aerodynamics for naval aviators 1965 edition

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					                                                                                           NAVAIR   00-8OT-80

       AVIATORS                                   BY
                                      H. H. HURT,              JR.
                        UNIVERSITY       OF SOUTHERN             CALIFORNIA

 DISTRIBUTION STATEMFNT C, Distribution authorized to U.S. Government agencies and
 their contractors to protect publications required for official use or for administrative or
 operational purposes only (January 1965). Other requests for this document shall be
 referred to Commanding      Officer, Naval Air Technical Services Facility, 700 Robbins
 Avenue, Philadelphia, PA 1911 l-5097.

 ,wNOTICE                   - For unclassified, limited documents, destroy by any method that
 will prevent disclosure of contents or reconstruction of the document.


                                     REVISED                                                  JANUARY    1965
Reproduction for non-military use of the information or ihstrations contained in &is
publication is not permitted without speciik approval of the ihip service (NAVAIR
or USAF). The policy for use of ClassifiedPublications is established the Air Force
in AFX 201-1 and for the Navy in Navy Regulations,Article 1509.
    The purpose of this textbook is to present the elements of applied
aerodynamics and aeronautical engineering which relate directly to
the problems of flying operations. All Naval Aviators possessa natural
interest in the basic aerodynamic factors which affect the performance
of all aircraft. Due .to the increasing complexity of modern aircraft,
this natural interest must be applied to develop a sound understanding
of basic engineering principles and an appreciation of some of the more
advanced problems of aerodynamics and engineering. The safety and
effectiveness of flying operations will depend greatly on the under-
standing and appreciation of how and why an airplane flies. The
principles of aerodynamics will provide the foundations for developing
exacting and precise flying techniques and operational procedures.
    The content of this textbook has been arranged to provide as com-
plete as possible a reference for all phases of flying in Naval Aviation.
Hence, the text material is applicable to the problems of flight train-
ing, transition training, and general flying operations. The manner
of presentation throughout the text has been designed to provide the
elements of both theory and application and will allow either directed
or unassisted study. As a result, the text material’   will be applicable
to supplement formal class Iectures and briefings and provide reading
material as a background for training and flying operations.
   Much of the specialized mathematical detail of aerodynamics has
been omitted wherever it was considered unnecessary in the field of
flying operations. Also, many of the basic assumptions and limita-
tions of certain parts of aerodynamic theory have been omitted for the
sake of simplicity and clarity of presentation. In order to contend with
these specific shortcomings, the Naval Aviator should rely on the
assistance of certain specially qualified individuals within Naval Avia-
tion. For example, graduate aeronautical engineers, graduates of the
Test Pilot Training School at the Naval Air Test Center, graduates of
the Naval Aviation Safety Officers Course, and technical representatives
of the manufacturers are qualified to assist in interpreting and applying
the more difficult parts of aerodynamics and aeronautical engineering.
To be sure, the specialized qualifications of these individuals should
be utilized wherever possible.
NAVWEPS 00-801-80
                The majority of aircraft accidents are due to some type of error of
             the pilot. This fact has been true in the past and, unfortunately, most
             probably will be true in the future. Each Naval Aviator should strive
             to arm himself with knowledge, training, and exacting, professional
             attitudes and techniques. The fundamentals of aerodynamics as pre-
             sented in this text will provide the knowledge and background for
             safe and effective flying operations. The flight handbooks for the air-
             craft will provide the particular techniques, procedures, and operating
             data which are necessary for each aircraft. Diligent study and continu-
             ous training are necessary to develop the professional skills and tech-
             niques for successful flying operations.
                The author takes this opportunity to express appreciation to those
             who have assisted in the preparation of the manuscript. In particular,
             thanks are due to Mr. J. E. Fairchild for his assistance with the por-
             tions dealing with helicopter aerodynamics and roll coupling phenom-
             ena. Also, thanks are due to Mr. J. F. Detwiler and Mr. E. Dimitruk
             for their review of the text material.
                                                        HUGH HARRISON HURT, Jr.
                August 1959
                University of Southern California
               Los Angelesj   Cnlif.

                                                                                         NAVWEPS OO-801-8O
                                                                                         TABLE OF CONTENTS

                        TABLE OF CONTENTS

PREFACE..         ,.,                                                        .                   iii
  WING   AND        AIRFOIL         FORCES
     PROPERTIES OF THE ATMOSPHERE.                                                                1
         Static pressure
         Standard atmosphere
         Pressure altitude
         Density altitude
     BERNOULLI’              PRINCIPLE            AND        SUBSONIC AIRFLOW..                   4
         Bernoulli’ equation,
                   s                                                                              6
              Incompressible tlow
              Variation of static pressure velocity
              Kinetic and porcntial energy of flow
              Static and dynamic prcssurc, 4
              Factors affecting dynamic pressure
         Airspeed measurement..                                                  ..               9
              Stagnation prcssurc
              Measurement of dynamic pressure
              Pitot and static sources
              Indicated airspeed

     DEVELOPMENT                 OF AERODYNAMIC                       FORCES..        .......    14
         Streamline pattern and pressure distribution.                                 .......   14
         Generatioaoflift..........................................                    .......   16
              Pressure distribution
         Airfoil terminology.                                                                    ,:
         Aerodynamic force coefficient                        ..
         Basic lift equation                                                                     23
               Lift coefficient
               Dynamic prcssurc and surface area
                    Interpretation of the lift equation..                                        .             .... . .              .    23
                          Lift cocfficicnt versus angle of attack
                          Stall speed and angle of attack
                          Angle of attack versus velocity
                          Primary control of airspeed
                     . . _ .. . _ .
                    mrfou un cnacactectsucs.                                                             . .              .               27
                          Section angle of attack and lift coefficient
                          Ty ical section chvactctistics
                          E&t of thickness and cambet
                    Drag characteristics,       .                                               . .                ....              :.   29
                          Drag equation
                          Drag cocficicnt versus angle of attack
                          Lift-drag ratio
                          Power-off glide pctformancc
                    Airfoil drag chanwteristics..                                                              )              .. .         33
                          Section drag cocfficicnt
                          Ty ical section characteristics
                          E 2 ect of thickness and cunbcr
                          Low drag sections
               FLIGHT AT HIGH LIFT CONDITIONS.                                                     ..              ...       . .           35
                  StaII speeds. .         . ....                                                 . . .,.                 ..... .           3.5
                         Maximum lift cc&cicnt
                         Stall angle of attack
                    ..,e     *   . .
                    Effect of maneuvering flight,.                                                                        .                ::
                           Load factor ~ets~s bank angle
                           Stall spad versus load factor
                    Effect of high lift devices.,                                                    .                                     37
                         Effect on stall speed
                    Stall angle of attack and stall recovery.                            ...             .         .                       39
               HIGH         LIFT DEVICES.                                                                                                  39
                    Types of high lift devices.,                                .                                                          41
                        Plain flap
                        S lit flap
                        SPotted flap
                        Fowler flap
                        Slots and slats
                        Boundary layer control
                    Operation of high lift devices.                                                                                        43
                        Flap retraction and extension
                           Chan es in lift, drag, and trim
                        Effect of power
               DEVELOPMENT                      OF AERODYNAMIC                                 PITCHING                MOMENTS
                    Pressure distribution.         .~.       : .     !        . :
                    Center of pressure and aerodynamic center.                                                                             a:
                    Pitching moment coefficient.          .            ,                                                                   49
                         Effect of camber
                         Effect of flaps
                         Relationship between center of pressure, aerodynamic centet, and
                            moment coefficient
                    Application to longitudinal stability. .                                                                               51
                         Stability and trim
                         Effect of supersonic flow
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                                                                                           TABLE OF CONTENTS

   FRICTION       EFFECTS.                                                                       52
       Viscous Bow..                                                                             52
       Boundarglayers....................................................                        52
           Laminar flow
           Turbulent flow
         ReyooldsNumber..................................................                        54
             Skin friction versus Reynolds Number
         Airflowseparatioa..................................................                     56
               Pressure distribution
               Prcswrc gradient and boundary layer energy
               Factors affecting separation
         Scaleeffect.........................................................                    59
              Effect on aerodynamic characteristics
              Reynolds Number correlation

PLANFORM              EFFECTS AND                    AIRPLANE                   DRAG
   EFFECT     OF WING        PLANFORM..                                                          61
             . .                                                                                 61
       Descr1puon of planform
           Area, span,, and chord
           Aspect ratm and taper
           Mean aerodynamic chord
       Development of lift by a wing..                                                 .         63
           vortex system
           Ti and bound vortices
           I&cd    flow and downwash
           Scction angle of attack
           Induced angle of attack
   INDUCED           DRAG.                                                  :                    66
       Induced angle of attack and inclined lift.                                                66
       Induced drag coefficient,                                                                 68
            Effect of lift coefficient
            Effect of aspect ratio
       Effectoflift........................................................                      68
       Effea of altitude..
       EffectofsPeed......................................................                       2;
       Effect of aspect ratio.                                                                   71
            Lift and dra characteristics
            Influcncc of f ow aspxt ratio configurations
   EFFECT            OF      TAPER            AND          StiEEPtiACK.                          74
          Spanwise lift distribution                                                             74
          localinducedflow.................................................                      76
          Effect on lift and drag characteristics.                          .‘
                                                                             ,                   76
   STALL          PATI’
                      ERNS.                                                                       77
          EffeaofpIanform..................................................                      ::
          Modifications for stall characteristics.                                                86
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               PARASITE             DRAG.                                                               87
                    Sources of parasite drag.                                                     .    87
                    Parasite drag coefficient.. . .                                               .
                    Parasite and induced drag.
                                 .?1 p”‘““ite dr2g CxEciczt
                          Airplane efficiency factor
                          Equivalent parasite area
                    Effect of configuration.                                                           91
                    Effect of altitude.,
                    Effectofspeed......................................................                ;:

               AIRPLANE               TOTAL            DRAG..                                          92
                    Drag variation with speed
                    Induced and parasite drag
                    Stall speed
                    Minimum drag
                    Specific performance conditions
                    Compressibility drag rise

         CHAPTER 2.               AIRPLANE PERFORMANCE
            REQUIRED         THRUST            AND         POWER
               DEFINITIONS.                                                                            96
                  Pan&e 14 ;n&Ced drw
                  _ _.-__.__._- _-                                                                     $6
                    Thrustandpowerrequir~~:::::::::::::::::::::::::::::::::::::::::                    97
               VARIATION                 OF THRUST                   AND         POWER REQUIRED
                    Effect of gross weight.                                                            99
                    Effect of configuratmn.                                                           101
                    Effect of altitude.                                                               101

            AVAILABLE              THRUST           AND         POWER
               PRINCIPLES                OF PROPULSION.                                               104
                    Mass flow, velocity change, momentum change..                                     104
                    Newton’ laws,
                            s                                                                         104
                    Wastedpower...............................:.....................                  104
                    Power available.                                                                  106
                    Propulsion efficiency.                                                            106
               TURBOJET               ENGINES
                    Operatingcycle....................................................                107
                    Function of the components.                                                       109
                           Inlet or diffuser
                           Combustion chamber
                           Exhaust nozzle
                     Turbojet       operating characteristics..                           :_          116
                           Thrust and power available
                           Effect of velocity
                           Effect of engine speed
                           Specific fuel consumption
                           Effect of altitude
                           Governing apparatus
                           Steady state, acceleration, deceleration
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                                                          TABLE OF CONTENTS
         Turbojet operating limitations                        124
             Exhaust gas temperature
             b&pr~$or    stall or surge

             Compressor inlet air temperature
             Engine speed
             Time limitations
         Thrust augmentation.                                  129
             Water injection
         The gas turbine-propeller  combination.               132
             Equivalent shaft horsepower
             Governing requirements
             Operating limitations
             performance characteristics
   THE     RECIPROCATING              ENGINE,                  135
                                . .
         Operating chatacterlsucs.                             135
             Operating cycle
             Brake horsepower
             Torque, RPM, and BMEP
             Normal combustion
             Preignition and detonation
             Fuel qualities
             Specific fuel consum tion
             Effect of altitude an 8 supercharging
             Effect of humidity
         Operating limitations.                                144
             Detonation and preignition
             Water injection
             Time limitations
             Reciprocating loads
         Operating   characteristics,                          145
             Flow patterns
             Propulsive cficiency
             Powerplant matching
             Governing and feathering
         Operating limitations..                               148

   STRAIGHT          AND      LEVEL       FLIGHT.              150
         Equilibrium conditions
         Thrust and power required
         Thrust and powec available
         Maximum and minimum speed
   CLIMB       PERFORMANCE.                                    150
         Steady and transient climb.                           150
             Forces acting on the airplane
             Climb angle and obstacle clcarancc
             Rate of climb, primary control of altitude
             Propeller and jet aircraft
         Climb performance.                                     156
             Effect of weight and altitude
             Descending flight
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               RANGE      PERFORMANCE.                                                                                  :;
                  General range performance.                                                                            158
                       Specific range, v&city, fuel flbw
                       Specific endurance
                       Cruise control and total range
                  Range, propeller driven airplanes.                                                                    160
                       Aerodynamic conditions
                       Effect of weight and altitude
                       Reciprocating and turboprop airplanes
                  Range, turbojet airplanes.                                                :.                          164
                       Aerodynamic conditions
                       Effect of weight and altitude
                       Constant altitude and cruise-climb profiles
                  Effect of wind oh ‘  PY~C........,....................................                                168
               ENDURANCE           PERFORMANCE.                                                                         170
                  General endurance performance..                                           :.                  .       170
                       Spxific cndurancc, velocity, fuel flow
                  Effect of altitude op endurance,                                         :..              ....        170
                       Propcllcr driven airplanes
                       Turbojet aitplaocs
               OFF-OPTIMUM        RANGE        AND ENDURANCE.                                                           172
                  Reciprocating powered airplane..                                                                      172
                  Turboprop powered airplane,      ,                                                 . ..               173
                  Turbojet powered airplane...              . . I..                                             .       175

               MANEUVERING                    PERFORMANCE.                                                              176
                    Relationships of turning flight. . . .                                       .          .       .   176
                         Steady turn, bank angle and load factor
                         Induced drag
                    Turning performance..                                                            . .                178
                         Tom radius and turn rate
                         Effect of bank aaglc and velocity
                    Tactical performance,                   .                                                           178
                         Maximum lift

                          FhZZF%3:~2:;                       pfOt”l~“CC
               TAKEOFF            AND        LANDING            PERFORMANCE..              .~,                          1132
                    Relationships of accelerated motion.                                                        .       182
                        Acceleration, vclocit    distance
                        Uniform and nonum,Jarm acceleration
                    Takeoff performance.. . . .                                                                         164
                        Forces acting on the airplane
                        Accelerated motion
                        Factors of technique
                    Factors affecting takeo# performance.                                                       .       187
                        Effect of gross weight
                        Rffcct of wind
                        Effect of runway slope
                        F’ qxt takeoff vcloclty.
                        Effect of altitude and tempcraturc
                        Handbook data
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                                                                                                        TABLE OF CONTENTS

          Landing performance..                                       ..                       .   .             192
              Forces acting on the airplane
              Accclanted motion
              Factors of technique
          Factors affecting landing performance.                                                       . . .     196
              E&t of gross weight
              Effect of wind

             Fg;     ~~~~~~~;mpcntwc
               ro   a
          Impmtance of handbook performance                       data.                                    ..    200

  GENERAL         CONCEPTS             AND        SUPERSONIC               FLOW        PATTERNS
     NATURE           OF COMPRESSIBILITY.                  ...............................                       201
          Definition of Mach number.    ........................................                                 202
          Sttbsonic, traasonic, supersonic, and hypersonic flight regimes. .......                               204
          Compressible flow conditions .......................................                                   204
          Comparison of compressible and incompressible flow. ...............                                    204
     TYPICAL      SUPERSONIC             FLOW             PATTERNS.,           ..................                207
         Obliqueshockwave     ................................................                                   207
         Normalshockwave     ................................................                                    207
         Ex nsionwave ....................................................                                       211
         E t9” on velocity, Mach number, density, pressure, energy. .. : ........
             ect                                                                                                 213
     SECTIONS     IN SUPERSONIC                           FLOW. ............................                     213
        nowpatterns     ......................................................                                   213
        Pressure distribution.          ..............................................                           213
        Wavedrag .........................................................                                       21s
        Location of aerodynamic center. ....................................                                     21s

  CONFIGURATION                  EFFECTS
     TRANSONIC       AND          SUPERSONIC                      FLIGHT.              .                         215
        Critical Mach ntlm~r                                                                                     2 15
        Shock wave formatton.                                                                  ... ...... .. .   218
        Shock induced separation..                          i..                                                  $2:
        Phenomena of transonic flight..                                                                     .    218
        Phenomena of supersonic Bight..                                                                     .    220
     TRANSONIC          AND     SUPERSONIC        CONFIGURATIONS.                                                220
        Airfoil sections..                                   .                                                   220
             Transonic sections
              Supctsonic sections
              Wave drag characteristics
              Effect of Mach number on airfoil characteristics
        Plaaform effects.                                         ,.......,.....                                 226
              Effect of swcc ack
              Advantages o p” swcepback
              Disadvantages of sweepback
              Effect of nspct ratio and tip shape
        Control surfaces.                                         .         .... ....                            236
              Powered controls
              All movable surfaces
NAWEPS 00-801-80

                    Supersonic engine inlets.                                                         .                             238
                        Internal and external comprcsrion inlets
                        Inlet performance and powerplant matching
                    Supersonic configurations.                                                                                      240
               AERODYNAMIC                     HEATING.                                                                             242
                    Ram temperature rise..           _.                                                                             242
                    Effect on structural materials and powerplant                         performance.                              242

               STATIC STABIL .ITY. ...............................................                                                  243
               DYNAMIC   STAB1 ‘LITY ....................................                                                           245
               TRIM AND CONTROLLABI ,LITY ..........................                                                                247
               AIRPLANE REFERENCE AXES. ...........................                                                                 249
            LONGITUDINAL                STABILITY            AND         CONTROL
               STATIC LONGITUDINAL                             STABILITY.                .........................                   250
                    Generalconsiderations:.             .. :,_~. ...... . .... . ...............                   .:..1...   ...      0.
                    Contribution of the component surfaces ..............................                                            253
                         Fuselage and nacelles
                         Horizontal tail
                    Power-off stability. ..................................................                                         259
                    Powereffects .......................................................                                            259
                    Control force stability. .............................................                                          264
                    Maneuveringstability         ...............................................                                    268
                    Tailoring control forces. ...........................................                                           270
               LONGITUDINAL                    CONTROL. ....................................                                        275
                    Maneuvering control requirement. ..................................                                             275
                    Takeoff control requirement. .......................................                                            275
                    Landing control requirement. .......................................                                            277
               LONGITUDINAL                     DYNAMIC                 STABILITY.             .....................                279
                    Phugoid ...........................................................                                             279
                    Short period motions ...............................................                                            281
               MODERN            CONTROL               SYSTEMS. .................................                                   281
                    Power operated
            DIRECTIONAL            STABILITY            AND        CONTROL
               DIRECTIONAL                 STABILITY.              ......................................                           284
                    Defimtuxu                                                                                                 ...   284
                    Contribution of the airplane components ............................                                            285
                          Vertical tail
                          Fuselage and nacelles
                          Power effects
                    Crawal conditions. ................................................                                             290
               DIRECTIONAL                  CONTROL .......................                               >................         290
                    Directional control requirements. ..................                                  ................          291
                    Adverseyaw .......................................................                                              291
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                                                                                                                 TABLE OF CONTENTS
      Spinrecovety..;   ...................................................                                           291
      Slipstream rotatmn. ................................................                                            294
      Cross wind takeoff and landing. ...................................                                             294
      Asymmetrical power. ...............................................                                             294
LATERAL       STABILITY                AND           CONTROL
   LATERAL             STABILITY,                  ...........................................                        294
             ...........................................................                                              295
   CONTRIBUTION                      OF THE AIRPLANE                                 COMPONENTS.                      295
      Wing.........~.........~                                                                                        298
      Fuselage and wmg powton,...................................................................................     298
      Sweepback .........................................................                                             298
      Vertical tail. ........................................................                                         298
   LATERAL             DYNAMIC                   EFFECTS, ................................                            299
      Directional divergence
      Spiral divergence
      Dutch roll
   CONTROL              IN ROLL ..............................................                                        300
            .           .                                                                                             300
      Rolhsg        motmn of an airplane. ......................................
      Roliing       performance, ..............................................                                       301
      Critical      requirements. ..............................................                                      305
MISCELLANEOUS                   STABILITY                PROBLEMS
   LANDING              GEAR CONFIGURATIONS                                          .........................        305
      Tail wheel type
      Tricyde type
      Bicycle type
   SPINS AND               PROBLEMS OF SPIN RECOVERY ................                                                 307
      Principal prospin moments
      Fundamental principle of recovery
      Effect of configuration
   PITCH-UP.,            .........................................................                                    313
      Contribution            of the airplane components
   EFFECTS OF HIGH                           MACH             NUMBER..                                                313
      Longitudinal stability and control
      Directional stability
      Dynamic stability and damping
   PILOT INDUCED                       OSCILLATIONS..                                                              _. 314
          Pilot.control system-airplane coupling
          High q aed low stick force stability
   ROLL       COUPLING.                                                                                               315
          Inertia and aerodynamic coupling
          Inertia and wind axes
          Natural pitch, yaw, and coupled pitch-yaw frequencies
          Critical roll rates
          Autorotative rolling
          Operating limitations
   HELICOPTER                  STABILITY                   AND CONTROL.                                               319
      Rotor gyroscopic effects
      Cyclic and collective pitch
      Lon itudinal, lateral, and directional                               control
      Ang f e of attack and velocity stability
      Dynamic stability

           GENERAL          OEFlNlTlONS              AND        STRUCTURAL              REQUlREMENTS

               STATIC STRENGTH .._..........                           ~.~~~.~           ~..~
                    Limit load
                    Factor of safety
                    Material properties

               SERVICE LIFE                                                                                       328
                    Pati e consideration
                    Loa r spectrum attd cumulative damage
                    Creep considerations

               AEROELASTIC                 EFFECTS.                                                              330
                    Stiffness and rigidity

           AIRCRAFT         LOADS           AND        OPERATING               LIMITATIONS
               FLIGHT         LOADS-MANEUVERS                             AND GUSTS.                             331
                    Loadfactor.....................................................                     ,...     331
                    Maneuvering load factors..                                                     .I   ,..,     331
                          Maximum lift capability
                          Effect of gross weight
                    ^      . ._
                    ClllStlOadtacfors..............,.................................                            332
                          Gust load increment
                         Effect of gust intensity and lift curve slope
                         Effect of wing loading and altitude
                    Effect of overstrea.                                                                       ,’ 334

              THE V-n OR V-g DIAGRAM.                                                                            334
                    Effect of weight, configuration;altihtde, and symmetry of Ior-Ang
                    Limit load factors
                    Ultitnute load facvxs
                    Maximum lift capability
                    Limit airspeed
                    Operating env+pe
                    Maneuver’ speed and penetration of turbulence

              EFFECT OF HIGH                      SPEED FLIGHT..                                                 339
                    Critical gust
                    Aileron reversal
                    Compressibility problems

              LANDING             AND GROUND                     LOADS.                                          343
                    Landing load factor
                    Effect of touchdown rate of descent
                    Effect of gross weight
                    Ported landing on unprepared .surfaces

           EFFECT OF OVERSTRESS         ON SERVICE                             LIFE                              344
                 Recognition of overstress’
                 Importance of operating limitations

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                                                                                              TABLE OF CONTENTS

  PRIMARY          CONTROL          OF     AIRSPEED        AND        ALTITUDE..                       349
     Angle of attack versus airspeed
     Rate of climb and descent
     Flying technique
  REGION        OF     REVERSED           COMMAND.                         .                           353
     Regions of normal and reversed command
     Features of flight in the normal and reversed regions of command

  THE ANGLE         OF ATTACK                  INDICATOR             AND         THE      MIRROR
    LANDING       SYSTEM.                                                                   .      .   357
     The angle of attack indicator
     The mirror landing system

  THE      APPROACH           AND        LANDING.,                                                     360
     The approach
     The landing flare and touchdown
     Typical errors

  THE       TAKEOFF..                                                                                  365
     Takeoff speed and distance
     Typical errors

  GUSTS AND       WIND      SHEAR..                  _.                    t,.                         367
    Vertical and horizontal gusts

   POWER-OFF         GLIDE    PERFORMANCE.                       .                                     369
     Glide angle and lift-drag ratio
     Factors affecting glide performance
     The flameout pattern

  EFFECTOF           ICE AND     FROST         ON AIRPLANE            PERFORMANCE..                    373
     Effect of ice
     Effect of frost

  ENGINE         FAILURE        ON       THE    MULTI-ENGINE                    AIRPLANE.              376
     Effecf of weight and altihtde
     Control requirements
     Effeti on performance
     Etrect of turning flight and configuration

   GROUND          EFFECT.,         _,                                                                 379
        Aerodynamic influence of ground effect
        Ground effect on specific flight conditions

   INTERFERENCE               BETWEEN           AIRPLANES            IN        FLIGHT..                383
        Effect of lateral, vertical, and IongiNdinal      separation
        Collision possibility
             BRAKING              PERFORMANCE.                     .........................................           387
                 Friction cbaracte~istics
                 Braking technique
                 Typical errors of braking technique
             REFCTSAL            SPEEDS , LINE                    SPEEDS, AND CRITICAL                         FIELD
                LENGTH.            .............................................................                       391
                 Refusal speed
                 Line speeds
                 Critical field length, multi-engine                operation
             SONIC BOOMS. .......................................................                                      396
                 Shock waves and audible sound
             HELICOPTER                 PROBLEMS. ...........................................                          399
                 Rotoraerodynamics         .....................................................                       400
                 Retreating blade stall ...................................................                            402
                 Compressjbility effects ..................................................                            404
                 Autorotatton charactertsttcs .............................................                            405
                 Powersettling   .........................................................                             408
             THE FLIGHT                 HANDBOOK.                  ........................................            411

        SELECTED       REFERENCES.           .....................................                                     413
        ,,“YL)\ .......................................................                                                414

                                                                             NAVWEPS 00-BOT-BO
                                                                            BASIC AERODYNAMICS

                                           Chapter 1

                              BASIC AERODYNAMKS

   In order to understand the characteristics of         WING    AND   AIRFOIL    FORCES
his aircraft and develop precision flying tech-
niques, the Naval Aviator must be familiar         PROPERTIES     OF THE ATMOSPHERE
with the fundamentals of aerodynamics. There
are certain physical laws which describe the         The aerodynamic forces and moments acting
behavior of airflow and define the various         on a surface are due in great part to the prop-
aerodynamic forces and moments acting on a         erties of the air mass in which the surface is
surface. These principles of aerodynamics pro-     operating.~ The composition, of the earth’    s
vide the foundations for good, precise flying      atmosphere by volume is approximately 78
techniques.                                        percent. nitrogen, 21 percent oxygen, and 1

percent water vapor, argon, carbon dioxide,            the proportion of the ambient air temperature
etc. For the majority of all aerodynamic con-          and the standard sea level air temperature.
siderations air is considered as a uniform             This temperature ratio is assigned the short-
mixture of these gases. The usual quantities           hand notation of 0 (theta).
used to define the properties of an air mass are           Temperature ratio
as follows:                                                             Ambient air temperature
   STATIC PRESSURE. The absolute static                           =Standard sea level air temperature
pressure of the air is a property of primary                    @=TITtl
importance. The static pressure of the air                      ,+273
at any altitude results from the mass of air                          288
supported above that level. At standard sea            Many items of compressibility effects and jet
level conditions the static pressure of the air        engine performance involve consideration of
is 2,116 psf (or 14.7 psi, 29.92 in. Hg, etc.)         the temperature ratio.
and at 40,000 feet altitude this static pressure          DENSITY.       The density of the air is a prop-
decreases to approximately 19 percent of the           erty of greatest importance in the study of
sea level value. The shorthand notation for            aerodynamics. The density of air is simply
the ambient static pressure is “p” and the             the mass of air per~cubic foot of volume and
standard sea level static pressure is given the        is a direct measure of the quantity of matter
subscript “a” for zero altitude, pa. A more            in each cubic foot of air. Air at standard sea
usual reference in aerodynamics and perform-           lcvcl conditions weighs 0.0765 pounds per cubic
ance is the proportion of the ambient sta~tic          foot and has a density of 0.002378 slugs per
pressure and the standard sea level static             cubic foot. At an altitude of 40,000 feet the
pressure. This static pressure ratio is assigned       air density is approximately 25 percent of the
the shorthand notation of 8 (delta).                   sea level value.
    Altitude pressure ratio                               The shorthand notation used for air density
                                                       is p (rho) and the standard sea level air density
                 Ambient static pressure
                                                       is then pO. In many parts of aerodynamics it
           =Standard sea level static pressure
                                                       is very convenient to consider the proportion
          6 = PIP0                                     of the ambient air density and standard sea
Many items of gas turbine engine perform-              level air density. This density ratio is assigned
ance are directly related to some parameter            the shorthand notation of c (sigma).
involving the altitude pressure ratio.                                          ambient air density
                                                           density ratio=
   TEMPERATURE.         The absolute tempera-                               standard sea level air density
cure of the air is another important property.                         a = PIP0

The ordinary temperature measurement by the               A general gas law defines the relationship of
Centigrade scale has a/datum at the freezing           pressure temperature, and density when there
point of water but absolute zero temperature           is no change of state or heat transfer. Simply
is obtained at a temperature of -273“ Centi-           stated this would be “density varies directly
grade. Thus, the standard sea level tcmpera-           with pressure, inversely with temperature.”
ture of 15” C. is an absolute temperature of           Using the properties previously defined,
288”. This scale of absolute temperature using
the Centigrade increments is the Kelvin scale,                density ratio=                    o.
                                                                                    Pressure rat’
                                                                                  temperature rat10
e.g., o K. The shorthand notation for the
ambient air temperature is “T” and the stand-
ard sea level air temperature of 288’ K. is
signified by Ta. The more usual reference is,
,.   n

         ,-g    #I
PlAVWEPS 00-8OT-80

This relationship has great application in               Thus, certain corrections must apply to the
aerodynamics and is quite fundamental and                instrumentation as well as the aircraft per-
necessary in certain parts of airplane perform-          formance if the operating conditions do not
ance.                                                    fit the standard atmosphere. In order to prop-
   VISCOSITY.      The viscosity of the air is           erly account for the nonstandard atmosphere
important in scale and friction effects. The             certain terms must be defined. Pressure.&itudc
coefficient of absolute viscosity is the propor-         is the altitude in the standard atmosphere
tion between the shearing stress and velocity            corresponditrg to a particular pressure. The
gradient for a fluid flow.      The viscosity of         aircraft altimeter is essentially a sensitive
gases is unusual in that the viscosity is gen-           barometer calibrated to indicate altitude in
erally a function of temperature alone and an            the staotlard atmosphere. If the altimeter is
increase in temperature increases the viscosity.          set for 29.92 in. Hg the altitude indicated is
The coefficient of absolute viscosity is assigned        the pressure altitude-the    altitude in the stand-
the shorthand notation I, (mu). Since many               ard atmosphere corresponding to the sensed
parts of aerodynamics involve consideration of           pressure. Of course, this indicated pressure
viscosity and density, a more usual form of               altitude may not be the actual height above
viscosity measure is the proportion of the co-            sea level due to variations in remperature,
efficient of absolute viscosity and density.            lapse rate; atniospheric pressure, and possible
This combination is termed the “kinematic                 errors in the sensed pressure.
viscosity” and is noted by Y (nu).                           The more appropriate term for correlating
                                                          aerodynamic performance in the nonstandard
     kinematic viscosity                                  atmosphere is density &it&-the         altitude in
                                                          the standard atmosphere corresponding to a
              cccoefficient of absolute viscosity         particular value of air density. The computa-
                             density                      tion of density altitude must certainly involve
                                                          consideration of pressure (pressure altitude)
             v=PlP                                        and temperature.      Figure 1.6 illustrates the
                                                          manner in which pressure altitude and tem-
The kinematic viscosity of air at standard sea            perature combine to produce a certain density
level conditions is 0.0001576 square feet per             altitude.   This chart is quite standard in use
second. At an altitude of 40,000 feet the                 and is usually included in the performance
kinematic viscosity is increased to 0.0005059             section of the flight handbook. Many subject
square foot per second.                                   areas of aerodynamics and aircraft performance
    In order to provide a common denominator              will emphasize density altitude and temperature
for comparison of various aircraft, a standard            as the most important factors requiring con-
atmosphere has been adopted. The standard                 sideration.
atmosphere actually represents the mean or
average properties of the atmosphere. Figure
1.1 illustrates the variation of the most im-                     S
                                                         BERNOULLI’       PRINCIPLE     AND SUBSONIC
portant properties of the air throughout the                AIRFLOW
standard atmosphere. Notice that the lapse
rate is constant in the troposphere and the                 All of the external aerodynamic forces on a
stratosphere begins with the isothermal region.          surface are the result of air pressureor air fric-
    Since all aircraft performance is compared           tion. Friction effects are generally confined to
 and,evaluated in the environment of the stand-          a thin layer of air in the immediate vicinity of
 ard atmosphere, all of the aircraft instrumenta-        the surface and friction forces are not the pre-
 tion is calibrated for the standard atmosphere.         dominating aerodynamic forces. Therefore,
                                         NAVWEPS OO-ROT-80
                                        BASIC AERODYNAMICS

Figure 1.7. Standard Altitude   Table
NAVWEPS 00401-80

  the pressure forces created on an aerodynamic                 be an unbalance of force to provide the ac-
 surface can be studied in a simple form which                 celeration. Since there is only air within the
 at first neglects the effect of friction and vis-             tube, the unbalance of force is provided by
 cosity of the airflow.     The most appropriate               the static pressure at station 1 being greater
 means of visualizing the effect of airflow and                than the static pressure at the constriction,
 the resulting aerodynamic pressures is to study                station 2.
 the fluid flow within a closed tube.                             (2) The total energy of the air stream in
     Suppose a stream of air is flowing through                the tube is unchanged. However, the air-
 the tube shown in figure 1.2. The airflow at              .’ stream energy may be in two forms. The
 station 1 in the tube has a certain velocity,                 airstream may have a potential energy which
 static pressure, and density. As the airstream                is related by the static pressure and a kimtic
 approaches the constriction at station 2 certain              energy by virtue of mass and motion.         As
 changes must take place. Since the airflow                    the total energy is unchanged, an increase in
 is enclosed within the tube, the mass flow at                 velocity (kinetic energy) will be accompa-
 any point along the tube must be the same and                 nied by a decrease in static pressure (poten-
 the velocity, pressure, or density must change                tial energy). This situation is analagous to
to accommodate this continuity of flow.                        a ball rolling along-a smooth surface. As
    BERNOULLI’   S     EQUATION.        A    distin-           the ball rolls downhill, the potential energy
guishing feature of submnic airflow is that                    due to position is exchanged for kinetic
changes in pressure and velocity take place                    energy of motion.      If .friction- were negli-
with sniall and negligible changes in density.                 gibie, the change of potential energy would
For this reason the study of subsonic airflow                  equal the change in ki,netic energy. This- is
can be simplified by neglecting the variation                  also the case for the airflow within the tube.
of density in the flow and assuming the flow                   The relationship of static pressure and veloc-
to be incomprmiblc. Of course, at high flow                 ity is maintained throughout the length of the
speeds whjch approach the speed of sound, the               tube. As the flow moves past the constriction
flow must be considered as compressible and                toward station 3, the velocity decreases and
“compressibility effects” taken into account.              the static pressure increases.
However, if the flow through the tube of                       The Bernoulli equation for incompressible
figure 1.2 is considered subsonic, the density of           flow is most readily explained ,by accounting
the airstream is essentially constant at all sta-          for the energy of the~airflow within the tube.
tions along the length.                                    As the airstream has no energy added or sub-
    If the density of the flow remains constant,           tracted at any point, the sum of the potential
static pressure and velocity are the variable              +id kinetic energy must be constant. The
quantities.     As the flow approaches the con-            kinetic energy of an object is found by:
striction of station 2 the velocity must increase                   “KE. =%MV=
to maintain the same mass flow. As the                     where K;E. = kinetic energy, ft.-lbs.
velocity increases the static pressure will de-                        M = mass, slugs
crease and the decrease in static pressure which                         =velocity, ft./set.
accompanies the increase in velocity can be                The kinetic energy of a cubic foot of air is:
verified in two ways:
       (I) Newton’ laws of motion state the
    requirement of an unbalanced force to pro-
    duce an acceleration (velocity change). If             where g=      kinetic energy per cu. ft., psf
    the airstream experiences an increase in veloc-                   p=air density, slugs per cu. ft.
    ity approaching the constriction, there must                      V=ait velocity, ft./set.
                                     NAWEPS DD-BDT-BD
                                    BASIC AERODYNAMICS


        PE + KE = CONSTANT
Ftaure 1.2. Airflow Within a Tube


         2500                                I

    I    1500                                        I
    ci                                               P

          500                                         I


                     P=21 16 PSF            P = 2014 PSF             P = 2133 PSF
                     q= 34 PSF              9 = 136 PSF              q= I7 PSF
                     H- 2150 PSF            H = 2150 PSF             H = 2150 PSF

                           Figure 1.3. Variation   o\ Pressure in Tube
                                                                                                 NAVWEPS 00-801-80
                                                                                                BASIC AERODYNAMICS

  If the potential energy is represented by the           TABLEl-l.     Effect of Speed and Altitvde   on Dwzmnic Prerrure

static pressure, p, the sum of the potential and
kinetic energy is the total pressure of the air-
stream.                                                               True air
                                                                        speed          -
         H=p+% P V’                                                   (fr./scc.)
                                                                                       ,I I
where H=total        pressure, psf (sometimes re-
              ferred to as “head ’ pressure)
                                                                        m=                  c
          p=static pressure, psf.                                                      _-
           p=density, siugs per cu. ft.
         V= velocity, ft./set.                                               338
This equation is the Bernoulli equation for                                  507
incompressible flow. It is important to ap-
‘                                                                            845
preciate that the term >$pV2has the units of                              I, 013
pressure, psf. This term is one of the most
important in all aerodynamics and appears so
frequently t&it       is given the name “dynamic
pressure” and the shorthand notation “4”.
              q= dynamic pressure, psf
                = jgpv2
With this definition it could be said that the
sum of static and dynamic pressure in the flow
tube remains constant.
    Figure 1.3 illustrates the variation of static,
dynamic, and total pressure of air flowing
through a closed tube. Note that the total                    AIRSPEED MEASUREMENT.             If a sym-
pressure is con,stant throughout the length               metrically shaped object were placed in a
 and any change in dynamic pressure produces              moving airstream, the flow pattern typical of
 the same magnitude change in static pressure.            figure 1.4 would result. The airstream at the
    The dynamic pressure of a free airstream is           very nose of the object would stagnate and the
 the one ‘   common denominator of all aero-              relative flow velocity at this point would be
 dynamic forces and moments. Dynamic pres-                zero. The airflow ahead of the object pos-
 sure represents the kinetic energy of the free           sesses some certain dynamic pressure and
 airstream and is a factor relating the capability        ambient static pressure. At the very nose of
for producing changes in static pressure on a             the object the local velocity will drop to zero
 surface. As defined, the dynamic, pressure               and the airstream dynamic pressure will be
 varies directly as the density and the square of         converted into an increase in static pressure at
 the velocity.     Typical values of dynamic pres-        the stagnation point.    In other words, there
 sure, 4, are shown in table l-1 for various true         will exist a static pressure at the stagnation
 airspeeds in the standard atmosphere. Notice             point which is equal to the airstream total
 that the dynamic pressure at some fixed veloc-           pressure-ambient static pressure plus dynamic
 ity varies directly with the density ratio at any        pressure.
 altitude.    Also, appreciate the fact that at an            Around the surface of the object the airflow
 altitude of 40,oM) feet (where the density ratio,        will divide and the local velocity will increase
 b, is 0.2462) it is necessary to have a true air         from zero at the stagnation point to some
 velocity twice that at sea level in order to              maximum on the sides of the object. If fric-
 product the same dynamic pressure.                        tion and viscosity effects are neglected, the

                   FORWARD STAGNATION                          AFT STAGNATION
                         POINT                                     POINT

           AIRSTREAM AHEAD                                             STAGNATION PRESSURE
         HAS AMBIENT    STATIC                                          IS AIRSTREAM TOTAL
        PRESSURE AND DYNAMIC                                                  PRESSURE
               PRESSURE                                                          P+q

                         Ftgure 1.4. Flow Pattern on a Symmetrical Object

surface anflow continues to the aft stagnation          pressure, q. The pressure gauge is then cali-
point where the local velocity is again zero.           brated to indicate flight speed in the standard
The important point of this example of aero-            sea level air mass. For example, a dynamic
dynamic flow is existence of the stagnation             pressure of 305 psf would be realized at a sea
point. The change in airflow static pressure            level flight ,speed of 300 knots.
which takes place at the stagnation point IS                Actually there can be many conditions of
equal to the free stream dynamic pressure, q.           flight where the airspeed indicator does not
   The measurement of free stream dynamic               truly reflect the actual velocity through the
pressure is fundamental to the indication of            air mass. The corrections that must be applied
airspeed. In fact, airspeed indicators are sim-         are many and lisred in sequence below:
ply pressure gauges which measure dynamic                      (1) The indicated airspeed (IAS) is the
pressure related to various airspeeds. Typical              actual instrument indication for some given
airspeed measuring systems are illustrated in
                                                            flight condition.   Factors such as an altitude
figure 1.5. The pitot head has no internal
                                                            other than standard sea level, errors of the
flow velocity and the pressure in the pitot tube
is equal to the total pressure of the airstream.            instrument and errors due to the installation,
The purpose of the static-ports is to sense the             compressibility, etc. may create great vari-
true static pressure of the free airstream. The             ance between this instrument indication and
total pressure and static pressure lines are                the actual flight speed.
attached to a differential pressure gauge and                   (2) The calibrated airspeed (CM) is the
the net pressure indicated is the dynamic                   result of correcting IAS for errors of the
                                                                                NAVWEPS 00-807-80
                                                                               BASIC AERODYNAMICS

                    PITOT-STATIC    SYSTEM                            PITOT WITH SEPARATE
                                                                         STATIC SOURCE

                          w/ q  :%
                                          PRESSURE INDICATED BY GAUGE IS
                                          DIFFERENCE BETWEEN TOTAL AND
                                              STATIC PRESSURE, H-p= q

                               Figure. 1.5. Airspeed   Measurement

instrument and errors due to position or lo-           0.05 psi position error is an airspeed error
cation of the installation.    The instrument          of 10 knots. A typical variation of air-
error must be small by design of the equip-            speed system position error is illustrated in
ment and is usually negligible in equjpment            figure 1.6.
which is properly maintained and cared for.                (3) The equivalent airspeed (PAS) is the
The position error of the installation must            result of correcting the (CAS) for compressi-
be small in the range of airspeeds involving           bility effects. At high flight speeds the
critical performance conditions.      Position         stagnation pressure recovered in the pitot
errors are most usually confine,d to the static        tube is not representative of the airstream
source in that the actual static pressure              dynamic pressure due to a magnification
sensed at the static port may be different              by compressibility.    Compressibility of the
from the free airstream static pressure.               airflow produces a stagnation pressure in
When the .,aircraft is operated through a              the pitot which is greater than if the flow
large range’ of angles of attack, the static           were incompressible. As a result, the air-
pressure distribution    varies ‘quite greatly          speed indication is given an erroneous mag-
and it becomes quite difficult to’   minimize          nihcation.     The standard airspeed indicator
 the static source error. In most instances a           is calibrated to read correct when at standard
compensating group of static sources may                sea level conditions and thus has a com-
 be combined to reduce the position error.              pressibility correction appropriate for these
 In order to appreciate the magnitude of this           conditions.    However, when the aircraft is
 problem, at flight speed near 100 knots a              operating above standard sea level altitude,
                                                                                 Revised January   1965
NAVWEPS 00-801-80

                              TYPICAL POSITION ERROR CORRECTION

                                   INDICATED AIRSPEED, KNOTS

                                 COMPRESSIBILITY    CORREt

                                  CALIBRATED AIRSPEED, KNOTS

                     Figure 1.6. Airspeed Corrections (sheet 1 of 2)

                                                           NAVWEPS 00-801-80
                                                          BASIC AERODYNAMICS


            ‘ -30fl1111v      AlISNxl

Figure    1.6. Airspeed    Corrections   (sheet 2 of 2)

  the inherent compensation is inadequate and                 Thus, the airspeed indicator system measures
  additional correction must be applied. The               dynamic pressure and will relate true flight
  subtractive corrections that must be applied             velocity when instrument, position, compress-
  to CA$ depend on pressure altitude and CAS               ibility, and density corrections are applied.
   and are shown on figure 1.6 for the subsonic            These corrections are quite necessary for ac-
  flight range. The equivalent airspeed (EAS)              curate determination of true airspeed and
   is the flight speed in the standard sea level           accurate navigation.
  air mass which would produce the same free                           s
                                                              Bernoulli’ principle and the concepts of
  stream dynamic pressure as the actual flight             static, dynamic, and total pressure are the basis
  condition.                                               of aerodynamic fundamentals. The pressure
      (4) The true airspeed (TAS) results when             distribution caused by the variation of local
  the &4X is corrected for density altitude.               stack and dynamic pressures on a surface is
  Since the airspeed indicator is calibrated               the source of the major aerodynamic forces
  for the dynamic pressures corresponding to               and moment.
  airspeeds at standard sea level conditions,
   variations in air density must be accounted             DEVELOPMENT        OF AERODYNAMIC
  for. To relate EAS and TAX requires con-                    FORCES
   sideration that the EAS coupled with stand-
  .ard sea level density produces the same dy-                The typical airflow patterns exemplify the
  namic pressure as the TAX Soupled with the               relationship of static pressure and velocity
   ^^_._^1 .:.. 2---:... ,.f L11Lbl:A.* C”IIUACI”L‘
  dCLUd, ‘ UcIIJIcy “I *L., “ 6°C rnrJ;r;m.. .
            all                   ‘                        defined by Bernoulli.   Any object placed in an
  From this reasoning, it can be shown that:               airstream will have the a& to impact or stag-
                                                           nate at some point near the leading edge. The
     (TAS)2p=(EAS)2      po                                pressure at this point of stagnation will be an
                       -                                   absolute static pressure equal to the total pres-
      or, TAS=EAS      62                                  sure of the airstream. In other words, the
                     d P                                   static pressure at the stagnation point will be
                                                           greater than the atmospheric pressure by the
        TAS= EAS 2
                   4                                       amount of the dynamic pressure of the air-
                                                           stream. As the flow divides and proceeds
  where TAX= true airspeed
                                                           around. the object, the increases in local ve-
        EAS=equivalent airspeed
                                                           locity produce decreases in static pressure.
           p=actual air density
                                                           This procedure of flow is best illustrated by the
          PO=standard sea level air density
                                                           flow patterns and pressure distributions of
          n=altitude density ratio, p/pa
                                                           figure 1.7.
   The result shows that the TAX is a function                STREAMLINE         PATTERN       AND    PRES-
of EAS and density altitude.  Figure 1.6 shows             SURE DISTRIBUTION.          The flow pattern of
a chart of density altitude as a function of               the cylinder of figure 1.7 is characterized by
pressure altitude and temperature. Each par-               the streamlines which denote the local flow
ticular density altitude fixes the proportion              direction.  Velocity distribution is noted by
between TAX and EAS. The use of a naviga-                  the streamline pattern since the streamlines
tion computer requires setting appropriate                 effect a boundary of flow, and the airflow
values of pressure altitude and temperature on             between the streamlines is similar to flow in a
the scales which then fixes rhe proportion be-             closed tube. When the streamlines contract
tween the scales of TAS and EAS (or TAS and                and are close together, high local velocities
CAS when compressibiliry        corrections are            exist; when the streamlines expand and are
applicable).                                               far apart, low local velocities exist. At the
Revlted   Jmuoy   1965
                                                                           NAVWEPS 00-8OT-80
                                                                          BASIC AERODYNAMICS

                         PRESSURE DISTRIBUTION       ON A 5v’     )ER


             (PERFECT FLUID)                                   (VISCOUS FLOW)


                       -PEAK      SUCTION

                                                             AFT STAGNATION POINT


                                                           VISCOUS FLOW

             Figure   1.7. Streamline Pattern and Pressure Distribution


forward stagnation point the local velocity                airfoil do not ,necessarily occtir at the point of
is zero and the maximum positive pressure re-              maximum thickness. However, a similarity
sults. As the flow proceeds from the forward               does exist in that the minimum pressure points
stagnation point the velocity increases as                 correspond to the points where the streamlines
shown by the change in streamlines. The                    are closest together and this condition exists
local velocities reach a maximum at the upper              when the streamlines are forced to the great-
and lower extremities and a peak suction pres-             est curvature.
sure is produced at these points on the cylinder.              GENERATION        OF LIFT.      An important
(NOTE: Positive pressures are pressures above              phenomenon associated with the production
atmospheric and negative or .ruction pressures             of lift by an airfoil is the “circulation” im-
are less than atmospheric.)          As the flow           parted to the airstream. The best practical
continues aft from the peak suction pressure,              illustration of this phenomenon is shown in
the diverging streamlines indicate decreasing              figure 1.8 by the streamlines and pressure dis-
local velocities and increasing local pressures.           tributions existing on cylinders in an airstream.
If friction and compressibility effects are not            The cylinder without circulation has a sym-
considered, the velocity would decrease to zero            metrical streamline pattern and a pressure dis-
 at the aft stagnation point and the full stagna-          tribution which creates n-0 n_et lift.       If the
 tion pressure would be recovered. The pressure            cylinder is given a clockwise rotation and
 distribution for the cylinder in perfect fluid            induces a rotational or circulatory flow, a dis-
 flow would be symmetrical and no net force                tinct change takes place in the streamline pat-
 (lift or dragj wvuid rcsuit. Of course, thr               tern and p’                “
                                                                        ess.~re &str~‘ u~~oii, The vriocitirs
 relationship between static pressure and ~eloc-           due to the vortex of circulatory flow cause
 ity along the surface is defined by Bernoulli’  s         increased 104 velocity on the upper surface
 equation.                                                 of the cylinder and decreased local velocity on
     The flow pattern for the cylinder in an actual        the lower surface of the cylinder. Also, the
 fluid   demonstrates the effect of friction or            circulatory flow produces an upwash immedi-
 viscosity. The viscosity of air produces a thin            ately ahead and downwash immediately be-
 layer of retarded flow immediately adjacent                hind the cylinder and both fore and aft stagna-
 to the surface. The energy expended in this                tion points are lowered.
  “boundary layer” can alter the pressure dis-                 The effect of the addition of circulatory flow
 tribution and destroy the symmetry of the                  is appreciated by the change in the pressure
 pattern. The force unbalance caused by the                 distribution on the cylinder.      The increased
 change in pressure distribution creates a drag             local velocity on the upper surface causes an
 force which is in addition to the drag due to              increase in upper surface suction while the
 skin friction.                                             decreased local velocity on the lower surface
     The streamline pattern for the symmetrical             causes a decrease in lower surface suction. As
 airfoil of figure 1.7 again provides the basis             a result, the cylinder with circulation will
 for the velocity and pressure distribution.                produce a net lift. This mechanically induced
  At the leading edge the streamlines are widely            circulation-called    Magnus effect-illustrates
  diverged in the vicinity of the positive pres-            the relationship between circulation and lift
  sures. The maximum local velocities and                   and is important to golfers, baseball and tennis
  suction (or negative) pressures exist where the           players as well as pilots and aerodynamicists.
  streamlines are the closest together,        One          The curvature of the flight path of a golf ball
  notable difference between the flow on the                 or baseball rcluites an unbalance df force
  cylinder and the airfoil is that the maximum               which is created by rotation of the ball. The
  velocity and minimum pressure points on the                pitcher that can accurately control a .powerful
                                                                                   NAVWEPS 00-8OT-80
                                                                                  BASIC AERODYNAMICS

                                INCREASED    LOCAL

                                       UPWASH         mSWNWASH

                                                                            LDECREASED     LOCAL

                                                            MAGNUS EFFECT BY
                                                            ROTATING CYLINDER

                                     AIRFOIL        LIFT

                                                                 -ZERO          LIFT

           7   INCREASED     LOCAL
           I      ,-VELOCITY

                                                                              POSITIVE    LIFT

                DECREASED    LOCAL

                     Figure 1.8. Generation of Lift (sheet 1 of 2)


                     Figure 7.8.   Generation        of Lift (sheet 2 of 2)

                                                      NAVWEPS GO-BOT-BO
                                                     BASIC AERODYNAMlCS

             AND ANGLE OF ATTACK


                                ORIGINAL ANGLE OF ATTACK
                             BUT INCREASED DYNAMIC PRESSURE



    Figure    1.9. Airfoil   Pressure Distribution

NAVWEPS 00-801-80

rotation will be quite a “curve ball artist”                   The effect of free stream density and velocity
the golfer that cannot control the lateral mo-              is a necessary consideration when studying the
tion of the club face striking the golf ball will           development of the various aerodynamic forces.
impart an uncontrollable spin and have trouble              Suppose that a particular shape of airfoil is
with a “hook” or “slice.”                                   fixed at a particular angle to the airstream.
    While a rotating cylinder can produce a net             The relative velocity and pressure distribution
lift from the circulatory flow, the method is               will be determined by the shape of the airfoil
relatively inefficient and only serves to point             and the angle to the airstream. The effect of
out the relationship between lift and circula-,             varying the airfoil size, air density and air-
tion. An airfoil is capable of producing lift               speed is shown in figure 1.9. If the same air-
with relatively high efficiency and the process             foil shape is placed at the same angle to an
is illustrated in figure 1.8. If a symmetrical              airstream with twice as great a dynamic pres-
airfoil is placed at zero angle of attack to the            sure the magnitude of the pressure distribution
airstream, the streamline pattern and pressure              will be twice as great but the r&rive shape of
distribution give evidence of zero lift.      HOW-          the pressure distribution will be the same.
ever, if the airfoil is given a positive angle of           With twice as great a pressure existing over
attack, changes occur in the streamline pattern             the surface, all aerodynamic forces and mo-
and pressure distribution similar to changes                ments will ~double. If a half-size airfoil ib
caused by the addition of circulation to the                placed at the same angle to the original air-
cylinder. The positive angle of attack causes               stream, the magnitude of the pressure distri-
increased velocity    on the upper surface with             bution is the same as the origina! airfoi! and
an increase in upper surface suction while the              again the relative shape of the pressure dis-
decreased velocity on the lower surface causes              tribution is identical. The same pressure act-
a decrease in lower surface suction. Also,                   ing on the half-size surface would reduce all
upwash is generated ahead of the airfoil, the                aerodynamic forces to one-half that of the
forward stagnation point moves under the                     original.   This similarity      of flow patterns
leading edge, and a downwash is evident aft                 means that the stagnation point occurs at the
of the airfoil.     The pressure distribution 0”             same place, the peak suction pressure occurs
the airfoil now provides a net force perpendicu-             at the same place, and the actual magnitude of
lar to the airstream-lift.                                   the aerodynamic forces and moments depends
     The generation of lift by an airfoil is depend-         upon the airstream dynamic pressure and the
 ent upon the airfoil being able to create circu-            surface area. This concept is extremely im-
 lation in the airstream and develop the lifting,            portant when attempting to separate and ana-
pressure distribution on the surface. In all                 lyze the most important factors affecting the
 cases, the generated lift will be the net force             development of aerodynamic forces.
 caused by the distribution of pressure over the                AIRFOIL      TERMINOLOGY.             Since the
 upper and lower surfaces of the airfoil.         At         shape of an airfoil and the inclination to the
 low angles of attack, suction pressures usually             airstream are so important in determining the
 will exist on both upper and lower surfaces.                pressure distribution, it is necessary to properly
 but the upper surface suction must be greater               define the airfoil terminology.        Figure 1.10
 for positive lift.    At high angles of attack               shows a typical airfoil and illustrates the
 near that for maximum lift, a positive pressure              various items of airfoil terminology
 will exist on the lower surface but this will                    (1) The chord line is a straight line connect-
 account for approximately one-third the net                    ing the leading and trailing edges of the
 lift.                                                          airfoil.

                                                                       NAVWEPS 00-8DT-80
                                                                      BASIC AERODYN,AMlCS

     LOCAT,ON DF                      THICKNESS


                                                               MEAN CAMBER

t              CA                              -I


     RE;L:r;                    &


                      Figure 1.10.   Airfoil   ~erminoh


    (2) The chord is the characteristic dimen-                angle of attack. Regardless of the condi-
 sion of the airfoil.                                         tion of flight, the instantaneous flight path
    (3) The mean-camberline is a line drawn                   of the surface determines the direction of the
 halfway between the upper and lower sur-                     oncoming relative wind and the angle of
 faces. Actually, the chord line connects the                 attack is the angle between the instantaneous
 ends of the mean-camber line.                                relative wind and the chord line. To respect
    (4) The shape of the mean-camber line is                  the definition of angle of attack, visualize
 very important in determining the aerody-                    the flight path of the aircraft during a loop
 namic characteristics of an airfoil section.                 and appreciate that the relative wind is
 The maximum camber (displacement of the                      defined by the flight path at any point dur-
 mean line from the chord line) and the Ioca-                 ing the maneuver.
 tion of the maximum camber help to define                    Notice that the description of an airfoil
 the shape of the mean-camber line. These                  profile is by dimensions which are fractions or
 quantities are expressed as fractions or per-             percent of the basic chord dimension. Thus,
 cent of the basic chord dimension. A typi-                when an airfoil. profile is specified a relative
 cal iow speed airfoil may have a maximum                  shape is described. (NOTB: A numerical sys-
 camber of 4 percent located 40 percent aft of             tem of designating airfoil profiles originated
 the leading edge.                                         by the National ~Advisory Committee for Aero-
    (5) The thickness and thickness distribu-              nautics [NACA] is used to describe the main
 tion of the profile are important properties              geometric features and certain aerodynamic
 of a section. The maximum tbicknus and                    properties. NACA Report Nol 824 wi!! pro-
 location of maximum thickness define thick-               vide the detail of this system.)
 ness and distribution of thickness and are                   AERODYNAMIC          FORCE COEFFICIENT.
 expressed as fractions or percent of the chord.           The aerodynamic forces of lift and drag depend
 A typical low speed airfoil may have a.                   on the combined effect of many different vari-
 maximum thickness of 12 percent located                   ables. The important single variables could
  30 percent aft of the leading edge.                      IX:
                                                                 (1) Airstream velocity
    (6) The leading edgeradius of the airfoil is
                                                                 (2) Air density
  the radius of curvature given the leading edge
                                                                 (3) Shape or profile of the surface
  shape. It is the radius of the circle centered
                                                                 (4) Angle of attack
 on a line tangent to the leading edge camber                    (5) Surface area
 and connecting tangency pcints of upper and                     (6) Compressibility effects
 lower surfaces with the leading edge. Typi-                     (7) Viscosity effects
 cal leading edge radii are zero (knife edge)              If the effects of viscosity and compressibility
  to 1 or 2 percent.                                       are not of immediate importance, the remain-
     (7) The Iift produced by an airfoil is the            ing items can be combined for consideration.
  net force produced perpendicular to the n&a-             Since the major aerodynamic forces are the
  tive wind.                                               result of various pressures distributed on a
     (8) The drag incurred by an airfoil is the             surface, the surface area will be a major factor.
  net force produced parallel to the relative wind.        Dynamic prcssurc of the airstream is another
     (9) The angle of attack is the angle between          common denominator of aerodynamic forces
   the chord line and the relative wind. Angle              and is a major factor since the magnitude of a
   of attack is given the shorthand notation                pressure distribution depends on the source
  a (alpha). Of course, it is important to dif-             energy of the free stream. The remaining
i ferentiate between pitch attitude angle and               major factor is the relative peJJ#re dittribution
                                                                                           NAVWEPS m-60T-30
                                                                                          BASIC AERODYNAMICS

existing on the surface. Of course, the ve-                      It is derived from the relative pressure and
locity distribution, and resulting pressure dis-                 velocity distribution.
tribution, is determmed by the.shape or pro-                        (2) Influenced only by the shape of the
file of the surface and the angle of a’        track.            surface and angle of attack since these factors
Thus, any aerodynamic force can be repre-                        determine the pressure distribution.
sented as the product df three major factors:                       (3) An index which allows evaluation of
      the surface area of the objects                           the effects of compressibility and viscosity.
      the dynamic pressure of the airstream                     Since the effects of area, density, and velocity
      the coefficient or index of force determined              are obviated by the coefficient form, com-
         by the relative pressure distribution                  pressibility and viscosity effects can be
This relationship is expressed by the following                 separated for study.
equation :                                                       THE BASIC LIFT EQUATION.                 Lift has
        F= C,qS                                              been dehned as the net force developed per-
where                                                        pendicular to the relative wind. The aero-
        F = aerodynamic force, lbs.                          dynamic force of lift on an airplane results
       C,=coeflicient of aerodynamic force                   from the generation of a pressure distribution
         ,iay;mic     pressure, psf                          on the wing. This lift force is described by
                                                             the following equation:
       S=surface area, sq. ft.                                           L=C&
   In order to fully appreciate the importance               where
of the aerodynamic force, coe&cient, C,, the                              L=lift, lbs.
above equation is rearranged to alternate                                C, = lift coefficient.
forms :                                                                   q= dy;:mic pressure, psf
                                                                          S= wing surface area, sq. ft.
                                                                 The lift coefhcient used in this equation is the
                                                             ratio of the lift pressure and dynamic pressure
                                                             and is a function of the shape of the wing and
In this form, the aerodynamic force coefficient              angle of attack. If the lift coefficient of a
Js appreciared as the aerodynamic force per                  conventional airplane wing planfoi-m were
surface area and dynamic pressure. In other                  plotted versus angle of attack, the result would
words, the force coefficient is a dimensionless              be typical of the graph of figure 1.11. Since
ratio between the average aerodynamic pres-                  the effects of speed, density, area, weight, alti-
sure (aerodynamic force.per ‘    area) and the air-          tude, etc., are eliminated by the coefficient form,
stream dynamic pressure. All the aerodynamic                 an indication of the true lift capability is ob-
forces of lift and drag are studied on this basis-           tained. Each angle of attack produces a par-
the common denominator in each case being                    ticular lift coefficient since the angle of attack
surface area and dynamic pressure. By such a                 is the controlling factor in the pressure dis-
definition, a “lift coefficient” would .be the               tribution.      Lift coeflicient increases with angle
ratio between lift pressure and dynamic pres-                 of attack up to the maximum lift coefficient,
sure; a “drag coefficient” would be the ratio                c L,,,~., and, as angle of attack is increased be-
between drag pressure and.:d.ynamic pressure.                 yond the maximum lift angle, the airflow is
The use of the coefficient form of an aero-                   unable to adhere to the upper surface. The
dynamic force is necessary since the force                    airflow then separates from the upper surface
coellicient is:                                               and stall occurs.
      (1) An index 04 the aerodynamic force                      JNTERPRETATION             OF THE LIFT EQUA-
   independent of area, density, and velocity.               TION.       Several important relationships are



H              L


                                       ANGLE    OF ATTACK,     DEGREES

                            Figure 7.7 1. Typical lib Characteristics
                                                                                        NAVWEPS 00.401-80
                                                                                       BASIC AERODYNAMICS

derived from study of the basic lift equation              Thus, a sea level airspeed (or EAS) of 100
and the typical wing lift curve. One impor-                knots would provide the dynamic pressure
tant fact to be appreciated is that the airplane           necessary at maximum lift to produce 14,250
shown in figure 1.11 stalls at the same angle              Ibs. of lift. If the airplane were operated at a
of attack regardless of weight, dynamic pres-              higher weight, a higher dynamic pressure
sure, bank angle, etc. Of course, the stall                would be required to furnish the greater lift
speedof the aircraft will be affected by weight,           and a higher stall speed would result. If the
bank angle, and other factors since the product            airplane were placed in a steep turn, the greater
 of dynamic pressure, wing area, and lift co-              lift required in the turn would increase the
 efficient must produce the required lift.      A          stall speed. If the airplane were flown at a
rearrangement of the basic lift equation de-               higher density altitude the TAX at stall would
 fines this relationship.                                  increase. However, one factor common to
                                                           each of these conditions is that the angle of
                     L = c&Y                               attack at C,,,, is the same. It is important to
    using q =$       (I’ in knots, TAX)                    realize that stall warning devices must sense
                                                           angle of attack (a) or pressure distribution
                                                           (related to CL).
                                                                Another important fact related by the basic
    solving for V,             -                           lift equation and lift curve is variation of angle
                 V=17.2        &                            of attack and lift coefficient with airspeed.
                           J       L,J                      Suppose that the example airplane is flown in
                                                            steady, wing 1eveJ flight at various airspeeds
Since the stall speed is the minimum flying                with lift equal to the weight.         It is obvious
speed necessary to sustain flight, the lift co-             that an increase in airspeed above the stall
efficient must be the maximum (CL,,,,).                     speed will require a corresponding decrease in
   Suppose that the airplane shown in’ figure               lift coeflicient and angle of attack to maintain
1.11 has the following properties:                          steady, lift-equal-weight     flight.    The exact
                Weight = 14,250 lbs                         relationship of lift coefficient and airspeed is
             Wing area=280 sq. ft.                          evolved from the basic lift equation assuming
                                                            constant lift (equal to weight) and equivaIent
If the airplane is flown in steady, level flight at
sea level with lift equal to weight the stall                                  C‘
                                                                              -=       v,
                                                                                       - p
speed would be:                                                               C%n.*   0V
           V.= 17.24&$                                     The example airplane was specified to have:
 where                                                                  Weight = 14,250 lbs.
          V.= stall speed, knots TAS                                      CL,,,=lS
          W= weight, lbs. (lift = weight)                                   V,= 100 knots EAS
                                                           The following table depicts the lift coefficients
          va= 17.2J (I.&4E;280)                            and angles of attack at various airspeeds in
             = 100 knots                                   steady flight.


                                                                                        NAVWEPS WOT-BO
                                                                                       BASIC AERODYNAMICS

                                                            angle of attack indicator allows precision con-
                                                            trol of the airspeed. The accomplished insttu-
                                                            ment pilot is the devotee of “attitude” flying
                                                            technique-his        creed being “attitude     plus
loo. .................   l.lm        1.30      20.00
110..................      ,826      1.24      15.P         power equals performance.” During a GCA
17.0..................     ,694      1.04      12.7’        approach, the professional instrument pilot
lY) ..................     .444       .61       8.20
200..................                 .38       4.6’
                                                            controls airspeed with stick (angle of attack)
MO. .................      ,111       .I7       2.10        and rate of descent with power adjustment.
4&l. .................     .c453      .o!J      1.10            Maneuvering flight and certain transient
30.7..................     ,040       .06        .T=
600..................      .028       .04        .5O        conditions of flight tend to complicate the
                                                            relationship of angle of attack and airspeed.
                                                            However, the majority of flight and, certainly,
Note that for the conditions of steady flight,               the most critical regime of flight (takeoff, ap-
each airspeed requites a specific angle of attack            proach, and landing), is conducted in essen-
and lift coefficient. This fact provides a fun-              tially steady flight condition.
damental concept of flying technique: Angle                     AIRFOIL LIFT CHARACTERISTICS.              Air-
of attack is tbs primary Controlof airspeedin steady         foil section properties differ from wing or
flight. Of course, the control stick or wheel                airplane properties because of the effect of the
allows the pilot to control the angle of attack              planform. Actually, the wing may have vati-
 and, thus, control the airspeed in steady flight.           ous airfoil sections from root to tip with taper,
 In the same sense, the throttle controls the                twist, sweepback and local flow components
 output of the powerplant and allows the pilot               in a spanwise direction.      The resulting aeto-
 to control rate of climb and descent at various             dynamic properties of the wing are determined
 airspeeds.                                                  by the action of each section along the span
    The teal believers of these concepts ate pro-            and the three-dimensional flow. Airfoil sec-
 fessional instrument pilots, LSO’ and glider                tion properties are derived from the basic shape
 pilots.. The glider pilot (or flameout enthusi-             or profile in two-dimensional flow and the force
 ast) has no recourse but to control airspeed by             coefficients are given a notation of lower case
 angle of attack and accept whatever rate of                 letters. For example, a wing or airplane lift
 descent is incurred at the various airspeeds.               coefficient is C, while an airfoil section lift
 The LSO must become quite proficient at judg-               coefficient is termed cr. Also, wing angle of
 ing the flight path and angle of attack of the              attack is Q while section angle of attack is
 airplane in the pattern. The more complete                  differentiated by the use of 01~. The study of
 visual reference field available to the LSO                  section properties allows an objective consider-
 allows him to judge the angle of attack of                  ation of the effects of camber, thickness, etc.
 the airplane mote accurately than the pilot.                    The lift characteristics of five illustrative
 When the airplane approaches the LSO, the                    airfoil sections are shown in figure 1.12. The
 precise judgment of airspeed is by the angle                section lift coe&icient, c,, is plotted versus
 of attack rather than the rate of closure. If                section angle of attack, olO,for five standard
 the LSO sees the airplane on the desired flight
                                                             NACA airfoil profiles. One characteristic fea-
 path but with too low an angle of attack, the
                                                              ture of all airfoil sections is that the slope of
  airspeed is too high; if the angle of attack is
  too high, the airspeed is too low and the ait-              the various lift curves is essentially the same.
 plane is approaching the stall. The mirror                   At low lift coefhcients, the section lift coeffi-
  landing system coupled with an angle of attack              cient increases approximately 0.1 for each
  indicator is an obvious refinement. The mit-                degree increase in angle of attack. For each
  tot indicates the desired flight path and the               of the airfoils shown, a S’ change in angle of

                       (DATA FROM NACA          REPORT NO. 824)

                               SECTION ANGLE OF ATTACK
                                     mo, DEGREES

                     Figure   1.12.   Lift Characteristics    of lypicol   Airfoil Sections

                                                                                               NAVWEPS OO-BOT-BO
                                                                                              BASIC AE,RODYMAMlCS

attack would produce an approximate 0.5                            sections have zero lift at zero angle of attack,
change in lift coefficient. Evidently, lift,~curve                 the sections with positive camber have nega-
slope is not a factor important in the selection                   tive angles for zero lift.
of an airfoil.                                                        The importance of maximum lift coefficient
    An important lift property affected by the                     is obvious. If the maximum lift coefficient is
airfoil shape is the section maximum lift co-                      high, the stall speed will be low. However,
efficient, ci-.  The effect of airfoil shape on                    the high thickness and camber necessary for
ci- can be appreciated by comparison of the                        high section maximum lift coefficients may
lift curves for the five airfoils of figure 1.12.                  produce low critical Mach numbers and large
The NACA airfoils 63X06,63-009, and 63i-012                        twisting moments at high speed. In other
ate symmetrical sections of a basic thickness                      words, a high maximum lift coefficient is just
distribution but maximum thicknesses of 6,                         one of the many features desired of an airfoil
9, and 12 percent respectively. The effect of                      section.
thickness on ~1% is obvious from an inspec-                           DRAG CHARACTERISTICS.            Drag is the
tion of these curves :                                             net aerodynamic force parallel to the relative
                                                                   wind and its source is the pressure distribution
                                                                   and skin friction on the surface. Large, thick
                                                                   bluff bodies in an airstream show a predomi-
                                       Cl.82          9.0°         nance of form drag due to the unbalanced pres-
NACA                  .~.        :.
NACA                                   1.10          10.5~         sure distribution.       However,    streamlined
NACA 63‘
       -01?,.                          1.40          13.80         bodies with smooth contours show a ptedomi-
                                                                   nance of drag due to skin friction.          In a
The 12-percent section has a cr- approxi-                          fashion similar to other aerodynamic forces,
mately 70 percent greater than the 6-percent                       drag forces may be considered in the form of a
thick section. In addition, the thicker airfoils                   coefficient which is independent of dynamic
have greater benefit from the use of various                       pressure and surface area. The basic drag
high lift devices.                                                 equation is as follows:
    The effect of camber is illustrated by the lift                            D=GqS
curves of the NACA 4412 and 631-412 sections.                                 D=drag, lbs.
The NACA 4412 section is a 12 percent thick                                   C,= drag coefficient
airfoil which has 4 percent maximum camber                                     q= dynamic pressure, psf
located at 40 percent of the chord. The                                            UP
NACA 63i-412 airfoil has the same thickness                                      =z    (V in knots, TAS)
and thickness distribution as the 631-012 but                                   S= wing surface area, sq. ft.
camber added to give a “design” lift coefficient                   The force of drag is shown as the product of
(c, for minimum section drag) of 0.4. The                          dynamic pressure, surface area, and drag co-
lift curves for these two airfoils show that                       efficient, C,. The drag coefficient in this
camber has a beneficial e&t       on cl-.                          equation is similar to any other aerodynamic
                                                                   force coefficient-it    is the ratio of drag pres-
                ScCdO”                %.I     a0 for “&*           sure to dynamic pressure. If the drag co-
                                                                   efficient of a conventional airplane were plotted
NACA 6h-312(symmctricd)     :.         1.40          13.e          versus angle of attack, the result would be
NACA 631-412Whmd).                     1.73          IS. z”
                                                                   typical of the graph shown in figure 1.13. At
                                                                   low angles of attack the drag coefficient is
An additional effect of camber is the change                       low and small changes in angle of attack create
in zero lift angle. While the symmetrical                          only slight changes in drag coefficient. At

                     I                                          a

                         Figure   7.73.   Drag Characteristics   (sheet   1 of 21


     Figure 7.13. Brag Characferistics (sheet 2 of 2)

higher    angles of attack the drag coefficient is              The configuration of an airplane has a great
much greater and small changes in angle of                   effect on the lift-drag ratio. Typical values
attack cause significant changes in drag. As                 of (L/D),..     are listed for various types of
stall occurs, a large increase in drag takes                 airplanes. While the high performance sail-
place.                                                       plane may have. extremely high lift-drag
    A factor more important in airplane per-                 ratios, such an aircraft has no real economic
formance considerations is the lift-drag ratio,              or tactical purpose. The supersonic fighter
L/D.     With the lift and drag data available for           may have seemingly low lift-drag ratios in
the airplane, the proportions of CL and CD can               subsonic flight but the airplane configurations
be calculated for each specific angle of attack.                                                           *
                                                             required for supersonic flight (and high [L/D]‘
The resulting plot of lift-drag ratio with angle             at high Mach numbers) precipitate this situa-
of attack shows that L/D increases to some                   tion.
maximum then decreases at the higher lift                       Many important items of airplane perform-
coefficients and angles of attack. Note that                 ance are obtained in flight at (L/D),...   Typi-
the maximum lift-drag ratio, (L/D),,,,        occurs         cal performance conditions which occur at
at one specific angle of attack and lift coefIi-             (L/D),.,   are:
cient. If the airplane is operated in steady                       maximum endurance of jet powered air-
flight at (L/D),,,,    the total drag is at a mini:
mum. Any angle of attack lower or higher                           maximum range of propeller driven air-
than that for (L/D),,,        reduces the lift-drag
ratio and consequently increases -the total                        maximum climb angle for jet powered air-
drag for a given airpiane iift.
    The airplane depicted by the curves of Figure
                                                                   maximum power-off glide range, jet or
 1.13 has a maximum lift-drag ratio of 12.5 at
 an angle of attack of 6”. Suppose this airplane                      Prop
 is operated in steady flight at a gross weight              The most immediately interesting of these
 of 12,500 lbs. If flown at the airspeed and                 items is the power-off glide range of an air-
 angle of attack corresponding to (L/D),..,                  plane. By examining the forces acting on an
 the drag would be 1,000 lbs. Any higher or                  airplane during a glide, it can be shown that
 lower airspeed would produce a drag greater                 the glide ratio is numerically equal to the
 than 1,000 lbs. Of course, this same airplane               lift-drag ratio. For example, if the airplane
 could be operated at higher or lower gross                  in a glide has an (L/D) of 15, each mile of alti-
 weights and the same maximum lift-drag ratio                tude is traded for 15 miles of horizontal dis-
 of 12.5 could be obtained at the same angle of              tance. Such a fact implies that the airplane
 attack of 6”. However, a change’ in gross                   should be flown at (L/D)-           to obtain the
 weight would require a change in airspeed to                greatest glide distance.
 support the new weight at the same lift co-                     An unbelievable feature of gliding perform-
 efficient and angle of attack.                              ance is the effect of airplane gross weight.
Type airplane:                                               Since the maximum lift-drag ratio of a given
                                     (L/D) emz
   High performance   sailplane.        25-40                airplane is an intrinsic property of the aero-
   Typical patrol or transport..       12-20                 dynamic configuration, gross weight will not
   High Performance   bomber.          2~25                  affect the gliding performance. If a typical
   Propellerpoweredtrainer..           1~15                  jet trainer has an (L/@-        of 15, the aircraft 1
   J et trainer..                      14-16                 can obtain a maximum of 15 miles horizontal
     Transonic fighter or attack..     lo-13                 distance for each mile of altitude.    This would
     Supersonic fighter or attack.     4-9 (subsonic)        be true of this particular airplane at any gross
Revised Januay     1965
                                                                                 NAVWEPS OO-EOT-RO
                                                                                BASIC AERODYNAMICS

weight if the airplane is flown at the angle         40 percent chord. When this section is com-
of attack for (L/D),.        Of course, the gross    pared with the NACA 0006 section the effect
weight would affect the glide airspeed neces-        of camber can be appreciated. At low lift
 sary for this particular angle of attack but the    coefficients the thtn, symmetrical section has
glide ratio would be unaffected.                     much lower drag. However, at lift coeffi-
    AIRFOIL      DRAG       CHARACTERISTICS.         cients above 03 the thicker, cambered section
The total drag of an airplane is composed of         has the lower drag. Thus, proper camber and
the drags of the individual components and           thickness can improve the lift-drag ratio of
the forces caused by interference between these      the section.
components. The drag of an airplane con-                 The NACA 63,412 is a cambered 12 percent
figuration must include the various drags due                                 “
                                                     thick airfoil of the ‘ laminar flow” type.
to lift, form, friction, interference, leakage,      This airfoil is shaped to produce a design lift
etc. To appreciate the factors which affect          coe5cient of 0.4. Notice that the drag curve
the drag of an airplane configuration, it is         of this airfoil has distinct aberrations with
most logical to consider the factors which           very low drag coefficients near the lift coeffi-
affect the drag of airfoil sections. In order to     cient of 0.4. This airfoil profile has its camber
allow an objective consideration of the effects      and thickness distributed to produce very low
of thickness, camber, etc., the properties of        uniform velocity on the forward surface (mini-
two-dimensional      sections must be studied.       mum pressure point well aft) at this lift coeffi-
Airfoil section properties are derived from the      cient.     The resulting pressure and velocity
basic profile in two-dimensional. flow and are       distribution enhance extensive laminar flow
provided the lower case shorthand notation           in the boundary layer and greatly reduce the
to distinguish them from wing or airplane            skin friction drag. The benefit of the laminar
properties, e.g., wing or airplane drag coe5-        flow is appreciated by comparing the minimum
cient is C, while airfoil section drag coefficient   drag of this airfoil with an airfoil which has
is c,.                                               one-half the maximum thickness-the         NACA
    The drag characteristics of three illustrative   ooo6.
airfoil sections are shown in figure 1.14. The           The choice of an airfoil section will depend
section drag coe&cient, c,, is plotted versus        on the consideration oftmany different factors.
the section lift coefficient, cr. The drag on        While the cI, of the section is an important
the airfoil section is composed of pressure drag     quality, a more appropriate factor for con-
and skin friction.     When the airfoil is at low    sideration is the maximum lift coefficient of
lift coe&cients, the drag due to skin friction       the section when various high lift devices are
predominates. The drag curve for a conven-           applied. Trailing edge flaps and leading edge
tional airfoil tends to be quite shallow in this     high lift devices are applied to increase the
region since there is very little variation of       cr,, for low speed performance.         Thus, an
skin friction with angle of attack. When the         appropriate factor for comparison is the ratio
airfoil is at high lift coefficients, form or        of section drag coe5cient to section maximum
pressure drag predominates and the drag co-          lift coefficient with flaps-cd/crm,. When this
efficient varies rapidly with lift coefficient.      quantity is corrected for compressibility,      a
The NACA 0006 is a thin symmetrical profile          preliminary selection of an airfoil section is
which has a maximum thickness of 6 percent           possible. The airfoil having the lowest value
located at 30 percent of the chord. This             of c&~, at the design flight condition (en-
section shows a typical variation of cd and cr.      durance, range, high speed, etc.) will create
    The NACA 4412 section is a 12 percent thick       the least section drag for a given .design stall
airfoil with 4 percent maximum camber at              speed.

                             (DATA FROM NACA REPORT ~0.824)

                    SMOOTH SURFAC

        -.2    Cl       .2       .4        .6    .8          ---I.2
                                                           LO’        1.4    1.6    1.8

                                      SECTION LIFT COEFFICIENT
                    Figure 1.14. Drag Characteristics of Typical Airfoil Sections

                                                                                      NAVWEPS 00-BOT-RO
                                                                                     BASIC AERODYNAMICS

PLIGHT AT HIGH LIFT CONDITIONS                            fuel. Hence, the gross weight and stall speed
                                                          of the airplane can vary considerably through-
    It is frequently stated that the career Naval         out the flight.    The effect of only weight on
 Aviator spends more than half his life “below            stall speed can be expressed by a modified form
 a thousand feet and a hundred knots.”        Re-         of the stall speed equation where density ratio,
 gardless of the implications of such a state-            c r,,,.,, and wing area are held constant.
ment, the thought does cunnute the relation-
                                                                  _i_z- K
ship of minimum flying speeds and carrier
aviation.     Only in Naval Aviation is there                     v.,- J K
such importance assigned to precision control             where
of the aircraft at high lift conditions.     Safe                 V*,=stall speed corresponding to some
operation in carrier aviation demands precision                         gross weight, WI
control of the airplane at high lift conditions.                  V@a=stall speed corresponding to a dif-
    The aerodynamic lift characteristics of an                          ferent gross weight, WP
airplane are portrayed by the curve of lift               As an illustration of this equation, assume
coefficient versus angle of attack.       Such a          that a particular airplane has a stall speed of
curve is illustrated in figure 1.15 for a specific        100 knots at a gross weight of 10,000 lbs.
airplane in the clean and flap down configura-            The stall speeds of this Sam: airplane at other
tions. A given aerodynamic configuration ex-
                                                          gross weights would be:
periences increases in lift coefficient with in-
creases in angle of attack until the maximum
lift coefficient is obtained. A further increase
in angIe of attack produces stall and the lift               ll,W        100x ‘&~=lO,
coefficient then decreases. Since the maximum                               4,
lift coefficient corresponds to the minimum                   12,ooO                    110
speed available in flight, it is an important                 14,4al                    120
point of reference. The stall speed of the air-                9mJ                       95
                                                               8,100                     90
craft in level flight is related by the equation:
                                                          Figure 1.15 illustrates the effect of weight on
          V7.=17.2      c w                               stall speed on a percentage basis and will be
                     J-- .ln2s                            valid for any airplane. Many specific condi-
where                                                     tions of flight are accomplished at certain fixed
           V.-stall   speed, knots TAS                    angles of attack and lift coefficients. The
           W=gross weight, lbs.                           effect of weight on a percentage basis on the
        c Lnoz=airplane maximum lift coefficient          speeds for any specific lift coefficient and angle
            csaltitude density ratio                      of attack is identical.      Note that at small
            S= wing area, sq. ft.                         variations of weight, a rule of thumb may
                                                          express the effect of weight on stall speed-
This equation illustrates the effect on stall             “a 2 percent change in weight causes a I per-
speed of weight and wing area (or wing load-              cent change in stall speed.”
ing, W/S), maximum lift coefficient, and alti-               EFFECT OF MANEUVERING                 FLIGHT.
tude. If the stall speed is desired in EAS, the           Turning flight and maneuvers produce an
density ratio will be that for sea level (u=              effect on stall speed which is similar to the
 1.000).                                                  effect of weight.    Inspection of the chart on
   EFFECT OF WEIGHT.            Modern configu-           figure 1.16 shows the forces acting on an airplane
rations of airplanes are characterized by a large         in a steady turn. Any steady turn requires
percent. of the maximum gross weight being                that the vertical component of Iift be equal to

                                      EFFECT OF FLAPS


                                          5     IO      I5     20      25

                                  I            ANGLE OtATTACK

                               EFFECT OF WEIGHT ON STALL SPEED

                           Figure 1.15.   Flight at High Lift Conditions

                                                                                              NAVWEPS 00-8OT-80
                                                                                             BASIC AERODYNAMICS

weight of the airplane and the horizontal com-                 EFFECT OF HIGH LIET DEVICES.                The
ponent of lift be equal to the centrifugal force.           primary purpose of high lift devices (flaps,
Thus, the aircraft in a steady turn develops a              slots, slats, etc.) is to increase the CLn, of the
lift greater than weight and experiences in-                airplane and reduce the stall speed. The take-
creased stall speeds.                                       off and landing speeds are consequently re-
    Trigonometric ‘ relationships allow deter-              duced. The effect of a typical high lift device
mination of the effect of bank angle on stall               is shown by the airplane lift curves of figure
speed and load factor. The load factor, B, is               1.15 and is summarized here:
the proportion between lift and weight and is
determined by:
                                                                        c.mip~tion                     L.                    ,
                                                                                                                    (II far C‘
                          W                                 clun(tla~Up) . . . .
                                                                       .               . . . .. .. .        1.5            200
                                                            Php down.                                       2.0            IS.9
                      n=- 1
                         cos I$
where                                                       The principal effect of the extension of flaps is
       n=load factor (or “G”)                               to increase the C,, and reduce the angle of
   cos 6 = cosine of the bank angle, + (phi)                attack for any given lift coefficient. The in-
                                                            crease in CL,, afforded by flap deflection re-
Typical values of load factor determined by                 duces the stall speed in a certain proportion,
this relationship are:
                                                            the effect described by the equation:
    .+.- 00   130     300      450      600    759                             -
                                                                    v,=v,      z%
    n-l.00    1.035   1.154    1.414                         J Ch,
The stall speed in a turn can be determined by:
                                                                     V,,= stall speed with flaps down

                                                                      v,=stall       speed without          flaps
  v,+= stall speed at some bank angle +                              C,=    maximum lift coefficient of
   V,= stall speed for wing level, lift-equal-
        weight flight                                                            the clean configuration
     n=load factor corresponding to the
                                                                    C&,= maximum lift coefficient
        bank angle
                                                                                 with flaps down
The percent increase in stall speed in a turn is
shown on figure l.i6.    Since this chart is predi-
                                                            For example, assume the airplane                 described by
cated on a steady turn and constant CL,, the                the lift curves of figure 1.15 has a            stall speed of
figures a!e valid for any airplane. The chart               100 knots at the landing weight                  in the clean
shows that no appreciable change in load fac-               configuration.     If the flaps are             lowered the
tor or stall speed occurs at bank angles less than          reduced stall speed is reduced to:
30“. Above 4S” of bank the increase in load
factor and stall speed is quite rapid. This fact
emphasizes the need for avoiding steep turns at
low airspeeds-a flight condition common to
stall-spin accidents.                                                                =86.5 knots
NAVWWS 00-8OT-80

                                                 .#a, GANK~ANGLE, DEGREES

                           EFFECT OF c            ONSTALL        SPEED



                            150                                                  %



                                        IO       20         30    40     50
                                                IN STALL SPEED

                             Figure   7.76.   Flight   at High Liff Conditions

  Revised Jarwary   1965
                                                                                            NAVWEPS OO-EOT-RO
                                                                                           BASIC AERODYNAMICS

Thus, wirh rhe higher lift coefficienr available,              angle of attack is unaffected. At any parricu-
less dynamic pressure is required to provide                   lar altitude, the indicated stall speed is a func-
the necessary lift.                                            tion of weight and load factor. An increase
   Because of the stated variation of stall speed              in altitude will produce a decrease in density
with C-, large changes in CL- are necessary                    and increase the true airspeed at stall. Also,
to produce significant changes in stall speed.                 an increase in altitude will alter compressibility
This effect is illustrated by the graph in figure              and viscosity effects and, generally speaking,
1.16 and certain typical values are shown                      cause the in,&ztcd stall speed to increase.
below:                                                         This parti&lar      consideration is usually sig-
                                                               nificant only above altitudes of 20,000 ft.
Percentincrease CL.        .~.    2   10 so   loo   300
                                                                  Recovery from stall involves a very simple
Percent reductionin stall speed   1   5 18     29   50         concept. Since stall is precipitated by an
                                                               excessive angle of attack, the angle of attack
The contribution of the high lift devices must                 must be dccmmd. This is a fundamental princi-
be considerable to cause large reduction in                    ple which is common to any airplane.
stall speed. The most elaborate combination                       An airplane may be designed to be “stall-
of flaps, slots, slats, and boundary layer con-                proof” simply by reducing the effectiveness of
trol throughout the span of the wing would                     the elevators. If the elevators are not power-
be required to increase C,- by 300 percent.                    ful enough to hold the airplane to high angles
A common case is that of a typical propeller                   of attack, the airplane cannot be stalled in any
driven transport which experiences a 70 per-                   condition of flight.     Such a requirement for a
cent increase in CzIM1by full flap deflection.                 tactical military airplane would seriously re-
A typical single engine jet fighter with a thin                duce performance. High lift coefficients near
swept wing obtains a 20 percent increase in                    the maximum are required for high maneuver-
CL- by full flap deflection. Thin airfoil sec-                 ability and low landing and takeoff speeds.
tions with sweepback impose distinct limita-                   Hence, the Naval Aviator must appreciate the
tions on the effectiveness of flaps and the 20                 effect of the many variables affecting the stall
percent increase in CL- by flaps is a typical-                 speed and regard “attitude flying,” angle of
                                                               attack indicators, and stall warning devices
if not high-value for such a configuration.
                                                               as techniques which allow more precise control
    One factor common to maximum lift condi-
                                                               of the airplane at high lift conditions.
tion is the angle of attack and pressure distri-
bution. The maximum lift coefficient of a
particular wing configuration is obtained at                   HIGH    LIFT DEVICES
one angle of attack and one pressure distribu-                    There are many different types of high lift
tion. Weight, bank angle, load factor, density                 devices used to increase the maximum lift co-
altitude, and airspeed have no direct effect on                efficient for low speed flight.     The high lift
the stall angle of attack. This fact is sufficient             devices applied to the trailing edge of a section
justification for the use of angle of attack indi-             consist of a flap which is usually 15 to 25 per-
cators and stall warning devices which sense                   cent of the chord. The deflection of a flap
pressure distribution    on the wing. During                   produces the effect of a large amount of camber
flight maneuvers, landing approach, takeoff,                   added well aft on the chord. The principal
turns, etc. the airplani will stall if the critical            types of flaps are shown applied to a basic sec-
angle of attack is cxcccdcd. The airspeed ar                   tion of airfoil.  The effect of a 30’ deflection of
which stall occurs will be determined by                       a 25 percent chord flap is shown on the lift
weight, load factor, and altitude but the stall                and drag curves of figure 1.17.


                                                BASIC     SECTION

                    PLAIN     FLAP                                             SPLIT    FLAP

                   SLOTTED         FLAP                                       FOWLER    FLAP

                                   EFFECT ON SECTION-LIFT   AND DRAG
                                   CHARACTERISTICS   OF A 25% CHORD
                                         FLAP DEFLECTED    30°

                                          SLOTTED                                      FOW&ER
                                                         3.0 -

                                                         2.5 -

                                                         2.0 -

                                                          1.5 -


                                                           .5 -

                                                           0 -I-
                  SECTION          ANGLE OF ATTACK                   SECTION     DRAG COEFFICIENT
                            o,,,     DEGREES                                           cd

                                       Figure   1.17.   Flap Configurations

Revised January   1965
                                                                                        NAVWEPS OO-BOT-BO
                                                                                       BASIC AERODYNAMICS

     The plainjap shown in figure 1.17 is a simple           loads on the structure and pitching moments
  hinged portion of the trailing edge. The effect            that must be controlled with the horizontal
  of the camber added well aft on the chord                  tail. Unfortunately, the flap types producing
 causes a significant increase in cbr. In addi-              the greatest increases in c,,- usually cause the
  tion, the zero lift angle changes to a more                greatest twisting moments. The Fowler flap
  negative value and the drag increases greatly.             causes the greatest change in twisting moment
 The split flap shown in figure 1.17 consist of              while the split flap causes the least. This
 plate deflected from the lower surface of the               factor-along with mechanical complexity of
 section and produces a slightly greater change              the installation-may      complicate the choice
 in cImoT than the plain flap. However, a much               of a flap configuration.
 larger change in drag results from the great                   The effectiveness of flaps on a wing con-
 turbulent wake produced by this type flap.                  figuration depend on many different factors.
 The greater drag’  may not be such a disadvan-              One important factor is the amount of the
 rage when ir is realized that it may be advan-              wing area affected by the flaps. Since a
 tageous to accomplish steeper landing ap-                   certain amount of the span is reserved for
 proaches over obstacles or require higher power             ailerons, the actual wing maximum lift prop-
 from the engine during approach (to minimize                erties will be less than that of the flapped
 engine acceleration time for waveoR).                       two-dimensional section. If the basic wing
     The slottedPap is similar to the plain flap but         has a low thickness, any type of flap will be
 the gap between the main section and flap                   less effective than on a wing of greater thick-
 leading edge is given specific contours. High               ness. Sweepback of the wing can cause an
energy air from the lower surface is ducted to               additional significant reduction in the effec-
 the flap upper surface. The high energy air                 tiveness of flaps.
from the slot accelerates the upper surface                     High lift devices applied to the leading edge
boundary layer and delays airflow separation                of a section consist of slots, slats, and small
to some higher lift coefficient. The slotted                 amounts of local camber. The fixed slot in a
flap can cause much greater increases in c,,,                wing conducts flow of high energy air into the
than the plain or split flap and section drags               boundary layer on the upper surface and delays
are much lower.                                              airflow separation to some higher angle of
     The Fowkr&zp arrangement is similar to the             attack and lift coefficient. Since the slot
slotted flap. The difference is that the de-                alone effects no change in camber, the higher
flected flap segment is moved aft along a set of
                                                            maximum lift coefficient will be obtained at a
tracks which increases the chord and effects
                                                            higher angle of attack, i.e., the slot simply
an increase in wing area. The Fowler flap is
characterized by large increases in c,,, with               delays stall to a higher angle of attack. An
minimum changes in drag. ,.                                 automatic slot arrangement consists of a
     One additional factor requiring consider-              leading edge segment (slat) which is free to
ation in a comparison of flap types is the aero-            move on tracks. At low angles of attack the
dynamic twisting        moments caused by the               slat is held flush against the leading edge by
flap. Positive camber produces a nose down                  the high positive local pressures. When the
twisting moment-especially        great when large          section is at high angles of attack, the high
camber is used well aft on the chord (an                    local suction pressures at the leading edge
obvious implication is that flaps are not prac-             create a chordwise force forward to actuate
tical on a flying wing or tailless airplane).               the slat. The slot formed then allows the
The deflection of a flap causes large nose down             section to continue to a higher angle of attack
moments which create important twisting                     and produce a clno. greater than that of the

                                                                  AUTOMATIC   SLOT


                                                          BOUNDARY LAYER CONTROL
                                                           BY FLAP AUGMENTATION

                                                      0     2.4
                     FIXED SLOT\

                                                                                              LOW SUCTION

                                                                                       ,BASIC SECTION
                                                                                         NO SUCTION

       0-l                                                     0~ :
  -5     0      5      IO       I5          20                    0     5       IO      I5    20    25
             SECTION ANGLE OF ATTACK                                    SECTION ANGLE OF ATTACK
                    00, DEGREES                                                00, DEGREES
                     Figure   7.18.   Ekt        of Slots and Boundary      Layer Control

                                                                                  NAVWEPS OO-BOT-RO
                                                                                 BASIC AERODYNAMICS

 basic section. The effect of a fixed slot on           stagnate and come to a stop. If this happens
 the lift characteristics is shown in figure 1.18.      the airflow will separate from the surface and
    .UO~Jana’ &Z~J can produce significant in-          stall occurs. Boundary layer control for high
 creases in cl, but the increased angle of              lift applications features various devices to
 attack for maximum lift can be a disadvantage.         maintain high velocity in the boundary layer
 If slots were the only high lift device on the         to allay separation of the airflow.    This con-
 wing, the high take off and landing angles of          trol of the boundary layer kinetic energy can
 attack may complicate the design of the                be accomplished in two ways. One method is
 landing gear. For this reason slots or slats           the application of a suction through ports to
 are usually used in conjunction with flaps             draw off low energy boundary layer and replace
 since the flaps provide reduction in the maxi-         it with high velocity air from outside the
 mum lift angle of attack. The use of a slot            boundary layer. The effect of surface suction
 has two important advantages: there is only a          boundary layer control on lift characteristics
negligible change in the pitching moment                is typified by figure 1.18. Increasing surface
 due to the slot and no significant change in           suction produces greater maximum lift coe5-
section drag at low angles of attack.       In fact,    cients which occur at higher angles of attack.
the slotted section will have less drag than            The effect is similar to that of a slot because
the basic section near the maximum lift angle          the slot is essentially a boundary layer control
for the basic section.                                  device ducting high energy air to the upper
    The slot-slat device finds great application        surface.
 in modern airplane configurations.      The tail-          Another method of boundary layer control
less airplane configuration can utilize only the        is accomplished by injecting a high speed jet
high lift devices which have negligible effect          of air into the boundary layer. This method
 on the pitching moments. The slot and slat            produces essentially the same results as the
are often used to increase the cl- in high speed       suction method and is the more practical in-
flight when compressibility effects are con-           stallation.    The suction type BLC requires the
siderable. The small change in twisting mo-            installation of a separate pump while the
ment is a favorable feature for any high lift           “blown” BLC system can utilize the high pres-
device to be used at high speed. Leading edge          sure source of a jet engine compressor. The
high lift devices are more effective on the            typical installation of a high pressure BU
highiy swept wing than trailing edge flaps             system would be the augmentation of a de-
since slats are quite powerful in controlling the      flected flap. Since any boundary layer control
flow pattern. Small amounts of local camber            tends to increase the angle of attack for maxi-
added to the leading edge as a high lift device        mum lift, it is important to combine the bound-
is most effective on wings of very low thick-          ary layer control with flaps since the flap de-
ness and sharp leading edges. Most usually             flection tends to reduce the angIe of attack for
the slope of the leading edge high lift device         maximum lift
is used to control the spanwise lift distribution           OPERATION OF HIGH LIFT DEVICES.
on the wing.                                           The management of the high lift devices on an
                                                       airplane is an important factor in flying opera-
   Boundary larcr control devices are additional
   ‘                                                   tions. The devices which are actuated auto-
means of increasing the maximum lift coe&-             matically-such     as automatic slats and slots-
cient of a section. The thin layer of airflow          are usually of little concern and cause little
adjacent to the surface of an airfoil shows re-        complication since relatively small changes in
duced local velocities from the effect of skin         drag and pitching moments take place. How-
friction.   When at high angles of attack this         ever, the flaps must be properly managed by
boundary layer on the upper surface tends to           the pilot to take advantage of the capability
S3lWvNAaOtl3v~ mva
 08-108-00 Sd3MAQN
                                                                                       NAVWEPS OO-EOT-SO
                                                                                      BASIC AERODYNAMICS

of such a device. To illustrate a few principles            When the flaps are lowered for landing essen-
 of flap management, figure 1.19 presents the               tially the same items must be considered. Ex-
lift and drag curves of a typical airplane in the           tending the flaps will cause these. changes to
 clean and flap down configurations.                        take place:
     In order to appreciate some of the factors                    (1) Lowering the flaps requires retrim-
 involved in flap management, assume that the                   ming to balance the nose down moment
 airpIane has just taken off and the flaps are                  change.
 extended. The pilot should not completely                         (2) The increase in drag requires a higher
 retract the flaps until the airplane has sufficient            power setting to maintain airspeed and
 speed. If the flaps are retracted prematurely                  altitude.
 at insufhcient airspeed, maximum lift coefi-                      (3) The angle of attack required to pro-
 cient of the clean configuration may not be                    duce the same lift coefficient is less, e.g.,
 able to support the airplane and the airplane                  flap extension tends to cause the airplane to
 will sink or stall. Of course, this same factor                “balloon.”
must be considered for intermediate flap posi-                  An additional factor which must be consid-
 tions between fully retracted and fully ex-                ered when rapidly accelerating after takeoff,
 tended. Assume that the airplane is allowed                or when lowering the flaps for landing, is the
 to gain speed and reduce the flight lift coefii-           limit airspeed for flap extension. Excessive
 cient to the point of flap retraction indicated            airspeeds in the flap down configuration may
 on figure 1.19. As the configuration is altered            cause structural damage.
 from the “cluttered” to the clean configura-                   In many aircraft the effect of intermediate
tion, three important changes take place:                   flap deflection is of primary importance in
       (1) The reduction in camber by flap re-              certain critical operating conditions.      Small
    traction changes the wing pitching moment               initial deflections of the flap cause noticeable
    and-for the majority of airplanes-requires                              s,,
                                                            changes in C’ without large changes in drag
    retrimming to balance the nose up moment                coefficient. This feature is especially true of
    change. Some airplanes feature an automat-              the airplane equipped with slotted or Fowler
    ic retrimming which is programmed with                  flaps (refer to fig. 1.17). Large flap deflections
    flap deflection.                                        past 30’ to 33’ do not create the same rate of
       (2) The retraction of flaps shown on                 change of Cs- but do cause greater changes in
    figure 1.19 causes a reduction of drag coeffi-          CD. A fact true of most airplanes is that the
    cient at that lift coefficient. This drag               first 50 percent of flap deflection causes mwc
    reduction improves the acceleration of the              than half of the total change in Cr.- and the
    airplane.                                               last 50 percent of flap deflection causes mo~c
       (3) The retraction of flaps requires an              than half of the total change in Cs.
    increase in angle of attack to maintain the                 The effect of power on the stall speed of an
    same lift coefficient. Thus, if airplane accel-         airplane is determined by many factors. The
    eration is low through the flap retraction              most important factors affecting this relation-
    speed range, angle of attack must be in-                ship are powerplant type (prop or jet), thrust-
    creased to prevent the airplane from sinking.           to-weight ratio, and inclination of the thrust
    This situation is typical after takeoff when            vector at maximum lift.       The effect of the
    gross weight, density altitude, and tempera-
                                                            propeller is illustrated in figure 1.20. The
    ture are high. However, some aircraft have
    such high acceleration through the flap re-             slisstream velocity behind the propeller is
    traction speed that the rapid gain in air-              different from the free stream velocity depend-
    speed requtres much less noticeable attitude            ing on the thrust developed. Thus, when the
    change.                                                 propeller driven airplane is at low air+ceds

                                          n  r
                                                       INDUCED FLOW
                                                      FROM PROPELLER

                     n            c;

                         figure 1.20. Power Effects

                                                                                       NAVWEPS 00-801~0
                                                                                      BASIC AERODYNAMICS

 and high power, the dynamic pressure in the               net lift produced by the airfoil is difference
 shaded area can be much greater than the free             between the lifts on the upper and lower sur-
 stream and this causes considerably greater               faces. The point along the chord where the
 lift than at zero thrust.     At high power con-          distributed lift is effectively concentrated is
 ditions the induced flow also causes an effect            termed the “center of pressure, c.p.“ The
 similar to boundary layer control and increases           center of pressure is essentially the “center of
the maximum lift angle of attack. The typical              gravity” of the distributed lift pressure and
four-engine propeller driven airplane may have             the location of the c.p. is a function of camber
60 to 80 percent of the wing area affected by              and section lift coe&cient
the induced flow and power effects on stall                    Another aerodynamic reference point is the
 speeds may be considerable. Also, the lift of              “aerodynamic center, d.e.” The aerodynamic
 the airplane at a given angle of attack and air-          center is defmed as the point along the chord
 speed will be greatly affected. Suppose the               where all changesin lift effectively take place.
 airplane shown is in the process of landing               To visualize the existence of such a point,
flare from a power-on approach. If there is                notice the change in pressure distribution with
 a sharp, sudden reduction of power, the air-              angle of attack for the symmetrical airfoil
plane may drop suddenly because of the reduced             of figure 1.21. When at zero lift, the upper
lift.                                                      and lower surface lifts are equal and located
     The typical jet aircraft does not experience          at the same point. With an increase in angle
the induced flow velocities encountered in                 of attack, the upper surface lift increases while
propeller driven airplanes, thus the only sig-             the lower surface lift decreases. The change
nificant factor is the vertical component of               ,of lift has taken place with no change in the
thrust. Since this vertical component con-                 center of pressure-a characteristic of sym-
tributes to supporting the airplane, less aero-            metrical airfoils.
dynamic lift is required to hold the airplane                  Next, consider the cambered airfoil of
in flight.    If the thrust is small and the thrust        figure 1.21 at zero lift. To produce zero lift,
inclination is slight at maximum lift angle,               the upper and lower surface lifts must be equal.
only negligible changes in stall speed will re-            One difference noted from the symmetrical air-
sult. On the other hand, if the thrust is very             foil is that the upper and lower surface lifts are
great and is given a large inclination at maxi-            not opposite one another. While no net lift
mum lift angle, the effect on stall speed can              exists on the airfoil, the couple produced by
be very large. One important relationship                  the upper and lower surface lifts creates a nose
remains-since there is very little induced flow            down moment. As the angle of attack is in-
from the jet, the angle of attack at stall is              creased, the upper surface lift increases while
 essentially the same power-on or power-off.               the lower surface lift decreases. While a
                                                           change in lift has taken place, no change in
  PITCHING MOMENTS                                         moment takes place about the point where
                                                           the lift change occurs. Since the moment
   The distribution of pressure over a surface
                                                           about the aerodynamic center is the product
is the ,source of the aerodynamic moments as
                                                           of a force (lift at the c.P.) and a lever arm
well as the aerodynamic forces. A typical
example of this fact is the pressure distribution          (distance from c.9. to a.~.), an increase in lift
acting on the cambered airfoil of figure 1.21.             moves the center of pressure toward the aero-
The upper surface has pressures distributed                dynamic center.
which produce the upper surface lift; the lower               It should be noted that the symmetrical air-
surface has pressures distributed which pro-               foil at zero lift has no pitching moment about
duce the lower surface lift.     Of course, the            the aerodynamic center because the upper and

                                      CAMBERED AIRFOIL
                               UPPER DEVELOPING POSITIVE


                         LOWER SURFACE LIFT

        SYMMETRICAL AIRFOIL                                 CAMBERED AIRFOIL
            AT ZERO LIFT                                       AT ZERO LIFT

                             UPPER SURFACE                                 A- UPPER SURFACE

                            LOWER SURFACE
                                 LIFT                          FLOWER        SURFACE LIFT

        SYMMETRICAL AIRFOIL                                CAMBERED AIRFOIL
           AT POSITIVE LIFT                                  AT POSITIVE LIFT

                            UPPER SURFACE LIFT                             A-UPPER SURFACE LIFT

                            LOWER SURFACE LIFT                        LOWER SURFACE LIFT

                            CHANGE IN LIFT                                 CHANGE IN LIFT
                     t                                              +
                     +                                          c          PITCHING MOMENT
                     O.C.                                           0.e.

                              Figure 1.27. Development of Pitching Moments

                                                                                     NAVWEPS O&601-80
                                                                                    BASIC AERODYNAMICS

lower surface lifts act along the same vertical          C%C. versus lift    coefficient for several repre-.
line. An increase in.lift on the symmetrical             sentative sections. The sign convention ap-
airfoil produces no change in this situation and         plied to moment coefficients is that the nose-up
the center of pressure remains fixed at the aero-        moment is positive.
dynamic center.                                             The NACA Ooog airfoil is a symmettical sec-
    The location of the aerodynamic center of an         tion of 9 percent maximum thickness. Since
airfoil is not affected by camber, thickness, and        the mean line of this airfoil has no camber,
angle of attack. In fact, two-dimensional in-            the coefhcient of moment about the aerody-
compressible airfoil theory will predict the             namic center is zero, i.e., the c.p. is at the ac.
aerodynamic center at the 25 percent chordpoint          The departure from zero cno.+ occurs only as the
for any airfoil regardless of camber, thickness,         airfoil approaches maximum lift and the stall
and angle of attack. Actual airfoils, which              produces a moment change in the negative
are subject to real fluid flow, may not have the         (nose-down) direction.        The NACA 4412 and
lift due to angle of .attack concentrated at the         63,-412 sections have noticeable positive cam-
exact 25 percent chord point. However, the               ber which cause relatively large moments about
actual location of the aerodynamic center for            the aerodynamic center. Notice that for each
various sections is rarely forward of 23 percent         sectionshowninfrgure 1.22, the c,,,....isconstant
or aft of 27 percent chord point.                        for all lift coefficients less than cl,-.
    The moment about the aerodynamic center                 The NACA 23012 airfoil is a very efficient
has its source in the relative pressure distribu-        conventional section which has been used on
tion and requires application of the coefficient         many airplanes. One of the features of the
form of expression for proper evaluation. The            ~section is a relatively high c& with only a
moment about the aerodynamic center is ex-               small c,,,,,,; The pitching moment coefficients 1
pressed by the following equation :                      for this section are shown on figure 1.22 along
                                                         with the effect of various type flaps added to
                                                         the basic section. Large amounts of camber
where                                                    applied well aft on the chord cause large nega-
                                                         tive moment coefficients. This fact is illus-
 A&, = moment about the aerodynamic center,
                                                         trated by the large negative moment coefli-
        a.c., ft.-lbs.
                                                         cients produced by the 30” deflection of a 25
CMa.c,=coefbcient of moment about the a.c.               percent chord flap.
                                                            me kc.      is a quantity determined by the
    q= dynamic pressure, psf                             shape of the mean-camber line. Symmetrical
                                                         airfoils have zero c,,,,. and the c.p. remains at
    S=wing     area, sq ft.                              the a.~. in unstalled flight.     The airfoil with
                                                         positive camber will have a negative c,,,~,~,
    c=chord,    ft.                                      which means the c.p. is behind the a.~. Since
                                                         the c5.c. is constant in unstalled flight a certain
The moment coefficient used in this equation is          relationship between lift coefficient and center
the dimensionless ratio of the moment pressure           of pressure can be evolved. An example of
to dynamic pressure moment and is a function             this relationship is shown in figure 1.22 for the
                                                         NACA 63i-412 airfoil by a plot of c.p. versus
                      c %.c. = p-                        c,. Note that at low lift coefficients the center
                                                         of pressure is well aft-even past the trailing
of. the shape of the airfoil mean camber line.           edge-and an increase in C~      moves the c.p, for-
Figure 1.22 shows the moment coefficient,                ward toward the a.~. The c.9. approaches the
                                                                                    Revised Jmuoy    1965
NAVWEPS 00-801-80

            5 -0.2                      1
                              NACA 23012 WITH SPLIT
                                                    I 25k FLAP ATI 3D”
            ”                                       I        I        1     I
                                        I                    1
                                  I         25%
                   -0.3   -
                              NACA 23012 WITH PLAIN FLAP AT 30’
                                                                      1 I                   .\
                                NACA 23012 WITH SLOTTED FLAP &T 30”
                                                                      I I            I


                                                    CP POSITION PERCENT CHORD
                                                       AFT OF LEADING EDGE

                               Figure       1.22.       Section Moment    Characteristics
 Revised January     1965
                                                                                          NAVWEPS D&801-80
                                                                                         BASIC AERODYNAMICS

              CHANGE IN LIFT                                  CHANGE IN LIFT
              DUE TO UPGUST                                   DUE TO UPGUST

                                                                       t    (UNSTABLE)

                C:G. 1

                                      t LIFT


                                Figure 1.23. Application     to Stability

AC. as a limit but as stall occurs, the drop in          aerodynamic center. This very necessary fea-
suction near the leading’ edge cause the c.p. to         ture can be visualized from the illustrations of
move aft.                                                figure 1.23.
   Of course, if the airfoil has negative camber,           If the two symmetrical airfoils are subject
or a strongly reflexed trailing edge, the moment         to an upgust, an increase in lift will take place
about the aerodynamic center will be positive.           at the 4.c. If the c.g. is ahead of the ax., the
In this case, the location of the aerodynamic            change in lift creates a nose down moment
center will be unchanged and will remain at              about the c.g. which tends to return the air-
the quarter-chord position.                              foil to the. equilibrium angle of attack. This
   The aerodynamic center is the point on the            stable, “weathercocking” tendency to return
chord where the coefficients of moment are               to equilibrium is a very necessary feature in
constant-the      point where all changes in lift        any airplane. If the c.g. is aft of the a.~., the
take place. The aerodynamic center is an cx-             change in lift due to the upgust takes place at
tremely important aerodynamic reference point            the AC. and creates a nose up moment about
and the most direct application is to the longi-         the c.g. This nose up moment tends to displace
tudinal stability of an airplane. To simplify            the airplane farther from the equilibrium and
the problem assume that the airplane is a                is unstable-the     airplane is similar to a ball
tailless or flying wing type. In order for this          balanced on a peak. Hence, to have a stable
type airplane to have longitudinal stability,            airplane, the c.g. must be located ahead of the
the center of gravity must be ahead of the               airplane rl.c.

    An additional requirement of stability is               boundary layer. This smooth laminar flow
that the airplane must stabilize and be trimmed             exists without the air particles moving from
for flight at positive lift.   When the c.g. is             a given elevation.
located ahead of d.c., the weight acting at the                As the flow continues back from the leading
c.g. is supported by the lift developed by the              edge, friction forces in the boundary layer
section. Negative camber is required to pro-                continue to dissipate energy of the airstream
duce the positive moment about the aerody-                  and the laminar boundary layer increases in
namic center which brings about equilibrium                 thickness with distance from the leading edge.
ot balance at positive lift.                                After some distance back from the leading
    Supersonic flow produces important changes              edge, the laminar boundary layer begins an
in the aerodynamic characteristics of sections.             oscillatory disturbance which is unstable. A
The aerodynamic center of airfoils in subsonic              waviness occurs in the laminar boundary layer
flow is located at the 25 percent chord point.              which ultimately       grows larger and more
As the airfoil is subject to supersonic flow, the           severe and destroys the smooth laminar flow.
aerodynamic center changes to the 50 percent                Thus, a transition takes place in which the
chord point.     Thus, the airplane in transonic            laminar boundary layer decays into a “turbu-
flight can experience large changes in longitu-             lent” boundary layer. The same sort of
dinal stability because of the large changes in             transition can be noticed inthe smoke from a
the position of the aerodynamic center.                     cigarette in still air. At, first, the smoke
                                                            ribbon is smooth and laminar, then develops
                                                            a definite waviness, and decays into a random
    &--v~se the +ir hAas.~~.v-~c~~vair -7ill ---
                           , .“I”., L, ,   I. 11 -11        turbulent smoke pattern.
 counter resistance to flow over a surface. The                As soon as the transition to. the turbulent
 viscous nature of airflow reduces the local                boundary layer takes place, the boundary
 velocities on a surface and accounts for the               layer thickens and grows at a more rapid rate.
drag of skin friction.     The retardation of air           (The small scale, turbulent flow within the
particles due to viscosity is greatest immedi-              boundary layer should not be confused with
 ately adjacent to the surface. At the very sur-            the large scale turbulence associated with
face of an object, the air particles are slowed to          airflow separation.) The flow in the turbu-
a relative velocity of near zero. Above this                lent boundary layer allows the air particles to
area other particles experience successively                travel from one layer to another producing an
 smaller retardation until finally, at some dis-            energy exchange. However, some small lami-
tance above surface, the local velocity reaches             nar flow continues to exist in the very lower
the full value of the airstream above the sur-              levels of the turbulent boundary layer and is
face. This layer of air over the surface which              referred to as the “laminar sub-layer.” The
shows local retardation of airflow from vis-                turbulence which exists in the turbulent bound-
cosity is termed the “boundary layer.” The
                                                            ary layer allows determination of the point of
characteristics of this boundary layer are illus-
                                                            transition by several means. Since the turbu-
trated in figure 1.24 with the flow of air over
a smooth flat plate.                                        lent boundary layer transfers heat more easily
   The beginning flow on a smooth surface gives             than the laminar layer, frost, water, and oil
evidence of a very thin boundary layer with                 films will be removed more rapidly from the
the flow occurring in smooth laminations,                   area aft of the transition point. Also, a-small
The boundary layer flow near the leading edge               probe may be attached to a stethoscope and
is similar to layers or laminations of air slid-            positioned at various points along a surface.
ing smoothly over one another and the obvi-                 When the probe is in the laminar area, a low
ous term for this type of flow is the “laminar”             “hiss” will be heard; when the probe is in
                      DEVELOPMENT        OF    BOUNDARY        L~AYER
                             ON   A   SMOOTH     FLAT    PLATE



                                              I                              I

-   LOW THICKNESS                                    -   GREATER THICKNESS
-   LOW SKIN FRICTION                                -   HIGHER SKIN FRICTION
                    figure   7.24. Boundary    Layer Charactorisfics

the turbulent area, a sharp “crackling” will          trays the relative magnitude of dynamic and
be audible.                                           viscous forces in the flow.
   In order to compare the characteristics of
the laminar and turbulent boundary layers, the
velocity profiles (the variation of boundary
layer velocity with height above the surface)
should be compared under conditions which               RiV=Reynolds       Number, dimensionless
could produce either laminar or turbulent
flow. The typical laminar and turbulent pro-              V= velocity, ft. per sec.
files are shown in figure 1.24. The velocity
                                                           x= distance from leading edge, ft.
profile of the turbulent boundary layer shows
a much sharper initial change of velocity but                 Y= kinematic viscosity, sq. ft. per sec.
a greater height (or boundary layer thickness)
required to reach the free stream velocity.           While the actual magnitude of the Reynolds
As a result of these differences, a comparison        Number has no physical significance, the
will show:                                            quantity is used as an index to predict and
       (1) The turbulent boundary layer has a         correlate various phenomena of viscous fluid,
    fuller velocity profile and has higher local      flow. When the RN is low, viscous or fric-
    velocities immediately adjacent to the sur-       tion forces predominate; when the RN is high,
    face. The turbulent boundary layer has            dynamic or inertia forces predominate. The
    higher kinetic energy in the airflow next to      effect of the variables in the equation for
    the surface.                                      Reynolds Number should be understood. The
       (2) At the surface, the laminar boundary       RN varies directly with velocity and distance
    layer has the less rapid change of velocity       back from the leading edge and inversely with
    with distance above the plate. Since the          kinematic viscosity.              s
                                                                              High RN’ are obtained
    shearing stress is proportional to the velocity   with large chord surfaces, high velocities, and
    gradient, the lower velocity gradient of the      low altitude; low RN’  sresult from small chord
    laminar boundary layer is evidence of a           surfaces, low velocities, and high altitudes-
    lower friction drag on the surface. If the        high altitudes producing high values for kine-
    conditions of flow were such that either a        matic viscosity.
    turbulent or a laminar boundary layer could          The most direct use of Reynolds Number is
    exist, the laminar skin friction would be         the indexing or correlating the skin friction
    about one-third that for turbulent flow.          drag of a surface. Figure 1.25 illustrates the
    The low friction drag of the laminar bound-       variation of the friction drag of a smooth,
 ary layer makes it quite desirable. However,         flat plate with a Reynolds Number which is
 the transition tends to take place in a natural      based on the length or chord of the plate.
fashion and limit the extensive development           The graph shows separate lines of drag coeffi-
 of the laminar boundary layer.                       cient if the flow should be entirely laminar or
    REYNOLDS NUMBER.               Whether a lam-     entirely turbulent.   The two curves for lam-
 inar or turbulent boundary layer exists depends      inar and turbulent friction drag illustrate the
 on the combined effects of velocity, viscosity,      relative magnitude of friction drag coefficient
 distance from the leading edge, density, etc.        if either type of boundary layer could exist.
 The effect of the most important factors is          The drag coefficients for either laminar or tur-
 combined in a dimensionless parameter called          bulent flow decrease with increasing RN since
 “Reynolds Number, RN.”             The Reynolds      the velocity gradient decreasesas the boundary
 Number is a dimensionless ratio which por-           layer thickens.
                                                                                                 NAWWEPS OD-EOT-SO
                                                                                                BASIC AERODYfflAMICS

                            FRICTION DRAG OF A SMOOTH
                                   FLAT PLATE

       ,020 -
D       ,010 -
iii    .008 -
yu’     .%2   -
0      :%   -
::     ,002 -                        \
2i                                         1
        .OOl *              1     I               1         1                              1
             0.1           0.5   1.0             5.0       10.0                50         100
                                     REYNOLDS NUMBER

                            CONVENTIONAL AfdD LAMINAR
                                 FLOW SECTIONS


                                               NACA                        /

                                                                       L       NACA 0009

                                           P       DRAG BUCKET”

                                                       I           I

                   -1.0     -3       0                .5          I.0               I.§
                          SECTION LIFT COEFFICIENT,                cl

                            Figure     7.25.   Skin Friction      Drag

                                                                                                  Weaised January   1965

    If the surface of the plate is smooth and the         delay the transition to some point farther aft
original airstream has no turbulence, the plate           on the chord. The subsequent reduction in
at low Reynolds Numbers will exist with pure              friction drag at the low angles of attack ac-
laminar flow. When the RN is increased to                 counts for the “drag bucket” shown on the
approximately 530,000, transition occurs on               graphs of cd and cI for these sections. Of
the plate and the flow is partly turbulent.               course, the advantages of the laminar flow
Once transition takes place, the drag coefficient         airfoil are apparent only for the smooth airfoil
of the plate increases from the laminar curve             since surface roughness or waviness may pre-
to the turbulent curve. As the RN approaches              clude extensive development of a laminar
very high values (20 to 50 million) the drag              boundary layer.
curve of the plate approaches and nearly equals               AIRFLOW SEPARATION.            The character
the values for the turbulent curve. At such               of the boundary layer on an aerodynamic
high RN the boundary layer is predominantly               surface is greatly influenced by the pressure
turbulent with very little laminar flow-the               gradient. In order to study this effect, the
transition point is very close to the leading             pressure distribution of a cylinder in a perfect
edge. While the smooth, flat plate is not ex-             fluid is repeated in figure 1.26. The airflows
actly representative of the typical airfoil, basic        depict a local velocity of !zero at the forward
fluid friction phenomena are illustrated.      At         stagnation point and a maximum local velocity
RN less than a half million the boundary layer            at the extreme surface. The airflow moves
will be entirely laminar unless there is extreme          from the high positive pressure to the minimum
surface roughness or turbulence induced in the            pressure point-a     favorable pressure gradient
airstream. Reynolds Numbers between one                   (high to low).      As the air moves from the
and five million produce boundary layer flow              extreme surface aft, the local velocity decreases
which is partly laminar and partly turbulent.             to zero at the aft stagnation point.    The static
At RN above ten million the boundary layer                pressure increases from the minimum (or max-
characteristics are predominantly turbulent.              imum suction) to the high positive pressure
   In order to obtain low drag sections, the              at the aft stagnation point-an       adverse pres-
transition from laminar to turbulent must be              sure gradient (low to high).
delayed so that a greater portion of the sur-                 The action of the pressure gradient is such
face will be influenced by the laminar bound-             that the favorable pressure gradient assists
ary layer. The conventional, low speed air-               the boundary layer while the adverse pressure
foil shapes are characterized, by minimum                 gradient impedes the flow of the boundary
pressure points very close to the leading edge.           layer. The effect of an adverse pressure gradi-
Since high local velocities enhance early                 ent is illustrated by the segment X-Y of figure
transition, very little surface is covered by             1.26. A corollary of the skin friction drag is
the laminar boundary layer, A comparison                  the continual reduction of boundary layer
of two 9 percent thick symmetrical airfoils is            energy as flow continues aft on a surface. * The
presented in figure 1.25. One section is the              velocity profiles of the boundary layer are
“conventional”      NACA C!UO~section which               shown on segment X-Y of figure 1.26. In the
has a minimum pressure point at approxi-                  area of adverse pressure gradient the bound-
mately 10 percent chord at zero lift. The other           ary layer flow is impeded and tends to show a
section is the NACA 66039 which has a                     reduction in velocity next to the surface. If
minimum pressure point at approximately 60                the boundary layer does not have sufhcient
percent chord at zero lift.       The lower local         kinetic energy in the presence of the adverse
velocities at the leading edge and the favor-             pressure gradient, the lower levels of the
able pressure gradient of the NACA 66-009                 boundary layer may stagnate prematurely.
                                                                   NAWWEPS 00-8OT-80
                                                                  BASIC AERODYNAMICS
                                              SEPARATION      1

                                BOUNDARY LAYER
                                          --‘ ION
                                  SEPAF iAT -.’



                                              b        SHOCK WAVE

                                 SHOCK WAVE INDUCED
                                   FLOW SEPARATION
             Figure 1.26. Airflow Separation (sheet 7 of 2)

Figure 7.26.   Airflow   Separation   (sheet 2 of 2)
                                                                                      NAVWEPS OO-SOT-80
                                                                                     BASIC AERODYNAMICS

 Premature stagnation of the boundary layer               to increase the kinetic energy of the upper sur-
means that all subsequent airflow will overrun            face boundary layer to withstand the more
 this point and the boundary layer will separate          severe pressure gradients common to the higher
from the surface. Surface flow which is aft of            lift coefficients. Extreme surface roughness
the separation point will indicate a local flow           on full scale aircraft (due to surface damage,
direction forward toward theseparation point-             heavy frost, etc.) causes higher skin friction
a flow reversal. If separation occurs the posi-           and greater energy loss in the boundary layer.
tive pressures are not recovered and form drag            The lower energy boundary layer may cause a
results. The points of separation on any aero-            noticeable change in C,-” and stall speed. In
dynamic surface may be noted by the reverse               the same sense, vortex generators applied to
flow area. Tufts of cloth or string tacked to             the surfaces of a high speed airplane may allay
the surface will lie streamlined in an area of            compressibility buffet to some degree. The
unseparated flow but will lie forward in an               function of the vortex generators is to create a
area behind the separation point.                         strong vortex which introduces high velocity,
    The basic feature of airflow separation is            high energy air next to the surface to reduce
stagnation of the lower levels of the boundary            or delay the shock induced separation. These
layer. Airjh      ~cparation muh when the lower           examples serve as a reminder that separation is
lcvcls of the boundary layer do not have sujicicnt         the result of premature stagnation of the
kinetic cncrgy in the prwncc of an advcm ps.wrc            boundary layer-insufficient     kinetic energy in
gradient. The most outstanding cases of air-               the presence of an adverse pressure gradient.
flow separation are shown in figure 1.26. An                  SCALE EFFECT. Since the boundary layer
airfoil at some high angle of attack creates a            friction and kinetic energy are dependent on
pressure gradient on the upper surface too                 the characteristics of the boundary layer,
severe to allow the boundary layer to adhere              Reynolds Number is important in correlating
to the surface. When the airflow does not                  aerodynamic characteristics.     The variation of
adhere to the surface near the leading edge                the aerodynamic characteristics with Reynolds
the high suction pressures are lost and stall              Number is termed “scale effect” and is ex-
occurs. When the shock wave forms on the                   tremely important in correlating wind tunnel
                                                           test data of scale models with the actual flight
upper surface of a wing at high subsonic speeds,
                                                          characteristics of the full size aircraft. The
the increase of static pressure through the
                                                           two most important section characteristics
shock’ wave creates a very strong obstacle for             affected by scale effects are drag and maximum
the boundary layer. If the shock wave is                  lift-the   effect on pitching moments usually
sufhciently strong, separation will follow and             being negligible.    From the known variation
 “compressibility   buffet” will result from the           of boundary layer characteristics with Rey-
turbulent wake or separated flow.                         nolds Number, certain general effects may be
    In order to prevent separation of a boundary          anticipated.    With increasing Reynolds Num-
layer in the presence of an adverse pressure               ber, it may be expected that the section maxi-
gradient, the boundary layer must have the                mum lift coefficient will increase (from the
highest possible kinetic energy. If a choice is           higher energy turbulent boundary layer) and
 available, the turbulent boundary layer would             that the section drag coefficient will decrease
 be preferable to the laminar boundary layer              (similar to that of the smooth plate). These
 because the turbulent velocity profile shows             effects are illustrated by the graphs of figure
 higher local velocities next to the surface.             1.27.
The most effective high lift devices (slots,                The characteristics depicted in figure 1.27
slotted flaps, BLC) utilize various techniques            are for the NACA 4412 airfoil (4 percent
                               RN                                                   RN -     1.5 MILLION

                        -6.0            11

                                     s               -I-              I
                                                                      I                       I       1-
           4   8   12   16 20                              -.5         0          .5         I.0      1.5
SECTION      ANGLE OF ATTACK                                     SECTION   LIFT         COEFFICIENT
          =o 1 DEGREES                                                            c.l
     figure 1.27. Effect of Reymafds Number on Section Ckacteristics       of NACA 4412
                                                                                NAVWEPS DD-RDT-80
                                                                               BASIC AERODYNAMICS

camber at 40 percent chord, 12 percent thick-       boundary layer obtained may reduce the form
ness at 30 percent chord)--a fairly typical         drag due to separation. In each instance, the
“conventionaal” airfoil section. The lift curve     forced transition will be beneficial if the reduc-
show a steady increase in cl with increasing        tion in form drag is greater than the increase
RN. However, note that a>maller change in           in skin friction.   Of course, this possibility
cr occurs between Reynolds Numbers of 6.0           exists only at low Reynolds Numbers.
ad 9.0 million than occurs between 0.1 and             1,n a similar sense, “trip” wires or small
3.0 million.     In other words, greater changes    surface protuberances on a wind tunnel model
in CI occur in the range of Reynolds Num-           may be used to force transition of the boundary
bers zhere the laminar (low energy) boundary        layer and simulate the effect of higher Reynolds
layer predominates. The drag curves for the         Numbers.
section show essentially the same feature-the
greatest variations occur at very low Reynolds               PLANFORM     EFFECTS AND
Numbers. Typical full scale Reynolds Num-                        AIRPLANE    DRAG
bers for aircraft in flight may be 3 to 5@O
where the boundary layer is predominately           EFFECT OF WING PLANFORM
turbulent.    Scale model tests may involve            The previous discussion of aerodynamic
Reynolds Numbers of 0.1 to 5 million where          forces concerned the properties of airfoil sec-
the boundary layer be predominately laminar.        tions in two-dimensional flow with no consid-
Hence, the “scale” corrections are very neces-      eration given to the influence of the planform.
sary to correlate the principal aerodynamic         When the effects of wing planform are intro-
characteristics.                                    duced, attention must be directed to the ex-
   The very large changes in aerodynamic            istence of flow components in the spanwise
characteristics at low Reynolds Numbers are         direction.    In other words, airfoil section
due in great part to the low energy laminar         properties deal with flow in two dimensions
boundary layer typical of low Reynolds Num-                     I
                                                    while plonform properties consider flow in
bers. Low Reynolds Numbers are the result           three dimensions.
of some combination of low velocity, small             In order to fully describe the planform of a
                                                    wing, several terms are required. The terms
size, and high kinematic viscosity   RN=
                                   (       3        having the greatest influence on the aerody-
Thus, small surfaces, low flight speeds, or very    namic characteristics are illustrated in figure
high altitudes can provide the regime of low        1.28.
Reynolds Numbers. One interesting phenom-                                       S,
                                                          (1) The wing r?rc11, is simply the plan
enon associated with low BN is the high form           surface area of the wing. Although a por-
drag due to separation of the low energy               tion of the area may be covered by fuselage
boundary layer. The ordinary golf ball oper-           or nacelles, the pressure carryover on these
ates at low RN and would have very high                surfaces allows legitimate consideration of
form drag without      dimpling.   The surface         the entire plan area.
roughness from dimpling disturbs the laminar              (2) The wing ~ptia, 6, is measured tip to
boundary layer forcing a premature transition          tip.
to turbulent.   The forced turbulence in the              (3) The avcragc chord, c, is the geometric
boundary layer reduces the form drag by pro-           average. The product of the span and the
                                                       average chord is the wing area (6X6=$).
viding a higher energy boundary layer to
                                                          (4) The aspect ratio, AR, is the proportion
allay separation. Essentially the same effect
                                                       of the span and the average chord.
can be produced on a model airplane wing by
roughening the leading edge-the turbulent                               AR=b/c

                                                        S= WING AREA, SO. FT.

                                                         b= SPAN, FT

                                                         c = AVERAGE CHORD, FT

                                                        AR = ASPECT RATIO

                                                        AR = b/c

                                                        AR=   b:s

             I       b ----_I
                                                        CR = ROOT CHORO, FT

                                                        Ct = TIP CHORD, FT

                                                         x = TAPER RATIO

                                                        A= SWEEP ANGLE, DEGREES

                                                        MAC : MEAN AERODYNAMIC CHORD, FT.

                        Figure 1.28.   Description   of Wing Planform

                                                                               NAVWEPS OO-BOT-BO
                                                                               BASIC AERODYNAMICS

If the planform has curvature and the aver-            root chord but an MAC equal to two-thirds
age chord is not easily determined, an                  of
                                                      ~‘ the root chord.
alternate expression is:                               The aspect ratio, taper ratio, and sweepback
                                                    of a planform are the principal factors which
                  AR = b2/.S                        determine the aerodynamic characteristics of a
                                                   .wing. These same quantities also have a defi-
The aspect ratio is a fineness ratio of the         nite influence on the structural weight and stiff-
wing and this quantity is very powerful in          ness of a wing.
determing the aerodynamic characteristics              DEVELOPMENT         OF LIFT BY A WING.
and structural weight.     Typical aspect ratios    In order to appreciate the effect of the planform
vary from 33 for a high performance sail-           on the aerodynamic characteristics, it is neces-
plane to 3.5 for a jet fighter to 1.28 for a        sary to study the manner in which a wing
flying saucer.                                      produces lift.’ Figure 1.29 illustrates the three-
   (5) The raat chord, c,, is the chord at the      dimensional flow pattern which results when
wing centerline and the rip chord, c,, is           the rectangular wing creates lift.
measured at the tip.                                   J.f a wing is producing lift, a pressure differ-
   (6) Considering the wing planform to             ential will exist between the upper and lower
have straight lines for the leading and trail-      surfaces, i.e., for positive lift, the static pres-
ing edges, the taper ratio, A (lambda), is the      sure on the upper surface will be less than on
ratio of the tip chord to the root chord.           the lower surface. At the tips of the wing,
                                                    the existence of this pressure differential creates
                   A=&                              the spanwise flow components shown in figure
                                                    1.29: For the rectangular wing, the lateral
The taper ratio affects the lift distribution
                                                    flow developed at the tip is quite strong and a
and the structural weight of the wing. A
                                                    strong vortex is created at the tip. The lateral
rectangular wing has a taper ratio of 1.0
while the pointed tip delta wing has a taper       ‘flow-and consequent vortex strength-reduces
ratio of 0.0.                                       inboard from the tip until it is zero at the
   (7) The sweep angle, A (cap lambda), is          centerline.
usually measured as the angle between the              The existence of the tip vortex is described
line of 25 percent chords and a perpendicular       by the drawings of figure 1.29. The rotational
to the root chord. The sweep of a wing              pressure flow combines with the local airstream
causes definite changes in compressibility,         flow to produce the resultant flow of the
maximum lift, and stall characteristics.            trailing vortex. Also, the downwash flow
   (8) The mean aerodynamic chord, MAC,             field behind a delta wing is illustrated by the
is the chord drawn through the centroid             photographs of figure 1.29. A tuft-grid is
(geographical center) of plan area. A rec-          mounted aft of the wing to visualize the local
tangular wing of this chord and the same            flow direction by deflection of th,e tuft ele-
span would have identical pitching moment
                                                    ments. This tuft-grid illustrates the existence
characteristics. The MAC is located on the
                                                    of the tip vortices and the deflected airstream
reference axis of the airplane and is a primary
reference for longitudinal stability considera-     aft of the wing. Note that an increase in
tions. Note that the MAC is not the average         angle of attack increases lift and increases the
chord but is the chord through the centroid         flow deflection and strength of the tip vortices.
of area. As an example, the pointed-tip                Figure 1.30 illustrates the principal effect
delta wing with a taper ratio of zero would         of the wing vortex system. The wing pro-
have an average chord equal to one-half the         ducing lift can be represented by a series of

                                            WING UPPER SURFACE

                                                                                       TIP VORTEX

                                           WING LOWER SURFACE
                                                                                 VORTICES     ALONG
                                                                                  TRAILING    EDGE

                                                                                           TRAILING EDGE

                                                              I                            UPPER     SURFACE
             LEADING EDGE


             LOW     PRESSURE-

             HIGH PRESSURE)

                           Figure   1.29. Wing Three Dimensional   Flow (sheet   1 of 2)

  Revised January   1965
                                                                               NAVWEPS OO-BOT-RD
                                                                              BASIC AERODYNAMICS

                    DOWNWASH FLOW FIELD BEHIND
                    A DELTA WING ILLUSTRATED
                    BY TUFT-GRID PHOTOGRAPHS AT
                    VARIOUS ANGLES OF ATTACK

                 --A-- II           30”   OF FLOW    ANGULARITY




I) TUFT GRID 6 INCHES              FROM           (b) TUFT GRID 24 INCHES FROM
       TRAILING EDGE.                                     TRAILING EDGE.

                                   FROM   NACA    TN 2674

       Figure   1.19.       Wing    Three Dimensional   Flow (sheet 2 of 2)


 vortex filaments which consist of the tip or              age relative wind which is different from the
 trailing vortices coupled with the bound or               remote free stream wind. Since the aerody-
line vortex. The tip vortices are coupled with             namic forces created by the airfoil sections of a
the bound vortex when circulation is induced               wing depend upon the immediate airstream in
with lift. The effect of this vortex system is             which they operate, consideration must be
to create certain vertical velocity components             given to the effect of the inclined average rela-
in the vicinity of the wing. The illustration              tive wind.
of these vertical velocities shows that ahead                 To create a certain lift coefficient with the
of the wing the bound vortex induces an up-                airfoil section, a certain angle must exist be-
wash. Behind the wing, the coupled action                  tween the airfoil chord line and the avcragc
 of the bound vortex and the tip vortices in-              relative wind. This angle of attack is a,,, the
 duces a downwash.        With the action of tip           section angle of attack. However, as this lift
 and bound vortices coupled, a final vertical              is developed on the wing, downwash is in-
 velocity (220) is imparted to the airstream by            curred and the average relative wind is in-
 the wing producing lift.       This result is an          clined. Thus, the wing must be given some
 inevitable consequence of a finite wing pro-              angle attack greater than the required section
 ducing lift.    The wing Producing lift applies           angle of attack to account for the inclination of
 the equal and opposite force to the airstream             the average relative wind. Since the wing
 and deflects it downward.      One of the impor-          must be given this additional angle of attack
 tant factors in this system is that a downward            because of the induced flow, the angle between
 velocity is created at the aerodynamic center             the average reiative wind arid tlie remote  fiCC

 (w) which is one half the final downward                  stream is termed the induced angle of attack,
 velocity imparted to the airstream (2~).                  ai. From this influence, the wing angle of
    The effect of the vertical velocities in the           attack is the sum of the section and induced
 vicinity of the wing is best appreciated when             angles of attack.
 they are added vectorially to the airstream                           a=ul)+a;
 velocity.    The remote free stream well ahead            where       a= wing angle of attack
 of the wing is unaffected and its direction is                       OLD= section angle of attack
 opposite the flight path of the airplane. ‘   Aft                    OI;= induced angle of attack
 of the wing, the vertical velocity (2~) adds to
 the airstream velocity to produce the down-               INDUCED     DRAG
 wash angle e (epsilon).      At the aerodynamic
 center of the wing, the vertical,velocity     (w)             Another important influence of the induced
 adds to the airstream velocity to produce a               flow is the orientation of the actual lift on a
 downward deflection of the airstream one-half             wing. Figure 1.30 illustrates the fact that the
 that of the downwash angle. In other words,               lift produced by the wing sections is perpen-
 the wing producing lift by the deflection of an           dicular to the average relative wind. Since
 airstream incurs a downward slant co the wind             the average relative wind is inclined down-
 in the immediate vicinity of the wing. Hence,             ward, the section lift is inclined aft, by the
 the JeCtionJof the wing operatein an average rela-        same amount-the       induced angle of attack,
tive wind which is inclined downward one-half the          ai. The lift and drag of a wing must continue
final dowraw& angle. This is one important                 to be referred perpendicular and parallel to the
feature which distinguishes the aerodynamic                remote free stream ahead of the wing. In this
properties of a wing from the aerodynamic                  respect, the lift on the wing has a component
properties of an airfoil section.                          of force parallel to the remote free stream.
    The induced velocities existing at the aero-           This component of lift in the drag direction
 dynamic center of a finite wing create an aver-           is the undesirable-but      unavoidable-conse-
                                                                                NAVWEPS DD-ROT-80
                                                                               BASIC AERODYNAMICS

                         BOUND OR :INE VORTEX

                                                                     , OR TIP VORTEX

                                                                      DEFLECTED AIRSTREAM


                                                                          BOUND VORTEX ONLY

              IN THE VICINITY OF
                   THE WING

                                                                      COUPLED BOUND AND
                                         AVERAGE RELATIVE WIND           TIP VORTICES
                                              AT WING A.C.
              t                                                                   DOWNWASH
REMOTE FREE STREAM                                                                 ANGLE

                                             D it INDUCED DRAG


                              REMOTE FREE STREAM

                     Figure 1.30. Wing    Vortex     System and Induced Flow

  quence of developing lift with a finite wing                 (3) The induced angle of attack can be
  and is termed INDUCED DRAG, D+ In-                         derived as:
  duced drag is separate from the drag due to
  form and friction and is due simply to the de-                        a~= 18.24 &   (degrees)
  velopment of lift.                                                             (  )
     By inspection of the force diagram of figure
  1.30, a relationship between induced drag, lift,           (NOTE:  the derivation of these relationships
  and induced angle of attack is apparent. The               may be found in any of the standard engi-
  induced drag coeficient, CDi, will vary directly           neering aerodynamics textbooks.)
  with the wing lift coefficient, C,, and the in-          These relationships facilitate an understanding
  duced angle of attack, as. The effective lift            and appreciation of induced drag.
  is the vertical component of the actual lift and,          The induced angle of attack         Eli= 18.~4$~
  if the induced angle of attack is small, will be                                             (              >
  essentially the same as the actual lift.      The         depends on the lift coefficient and aspect ratio.
J horizontal and vertical component of drag is              Flight at high lift conditions such as low speed
  insignificant under the same conditions.     By a         or maneuvering flight will create high induced
  detailed study of the factors involved, the fol-          angles of attack while high speed, low lift
  lowing relationships can be derived for a wing            flight will create very small induced angles .of
  with an elliptical lift distribution:                     attack. The inference is that high lift coefli-
       (1) The induced drag equation follows the            cients require large downwash and result in
     same form as applied to any other aerody-              large ,induced angles of attack. The effect of
     namic force.                                           aspect ratio is significant since a very high
                                                            aspect ratio would produce a negligible induced
             Di=CDigS                                       angle of attack. If the aspect ratio were in-
   where                                                    finite, the induced angle of attack would be
             Di=induced     drag, lbs.                      zero and the aerodynamic characteristics of the
              4= :Vymic      pressures; psf                 wing would be identical with the airfoil sec-
                                                            tion properties.     On the other hand, if the
               =295                                         wing aspect ratio is low, the induced angle of
            Cni= induced drag coefficient                   attack will be large and the low aspect ratio
                                                            airplane must operate at high angles of attack
             S=wing area, sq. ft.
                                                            at maximum lift. Essentially, the low aspect
     (2) The induced drag coefficient can be               ratio wing affects a relatively small mass of
   derived as :                                             air and consequently must provide a large de-
                                                            flection (downwash) to produce lift.
                    CD,-C, sin ai                              EFFECT OF LIFT.          The induced drag co-
   or                                                                              C&l
                                                            e&cient CDi=0.31E -          shows somewhat sim-
                                                                     (             AR
                                                           ilar effects of lift coefficient and aspect ratio.
                                    c,P                    Becauseof the power of variation of induced drag
                       =0.318       -Jjj
                                (          )               coefficient with lift coefficient, high lift coefli-
   where                                                   cients provide very high induced drag and low
            C,= lift coefficient                           lift coefficients very low induced drag. The di-
        sin ai=natural sine of the induced angle           rect effect of C, can be best appreciated by assum-
                    of attack, Eli, degrees                ing an airplane is flying at a givenweight, alti-
             r=3.1416, constant                            tude, and airspeed. If the airplane is maneuvered
           AR= wing aspect ratio                           from steady level flight to a load factor of two,
 hWd       Jonua~    1965
                                                                                NAVWEPS 0040240
                                                                               BASIC AERODYNAMICS

the lift coefficient is doubled and the induced     air density requires a greater deflection of the
drag is four times 0.1 grsat. If the flight load    airstream to produce the same lift.    However,
factor is changed from one to five, the induced     if the airplane is flown at the same EAS, the
drag is twenty-five times as great. If all other    dynamic pressure will be the same and induced
factors are held constant to single out this        drag will not vary. In this case, the TAS
effect, it could be stated that “induced drag       would be higher at altitude to provide the
varies as the square of the lift”                   same EAS.
                                                       EFFECT OF SPEED. The general effect of
                  Di,    L! ’                       speed on induced drag is unusual since low air-
                  Di,= 0 L1                         speeds are’ associated with high lift coefficients
                                                    and high lift coefficients create high induced
where                                               drag coefficients. The immediate implication
       Di,= induced drag corresponding to           is that induced drag inmaw with decreasingair
               some original lift, L1               J@.     If all other factors are held constant to
       Di,= induced drag corresponding to           single out the effect of airspeed, a rearrange-
               some new lift, Lp                    ment of the previous equations would predict
      (and q (or EAS), S, AR are constant)          that “induced drag varies inversely as ,the
This expression defines the effect of gross          square of the airspeed.”
weight, maneuvers, and steep turns on the
induced drag, e.g., 10 percent higher gross
weight increases induced drag 21 percent, 4G
maneuvers cause 16 times as much induced
drag, a turn with 4s0 bank requires a load          where
factor of 1.41 and this doubles the induced         Dil= induced drag corresponding to some orig-
drag.                                                    inal speed, Vi
   EFFECT OF ALTITUDE.              The effect of
altitude on induced drag can be appreciated by      Di,= induced drag corresponding to some new
holding all other factors constant. The gen-             speed, Vs
eral effect of altitude is expressed by:                     (and L, S, AR, ,J are constant)

                                                       Such an effect would imply that a given air-
                                                    plane in steady flight would incur one-fourth
where                                               as great an induced drag at twice as great a
                                                    speed or four times as great an induced drag at
Dil= induced drag corresponding to some orig-       half the original speed. This variation may
     inal altitude density ratio, 0,                be illustrated by assuming that an airplane in
D&= induced drag corresponding to some new          steady level flight is slowed from 300 to 150
    altitude density ratio, q                       knots. The dynamic pressure at 1% knots is
                                                    one-fourth the dynamic pressure at 300 knots
        (and L, S, AR, V are constant)              and the wing must deflect the airstream four
This relationship implies that induced drag         times as greatly to create the same lift.   The
would increase with altitude, e.g., a given         same lift force is then slanted aft four times
airplane flying in level flight at a given TAS      as greatly and the induced drag is four times
at 40,000 ft. (u=O.25) would have four times        as great.
as much induced drag than when at sea level            The expressed variation of induced drag with
(u= 1.00). This effect results when the lower       speed points out that induced drag will be of
                                                                                        NAVWEPS OD-SOT-BO
                                                                                       BASIC AERODYNAMICS

greatest importance at low speeds and prac-                 typical only of a wing planform of extremely
tically insignificant in flight at high dynamic             high (infinite) aspect ratio. When a wing of
pressures. For example, a typical single en-                some finite aspect ratio is constructed of this
gine jet airplane at low altitude and maximum               basic section, the principal differences will be
level flight airspeed has an induced drag which             in the lift and drag characteristics-the     mo-
is less than 1 pcrccont the total drag. How-
                       of                                   ment characteristics remain essentially the
ever, this same airplane in steady flight just              same. The effect of decreasing aspect ratio on
above the stall speed could have an induced                 the lift curve is to increase the wing angle of
drag which is approximately 75 pnrcnt of the                attack necessary to produce a given lift co-
total drag.                                                 efficient. The difference between the wing
   EFFECT OF ASPECT RATIO.             The effect           angle of attack and the section angle of attack
of aspect ratio on the induced drag
                                                            is the induced angle of attack, orit18.24     L
                                                            which increases with decreasing aspect ratio.
                                                            The wing with the lower aspect ratio is less
                                                            sensitive to changes in angle of attack and re-
is the principal effect of the wing planform.               quires higher angles of attack for maximum
The relationship for induced drag coefIicient               lift.   When the aspect ratio is very low (below
emphasizes the need of a high aspect ratio                  3 or 6) the induced angles of attack are not
for the airplane which            is continually            accurately predicted by the elementary equa-
operated at high lift coefficients. In other                            and
                                                            tion for 01~ the graph of C, versus 01    develops
words, airplane configurations designed to                  distinct curvature. This effect is especially
operate at high lift coefficients during the                true at high lift coefhcients where the lift
major portion of their flight (sailplanes, cargo,           curve for the very low aspect ratio wing is
transport; patrol, and antisubmarine types)                 very shallow and CL- and stall angle of attack
demand a high aspect ratio wing to minimize                 are less sharply defined.
the induced drag. While the high aspect                         The effect of aspect ratio on wing drag char-.
ratio wing will minimize induced drag, long,                acteristics may be appreciated from inspection of
thin wings increase structural weight and have              figure 1.31. The basic section properties are
relatively poor stiffness characteristics.      This        shown as the drag characteristics of an infinite
fact will temper the preference for a very high             aspect ratio wing. When a planform of some
aspect ratio. Airplane configurations which                 finite aspect ratio is constructed, the wing drag
 are developed for very high speed flight (es-              coefficient is the rtlm of the induced drag coe&-
 specially supersonic flight) operate at relatively
                                                            cient, C,,=O.318 AR, and the section drag co-
 low lift coefficients and demand great aero-
 dynamic cleanness. These configurations of                 efhcient. Decreasing aspect ratio increases the
 airplanes do not have the same preference for              wing drag coefficient at any lift coefficient since
 high aspect ratio as the airplanes which op-               the induced drag coefficient varies inversely
 erate continually    at high lift coefficients.            with aspect ratio. When the aspect ratio is
 This usually results in the development of low
                                                            very low, the induced drag varies greatly with
 aspect ratio planforms for these airplane con-
                                                            lift and at high lift coefficients, the induced
    The effect of aspect ratio on the lift and drag         drag is very high and increases very rapidly
 characteristics is shown in figure 1.31 for                with lift coefficient.
 wings of a basic 9 percent symmetrical section.                While the effect of aspect ratio on lift curve
 The basic airfoil section properties are shown             slope and drag due to lift is an important re-
  on these curves and these properties would be             lationship, it must be realized that design for

       t                                                              (NO SWEEPBACK)

                       BASIC SECTION       WING ANGLE OF ATTACK
             I .4                                a DEGREES
                    1 \A”=‘
                                                            AR,=5                AR = 2.5

                                               I      I       I    (LOW MACH NUMBER)        I

                                               .I0           .I5           .20              .25
                    I                    WING DRAG COEFFICIENT,     CD

                        Figure 1.31. Effect of Aspect Ratio on Wing Characteristics

                                                                                   NAWEPS OO-BOT-BO
                                                                                  BASIC AERODYNAMICS

very high speed flight does not favor the use of          takeoff distance may occur. Also, the initial
high aspect ratio planforms. Low aspect ratio             climb performance may be marginal at an
planforms have structural advantages and                  excessively low airspeed. There are modern
allow the use of thin, low drag sections for high         configurations of airplanes of very low aspect
speed flight.     The aerodynamics of transonic           ratio (plus sweepback) which-if           over-
and supersonic flight also favor short span, low          rotated during a high altitude, high gross
aspect ratio surfaces. Thus, the modern con-              weight takeoff-cannot       fly out of ground
figuration of airplane designed for high speed            effect. With the more conventional airplane
flight will have a low aspect ratio planform              configuration, an excess angle of attack pro-
with characteristic aspect ratios of two to four.         duces a well defined stall. However, the
The most important impression that should                 modern airplane configuration at an excessive
result is that the typical modern configuration           angle of attack has no sharply defined stall
will have high angles of attack for maximum               but developes an excessive amount of induced
lift and very prodigious drag due to lift at low          drag. To be sure that it will not go unsaid,
flight speeds. This fact is of importance to              an excessively low angle of attack on takeoff
theNaval Aviator becausethe majority of pilot-            creates its own problems-excess takeoff
caused accidents occur during this regime of              speed and distance and critical tire loads.
flight-during     takeoff, approach, and landing.             (2) During appra& where the pilot must
Induced drag predominates in these regimes of             exercise proper technique to control the
flight.                                                   flight path. “Attitude      plus power equals
    The modern configuration of high speed air-           performance.” The modern high speed con-
plane usually has a low aspect ratio planform             figuration at low speeds will have low lift-
with high wing loading. When wing sweep-                  drag ratios due to the high induced drag 1
back is coupled with low aspect ratio, the wing           and can require relatively high power set-
lift curve has distinct curvature and is very flat        tings during the power approach. If the
at high angles of attack, i.e., at high CL, C, in-        pilot interprets that his airplane is below
creases very slowly with an increase in 01. In            the desired glide path, his first reaction rnu~t
addition, the drag curve shows extremely rapid            trot be to just ease the nose up. An increase
rise at high lift coefficients since the drag due         in angle of attack without an increase in
to lift is so very large. These effects produce           power will lower the airspeed and greatly
flying qualities which are distinctly different           increase the induced drag. Such a reaction
from a more “conventional” high aspect ratio              could create a high rate of descent and lead
airplane configuration.                                   to very undesirable consequences. The an-
    Some of the most important ramifications of           gle of attack indicator coupled with the
the modern high speed configuration are:                  mirror landing system provides reference to
       (1) During takeoff where the airplane must         the pilot and emphasizes that during the
    not be over-rotated to an excessive angle of          steady approach “angle of attack is the
    attack. Any given airplane will have some             primary control of airspeed and power is the
    fixed angle of attack (and CJ which produces          primary control of rate of climb or descent.”
    the best takeoff performance and this angle           Steep turns during approach at low airspeed
    of attack will not vary with weight, density          are always undesirable in any type of air-
    altitude, or temperature. An excessive angle          plane because of the increased stall speed and
    of attack produces additional induced drag            induced drag. Steep turns at low airspeeds
    and may have an undesirable effect on takeoff         in a low aspect ratio airplane can create
    performance. Takeoff acceleration may be              extremely high induced drag and can incur
    seriously reduced and a large increase in             dangerous sink rates.
                                                                                   Revised January   1965

       (3) During the landing phase where an               speed for (L/D)-.     The additional speed pro-
   excessive angle of attack (or excessively low           vides a more favorable margin of flare capabil-
   airspeed) would create high induced drag                ity for flameout landing from a steep glide path
   and a high power setting to control rate of             (low aspect ratio, low (L/D)-,        low glide
   descent. A common error in the technique                ratio).
   of landing modern conbgurations is a steep,                 The landing technique must emphasize
   low power approach to landing. The steep                proper control of angle of attack and rate of
   flight path requires considerable maneuver              descent to prevent high sink rates and hard
   to flare the airplane for touchdown and                 landings. As before, to be sure that it will
   necessitates a definite increase in angle of            not go unsaid, excessive airspeed at landing
   attack. Since the maneuver of the flare is a            creates its own problems-excessive wear and
   transient condition, the variation of both              tear on tires and brakes, excessive landing
   lift and drag with angle of attack must be               distance, etc.
   considered. The lift and drag curves for a                  The effect of the low aspect ratio planform
   high aspect ratio wing (fig. 1.31) show con-             of modern airplanes emphasizes the need for
   tinued strong increase in C, with 01up to stall          proper flying techniques at low airspeeds.
   and large changes in Co only at the point of             Excessive angles of attack create enormous
    stall. These characteristics imply that the             induced drag which can hinder takeoff per-
   high aspect ratio airplane is usually capable            formance and incur high sink rates at landing.
    of flare without unusual results. The in-               Since such aircraft have intrinsic high mini-
    __^_“^ 111
            :- ---I.. -c _&-__ .-* *we -..- : 1
    C,LaLDC a,l5~~ VI ~LL~CLdo n.-. p~ovmes the             mum flying speeds, an excessively low angle of
    increase in lift to change the flight path              attack at takeoff or landing creates its own
    direction without large changes in drag to              problems. These facts underscore the im-
    decelerate the airplane.                                portance of a “thread-the-needle,” professional
    The lift and drag curves for a low aspect               flying technique.
ratio wing (fig. 1.31) show that at high angles
of attack the lift curve is shallow, i.e., small
                                                           EFFECT OF TAPER AND SWEEPBACK
changes in C, with increased a. This implies
a large rotation needed to provide the lift to
                                                              The aspect ratio of a wing is the primary
flare the airplane from a steep approach. The
                                                           factor in determining the three-dimensional
drag curve for the low aspect ratio wing shows
                                                           characteristics of the ordinary wing and its
large, powerful increases in C, with Cr. well
                                                           drag due to lift.  However, certain local effects
below the stall. These lift and drag charac-
                                                           take place throughout the span of the wing and
teristics of the low aspect ratio wing create
                                                           these effects are due to the distribution of area
a distinct change in the flare characteristics.
                                                           throughout the span. The distribution of lift
If a flare is attempted from a steep approach at
                                                           along the span of a wing cannot have sharp
low airspeed, the increased angle of attack
                                                           discontinuities.                         t
                                                                              (Nature just doesn’ arrange
may provide such increased induced drag and
                                                           natural forces with sharp discontinuities.)
rapid loss of airspeed that the airplane does not          The typical lift distribution is arranged in
actually flare. A possible result is that an               some elliptical fashion. A representative dis-
even higher sink rate may be incurred. This                tribution of the lift per foot of span along the
is one factor favoring the use of the “no-flare”           scan of a wing is shown in figure 1.32.
or “minimum flare” type landing technique                     The natural distribution of lift along the
for certain modern configurations.       These same        span of a wing provides a basis for appreciating
aerodynamic properties set the best glide                  the effect of area distribution and taper along
speeds of low aspect ratio airplanes above the             the span. If the elliptical lift distribution is
                                                NAVWEPS OfJ-RDT-8D
                                               BASIC AERODYNAMICS

   A               I       I

    TYPlChL                      SPAN ’
                 L&i. PER kT. OF ‘
               LIFT DISTRIBUTION

Figure 4.32.    Sponwise   Lift Distribution

matched with a planformwhose chord is dis-                 exists. This situation creates an induced angle
tributed in an elliptical fashion (the elliptical          of attack at the root which is less than the
wing), each square foot of area along the span             average for the wing and a local section angle
produces exactly the same lift pressure. The               of attack higher than the average for the wing.
elliptical wing planform then has each section             The result is shown by the graph of figure 1.32
of the wing working at exactly the same local              which depicts a local lift coefficient at the root
lift coefhcient and the induced downflow at                almost 20 percent greater than the wing lift
the wing is uniform throughout the span. In                coefficient.
the aerodynamic sense, the elliptical. wing is                 The effect of the rectangular planform may
the most efficient planform because the uni-               be appreciated by matching a near elliptical
formity of lift coefficient and downwash incurs            lift distribution    with a planform with a
rbt iea$t induced drag for a given aspect ratio.           constant chord.       The chords near ‘   the tip
The merit of any wing @anform is then meas-                develop less lift pressure than the root and
ured by the closeness with which the distribu-             consequently have lower section lift coe&-
tion of lift coefficient and downwash approach             cients. The great nonuniformity of local lift
that of the elliptical planform.                           coefficient along the span implies that some
    The effect of the elliptical planform is illus-        sections carry .more than their share of the
trated in figure 1.32 by the plot of local lift            load while others carry less than their share
                                                           of the load. Hence, for a given aspect ratio,
coefficient to wing lift coefficient, f! versus
                                      G’                   the rectangular planform will be less efficient
scm:spnn L.“CY.ICG. Tbac e!liptical wing p*
            ,4;..t,or,                                             UK -11:.
                                                            LlLill -L. C‘ -!-~I wing.
                                                           -t--           lqJLlCal          For exampie, a
duces a constant value of$=J.O        throughout           rectangular wing of AR=6 would have 16
                                                           percent higher induced angle of attack for the
the span from root to tip.‘ Thus, the local                wing and 5 percent higher induced drag than
section angle of attack, LYE,   and local induced           an elliptical wing of the same aspect ratio.
angle of attack, CY,,are constant throughout                   At the other extreme of taper is the pointed
the span. If the planform area distribution is              wing which has a taper ratio of zero. The
anything other than elliptical, it may be ex-              extremely small parcel of area at the pointed
pected that the local section and induced angles            tip is not capable of holding the main tip
of attack will not be constant along the span.              vortex at the tip and a drastic change in down-
   A planform previously considered is the                  wash distribution results. The pointed wing
simple rectangular wing which has a taper                   has greatest downwash at the root and this
ratio of 1.0. A characteristic of the rectangular           downwash decreases toward the tip. In the
wing is a strong vortex at the tip with local               immediate vicinity of the pointed tip, an
downwash behind the wing which is high at                   upwash is encountered which indicates that
the tip and low at the root. This large non-                negative induced angles of attack exist in this
uniformity in downwash causes similar varia-                area. The resulting variation of local lift
tion in the local induced angles of attack along            coefficient shows low cr at the root and very
the span. At the tip, where high downwash                   high c, at the tip. This effect may be appre-
exists, the local induced angle of attack is                ciated by realizing that the wide chords at
greater than the average for the wing. Since                the root produce low lift pressures while the
the wing angle of attack is composed of the                 very narrow chords toward the tip are sub-
sum of at and aor a large local (x, reduces the             ject to very high lift pressures.. The varia-
local a0 creating low local lift coefficients at
                                                           tion of 2 throughout the span of the wing of
the tip. ‘  Ihe reverse is true at the root of the                   L
rectangular   wing where low local downwash                taper ratio==0 is shown on the graph of figure
                                                                                    NAVWEPS OD-ROT-RO
                                                                                   RASIC AERODYNAM!CS

1.32. As with the rectangular wing, the non-           advantages of root stall first are that ailerons
uniformity of downwash and lift distribution           remain effective at high angles of attack,
result in inefficiency of rhis planform.    For        favorable stall warning results from the buffet
example, a pointed wing of AR=6 would have             on the empennage and aft portion of the fuse-
17 percent higher induced angle of attack for          lage, and the loss of downwash behind the root
the wing and 13 percent higher induced drag            usually ptovides a stable nose down moment
than an elliptical wing of thesame aspect ratio.       to the airplane. Such a stall pattern is favored
   Between the two extremes of taper will              but may be difficult to obtain with certain wing
exist planforms of more tolerable efficiency.          configurations.      The types of stall patterns in-
The variations of 2 for a wing of taper ratio          herent with various planforms are illustrated
                                                       in figure 1.33. The various planform effects
=0.5 closely approxtmates the lift distribution         are separated as follows :
of the elliptical wing and the drag due to lift             (A) The elliptical planform has constant
characteristics are nearly identical.       A wing      local lift coefficients throughout the span from
of AR=6 and taper ratio=0.5            has only 3      root to tip. Such a lift distribution means that
percent higher ai and 1 percent greater CD: than        all sections will reach stall at essentially the
an elliptical wing of the same aspect ratio.            same wing angle of attack and stall will begin
    ,A separate effect on the spanwise lift dis-        and progress uniformly throughout the span.
tribution is contributed by wing sweepback.             While the elliptical wing would reach high
Sweepback of the planform tends to alter the            lift coefficients before incipient stall, there
lift distribution similar to decreasing the taper       would be little advance warning of complete
ratio. Also, large sweepback tends to increase           stall. Also, the ailerons may lack effectiveness
induced drag.                                           when the wing operates near the stall and lat-
    The elliptical wing is the ideal of the sub-        eral control may be difficult.
sonic aerodynamic planform since it provides                (B) The lift distribution of the rectangular
a minimum of induced drag for a given aspect            wing exhibits low local lift coefficients at the
ratio. However, the major objection to the               tip and high local lift coe5cients at the root.
elliptical planform is the extreme difficulty of         Since the wing will initiate stall in the area of
mechanical layout and construction. A highly            highest local lift coefficients, the rectangular
tapered planform is desirable from the stand-            wing is characterized by a strong root stall
point of structural weight and stiffness and             tendency. Of course, this stall pattern is fav-
the usual wing planform may have a taper                 orable since there is adequate stall warning
ratio from 0.45 to 0.20. Since structural con-           buffet, adequate aileron effectiveness, and usu-
 siderations are quite important in the develop-         ally strong stable moment changes on the ait-
 ment of an airplane configuration, the tapered          plane. Because of the great aerodynamic and
planform is a necessity for an efficient configu-        structural ine&ciency of this planform, the
 ration. In order to preserve the aerodynamic            rectangular wing finds limited application only
 efficiency, the resulting planform is tailored          to low cost, low speed light planes. The sim-
 by wing twist and section variation to obtain           plicity of construction and favorable stall
 as near as possible the elliptic lift distribution.     characteristics are predominating requirements
                                                         of such an airplane. The stall sequence fot a
STALL PATTERNS                                           rectangular wing is shown by the tuft-grid
   An additional effect of the planfotm        area      pictures. The progressive flow separation il-
distribution is on stall pattern of wing.       The      lustrates the strong root stall tendency.
desirable stall pattern of any wing is a       stall         (C) The wing of moderate taper (taper
which begins on the root sections first.        The      ratio=0.5) has a lift distribution which closely

                                                   SPANWISE LIFT

                                  ROOT                                       TIP

                          ELLIPTICAL                                 RECTANGULAR, X=1.0

                  n      ~PROGRE,,,s=

                         MODERATE TAPER, A= 0.5                      HIGH TAPER, A=O.25

                                  Figure   1.33.   Stall Patterns (sheet I of 8)

Revised January   1965
                                                                     NAVWEPS OeBOT-80
                                                                    BASIC AERODYNAMICS

                                AR=2.31, k=l.O

             -II-              30°    OF FLOW     ANGULARITY







(a) TUFT GRID 6 INCHES         FROM           (b) TUFT GRID 24 INCHES   FROM
        TRAILING EDGE                                 TRAILING EDGE

                           FROM       NACA    TN 2674

              F;gure   1.33.    Stall Patterns   (sheet 2 of 8)

NAWEPS oD-80~~0

                       SURFACE TUFT PHOTOGRAPHS
                          FOR RECTANGULAR    WING
                              AR=2.31, k-l.0




                              FROM    NACA    TN 2674

                     Figuse 1.33. Stall Patterns (sheet 3 of 8)

                                                               NAVWEPS Oo-8OT-80
                                                              BASIC AERODYNAMICS

                     45’ DELTA, AR=4.0,X=O

                          30°    OF FLOW     ANGULARITY






        TRAILING EDGE                            TRALLING EDGE

                       FROM     NACA     TN 2674

              Figure 1.33. Staff Patterns (sheet 4 of 81


                                  SURFACE TUFT PHOTOGRAPHS
                                  FOR A SWEPT, TAPERED WING
                                    45O DELTA, AR=4.0. x=0

                 i =0   DEGREES                                    a = 8 DEGREES

                 a = 12 DEGREES                                    B = 16 DEGREES

                                         a = 20   DEGREES

                                     FROM   NACA    TN 2674

                            Figure 1.33. Stall Patterns (sheet 5 of 8’
                                             NAVWEPS OO-SOT-80
    )YE STREAMERS       OhI F!ilJ   MOnFl

Ftgure 7.33. Staff Patterns (sheet 6 of 8)

                                   60° DELTA, AR=2.31, X = 0

                                             30” OF FLOW ANGULARITY







         (a) TUFT     GRID 6 INCHES         FROM           (b) TUFT      GRID 24 INCHES   FROM
                    TRAILING  EDGE                                     TRAILING   EDGE

                                      FROM         NACA    TN 2674

                           Figure   1.33.    Stall Patterns   (sheet   7 of 8)

                                                               NAVWEPS OD-801-80
                                                              BASIC AERODYNAMICS

                   A SWEPT, TAPERED WlNG
                   60° DELTA, AR=2.31, A=0

a = 0 DEGEES


                    a =32   DEGREES

                  FROM   NACA   TN 2674

         Figure 1.33. Std   Patterns (sheet 8 018)
NAVWEPS 00-801-80

approximates that of the elliptical wing.               practical application to an airplane which is
Hence, the stall pattern is much the same as the        definitely subsonic in performance.
elliptical wing.                                              (F) Sweepback applied to a wing planform
      (D) The highly tapered wing of taper              alters the lift distribution similar to decreasing
ratio=0.25 shows the stall tendency inherent            taper ratio. Also, a predominating influence
with high taper. The lift distribution of such          of the swept planform is the tendency for a
a wing has distinct peaks just inboard from the         strong crossflow of the boundary layer at high
tip. Since the wing stall is started in the             lift coefficients. Since the outboard sections
vicinity of the highest local lift coefficient,         of the wing trail the inboard sections, the out-
this planform has a strong “tip stall” tendency.        board suction pressures tend to draw the
The initial stall is not started at the exact tip       boundary layer toward the tip. The result is
but at the station inboard from the tip where           a thickened low energy boundary layer at the
highest local lift c,oefficients prevail. If an         tips which is easily separated. The develop
actual wing were allowed to stall in this               ment of the spanwise flow in the boundary
fashion the occurrence of stall would be typi-           layer is illustrated by the photographs of
 fied by aileron buffet and wing drop. There             figure 1.33. Note that the dye streamers on
would be no buffet of the empennage or aft               the upper surface of the~swept wing develop a
fuselage, no strong nose down moment, and                strong spanwise crossflow at high angles of
 very little-if      any-aileron   effectiveness. In     attack. Slots, slats, and flow fences help to
 order to prevent such undesirable happenings,           allay the strong tendency for spanwise flow.
 the wing must be tailored to favor the stall                  When sweepback and taper are combined in
 pattern. The wing may be given a geometric.             a planform, the inherent tip stall tendency is
 twist or “washout” to decrease the local                 considerable. If tip stall of any significance is
  angles of attack at the tip. In addition, the           allowed to occur on the swept wing, an addi-
  airfoil section may be varied throughout the            tional complication results: the forward shift
  span such that sections with greater thickness          in the wing center of pressure creates an un-
  and camber are located in the areas of highest          stable nose up pitching moment. The stall
  local lift coefhcients. The higher ct- of               sequence of a swept, tapered wing is indicated
  such sections can then develop the higher local         by the tuft-grid photographs of figure 1.33.
                                                               An additional effect on sweepback is the re-
  C~S and be less likely to stall. The addition
                                                          duction in the slope of the lift curve and maxi-
  of leading edge slots or slats toward the tip
                                                          mum lift coeflicient. When the sweepback is
   increase the local c t- and stall angle of attack      large and combined with low aspect ratio the
   and are useful in allaying tip stall and loss of        lift curve is very shallow and maximum lift
   aileron effectiveness. Another device for im-           coefficient can occur at tremendous angles.of
   proving the stall pattern would be the forcing          attack. The lift curve of one typical low
   of stall in the desired location by decrctisingthe      aspect ratio, highly tapered, swept wing air-
   section ctmarin this vicinity.   The use of sharp       plane depicts a maximum lift coefficient at
   leading edges or “stall strips” is a powerful           approximately 43’ angle of attack.    Such dras-
    device to control the stall pattern.                   tic angles of attack are impractical in many
        .(E) The pointed tip wing of taper ratio           respects. If the airplane is operated at such
   equal to zero develops extremely high local             high angles of attack an extreme landing gear
    lift coefficients at the tip. For all practical        configuration is required, induced drag is ex-
    purposes, the pointed tip will be stalled at any        tremely high, and the stability of the airplane
    condition of lift unless extensive tailoring is        may seriously deteriorate. Thus, the modern
   applied to the wing. Such a planform has no             conhguration of airplane may have “minimum
                                                                                      NAVWEPS OO-ROl-80
                                                                                     BASIC AERODYNAMICS

control speeds” set by these factors rather than          the wing root boundary layer to be more easily
simple stall speeds based on C&,.                         separated in the presence of an adverse pressure
    When a wing of a given planform has various           gradient. Since the upper wing surface has the
high lift devices added, the lift distribution and        more critical pressure gradients, a low wing
stall pattern can be greatly affected. Deflec-            position on a circular fuselage would create
tion of trailing edge flaps increases the local           greater interference drag than a high wing
lift coe5cients in the flapped areas and since            position.    Adequate filleting and control of
the stall angle of the flapped section is de-             local pressure gradients is necessary to mini-
creased, initial stall usually begins in the              mize such additional drag due to interference.
flapped area. The extension of slats simply                   The sum of all the drags due to form, fric-
allows the slatted areas to go to higher lift             tion, leakage and momentum losses, and inter-
coe5cients and angles of attack and generally             ference drag is termed “parasite” drag since
delays stall in that vicinity.        Also, power         it is not directly associated with the develop-
effects may adversely affect the stall pattern of         ment of lift. While this parasite drag is not
the propeller powered airplane. When the                  directly associated with the production of lift
propeller powered airplane is at high power               it is a variable with lift.     The variation of
and low speed, the flow induced at the wing               parasite drag coefficient, C+, with lift coef-
root by the slipstream may cause considerable             ficient, C,, is shown for a typical airplane in
delay in the stall of the root sections. Hence,           figure 1.34. The minimum parasite drag co-
the propeller powered airplane may have its               efficient, CDpmi,, usually occurs at or near zero
most undesirable stall characteristics during the         lift and parasite drag coefficient increases
power-on stall rather than the power-off stall.           above this point,in a smooth curve. The in-
                                                          duced drag coefficient is shown on the same
PARASITE     DRAG                                         graph for purposes of comparison since the
                                                          total drag of the airplane is a sum of the
   In addition to the drag caused by the de-
                                                          parasite and induced drag.
velopment of lift (induced drag) there is the
                                                              In many parts of airplane performance it is
obvious drag which is nor due to the develop
                                                          necessary to completely distinguish between
ment of lift.   A wing surface even at zero lift
                                                          drag due to lift and drag not due to lift. The
will have “profile” drag due to skin friction
                                                          total drag of an airplane is the sum of the para-
and form. The other components of the air-
                                                          site and induced drags.
plane such as the fuselage, tail, nacelles, etc.,
contribute to drag because of their own form                               G=c++cD;
and skin friction.    Any loss of momentum of             where
the airstream due to powerplant cooling, air                        C, = airplane drag coefficient
conditioning, or leakage through construction
                                                                   C+=parasite    drag coefficient
or access gaps is, in effect, an additional drag.
When the various components of the airplane                        C,,= induced drag coeaicient
are put together the total drag will be greater
than the sum of the individual components
because of “interference” of one surface on the
other.                                                    From inspection of figure 1.34 it is seen that
  The most usual interference of importance               both CD, and CD, vary with lift coefticient.
occurs at the wing-body intersection where the            However, the usual variation of parasite drag
growth of boundary layer on the fuselage re-              allows a simple correlation with the induced
duces the boundary layer velocities on the wing           drag term. In effect, the part of parasite drag
root surface. This reduction in energy allows             above the minimum at zero lift can be “lumped”
NAVWEPS 00-801-80



                    i 0.4


                               0                   .05               ;!O              .!5
                                                   DRAG COEFFICIENT,       CD



                j       1.0
                t       0.6
                $       0.6

                i       0.4



                                                   DRAG COEFFICIENT,       CD

                              Figure   1.34.   Airplane   Parasite and Induced Drag
                                                                                         NAVWEPS 00-8OT-80
                                                                                        BASIC AERODYNAMICS

in with the induced drag coefficient by a con-            ure is not too accurate because of the sharper
stant factor which is defined as the “airplane            variation of parasite drag at high angles of
e5ciency factor”, c. By this method of ac-                attack. In a sense, the airplane efficiency fac-
counting the airplane drag coe5cient is ex-               tor would change from the constant value and
pressed as :                                              decrease. The deviation of the actual airplane
                                                          drag from the approximating curve is quite
                                                          noticeable for airplanes with low aspect ratio
                                                          and sweepback. Another factor to consider is
                                                          the effect of compressibility.   Since compressi-
                                                          bility effects would destroy this relationship,
where                                                     the greatest application is for subsonic perform-
                minimum parasite drag                     ance analysis.
        C DPmB=
                coefficient                                  The total airplane drag is the sum of the
           CD;= induced drag coe5cient                    parasite and induced drags.
            e= airplane e5ciency factor                                   D= D,+D<
In this form, the airplane drag coefficient is                            Di= induced drag
expressed as the sum of drag not due to lift
        ) and drag due to lift (G).     The air-                             =(0.318 $+S
plane efficiency factor is some co&ant (usually           and
less than unity) which includes parasite drag                             D,= parasite drag
due to lift with the drag induced by lift.
CDpmr” invariant with lift and represents the
parasite drag at zero lift.   A typical value of          When expressed in this form the induced drag,
Cr,Pminwould be 0.020, of which the wing may              Di, includes all drags due to lift and is solely
account for 50 percent, the fuselage and nacelles         a function of lift.   The parasite drag, D,, is
40 percent, and the tail 10 percent. The term             the parasite drag and is completely independent
                                                          of lift-it   could be called the “barn door”
of 0.318 g         accounts for all drag due’ to          drag of the airplane.
     (          >
lift-the   drag induced by lift and the extra                 An alternate expression for the parasite drag
parasite drag due to lift.      Typical values of         is:
the airplane efficiency factor range from 0.6 to
0.9 depending on the airplane configuration
and its characteristics. While the term of                where
drag due to lift does include some parasite                        f = equivalent   parasite area, sq. ft.
drag, it is still generally referred to as induced
                                                                   f = CDPmi,S
     The second graph of figure 1.34 shows that                    q= dynamic pressure, psf
the sum of CD,-mm   and G can approximate the
                         e                                          =- UP
actual airplane CD through a large range of lift                       295
coefficients. For airplanes of moderate aspect             or
ratio, this representation of the airplane total                  DpEfg
drag is quite accurate in the ordinary range of
lift coefficients up to near 70 percent of CL,,.           In this form, the equivalent parasite area, f,
At high lift coefficients near CL-, the proced-            is the product of CDPml”and S and relates an
I   Y   B
                                                                                      NAVWEK OD-BOT-BO
                                                                                     BASIC AERODYNAMICS

 impression of the “barn door” size. Hence,               be appreciated. The general effect of altitude
parasite drag can be appreciated as the result            is expressed by:
of the dynamic pressure, 4, acting on the
equivalent parasite area, j. The “equivalent”
parasite area is defmed by this relationship as
a hypothetical surface with a C,=l.O which
produces the same parasite drag as the air-               where
plane. An analogy would be a barn door in                 D,, = parasite drag corresponding to some orig-
the airstream which is equivalent to the air-                   inal altitude density ratio, 0,
plane. Typical values for the equivalent para-
site area range from 4 sq. ft. for a clean fighter        D,,=parasite drag corresponding to some new
type airplane to 40 sq. ft. for a large transport               altitude density ratio, (ra
type airplane. Of course, when any airplane
is changed from the clean configuration to the                        (and f, V are constant)
landing configuration, the equivalent parasite
                                                          This relationship implies that parasite drag
area increases.
                                                          would decrease at altitude, e.g., a given air-
   EFFECT OF CONFIGURATION.              The par-
                                                          plane in flight at a given T.4.Y at 40,COOft.
 asite drag, D,, is unaffected by lift, but is
                                                          (e=O.29 would have one-fourth the parasite
variable with dynamic pressure and equivalent
                                                          drag when at sea level (u=l.OO).       This effect
parasite area. This principle furnishes the
                                                          results when the lower air density produces
 basis for illustrating the variation of parasite
                                                          less dynamic pressure. However, if the air-
drag with the various conditions of flight.
                                                          plane is flown at a constant EAS, the dynamic
If all other factors are held constant, the para-
                                                          pressure and, thus, parasite drag do not vary.
site drag varies directly with the equivalent
                                                          In this case, the TASwould be higher at altitude
parasite area.
                                                          to provide the same EAS.
                                                             EFFECT OF SPEED. The effect of speed
                   D,,= b                                 alone on parasite drag is the most important.
                   D,, C)I                                If all other factors are held constant, the effect
                                                          of velocity on parasite drag is expressed as:
                                                                            -=- V, *
D,,= parasite drag corresponding to some orig-                              D,, (3
     inal parasite area, fi
D,,==parasite drag corresponding to some new
      parasite area, fi                                   D,,=parasite drag corresponding to some orig-
                                                                inal speed, Vi
             (V and (r are constant)
                                                          D,,=parasite drag corresponding to some new
                                                                speed, VS
As an example, the lowering of the landing
gear and flaps may increase the parasite area                          (j and o are constant)
80 percent. At any given speed and altitude
this airplane would experience an 80 percent              This relationship expresses a powerful effect
increase in parasite drag.                                of speed on parasite drag. As an example, a
   EFFECT OF ALTITUDE.         In a similar man-          given airplane in flight at some altitude would
ner the effect of altitude on parasite drag may           have four times as much parasite drag at twice
NAVWEPS 00-801-80

as great a speed or one-fourth as much parasite              fuselage and nacelles of high fineness ratio,
drag at half the original speed. This fact may               well faired canopies, and thin wing sections
be appreciated by the relationship of dynamic                which have very smooth uniform pressure dis-
pressure with speed-twice as much V, four                    tributions.   -Low aspect ratios and sweepback
times as much 4, and four times as much D,.                  are favorable in delaying and reducing the
This expressed variation of parasite drag with               compressibility drag rise. In addition, inter-
speed points out that parasite drag will be of               ference effects are quite important in transonic
greatest importance at high speeds and prac-                 and supersonic flight and the airplane cross
tically insignificant in flight at low dynamic               section area distribution must be controlled
pressures. To illustrate this fact, an airplane              to minimize local velocity peaks which could
in flight just above the stall speed could have a            create premature strong shock wave formation.
parasite drag which is only 25 percent of the                    The modern configuration of airplane will
total drag. However, this same airpfane at                   illustrate the features required to effect very
maximum level flight speed at low altitude                   high speed performance-low         aspect ratio,
would have a parasite drag which’ is very                    sweepback, thin low drag sections, etc. These
nearly 100 percent of the total drag. The                    same features produce flight characteristics at
predominance of parasite drag at high flight                 low airspeeds which necessitate .proper flying
speeds emphasizes the necessity for great aero-              technique.
dynamic cleanness (low j) to obtain high speed               AIRPLANE TOTAL DRAG
                                                                 AI&CCYCYl Ye nf ~ln eimlooe
                                                                I%,- rn+ql Jr,, v YIL L”y’““c in fl.jght is the
   In the subsonic regime of flight, the ordinary
configuration of airplane has a very large por-              sum of the induced and parasite drag. Figure
tion of the equivalent parasite area determined              I.35 illustrates the variation of toral drag
by skin friction drag. As the wing contrib-                  with speed for a given airplane in level flight
utes nearly half of the total parasite drag, the             at a particular weight, configuration, and alti-
profile drag of the wing can be minimized by                 tude. The parasite drag increases with speed
the use of the airfoil sections which produce                varying as the square of the velocity while the
extensive laminar flow. A subtle effect on                   induced drag decreases with speed varying in-
parasite drag occurs from the influence of the               versely as the square of the velocity.         The
wing area. Since the wing area (S) appears                   total drag of the airplane shows the predomi-
directly in the parasite drag equation, a reduc-             nance of induced drag at low speed and parasite
tion in wing area would reduce the parasite                  drag at high speed. Specific points of interest
drag if all other factors were unchanged.                    on the drag curve are as follows:
While the exact relationship involves con-                       (A) Stall of this particular airplane occurs
 sideration of many factors, most optimum                    at 100 knots and is indicated by a sharp rise
airplane configurations have a strong preference             in the actual drag. Since the generalized iqua-
                                                             tions for induced and parasite do not account
for the highest practical wing loading and
                                                             for conditions at stall, the actual drag of the
 minimum wing surface area.
                                                              airplane is depicted by the “hook” of the
    As the flight speeds of aircraft approach the             dotted line.
 speed of sound, great care must be taken to                     (B) At a speed of 124 knots, the airplane
 delay and alleviate compressibility         effects.         would incur a minimum rate of descent in
 In order to delay and teduce the drag rise                   power-off flight. Note that at this speed the
 associated with compressibility       effects, the           induced drag comprises 75 percent of the total
 components of the airplanes must be arranged                 drag. If this airplane were powered with a
 to reduce the early formation of shock waves                 reciprocating-propeller type powerplant, maxi-
 on the airplane. This will generally require                 mum endurance would occur at this airspeed.
                                             NAVWEPS OO-ROT-80
                                            BASIC AERODYNAMICS

                VELOCITY   KNOTS

Figure 9.35. Typical Airplane Drag Curves


    (C) The point of minimum total drag occurs              215 knots. This point on the drag curve pro-
at a speed of 163 knots. Since this speed in-               duces the highest proportion between velocity
curs the least total drag for lift-equal-weight             and drag and would be the point for maximum
flight, the airplane is operating at (L/D)ma,.              range if the airplane were jet powered. Be-
Because of the particular manner in which                   cause of the high proportion of parasite drag
parasite and induced drags vary with speed                  at this point the long range jet airplane has
(parasite drag directly as the speed squared;               great preference for great aerodynamic clean-
induced drag inversely as the speed squared)                ness and less demand for a high aspect ratio
the minimum total drag occurs when the in-                  than the long range propeller powered airplane.
duced and parasite drags are equal. The speed                   (E) At a speed of 400 knots, the induced
for minimum drag is an important reference for              drag is an extremely small part of the total
many items of airplane performance. One                     drag and parasite drag predominates.
item previously ,presented related glide per-                   (P) As the airplane reaches very high flight
formance and lift-drag ratio. At the speed of               speeds, the drag rises in a very rapid fashion
163 knots this airplane incurs a total drag of              due to compressibility.     Since the generalized
778 lbs. while producing 12,000 lbs. of lift.               equation for parasite drag does not account for
 These figures indicate a maximum lift-drag                 compressibility effects, the actual drag rise is
ratio of 15.4.and relate a glide ratio of 15.4.~            typified by the dashed line.
In addition, if this airplane were jet powered,                 The airplane drag curve shown in figure 1.34
the airplane would achieve maximum en-                      is particular to one weight, configuration, and
durance at this airspeed for ‘   the specified alti-         altitude in level flight. Any change in one of
 tude. If this airplane were propeller powered,              these variables will affect the specific drags at
 the airplane would achieve maximum range at                 specific velocities.
 this airspeed for the specified altitude.                      The airplane drag curve is a major factor in
     (D) Point (D) is at an airspeed approxi-                many items of airplane performance. Range,
mately 32 percent greater than the speed for                 endurance, climb, maneuver, landing, takeoff,
 (L/D),.,.    Note that the parasite drag com-               etc., performance are based on some relation-
prises 75 percent of the total drag at a speed of            ship involving the airplane drag curve.

                                                                                  NAVWEPS 00-8OT-80
                                                                              AIRPLANE PERFORMANCE

   The performance of an aircraft is. the most         operating limitations and insight to obtain
important feature which defines its suitability        the design performance of his aircraft. The
for specific missions. The principal items of          performance section of the flight handbook
airplane performance deserve detailed consid-          provides the specific information regarding the
eration in order to better understand and              capabilities and limitations of each airplane.
appreciate the capabilities of each airplane.          Every Naval Aviator must rely upon these
Knowledge of the various items of airplane             handbook data as the guide to safe and effec-
performance will provide the Naval Aviator             rive operation of his aircraft.
with a more complete appreciation of the

     REQUIRED      THRUST    AND    POWER                   knots requires one horsepower of propulsive
                                                            power. However, each pound of drag at 650
DEFINITIONS                                                 knots requires two horsepower while each
    All of the principal items of flight perform-           pound of drag at 162.5 knots requires one-half
ance involve steady state flight conditions and             horsepower. The term “power” implies work
equilibrium of the airplane. For the airplane               rate and, as such, will be a function of the speed
to remain in steady level flight, equilibrium               at which a particular force is developed.
must be obtained by a lift equal to the air-                    Distinction    between thrust required and
plane weight and a powerplant thrust equal to               pawcr required is necessary for several reasons.
the airplane drag. Thus, the airplane drag                  For the items of performance such as range and
defines the thrust required to maintain steady              endurance, it is necessary to relate powerplant
level flight.                                               fuel flow with the propulsive requirement for
     The total drag of the airplane is the sum of           steady IeveI flight.     Some powerplants incur
the parasite and induced drags: Parasite drag               fuel flow rate according to output thrust while
is the sum of pressure and friction drag which              other powerplants incur fuel flow rate depend-
is due to the basic configuration and, as de-               ing on output power. For example, the turbo-
fined, is independent of lift. Induced drag is               jet engine is principally. a thrust producing
the undesirable but unavoidable consequence                 machine and fuel flow is most directly related
 of the development of lift. In the process of              to thrust output. The reciprocating engine is
 creating lift by the deflection of an airstream,           principally a power producing machine and
 the actuai iift is inclined and a coimponcn: of            fuei flow is most directiy reiated to power
 lift is incurred parallel to the flight path direc-         output.      For these reasons the variation of
 tion. This component of lift combines with                 thrust required wil1 be of greatest interest in
 any change in pressure and friction drag due                the performance of the turbojet powered air-
 to change in lift to form the induced drag.                 plane while the variation of power required
 While the parasite drag predominates at high                will be of greatest interest in the performance
  speed, induced drag predominates at low speed.             of the propeller powered airplane. Also, dis-
 Figure 2.1 illustrates the variation with speed             tinction between power and thrust required is
  of the induced, parasite, and total drag for a             necessary in the study of climb performance.
 specific airplane configuration in steady level
                                                             During a steady climb, the rate of climb will
                                                             depend on excess power while the angle of
      The power required for flight depends on the
  thrust required and the flight velocity.        By         climb is a function of excess thrust.
 definition, the propulsive horsepower required                 The total power required for flight can be
  is related to thrust required and flight velocity          considered as the sum of induced and parasite
  by the following equation:                                 effects similar to the total drag of the airplane.
                                                             The induced power required is a function of the
                     pr= Trv                                 induced drag and velocity.
 where                                                                          p,,,!g
     Pr=power required, h.p.
     Tr= thrust required (total    drag), Ibs.              where
     V= true airspeed, knots                                        Pri= induced power required, h.p.
 By inspection of this relationship, it is appar-                   D<=induced drag, lbs.
 ent that each’pound of drag incurred at 325                         V= true airspeed, knots

                                                                                       NAVWEPS 00-8OT-80
                                                                                   AIRPLANE PERFORMAN:CE

Thus, induced power required will vary with               PrPs=parasite power required corresponding to
lift, aspect ratio, altitude, etc., in the same                                       ,
                                                               some different speed, I’
manner as the induced drag. The only differ-              For example, if an airplane in steady     flight is
ence will be the variation with speed. If all             operated at twice as great a speed, the   parasite
other factors remain constant, the induced                drag is four times as great but the       parasite
power required varies inversely with velocity             ~;;zr   required is eight times the       original
while induced’  drag varies inversely with the
square of the velocity.                                      Figure 2.1 presents the thrust required and
                                                          power required for a specific airplane configu-
                                                          ration and altitude.      The curves of figure 2.1
                                                          are applicable for the following airplane data:
                                                               gross weight, W= 15,000 Ibs.
                                                                span, b=40 ft.
Pri,=induced power required corresponding to                    equivalent parasite area, f=7.2 sq. ft.
       some original speed, Vi                                  airplane efficiency factor, c= ,827
I+;,= induced power required corresponding to                   sea level altitude, C= 1.000
       some different speed, V,                                 compressibility corrections neglected
For example, if an airplane in steady level flight        The curve of drag or thrust required versus
is operated at.twice as great a speed, the in-            velocity shows the variation of induced, para-
duced drag is one-fourth the original value but           site, and total drag. Induced drag predomi-
the induced power required is one-half the                nates at low speeds. When the airplane is
original value.                                           operated at maximum lift-drag ratio, (L/D)-,
   The parasite power required is a function              the total drag is at a minimum and the induced
of the parasite drag and velocity.                        and parasite drags are equal. For the specific
                                                          airplane of figure 2.1, (,L/D),, and minimum
                                                          total drag are obtained at a speed of 160 knots.
                                                             The curve of power required versus velocity
where                                                     shows the variation of induced, parasite, and
        Pr,=parasite power required, h.p.                 total power required. As before, induced
        D,=paraSite drag, lbs.                            power required predominates at low speeds and
         V= true airspeed, knots                          parasite power required predominates at high
                                                          speeds and the induced and parasite power are
Thus, parasite power required will vary with
                                                          equal at (L/D),,.      However, the condition of
altitude and equivalent parasite area ( f) in the
                                                          (L/D&-     defines only the point of minimum
same manner as ‘ parasite drag. However,
                                                          drag and does not define the point of minimum
the variation with speed will be different. If
                                                          pozverrequired. Ordinarily, the point of mini-
all other factors are constant, the parasite drag
                                                          mum power required will occur at a speed
varies as the square of velocity but parasite
                                                          which is 76 percent of the speed for minimum
power varies as the cube of velocity.
                                                          drag and, in the case of the airplane configura-
                                                          tion of figure 2.1, the speed for minimum power
                   Pb% v* 3                               required would be 122 knots. The total drag
                   -=(-I VI                               at the speed for minimum power required is 15
where                                                     percent higher than the drag at (L/D)-    but the
Prpl= parasite power required corresponding to            minimum power required is 12 percent lower
      some original speed, Vi                              than the power required at (L/D)-.


                       Figure 2.1.   Airplane   Thrust and Power Required
                                                                                         NAVWEPS OO-.ROT-80
                                                                                     AtRPlANE PERFORMANCE

    Induced drag predominates at speeds below
 the point of minimum total drag. When the                                      v, Tg
 airplane is operated at the condition of mini-                                 -=J E
 mum power required, the total drag is 75
 percent induced drag and 25 percent parasite
 drag. Thus, the induced drag is three times as                Vi = speed corresponding to a specific C,
 great as the parasite drag when at minimum                           and weight, W,
 power required.
                                                               Va=speed corresponding to the same C,
 VARIATIONS OF THRUST REQUIRED AND                                   but a different weight, Ws
                                                            For the example airplane of figure 2.2, a change
      The curves of thrust required and power
                                                            of gross weight from 15,000 to 22,500 lbs. re-
  required versus velocity provide the basis for
                                                            quires that the airplane operate at speedswhich
  comprehensive analysis of all the major items
                                                            are 22.5 percent greater to maintain a specific
  of airplane performance. The changes in the
                                                            lift coefficient. For example, if the 15,000-lb.
  drag and power curves with variations of air--
                                                            airplane operates at 160 knots for (L/D)-,   the
  plane gross weight, configuration, and altitude
                                                            speed for (L/D)mz at 22,500 lbs. is:
  furnish insight for the ‘     variation of range,
  endurance, climb performance, etc., with these
  same items.                                                              v, = VI@
      The effect of a change in weight on the thrust
  and power required is illustrated by figure 2.2.                            =I&) 22,500
1 The primary effect of a weight change is a                                      -\i-
  change in the induced drag and induced power
                                                                              = (160) (1.225)
  required at any given speed. Thus, the great-
  est changes in the curves of thrust and power                               = 196 knots
  required will take place in the range of low
  speed flight where the induced effects pre-               The same situation exists with respect to the
  dominate. The changes in thrust and power                 curves of power required where a change in
  required in the range of high speed flight are            weight requires a change of speed to maintain
  relatively slight because parasite effects pre-           flight at a particular CL. For example, if the
  dominate at high speed. The induced effects               15,000-lb. airplane achieves minimum power
  at high speed are relatively small and changes            required at 122 knots, an increase in weight to
  in these items produce a small effect on the              22,500 Ibs. increases the speed for minimum
  total thrust or power required.                           power required to 149 knots.
      In addition to the general effect on .the in-             0f course, the thrust and power required at
  duced drag and power required at particular               specific lift coefficients are altered by changes in
  speeds, a change in weight will require that the          weight.      At a specific C,, any change in weight
  airplane operate at different airspeeds to main-          causes a like change in thrust required, e.g., a
  tain conditions of a specific lift coefficient and        50-percent increase in weight causes a 50-per-
  angle of attack. If the airplane is in steady             cent increase in thrust required at the same C,.
  flight at a particular C,,, the airpseed required         The effect of a weight change on the power re-
  for this CL will vary with weight in the fol-             quired at a specific CL is a bit more complex be-
  lowing manner :                                           cause a change in speed accompanies the change

                                                                                            Revised January   1965

                  Figure 2.2. Effect of Weight on Thrust and Power Required
                                                                                      NAVWEPS 00-501-50
                                                                                   AMPLANE PERFORMANCE

 in drag and there is a two-fold effect. A 50-           an increase in f to account for the additional
 percent increase in weight produces an increase         changes in parasite drag which may vary with
 of 83.8 percent in the power required to main-          C‘  .
 tain a specific CL. This is the result of a 50-              A change in altitude can produce signifi-
 percent increase in thrust required coupled with        cant changes in the curves of thrust and power
 a 22.5-percent increase in speed. The effect of a       required. The effects of altitude on these
 weight change on thrust required, power re-             curves providea great part of the explanation of
 quired, and airspeed at specific angles of attack       the effect of altitude on range and endurance.
 and lift coefficients provides an important basis       Figure 2.4 illustrates the effect of a change in
 for various techniques of cruise and endurance          altitude on the curves of thrust and power re-
 conditions of flight.                                   quired for a specific airplane configuration and
1 Figure 2.3 illustrates the effect on the curves        gross weight.        As long as compressibility
 of thrust and power required of a change in the         effects are negligible, the principal effect of
  equivalent parasite area,!, of the configuration.      increased altitude on the curve of thrust re-
 Since parasite drag predominates in the region          quired is that specific aerodynamic conditions
 of high flight speed, a change in f will produce        occur at higher true airspeeds. For example,
 the greatest change in thrust and power re-             the subject airplane at sea level has a minimum
 quired at high speed. Since parasite drag is            drag of 1,250 lbs. at 160 knots. The same
  relatively small in the region of low speed            airplane would incur the same drag at altitude
  flight, a change in f will produce relatively          if operated at the same cqthdcnt airsprcd of 160
  small changes in thrust and power required at           knots. However, the equivalent airspeed of
  low speeds. The principal effect of a change in         160 knots at 22,000 ft. altitude would produce
  equivalent parasite area of the configuration is        a true airspeed of 227 knots. Thus, an in-
  to change the parasite drag at any given air-           crease in altitude will cause the curve of thrust
  speed.                                                  required to flatten out and move to the direc-
      The curves of figure 2.3 depict the changes in      tion of higher velocity.        Note that altitude
  the curves of thrust and power required due             alone will not alter the value of minimum drag.
  to a 50 percent increase in equivalent parasite              The effect of altitude on the curve of power
  area of the configuration.     The minimum total        required can best be considered from the effect
   drag is increased by an increase in f and the          on true airspeed to achieve a specific aero-
  GWL         is reduced. ‘ Also, the increase in f       dynamic condition.         The sea level power re-
   will increase the CL for (L/D)-     and require a      quired curve of figure 2.4 indicates that
   reduction in speed at the new, but decreased,          CW>mz occurs at 160 knots and requires 615
   (L/D)-.      The point of minimum power re-            h.p. If this same airplane is operated at
   quired occurs at a lower airspeed and the value        WD)ma at an altitude of 22,000 ft., the same
   of the minimum power required is increased             drag is incurred at a higher velocity and re-
   slightly.    Generally, the effect on the mini-        quires a higher power. The increase in ve-
   mum power required is slight because the para-          locity to 227 knots accounts for the increase
   site drag is only 25 percent of the total at this       in power required to 872 hp.         Actually, the
   specific condition of flight.                           various points on the curve of power required
       An increase in the equivalent parasite area         can be considered affected in this same fashion.
   of an airplane may he brought about by the              At specific lift coefficients and angles of attack,
    deflection of flaps, extension of landing gear,        a change in altitude will alter the true airspeed
    extension of speed brakes, addition of external        particular to these points and cause a change
    stores, etc. In such instances a decrease in the       in power required because of the change in
    airplane efficiency factor, c, may accompany           true airspeed. An increase in altitude will
                                                                                        Revised Januaty   1965



           Figure 2.3. Effect of Equivalent Parasite Area, f, on Thrust and Power Required
                                                                             NAVWEPS Oo-8oT-80
                                                                         AIRPLANE PERFORMANCE


                                      VELOCITY-KNOTS        (TAS)


                                        VELOCITY-KNOTS       (TAS)

              Figure 2.4.   Ekf   of Altitude    on Thrust and Power Required

cause the power required curve to flatten out           The development of thrust by a turbojet or
and move to higher velocities and powers             ramjet powerplant is illustrated by figure 2.5.
required.                                            Air approaches at a velocity, Vi, depending on
   The curves of thrust and power required and       the flight speed and the powerplant operates
their variation with weight, altitude, and con-      on a certain mass flow of air, Q, which passes
figuration are the basis of all phases of airplane   through the engine. Within the powerplant
performance. These curves define the require-        the air is compressed, energy is added by the
lnent~ of the airplane and must be considered        burning of fuel, and the mass flow is expelled
with the power and thrust available from the         from the nozzle finally reaching a velocity,
powerplants to provide detailed study of the         V;. The momentum change accomplished bv
various items of airplane performance.               this action produces the thrust,

     AVAILABLE       THRUST     AND   POWER                          Ttz=Q (V,V,)
   All powerplants have in common certain                Ta= thrust, lbs.
general principles. Regardless of the type of
propulsion device, the development of thrust is           Q= mass flow, slugs per sec.
related by Newton’ laws of motion.
                                                         Vi= inlet (or flight) velocity, ft. per sec.
or                                                        V,= jet velocity, ft. per sec.
                           df                        The typical ramjct or turbojet powerplane de-
where                                                rives its thrust by working with a mass flow
                                                     relatively smaller than that of a propeller but
        $=force   or thrust, lbs.
                                                     a relatively greater change of velocity.    From
        m=mass, slugs                                the previous equation it should be appreciated
                                                     that the jet thrust varies directly with the mass
        a=acceleration,   ft. per sec.%              flow Q, and velocity change, Va-Vi.          This
                                                     fact is useful in accounting for many of the
        d=derivative  with respect to time, e.g.,
        dr rate of change with time                  performance characteristics of the jet power-
      mV=momentum, lb.-sec., product of mass            In the process of creating thrust by mo-
          and velocity                               mentum change of the airstream, a relative
                                                     velocity, Vz-V1, is imparted to the airstream.
The force of thrust results from the accelera-       Thus, some of the available energy is essen-
tion provided the mass of working fluid. The         tially wasted by this addition of kinetic energy
magnitude of thrust is accounted for by the          to the airstream. The change of kinetic energy
rate of change of momentum produced by the           per time can account for the power wasted in
powerplant.     A rocket powerplant creates          the airstream.
thrust by creating a very large change in veloc-
ity of a relatively small mass of propellants.                       Pw=KE/t
A propeller produces thrust by creating a com-
paratively small change in velocity of a rela-
tively large mass of air.
                                                                                         NAVWEPS Oo-ROT-80
                                                                                     AIRPLANE PERFORMANCE


                               T, = Q (V,-V,)
                                      Pa= T,, V,


                                  7)p=-        2VI
                                          v2 +v,

7p    .5
           0   .I   .2    .3     .4       .5         .6    .?    .6       .9   1.0


                         Figure 2.5.      Principles      of Propulsion

NAWEPS 0040140

Of course, the development of thrus,t with              to produce the required thrust with the highest
some finite mass flow will require some finite          possible mass flow and lowest possible velocity
velocity change and there will be the inevita-          change.
ble waste of power in the airstream. In order              The graph of figure 2.5 shows the variation
to achieve high efficiency of propulsion, the           of propulsion efficiency, qP, with the ratio of
thrust should be developed with a minimum               flight speed to jet velocity, VJV,. To achieve
of wasted power.                                        a propulsion efficiency of 0.85 requires that the
   The propulsion efficiency of the jet power-          flight velocity be approximately 75 percent of
plant can be evaluated by comparing the                 the slipstream speed relative to the airplane.
propulsive output power with the input power.           Such a propulsive efficiency could be typical
Since the input power is the sum of the output          of a propeller powered airplane which derives
power and wasted power, an expression for               its thrust by the propeller handling a large
propulsion efficiency can be derived.                   mass flow of air. The typical turbojet power-
                                                        plant cannot achieve such high propulsive
                         Pa                             ethciency because the thrust is derived with a
                    vp=Pa+Pw                            relatively smaller mass flow and larger vcloc-
                                                        ity change. For example, if the jet velocity is
                           zv,                          1,200 ft. per sec. at a flight velocity of 600 ft.
                    ')p= v*+v1                          per sec., the propulsion efficiency is 0.67. The
where                                                   ducted fan, bypass jet, and turboprop are vari-
                                                        aCon -which impiove tliC propulsive efIiciency
        trp= propulsion efficiency
                                                        of a type of powerplant which has very high
         9=“eta”                                        power capability.
                                                            When the conditions of range, endurance, or
     Pa = propulsive power available                    economy of operation are predominant, high
                                                        propulsion efhciency is necessary. Thus, the
          = TCZV~                                       propeller powered airplane with its inherent
    Pw= power wasted                                    high propulsive efliciency will always find ap
                                                        plication.     The requirements of very high
The resulting expression for propulsion effi-           speed and high altitude demand very high
ciency, v,,, shows a dependency on the flight           propulsive power from relatively small powcr-
velocity, V,, and the jet velocity, VZ. When             plants. When there are practical limits to the
the flight velocity is zero, the propulsion              increase of mass flow, high output is obtained
efficiency is zero since all power generated is          by large velocity changes and low propulsive
wasted in the slipstream and the propulsive              efficiency is an inevitable consequence.
power is zero. The propulsion efliciency would
be I.00 (or 100 percent) only when the flight           TURBOJET      ENGINES
velocity, Vi, equals the jet velocity, Vz.                 The turbojet engine has foundwidespread USC
Actually, it would not be possible to produce           in aircraft propulsion because of the relatively
thrust under such conditions with a finite mass         high power output per powerplant weight and
flow. While 100 percent efficiency of propul-           size. Very few aircraft powerplants can com-
sion can not be attained practically, some              pare with the high output, flexibility, simplic-
insight is furnished to the means of creating           ity, and small size of the aircraft gas turbine.
high values of propulsion efficiency. To ob             The coupling of the propeller and recipro-
tain high propulsion efficiency it is necessary         cating engine is one of the most efficient means

                                                                                     NAVWEPS 00-801-80
                                                                                  ARPLANE PERFORMANCE

known for converting fuel energy into propul-             compressor pressure ratio should be high to
sive energy. However, the intermittent action             produce a high thermal efliciency in the engine
of the reciprocating engine places practical              The area XCDZ represents the work done by
limits to the airflow that can be processed and           the compressor during the compression of the
restricts the development of power. The con-              unit weight of air. Of course, certain losses
tinuous, steady flow feature of the gas turbine           and inefliciencies are incurred during the com-
allows such a powerplant to process consider-             pression and the power required to operate the
ably greater airflow and, thus, utilize a greater         compressor will be greater than that indicated
expenditure of fuel energy. While the pro-                by the work done on the engine airflow.
pulsive efficiency of the turbojet engine is con-            Compressed air is discharged from the com-
siderably below that of the reciprocating en-             pressor to the combustion chamber at condition
gine-propeller combination, the specific power            D. Fuel is added in the combustion chamber,
 output of the turbojet at high speeds is quite           and the combustion of fuel liberates consider-
 superior.                                                able heat energy. The combustion process in
    The operation of the turbojet engine involves         the gas turbine differs from that of the recipro-
 a relatively large change in velocity being im-          cating engine in that the process is essentially
parted to the mass flow through the engine.               a constant pressure addition of heat energy.
Figure 2.6 illustrates the operation of a typical         As a result, the combustion of fuel causes a
 turbojet engine by considering the processing            large change in temperature and large change
 given a unit weight of inlet airflow.   Consider         of volume of the unit weight of airflow.      The
 a unit weight of ambient air approaching the             process in the combustion chamber is repre-
 inlet to the engine then experiencing the                sented by the change from point D to point E of
changes in pressure and volume as it is proc-             the pressure-volume diagram of figure 2.6.
 essed by’  the turbojet.  The chart of pressure              The combustion products are delivered to the
 versus volume of figure 2.6 shows that the unit          turbine section where sufficient work must be
 weight of airflow at atmospheric condition A             extracted to power the compressor section.
 is delivered to the inlet entrance at condition          The combustion chamber discharges high tem-
B. The purpose of the inlet or diffuser as to             perature, high pressure gas to the turbine where
reduce the velocity and increase the pressure
                                                          a partial expansion is accomplished with a drop
 of the flow entering the compressor section.
                                                          in pressure and increase in volume to point F
 Thus, the aerodynamic compression produces
 an increase in pressure and decrease in volume           on the pressure-volume diagram. The work
 of the unit weight of air and delivers air to            extracted from the unit weight of air by the
the compressor at condition C. The work done              turbine section is represented by the area
by the aerodynamic compression of the inlet               ZEFY.      As with the compressor, the actual
ot diffuser is represented by the area ABCX.              shaft work extracted by the turbine will differ
 Generally, most conventional turbojet engines            from that indicated by the pressure-volume
 require that the compressor inlet flow be sub-            diagram because of certain losses incurred
 sonic and supersonic flight will involve con-             through the turbine section. For steady, sta-
 siderable aerodynamic compression in the inlet.           bilized operation of the turbojet engine the
    Air delivered to the compressor inlet at con-          power extracted by the turbine will equal the
 dition C is then subject to further compression           power required to operate the compressor. If
 through the compressor section. As a result               the turbine power exceeds the compressor
 of the function of the compressor, the unit               power required, the engine will accelerate; if
 weight of air is subject to a decrease in volume          the turbine power is less than the compressor
 and increase in pressure to condition D. The              power required, the engine will decelerate.
NAVWEPS 00-807-80

                                                      COMBUSTION                 TAILPIPE
             INLET OR                                                             NOZZLE
             DIFFUSER           COMPRESSOR                 CHAMBER     TURBINE

                                   TURBOJET      ENGINE CYCLE


                    .                                        TURBINE     WORK
                 E      Y


                            1                                                               c
                                           VOLUME. CU. FT.

                                  Figure 2.6.   Turbojet   Engines

                                                                                      NAVWEPS OO-ROT-RO
                                                                                  AtRPlANE PERFORMANCE

   The partial expansion of the gases through             boundary layer along the fuselage surface. At
the turbine will provide the power to operate             supersonic flight speeds, the diffuser must slow
the engine. As. the gases are discharged from             the air to subsonic with the least waste of
the turbine at point F, expansion will continue           energy in the inlet air and accomplish the
through the tailpipe nozzle. until atmospheric            process with a minimum of aerodynamic drag.
pressure is achieved in the exhaust. Thus,                In addition, the inlet must be efIicient and
continued expansion in the jet nozzle will re-            stable in operation throughout the range of
duce the pressure and increase the volume of              angles of attack and Mach numbers of which
the unit weight of air to point G on the pressure         the airplane is capable.
volume diagram. As a result, the final jet                   The operation of the compressor can be af-
velocity is greater than the inlet velocity and           fected greatly by the uniformity of flow at the
the momentum change necessary for the .de-                compressor face. When large variations in
velopment of thrust ha~s’    been created. The            flow velocity and direction exist at the face of
area YFGA represents the work remaining to                the axial compressor, the efficiency and stall-
provide the expansion to jet velocity after the           surge limits are lowered. Thus, the flight
turbine has extracted the work requited to                conditions which involve high angle of attack
operate the compressor.                                   and high sideslip can cause deterioration of
   Of course, the combustion chamber discharge            inlet performance.
could be more completely expanded through a                  The compreJ.ror s&on is one of the most im-
larger turbine section and the net power could            portant components of the turbojet engine.
be used to operate a propeller rather than pro-           The compressor must furnish the combustion
vide high exhaust gas velocity.       For certain         chamber with large quantities of high pressure
applications, the gas turbine-propeller combi-            air in a most efficient manner. Since the com-
nation could utilize the high power capability            pressor of a jet engine has no direct cooling,
of the gas turbine with greater propulsive                the compression process takes place with a
efficiency.                                               minimum of heat Ioss of the compressed air.
   FUNCTION       OF THE COMPONENTS.                      Any friction loss or inefficiency of the com-
Each of the engine components previously de-              pression process is manifested as an undesirable
scribed will contribute some function affecting           additional increase in the temperature of the
the efficiency and output of the turbojet engine.         compressor discharge air. Hence, compressor
For this reason, each of these components                 efficiency will determine the compressor power
should be analyzed to determine the requite-              necessary to create the pressure rise of a given
ments for satisfactory operating characteristics.         airflow and will affect the temperature change
   The i&t or &@er must be matched to the                 which can take place in the combustion
powerplant to provide the compressor entry                chamber.
with the required airflow.        Generally, the             The compressor section of a jet engine may
compressor inlet must receive the required air-           be an axial flow or centrifugal flow compressor.
flow at subsonic velocity with uniform dis-               The centrifugal flow compressor has great util-
tribution of velocity and direction at the                ity, simplicity, and flexibility    of operation.
compressor face. The diffuser must capture                The operation of the centrifugal compressor
high energy air and deliver it at low Mach                requires relatively low inlet velocities and a
number uniformly to the compressor. When                  plenum chamber or expansion space must be
the inlet is along the sides of the fuselage, the         provided for the inlet. The impeller rotating
edges of the inlet must be located such that              at high speed receives the inlet air and pto-
the inlet receives only high energy air and               vides high acceleration by virtue of centrifugal
provision must be made to dispose of the                  force. As a result, the air leaves the impeller
                                CENTRIFUGAL COMPRESSOR

               DWGLE ENTRY

                                AXIAL FLOW COMPRESSOR

                                VM BLADES7

         INLET                                                       USCHARGE


                                   COMPRESSOR BLADING


                                 Figure 2.7.   Compressor   Types
                                                                                          NAWEPS 00-8OT-80
                                                                                      AIRPLANE PERFORMANCE

   at very high velocity and high kinetic energy.            from five to ten (or greater) with efficiencies
   A pressure rise is produced by subsequent ex-              which cannot be approached with a multi-
   pansion in the diffuser manifold by converting             stage centrifugal compressor.
   the kinetic energy into static pressure energy.               The axial flow compressor can provide
   The manifold then distributes the high pres-               efficiently the high. pressure ratios necessary
   sure discharge to the combustion chambers.                for low fuel consumption.          Also, the axial
   A double entry impeller allows a given diam-              compressor is capable of providing high air-
  eter compressor to process a greater airflow.              flow with a minimum of compressor diameter.
   The major components of the centrifugal com-              When compared with the centrifugal com-
  pressor are illustrated in figure 2.7.                     pressor, the design and construction of the
      The centrifugal compressor can provide a                axial compressor is relatively complex and
   relatively high pressure ratio per stage but the          costly and the high efficiency is sustained over
   provision of more than one or two stages is               a much narrower range of operating conditions.
   rarely feasible for aircraft turbine engines.             For these reasons, the axial compressor finds
   The single stage centrifugal compressor is                greatest application where rhe demands of
   capable of producing pressure ratios of about             efficiency and output predominate over con-
   three or four with reasonable efficiency. &es-            siderations. of cost, simplicity, flexibility    of
   sure ratios greater than four require such high            operation, etc. Multispool compressors and
   impeller tip speed that compressor efficiency              variable statot blades serve to improve the
   decreases very rapidly.       Since high pressure         operating characteristics of the axial com-
   ratios are necessary to achieve low fuel con-             pressor and increase the flexibility of operation.
   sumption, the centrifugal compressor finds                    The combustionchambermust convert the fuel
   greatest application to the smaller engines               chemical energy into heat energy and cause a
   where simplicity and flexibility of operation are         large increase in the total energy of the engine
   the principal requirements rather than high               airflow.     The combustion chamber will opet-
   efficiency.                                               ate with one principal limitation: the dis-
      The axial flow compressor consists of altet-           charge from the combustion chamber must be
  nate rows of rotating and stationary airfoils.             at temperatures which can be tolerated by the
   The major components of the axial flow com-               turbine section. The combustion of liquid
   pressor ate illustrated in figure 2.7. A pressure         hydrocarbon fuels can produce gas temperatures
  rise occurs through the row of rotating blades             which are in excess of 1,700 to 1,800° C.
  since the airfoils cause a decrease in velocity            However, the maximum continuous turbine
  relative to the blades. Additional        pressure         blade operating temperatures rarely exceed
  rise takes place through the row of stationary                               C
                                                             NO0 to J,OOO” and considerable excess air
   blades since these airfoils cause a decrease in           must be used in the combustion chamber to
  the absolute velocity of flow. The decrease                prevent exceeding these temperature limits.
I in velocity, relative or absolute, eEeLts a com-               While the combustion chamber design may
1 ptession of the flow and causes the increase in            .take various forms and configurations, the
  static pressure. While the pressure rise pet               main features of a typical combustion chamber
  stage of the axial compressor is relatively Jo%-,          ate illustrated by figure 2.8. The combustion
  the efficiency is very high and high pressure              chamber receives the high pressure discharge
  ratios can be obtained efficiently by successive           from the compressor and introduces apptoxi-
  axial stages. Of course, the eficient pressure             mately one half of this air into the immediate
  rise in each stage is limited by excessive gas             area of the fuel spray. This primary combus-
  velocities.     The multistage axial flow com-             tion air must be introduced with relatively
  pressor is capable of providing pressure ratios            high turbulence and quite low velocities to
                                                                                          Revised Januwy   1965
NAVWEPS 00-80T-80

                                     TYPICAL COMBUSTION CHAMBER
                                            SECONDARY Al R
                                            OR COOLING FLOW

       FUEL                                                                           DISCHARGE
       SPRAY                                                                          TO TURBINE
      NOZZLE                                                                            NOZZLES


                                                            / 11
                                            TURBINE    SECTION
                                                                 TUR’      NOZZLE    VANES

                                                                       TmaiNt    BLADES

               SHAFT                                                   TURBINE    WHEEL

                                            TURBIhE    BLADING


        (ROTATING)                                                               TURBINE     BLADES

                       Figure 2.8.   Combustion   Chamber   and Turbine Components
                                                                                        NAVWEPS O(L8OT-80
                                                                                    AIRPLANE PERFORMANCE

 maintain a nucleus of combustion in the com-               energy to drive the propeller in addition to the
 bustion chamber. In rhe normal combustion                  compressor and accessories.
process, the speed of flame propagation is quite                The combustion chamber delivers high en-
low and, if the local velocities are too high at            ergy combustion gases to the turbine section at
 the forward end of the combustion chamber,                 high pressure and tolerable temperature. The
 poor combustion will result and it is likely               turbine nozzle vanes are a row of stationary
 rhar the flame will blow out. The secondary                 blades immediately ahead of the rotating tur-
air-or cooling flow-is introduced downstream                bine. These blades form the nozzles which
from the combustion nucleus to dilute the com-              discharge the combustion gases as high ve-
 bustion products and lower the discharge gas               locity jets onto the rotating turbine. In this
 temperature.                                               manner, the high pressure energy of the com-
   The fuel nozzle must provide a finely                    bustion gases is converted into kinetic energy
atomized, evenly distributed spray of fuel                  and a pressure and temperature drop takes
through a wide range of flow rates. Very                    place. The function of the turbine blades
specialized design is necessary to provide a                operating in these jets is to develop a tangen-
nozzle with        suitable characteristics.    The          tial force along the turbine wheel thus extract-
spray parrern and circulation in the combustion              ing mechanical energy from the combustion
chamber must make efficient use of the fuel by              gases. This is illustrated in figure 2.8.
complete combustion. The temperatures in                        The form of the turbine blades may be a com-
the combustion nucleus can exceed 1,700” to                 bination of two distinct types. The imp&c
1,SW’ C but the secondary air will dilute the               type turbine relies upon the nozzle vanes to
gas and reduce the temperature to some value                accomplish the conversion of combustion gas
which can be tolerated in the turbine section.              static pressure to high velocity jets. The
A pressure drop will occur through the com-                 impulse turbine blades are shaped to produce
bustion chamber to accelerate the combustion                a large deflection of the gas and develop the
gas rearward. In addition, turbulence and                   tangential force by the flow direction change.
fluid friction will cause a pressure drop but this          In such a design, negligible velocity and pres-
loss must be held to the minimum incurred by                sure drop occurs with the flow across the tur-
providing complete combustion.         Heat trans-          bine rotor blades. The reaction type turbine
ferred through the walls of the combustion                  differs in that large velocity and pressure
chamber constitutes a loss of thermal energy                changes occur across the turbine rotor blades.
and should be held to a minimum.          Thus, the         In the reaction turbine, rhe stationary nozzle
combustion chamber should enclose the com-                  vanes serve only to guide the combustion gas
bustion space with a minimum of surface area                onto the turbine rotor with negligible changes
to minimize heat and friction losses. Hence,                in velocity and pressure. The reaction tur-
 the “annular” typ: combustion chamber offers               bine rotor blades are shaped to provide a pres-
certain advantages over the multiple “can”                  sure drop and velocity increase across the
type combustion chamber.                                    blades and the reaction from this velocity in-
   The tur6inc sectionis the most critical element          crease provides the tangential force on the
of the turbojet engine. The function of the                 wheel. Generally, the turbine design is a
turbine is to extract energy from the combus-               form utilizing some feature of each of the two
tion gases and furnish power to drive the com-              types.
pressor and accessories. In the case of the                     The turbine blade is subjected to high
turboprop engine, the turbine section must ex-              centrifugal stresses which vary as the square
tract a very large portion of the exhaust gas               of the rorative speed. In addition, the blade

                                                                                        Revised January   1965
NAVWEPS 00-801-80

 is subjected to the bending and torsion of                   area is too large, incomplete expansion will
 the tangential impulse-reaction forces. The                  take place; if the exit area is too small, an over
 blade must wirhstand these stresses which are                expansion tendency results. The exit area can
generally of a vibratory and cyclic nature                    affect the upstream conditions and must be
while at high temperatures. The elevated                      properly proportioned for overall performance.
 temperatures at which the turbine must func-                    When the ratio of exhaust gas pressure to
 tion produce extreme conditions for struc-                   ambient pressure is greater than some critical
tural creep and fatigue considerations. Conse-                 due, sonic flow can exist and the nozzle will
quently, the engine speed and temperature op-                  be choked or limited to some maximum flow.
erating limits demand very careful considera-                 When supersonic exhaust gas velocities are re-
tion. Excessive engine temperatures or speeds                 quired to produce the necessary momentum
may produce damage which is immediately                        change, the expansion process will require the
 apparent. However, creep and fatigue damage                  convergent-divergent nozzle illustrated in fig-
 is cumulative and even though damage may                      ure 2.9. With sui?icient pressure available the
not be immediately apparent by visual inspec-                 initial expansion in the converging portion is
 tion, proper inspection methods (other than                   subsonic increasing to sonic velocity at the
 visual) must be utilized and proper records                   throat. Subsequent expansion in the divergent
 kept regarding the occurrence.                               portion of the nozzle is supersonic and the re-
    Actually, the development of high tempera-                sult is the highest exit velocity for a given
 ture alloys for turbines is a critical factor in the         pressure ratio and mass flow. When the pres-
 develop,mcnt of high ei%ciciicy, high output                 sure ratio is very high the final exit diameter
 aircraft gas turbines. The higher the tem-                   required to expand to ambient pressure may be
peratute of gases entering the turbine, the                    very large but is practically. limited to the
 higher can be the temperature and pressure of                fuselage or nacelle afterbody diameter. If the
the gases at discharge from the turbine with                  exhaust gases exceed sonic velocity, as is porsi-
greater exhaust jet velocity and thrust.                       ble in a ramjet combustion chamber or after-
    The function of the t&pipe or exhaust no?&                 burner section, only the divergent portion of
is to discharge the exhaust gases to the atmos-                the nozzle may be necessary.
phere at the highest possible velocity to pro-                   Figure 2.9 provides illustration of the func-
duce the greatest momentum change and thrust.                 tion of the various engine components and the
If a majority of the expansion occurs through                 changes in static pressure, temperature, and
the turbine section, there remains only to con-               velocity through the engine. The conditions
duct the exhaust gases rearward with a mini-                  at the inlet provide the initial properties of the
mum energy loss. However, if the turbine                       engine airflow.   The compressor section fur-
operates against a noticeable back pressure, the              nishes the compression pressure rise with a
nozzle must convert the remaining pressure                    certain unavoidable but undesirable increase in
energy into exhaust gas velocity.        Under ideal          temperature. High pressure air delivered to
conditions, the nozzle would expand the flow                  combustion chamber receives heat from the
to the ambient static pressure at the exhaust                 combustion of fuel and experiences a rise in
and the area distribution in the nozzle must                  temperature. The fuel flow is limited so that
provide these conditions.       When the ratio af             the turbine inlet temperature is within limits
exhaust gas pressure to ambient pressure is                   which can be tolerated by the turbine structure.
relatively low and incapable of producing sonic               The combustion takes place at relatively con-
flow, a converging nozzle provides the expan-                 stant pressure and initially low velocity. Heat
sion. The exit area must be of proper size to                 addition then causes large increases in gas vol-
bring about proper exit conditions.       If the exit         ume and flow velocity.
                                                                                 NAVWEPS 00-801-80
                                                                             AIRPLANE PERFORMANCE

                                         NOZZLE TYPES
      CONVERGENT NOZZLE                                CONMRGPIT-DDMRGENT NOZZLE

           --3-                                        ~--

                                 ENGINE OPERATING CONOITIONS

                    COMPRESSOR                                                EXHAUST
                                                               TURBlElE       NOZZLE







              Figure 2.9.   Exhaust Nozzle   Types and Engine Operating   Conditions
NAVWEPS 00-801-80

   Generally, the overall fuel-air ratio of the         obtained only if there is an increase in mass
turbojet is quite low because of the limiting           flow, Q, or jet velocity, Vs, When at low
turbine inlet temperature. The overall air-             velocity, an increase in velocity will reduce
fuel ratio is usually some value between 80 to          the velocity change through the engine with-
40 during ordinary operating conditions be-             out a corresponding increase in mass flow and
cause of the large amount of secondary air or           the available thrust will decrease. At higher
cooling flow.                                           velocity, the beneficial ram helps to overcome
   High temperature, high energy combustion             this effect and the available thrust no longer
gas is delivered to the turbine section where           decreases, but increases with speed.
power is extracted to operate the compressor               The propulsive power available from the
section. Partial or near-complete expansion             turbojet engine is the roduct of available
can take place through the turbine section with         thrust and velocity.     T t e propulsive horsc-
the accompanying pressure and tempcratute               power available from the turbojet engine’    is
drop. The exhaust nozzle completes the ex-              related by the following expression:
pansion by producing the final jet velocity and
momentum change necessary in the develop-                                      --
ment of thrust.                                                                     325
   TURBOJET OPERATING            CHARACTER-             where
ISTICS. The turbojet engine has many oper-
                                                            Pa=propulsive    power available, h.p.
ating characteristics which are of great im-
portance to the various items of jet airp!ane               T.-*Le..;-
                                                            LC‘          ‘;--;11.1*~
                                                                --LL,IlLSLt”.uiaOK, ibs.
performance. Certain of these operating char-
acteristics will provide a strong influence on               V= flight velocity, knots
 the range, endurance, etc., of the jet-powered
airplane. Other operating characteristics will          The factor of 321 evolves from the use of the
require operating techniques which differ               nautical unit of velocity and implies that
greatly from more conventional powerplants.             each pound of thrust developed at 325 knots
   The turbojet engine is essentially a thrust-         is the equivalent of one horsepower of propul-
producing powerplant and the propulsive                 sive power. Since the thrust of the turbojet
power produced is a result of the flight speed.         engine is essentially constant with speed, tht
The variation of available thrust with speed is         power available increases almost linearly with
relatively small and the engine output is very          speed. In this sense, a turbojet with 5000 Ibs.
nearly constant with flight speed. The mo-              of thrust available could produce a propulsive
mentum change given the engine airflow de-              power of 3,ooO h.p. at 325 knots or 10,000
velops thrust by the following relationship:            h.p. at 650 knots. The tremendous propulsive
                                                        power at high velocities is one of the principal
                                                        features of the turbojet engine. When the
                                                        engine RPM and operating altitude arc fixed,
where                                                   the variation with speed of turbolet thrust and
    Ta= thrust available, lbs.                          power available is typified by the first graph
                                                        of figure 2.10.
     Q=mass flow, slugs per sec.                          The variation of thrust output with engine
    vi=inlet or flight velocity, ft. per sec.           speed is a factor of great importance in the
    Va= jet velocity, ft. per see.                      operation of the turbojet engine. By reason-
                                                        ing that static pressure changes depend on the
Since an increase in flight speed will increase         square of the flow velocity, the changer of
the magnitude of Vi, a constant thrust will be          pressure throughout the turbojet engine would
                                                                                NAVWEPS 00-801-80
                                                                            AlR,PlANE PERFORMANCE

be expected to vary as the square of the rota-     be appreciated. If the turbojet powerplant
tive speed, N. However, since a variation in       operates at less than the “trimmed” or adjusted
rotative speed will alter airflow, fuel flow,      speed for maximum thrust, the deficiency of
compressor and turbine efficiency, etc., the       thrust for takeoff may cause a considerable
thrust variation will be much greater than         increase in takeoff distance. During approach,
just the second power of rotative speed. In-       an excessively low RPM may cause very low
stead of thrust being proportional to iV2, the     thrust and produce a very steep glide path.
typical fixed geometry engine develops thrust      In addition, the low RPM range involves the
approximately proportional to N3.6. Of course,     much greater engine acceleration time to pro-
such a variation is particular to constant alti-   duce thrust for a waveoff. Another compli-
tude and speed.                                    cation exists when the thrust is proportional
   Figure 2.10 illustrates the variation of per-   to some large power of rotative speed, e.g.,
cent maximum thrust with percent maximum           Nb.O. The small changes in RPM produce
RPM for a ‘    typical fixed geometry engine.      such large variations in thrust that instruments
Typical values from this graph are as follows:     other than the tachometer must be furnished
       P<m#r RPM
            ma%.                    IMX.
                               Pmwit tlJrw,r       for accurate indication of thrust output.
          100                loo (of course)          The “specific fuel consumption, ci’ is an
           99                 96.5                 important factor for evaluating the perform-
           95                 83.6                 ance and efficiency of operation of a turbojet
           90                 69.2
                                                   engine. The specific fuel consumption is the
           70                 28.7                 proportion between the fuel flow (in lbs. per
                                                   hr.) and the thrust (in lbs.). For example,
Note that in the top end of power output, each     an engine which has a fuel flow of 14,000 lbs.
1 percent RPM change causes a 3.5-percent          per hr. and a thrust of 12,500 lbs. has a specific
change in thrust output. This illustrates the      fuel consumption of:
power of variation of thrust with rotative
speed which, iii this example, is N3.“. Also                        Fuel flow
note that the top 20 percent of RPM controls                     “= Thrust
more than half of the output thrust.
                                                                    14,000 lbs./hr.
   While the fixed geometry engine develops
                                                                 I=  12,500 lbs.
thrust approximately proportional to Na.“, the
engine with variable geometrywill demonstrate                    c,=1.12 lbs./hr./lb.
a much more powerful effect of rotative speed.
When the jet engine is equipped with a vari-       Thus, each unit pound of thrust requires 1.12
able nozzle, multispool compressor, variable       lbs. per hr. fuel flow. Obviously, high engine
stator blades, etc., the engine is more likely     efficiency would be indicated by a low value of
to develop thrust proportional to rotative         c,. Typical values for turbojet engines with
speed from values of N4.6 to N6.0. For ex-         relatively high pressure ratios range from 0.8
ample, if a variable geometry engine develops      to 1.2 at design operating conditions in sub-
thrust proportional to Ns.‘ each one per cent      sonic flight.    High energy fuels and greater
RPM change causes a 5.0-percent thrust change      pressure ratios tend to produce the lower values
at the top end of power output.       Also, the    of ct. Supersonic flight with the attendant in-
top 13 percent of RPM would control the top        let losses and high compressor inlet air tem-
50 percent of thrust output.                       peratures tend to increase the specific fuel con-
   The powerful variation of thrust with engine    sumption to values of 1.2 to 2.0. Of course,
 speed has certain ramifications which should      the use of an afterburner is quite inefficient
NAVWEPS 00-801-80
                                               VARIATION OF THRUST AN0 POWER WITH VELOCITY
                           /STATIC                           THRUST

          THRUST                              1
           &?eLE                          AVAILABLE
          POWER                                                                                       /
        AVAILABLE                                        /                                                AV!$%EHp’              E

                                                                                                                             (CONSTANT ALTITUDE 8 RPM)

                                                                                       VELOCITY,               KNOTS

            100                                                   VARIATION OF THRUST WITH RPM

                             (CONSTANT ALTITUDE
            80                            a

    PERCENT 6o                             ThrN3.5
    mmlgTM  50

              04              I                                   I                                           1          0              1
                   0         IO               20                 30           40             50               SO        70       80    90    100
                                                                          PERCENT MAXIMUM RPM

                                                       VARIATION OF SPECIFIC FUEL
                                           I             CONSUMPTION WITH RPM
                                                                                                              (CONSTANT ALTITUDE
                                                                                                                  8 VELOCITY)
            sEzc                  2.0

                                    .T,            *         I        I   I        I     I        I       I        I.

                                           0       IO 20 30 40 50 60 70 80 90 100
                                                      PERCENT MAXIMUM RPM

                                               Figure 2.10.                    Turbojet               Performance
                                                                                                                                               NAVWEPS 00-8OT-80
                                                                                                                                           AtRPlANE PERFORMANCE

due to thc~ low combustion pressure and values                                                   If the fixed geometry engine is operated at a
of c, from 2.0 to 4.0 are typical with aftet-                                                 constant V (TAS) in subsonic flight and con-
burner operation.                                                                             stant N (RPM) the inlet velocity, inlet ram,
    The turbojet engine usually has a strong                                                  and compressor pressure ratio are essentially
preference fot high RPM to produce low specif-                                                constant with altitude.    An increase in alti-
ic fuel consumption.      Since the normal rated                                              tude then causes the engine air mass flow to
thrust condition is a particular design point                                                 decrease in a manner very nearly identical to
for the engine, the minimum value of c, will                                                  the altitude density ratio. Of coutsc, this de-
occur at or near this range of RPM. The                                                       crease in mass flow will produce a significant
illustration of figure 2.10 shows a typical vati-                                             e&ct on the output thrust of the engine.
ation of c, with percent maximum RPM where                                                    Actually, the variation of thrust with altitude
values of RPM less than 80 to 85 percent pro-                                                 is not quite as severe as the density variation
duce a specific fuel consumption much greater                                                 because favorable decreases in temperature
than the minimum obtainable. This pref-                                                       occut. The decrease in inlet air temperature
erence for high.RPM to obtain low values of                                                   will provide a relatively greater combustion
C, is very pronounced in the fixed geometry                                                   gas &ergy and allow a greater jet velocity.
engine. Turbojet engines with multispool                                                      The increase in jet velocity somewhat offsets
compressors tend to be less sensitive in this                                                 the decrease in mass flow. Of course, an in-
respect and are more flexible in their operating                                              crease in altitude provides lower temperatures
characteristics.   Whenever low values of cI ate                                              below the tropopause. Above the tropopause,
necessary to obtain range or endurance, the                                                   no further favorable decrease in temperature
preference of the turboiet engine for the design                                              takes place so a more rapid variation of thrust
operating RPM can be a factor of great                                                        will take place. The approximate variation
influence.                                                                                    of thrust with altitude is represented by figure
    Altitude is one factor which strongly affects                                             2.11 and some typical values at specific alti-
                                                                                              tudes ate as follows :
the performance of the turbojet engine. An
increase in altitude produces a decrease in                                                                               RIrioof Tbrvrtat dri14
                                                                                                  Altitude, ft. :                                   ( Thi   ti I,‘ bwl )
density and pressure and, if below the tropo-                                                          Scalevel.............................                      1.m
pause, a decrease in temperature. If a typical                                                         5,ooo................................                        ,888
                                                                                                       lO,ooo...............................                       .785
nonaftcrbutning turbojet engine is operated at
                                                                                                       2o,ooo...............................                       ,604
a constant RPM and true airspeed, the vatia-                                                           35,Mx)...............................                       .392
tion of thtust and specific fuel consumption                                                           40,Ko.                                                      .315
with altitude can be approximated from figure                                                          =Jo,ocQ._._..,...._....._,.,.__.,.....                      .180
221. The variation of density in the standard                                                 Since the change in density with altitude is
atmosphere is shown by the values of density                                                  quite rapid at low altitude turbojet takeoff pet-
ratio at vatious altitudes.    Typical values of                                              formance wil1 Abegreatly affected at high alti-
the density ratio at specific altitudes are as                                                tude. Also note that the thrust at 35,000 ft.
follows:                                                                                      is approximately 39 percent of the sea level
    Altitude, ft.:                                                      Dews@   ra#ie
          scaleeel . . . . . . . .. . . . . . . . . . . . . . . . . . . . . Loo0                 The thrust added by the afterburner of a
          5,ooo..          :.          .                                     .a617            turbojet engine is not affected so greatly by
          lO,coo..............................                               .7385            altitude as the basic engine thrust. The use of
          .?2#XQ.                                                            .4976
                                                                                              afterburner may provide a thrust increase of 50
          35,cao . . . . . . . . . . . . . . .            .. .. ..           .3099
          40,oal.. . . .                                                     .2462            percent at low altitude or as much as 100 per-
          ~,OUO. . .                   .                                     .lS32            cent at high altitude.

                                 \ I
                                  \\                                                !


    2 25,000



                          ,FIXED GEOMETRY

                     0     0.1    0.2      0.3   0.4       0.5     0.6    0.7    0.6    0.9      1.0
                                        RATIO OF WANTITY)         AT ALTITUDE
                                                 (QUANTIT’       AT SEA LEVEL

                     Figure 2.7 1. Approximate    Eftect   of Altitude   on Engine Performance

                                                                                       NAVWEPS 00-8OT-80
                                                                                   AIRPLANE PERFORMANCE

    When the inlet ram and compressor pressure             flow, nozzle area, etc. to provide engine per-
ratio is fixed, the principal factor affecting the         formance scheduled by the throttle or power
specific fuel consumption is the inlet air temp-           lever. These regulatory functions provided
erature. When the inlet air temperature is                 must account for variations in altitude, tem-
lowered, a given heat addition can provide                 perature, and flight velocity.
relatively greater changes in pressure or vol-                 One principal governing factor which must
 ume. As a result, a given thrust output                   be available is that a selected power setting
requires less fuel flow and the specific fuel con-         (RPM) must be maintained throughout a wide
 sumption, c,, is reduced. While the effect of             range of flight conditions. Figure 2.12 illus-
altitude on specific fuel consumption does not             trates the sariation of fuel flow with RPM for
compare with the effect on thrust output, the              a turbojet operating at a particular set of
variation is large enough to strongly influence            flight conditions.    Curve 1 depicts the varia-
range and endurance conditions.        Figure 2.11         tion with RPM of the fuel flow required for
illustrates a typical variation of specific fuel           stabilized, ste,ady state operation of the engine.
consumption with altitude.         Generally, the          Each point along this curve 1 defines the fuel
 specific fuel consumption decreases steadily              flow which is necessary to achieve equilib-
with altitude until the tropopause is reached              rium at a given RPM. The steady state fuel
and the specific fuel consumption at this point            flow produces a turbine, power to equal the
is approximately 80 percent of the sea level               compressor power requirement at a particular
value.                                                     RPM. The throttle position primarily com-
    Above the tropopause the temperature is con-           mands .a given, engine speed and, as changes
stant and altitudes slightly above the tropo-              occur in the ambient pressure, temperature,
pause cause no further decrease in specific fuel           and flight speed, the .steady state fuel flow will
 consumption. Actually, altitudes much above               vary. The governing’ apparatus must account
 the tropopause bring about a general deteriora-           for these variations in flight conditions and
tion of overall engine efficiency and the~spkific          maintain the power setting scheduled by
fuel consumption begins an increase with                   throtrle position.
altitude.    The extreme altitudes above the                   In addition to the maintenance of steady
 tropopause produce low combustion chamber                 state operation, the fuel control and associ-
pressures, low compressor Reynolds Numbers,                ated engine control itemsmust provide for the
low fuel flow, etc. which are notconduci,ve to             transient conditions of engine acceleration and
 high engine efficiency.                                   deceleration. In order to accelerate the en-
    Because of the variation of c, with altitude,          gine, the fuel control must supply a fuel flow
 the majority of turbojet engines achieve maxi-            greater than that required for steady state
 mum efficiency at or above 35,000 ft. For this            operation to ,produce a’turbine power greater
 reason, the turbojet airplane will find optimum           than the compressor power requirement. How-
 range and endurance conditions at. or above               ever, the additional fuel flow to accelerate the
 35,000 ft. provided the aircraft is not thrust            engine must be controlled and regulated to
 or compressibility limited at these altitudes.            prevent any one or combination of the follow-
    The governingapparatus of the turbojet engine          ing items:
 consists primarily of the, items which control                  (1) compressor stall or surge
                                                                 (2) excessive turbine inlet temperature
 the flow of fuel to the engine. In addition,                    (3) excessively rich fuel-air ratio which
 there may be included certain functions which                          may not sustain combustion
 operate variable nozzles, variable stator vanes,          Generally, the stall-surge and turbine tem-
 variable inlets, etc. Generally, the fuel con-            perature limits predominate to form an ac-
 trol and associated items should regulate fuel            celeration fuel flow boundary typified by curve
NAVWEPS 00-807-80

                  ALL CURVES APPROPRIATE
                  FOR A PARTICULAR:
                         rM&N NUMBER

                                BOUNDARY          A&

                                   E                            I
                               (IDLE)         N-RPM           (MA%)

                                                         EXHAUST GAS

         RPM c

                                        . _ . _ _- - -                      rAILPIPE TOTAL
             PRESSURE                   TEMPERATURE                           PRESSURE

                        Figure 2.12. Engine Governing and Instrumentation

                                                                                       NAVWEPS 00-8OT-30
                                                                                   AIRPLANE PERFORMANCE

2 of figure 2.12. Curve 2 of this illustration                 During deceleration conditions, the mini-
defines an upper limit of fuel flow which can              mum allowable fuel flow is defined by the lean
be tolerated within stall-surge and tempera-               limit to support combustion. If the fuel flow
ture limits.    The governing apparatus of the             is reduced below some critical value at each
engine must limit the acceleration fuel flow               RPM, lean blowout or flameout will occur.
within this boundary.                                      This condition is illustrated by curve 3 of
    To appreciate the governing requirements               figure 2.12 which forms the deceleration fuel
during the acceleration process, assume the                flow boundary. The governing apparatus must
engine described in figure 2.12 is in steady state         regulate the deceleration fuel flow within this
stabilized operation at point A and it is desired          boundary.
to acceler&the engine to maximum RPM and                       To appreciate the governing requirements
stabilize:at point C. As the throttle is placed            during the deceleration process, assume the
at the position for maximum RPM, the fuel                  engine described in figure 2.12 is in stabilized,
control will increase the fuel flow to point B             steady state operation at point C and it is
to provide acceleration fuel flow. As the                  desired to decelerate to idle conditions and
engine accelerates and increases RPM, the fuel             stabilize at point E. As the throttle is placed
control will continue to increase the fuel flow            at the position for idle RPM, the fuel control
within the acceleration boundary until the                 will decreasethe fuel flow to point D to provide
engine speed approaches the controlled maxi-               the deceleration fuel flow. As the engine
mum RPM at point C. As the engine speed                    decelerates and decreases RPM, the fuel gov-
nears the maximum at point C, the fuel contrcl’            erning will continue to decrease the fuel flow
will reduce fuel flow to produce stabilized oper-           within the deceleration boundary until the idle
ation at this point and prevent the engine                 fuel flow is reached and RPM is established at
overspeeding the commanded RPM. Of course,                  point E. Of course, if the throttle is closed
if the throttle is opened very gradually, the               very slowly, the deceleration fuel flow is barely
acceleration fuel flow is barely above the steady           below the steady state condition and the engine
state condition and the engine does not ap-                 does not approach the deceleration fuel flow
proach the acceleration fuel flow boundary.                 boundary. The fuel control must provide a
 While this technique is recommended for                    deceleration flow close to the boundary to
 ordinary conditions to achieve trouble free                provide rapid decrease in thrust and satisfactory
operation and good service life, the engine must            flight control.
be capable of good acceleration to produce                      In most cases, the deceleration fuel flow
 rapid thrust changes for satisfactory flight               boundary is considerably below the steady
 control.                                                   state fuel flow and no great problem exists in
    In order for the powerplant to achieve mini-            obtaining satisfactory deceleration character-
mum acceleration times, the fuel control must               istics. In fact, the greater problem is con-
 provide acceleration fuel flow as close as                 cerned with obtaining proper acceleration
 practical to the acceleration boundary. Thus,              characteristics.  For the majority of centrifu-
 a maximum controlled acceleration may pro-                 gal flow engines, the acceleration boundary is
 duce limiting turbine inlet temperatures or                set usually by temperature limiting conditions
 slight incipient stall-surge of the compressor.            rather than compressor surge conditions. Peak
 Proper maintenance and adjustment of the                   operating efficiency of the centrifugal com-
 engine governing apparatus is essential to                 pressor is obtained at flow conditions which
 produce minimum acceleration times without                  are below the surge limit, hence acceleration
 incurring excessive temperatures or heavy stall-            fuel flow boundary is determined by turbine
  surge conditions.                                          temperature limits.   The usual result is that
NAVWEPS 00-801-80

the centrifugal flow engine has relatively large         RPM. Since the variation of thrust with
acceleration margins and good acceleration               RPM is quite powerful, the tachometer in-
characteristics result with the low rotational           dication is a powerful reference.
inertia. The axial flow compressor must oper-               (2) The exhaust gas temperature gauge
ate relatively close to the stall-surge limit to         provides an important reference for engine
obtain peak efficiency. Thus, the acceleration           operating limitations.     While the tempera-
fuel flow boundary for the axial flow engine is          ture probe may be located downstream from
set by these stall-surge limits which are more           the turbine (tailpipe or turbine discharge
immediate to steady state conditions than tur-           temperature) the instrument should provide
bine temperature limits.       The fixed geometry        an accurate reflection of temperatures up-
axial flow engine encounters relatively small            stream in the turbine section. The exhaust
acceleration margins and, when compared to               gas temperature relates the energy change
the centrifugal flow engine with larger accel-           accomplished by fuel addition.
eration margins and lower rotational inertia,                (3) The fuel flowmeter can provide a fair
has inferior acceleration characteristics. Cer-          reflection of thrust output. and operating
tain variation of the axial flow engine such as          efficiency. Operation at high density alti-
variable nozzles, variable stator blades, multi-         tude or high inlet air temperatures-reduces
ple-spool compressors, etc., greatly improve             the output thrust and this effect is related by
the acceleration characteristics.                        a reduction of fuel flow.
    A note of caution is appropriate at this                 (4) The’ tailpipe total pressure (p+q in
point.     If the main fuel control and govern-          the tailpipe) can be correlated with the jet
 ing apparatus should malfunction or become              thrust for a given engine geometry and set of
 inoperative and an unmodulated secondary or             operating conditions.      The output thrust
 emergency system be substitued, extreme care            can be related accurately with various com-
must be taken to avoid abrupt changes in                  binations of compressor inlet total pressure,
throttle position.     In such a case, very gradual       tailpipe total pressure, ambient pressure and
 movement of the throttle is necessary to ac-            temperature. Hence; pressure differential
complish changes in power setting without                 (Ap), pressure ratio, and ,tailpipe total pres-
 excessive turbine temperatures, compressor               sure instruments can provide more accurate
 stall or surge, or flameout.                             immediate indications of output thrust than
    There are various instruments to relate irnr          combined indications of RPM and EGT.
 portant items of turbojet engine performance.            This is especially true with variable geom-
 Certain combinations of these instruments are            etry or multiple spool engines.
 capable of immediately relating the thrust               Many other specialized instruments furnish
  output of the powerplant in a qualitative man-       additional information for more detailed items
  ner. It is difficult to provide an instrument or     of engine performance. Various additional
  combination of instruments which immedi-             engine information is realized from fuel pres-
  ately relate the thrust output in a ~arrantitativ~   sure, nozzle positions, compressor inlet air
  manner. As a result, the pilot must rely on          temperature, etc.
  a combination of instrument readings and judge
  the output performance according to standard           TURBOJET      OPERATING       LIMITATIONS.
  values particular to the powerplant.      Some of    The operating characteristics of the turbojet
  the usual engine indicating instruments are as       engine provide various operating limitations
  follows :                                            which must be given due respect. Operation
       (1) The tachometer provides indication of       of the powerplant within the specified limita-
     engine speed, N, by percent of the maximum        tions is absolutely necessary in order to obtain
                                                                                        NAVWEPS OO-SOT-RO
                                                                                    AIR.PLANE PERFORMANCE

the design service life with  trouble-free opera-          excess of the operational limits for these con-
tion. The following items describe the critical            ditions will increase the possibility of early
areas encountered during the operational use               failure of the turbine components.
of the turbojet engine:                                       While the turbine components are the most
   (1) The limiting exhaust gag tcmpcra;wcs pro-           critically stressed high temperature elements
vide the most important restrictions to the op-            they are not the only items. The combustion
eration of the turbojet engine. The turbine                chamber components may be critical at low
components are subject to centrifugal loads of             altitude where high combustion chamber pres-
rotation, impulse and reaction loads on the                 sures exist. Also, the airframe structure and
blades, and various vibratory loads which may               equipment adjacent to the engine may be sub-
be inherent with the design. When the turbine               ject to quite high temperatures and require
components are subject to this variety of stress            provision to prevent damage by excess time at
in the presence of high temperature, two types              high temperature.
of structural phenomena must be considered.                    (2) The c~mprcs~or  Jtall or surge has the pos-
when a part is subject to a certain stress at some          sibility of producing damaging temperatures
high temperature, weep failure will take place              in the turbine and combustion chamber or un-
after a period of time. Of course, an increase              usual transient loads in the compressor. While
in .tcmperature or stress will increase the rate            the stall-surge phenomenon is possible with
at which creep damage is accumulated and                    the centrifugal compressor, the more common
reduce the time required to cause failure. An-             .occurrence is with the axial flow compressor.
other problem results when a part is subjected              Figure 2.13 depicts the pressure distribution
to a repeated or cyclic stress. F&&e failure                that may exist for steady state operation of
will occur after a number of cycles of a varying            the engine. In order to accelerate the engine
stress. An increase in temperature or magni-                to a greater speed, more fuel must be added to
tude of cyclic stress will increase the rate of             increase the turbine power above that required
fatigue damage and reduce the number of cycles              to operate the compressor.
necessary to produce failure. It is important                  Suppose that the fuel flow is increased be-
to note that both fatigue and creep damage are              yond the steady state requirement without a
cumulative.                                                 change in rotative speed. The increased com-
   A gross overstress or overtemperature of the             bustion chamber pressure due to the greater
turbine section will produce damage that is                 fuel flow requires that the compressor dis-
immediately apparent. However, the creep                    charge pressure be higher. For the instant
and fatigue damage accumulated through pe-                  before an engine speed change occurs, an in-
riods of less extreme’ overstress or overtem-               crease in compressor discharge pressure will be
perature is more subtle. If the turbine is                  accompanied by a decrease in compressor flow
sibject to repeated excessive temperatures, the             velocity.   The equivalent effect is illustrated
greatly increased rate of creep and fatigue                 by the flow components onto the rotating com-
damage wiIl produce failure early within the                pressor blade of figure 2.13. One component
anticipated service life.                                   of velocity is due to rotation and this compo-
   Generally, the operations which produce                  nent remains unchanged for a given rotative
 the highest exhaust gas temperatures are                   velocity of the single blade. The axial flow
starting, acceleration, and maximum thrust                  velocity for steady state operation combines
at high altitude.     The time spent at these               with rotational component to define a result-
temperatures must be limited arbitrarily to                 ant velocity and direction. If the axial flow
prevent excessive accumulation of creep and                 component is reduced, the resultant velocity
fatigue. Any time spent at temperatures in                  and direction provide an increase in angle of
                                                 COMPRESSOR     STALL

                                                         COMBUSTION                EXHAUST
                           COMPRESSOR                     CHAMBER T”RB,NE          NOZZLE

                           PRESSURE       RISE
                             LIMITED      BY



                                        BLADE ANGLE
                                                                                  ,STEADY STATE
                                                                                   AXIAL FLOW VEL .OCITY
                                                                                  -REDUCED AXIAL
                                                                                   FLOW VELOCITY

                                            VELOCITY  COMPONENT
                                              DUE TO ROTATION

                                           EFFECT    OF INLET    TEMPERATURE

     TEMPERATURE                                                                                     EXHAUST
        CHANGE                                                     TEMPERATURE  RISE
                                                                  THROUGH COMBUSTION
                      --                                                CHAMBER

                           COMPRESSOR                   COMBUSTION       TURBINE           EXHAUST
                                                          CHAMBER                          NOZZLE
       Figure 2.13.    Effect       of Compressor   Stall ond Inlet Temperature     on Engine Operation
                                                                                       NAVWEPS 00-801-80
                                                                                   AIRMANE Pl?RFORMANCE

attack for the rotating blade with a subsequent                  (c) Very high altitude flight produces low
increase in pressure rise. Of course, if the                 compressor Reynolds numbers and an effect
change in angle of attack or pressure rise is                similar to that of airfoil sections. As a
beyond some critical value, stall will occur.                decrease to low Reynolds numbers reduces
While the stall phenomenon of a series of                    the section c&, very high altitudes reduce
rotating compressor blades differs from that                 the maximum pressure ratio of the com-
of a single airfoil section in a free airstream,             pressor. The reduced stall margins increase
the cause and effect are essentially the same.               the likelihood of compressor stall.
   If an excessive pressure rise is required              Thus, the recovery from a compressor stall
through the compressor, stall may occur with              must entail reduction of throttle setting to
the attendant breakdown of stable, steady flow            reduce fuel flow, lowering angle of attack and
through the compressor. As stall occurs, the              sideslip and increasing airspeed to improve
pressure rise drops and the compressor does not           inlet condition, and reducing altitude if high
furnish discharge at a pressure equal to the              altitude is a contributing factor.
combustion chamber pressure. As a result, a                  (3) While the j7ameout is a rare occurrence
flow reversal or backfire takes place. If the             with modern engines, various malfunctions
stall is transient and intermittent, the indica-          and operating conditions allow the flameout to
tion will be the intermittent “bang” as back-             remain a possibility.      A uniform mixture of
fire and flow reversal take place. If the stall           fuel and air will sustain combustion within a
develops and becomes steady, strong vibration             relatively wide range of fuel-air ratios. Com-
and a loud (and possibly expensive) roar                  bustion can be sustained with a fuel-air ratio
develops from the continuous flow reversal.               as rich as one to five or as lean as one to twenty-
The increase in compressor power required                 five. Fuel air ratios outside these limits will
tends to reduce RPM and the reduced airflow               not support combustion due to the deficiency
and increased fuel flow cause rapid, immediate            of air or deficiency of fuel. The characteristics
rise in exhaust gas temperature. The pos-                 of the fuel nozzle and spray pattern as well as
sibility of damage is immediate with the steady           the governing apoaratus must insure that the
stall and recovery must be accomplished                   nucleus of combt .,on is maintained through-
quickly by reducing throttle setting, lowering            out the range of engine operation.
the airplane angle of attack, and increasing                 If the rich limit of fuel-air ratio is exceeded
airspeed. Generally, the compressor stall is              in the combustion chamber, the flame will
caused by one or a combination of the fol-                blow out. While this condition is a pos-
lowing items:                                             sibility the more usual cause of a flameout is
       (ti) A malfunctioning fuel control or gov-         exceeding the lean blowout limit.         Any con-
   erning apparatus is a common cause. Proper             dition which produces some fuel-air ratio
    maintenance and adjustment is a necessity for         leaner than the lean limit of combustion will
    stall-free operation. The malfunctioning is           produce a flameout. Any interruption of the
   most usually        apparent during     engine         fuel supply could bring on this condition.
   acceleration.                                          Fuel system failure, fuel system icing, or pro-
       (6) Poor inlet conditions are typical at           longed unusual attitudes could starve the flows
   high angles of attack and sideslip. These              of fuel to the engine. It should be noted the
   conditions reduce inlet airflow and create             majority of aviation fuels are capable of
   nonuniform flow conditions at the com-                 holding in solution a certain small amount of
   pressor face. Of course, these conditions are          water. If the aircraft is refueled with rela-
   at the immediate control of the pilot.                 tively w&m fuel then flown to high altitude,


the lower temperatures can precipitate this                      provide a convenient limit to sustained high
water out of solution in liquid or ice crystal                   speed flight.
form.                                                                                                  or
                                                                     (5) The effect of engine overspeed critical vi-
   High altitude flight produces relatively small                bration speedranger is important in the service
air mass   flow through the engine and the rela-                 life of an engine. One of the principal sources
tively low fuel flow rate. At these conditions                   of turbine loads is the centrifugal loads due to
a malfunction of the fuel control and governing                  rotation.     Since the centrifugal loads vary as
apparatus could cause flameout. If the fuel                      the square of the rotative speed, a 5 percent
control allows excessively low fuel flow during                  overspeed would produce 10.25 percent over-
controlled deceleration, the lean blow out limit                 stress (1.05*= 1.1025). The large increase in
may be exceeded. Also, if the governed idle                      stress with rorative speed could produce very
condition allows any deceleration below the                      rapid accumulation of creep and fatigue dam-
idle condition the engine will usually continue                  age at high temperature. Repeated overspeed
to lose speed and flameout.                                      and, hence, overstress can cause failure early
   Restarting the engine in flight requires sufli-               in the anticipated service life.
cient RPM and airflow to allow stabilized op-                        Since the turbojet engine is composed of
eration. Generally, the extremes of altitude                     many different distributed masses and elastic
 are most critical for attempted airstart.                       structure, there are certain vibra~tory modes
   (4) An increased compressor   inlet air tcmpcra-              and frequencies for the shaft, blades, etc.
tare can have a profound effect on the output                    While it is necessary to prevent any resonant
tbLrust   of      2 rnrhniet
                    ---“-,--   m&n,=
                               --o---.   As   shown   in         conditions from existing within the normal
figure 2.13, an increase in compressor inlet                     operating range, there may be certain vibra-
temperature produces an even greater increase                     tory modes encountered in the low power range
in the compressor discharge temperature. Since                   common to ground operation, low altitude
the turbine inlet temperature is limited to                       endurance, acceleration or deceleration. If
some maximum value, any increase in com-                         certain operating RPM range restrictions are
pressor discharge temperature will reduce the                     specified due to vibratory conditions, opera-
temperature change which can take place in                        tions must be conducted with a minimum of
the combustion chamber. Hence, the fuel flow                      time in this area. The greatly increased
will be limited and a reduction in thrust is                      stresses common to vibratory conditions are
incurred.                                                        quite likely to cause fatigue failures of the
    The effect of inlet air temperature on thrust                 offending components.
output has two special ramifications.     At rakc-                   The operating limitations of the engine are
off, a high ambient air temperature at a given                    usually specified by various combinations of
pressure altitude relates a high density altitude.                RPM, exhaust gas temperature, and allowable
Thus, the takeoff thrust is reduced because of                    time. The conditions of high power output
low density and low mass flow. In addition                        and acceleration have relatively short times
to the loss of thrust due to reduced mass flow,                   allowable to prevent abuse of the powerplant
thrust and fuel flow are reduced further be-                      and obtain good service life. While the al-
cause of the high compressor inlet temperature.                   lowable times at various high power and
In flight at Sigh Mach number, the aerodynamic                    acceleration condition appear arbitrary, the
 heating will provide an increase in compressor                   purpose is to reduce the spectrum of loading
 inlet temperature. Since the compressor inlet                    which contributes the most rapid accumulation
 temperature will reflect the compressor dis-                     of creep and fatigue damage. In fact, in some
 charge temperature and the allowable fuel                        instances, the arbitrary time standards can be
 flow, the compressor inlet air temperature may                   set to suit the particular requirements of a
                                                                                        NAVWEPS OO-EOT-80
                                                                                    AIRPLANE PERFORMANCE

certain type of operation. Of course, the                  afterburner and very high temperatures can be
effect on service life of any particular load              tolerated. The combustion of fuel in the after-
spectrum must be anticipated.                              burner brings additional increase in tempera-
    One exception to the arbitrary time standard           ture and volume and\ adds considerable energy
for operation at high temperatures or sus-                 to the exhaust. gases producing increased jet
tained high powers is the case of the after-               velocity. The major components of the after-
burner operation. When the cooling flow is                 burner are illustrated in figure 2.14.
only that necessary to prevent excessive tem-                 One necessary feature of the turbojet engine
peratures for adjacent structure and equipment,            equipped with afterburner is a variable nozzle
sustained operation past a time limit may cause            area. As the afterburner begins functioning,
damage to these items.                                     the exit nozzle area must increase to accom-
    THRUST AUGMENTATION.               Many op-            modate the increased combustion products.
erating performance conditions may require                 If the afterburner were to begin functioning
that additional thrust be provided for short               without an increase in exit area, the mass flow
periods of time. Any means of augmenting                   through the engine would drop and the tem-
the thrust of the turbojet engine must be ac-              peratures would increase rapidly. The nozzle
complished without an increase in engine speed             area must be controlled to increase as after-
or maximum turbine section temperature. The                burner combustion, begins. As a result, the
various forms of afterburning or water injection           engine mass flow is given a large increase in
allow the use of additional fuel to provide                jet velocity with the corresponding increase in
thrust augmentation without increase in engine             thrust.              .,
speed or turbine temperature.                                  The combustion of fuel in the afterburner
    The aftsrbumer is a relatively simple means            takes place at low pressures and is relatively
of thrust augmentation and the principal fea-              inefficient. This basic inefficiency of the low
 tures are light weight and large thrust increase.         pressure combustion is given evidence by the
 A typical afterburner installation may add only           large increase in specific fuel combustion.
 10 to 20 percent of the basic engine wei,ght but          Generally, the use of afterburner at least will
 can provide a 40- to 60-percent increase in the           double the specihtfuel consumption.          As an
 static sea level thrust. The afterburner con-             example, consider a turbojet engine capable
 sists of an additional combustion area aft of              of producing 10,000 lbs. of thrust which can
 the turbine section with an arrangement of                develop 15,ooO lbs.. of thrust with the use of
fuel nozzles and flameholders.       Because the           afterburner.      Typical values for specific fuel
local flow velocities in the afterburner are               consumption would. be c,= 1.05 for the basic
 quite high, the flameholders are necessary to              engine or t,= 2.1 when the afterburner is in
 provide the turbulence to maintain combustion              use. The fuel flow during operation would be
 within the afterburner section. The turbojet               as follows:
 engine operates with airflows greatly in excess                 fuel flow = (thrust) (specific fuel consump-
 of that chemically required to support combus-                                  tion)
 tion of engine fuel. This is necessary because                   without afterburner,
 of cooling requirements and turbine tempera-                          fuel flow=(10,000) (1.05)
                                                                                 = 10,500 lbs./hr.
 ture limitations.   Since only 15 to 30 percent
                                                                 with afterburner,
 of the engine airflow is used in the combustion                       fuel flow=(15,COO) (2.1)
 chamber, the large excess air in the turbine                                    =31,500 lbs./hr.
 discharge can support combustion of large                  The low efficiency of the afterburner is illus-
 amounts of additional fuel. Also, there are                trated by the additional 21,CCOlbs./hr. of fuel
  no highly stressed, rotating members in the               flow to create the additional 5,ooO lbs. of
NAVWEPS 0040T-80
                                       AFTERBURNER        COMPONENTS


                                                WATER     INJECTION

                                                WATER INJECTION

        PRE -COMPRESSOR                                   CHAMBER         NOZZLE

                                     TURBINE-PROPELLER         COMBINATION


                                                                CHAMBER              NOZZLE

          Figure 2.14.    Thrust Augmentation    and the Gas Turbine-Propeller     Combination

                                                                                      NAVWEPS 00-30T-30
                                                                                  AIRPLANE PERFORMAPJCE

thrust. Because of the high fuel consumption               immediate advantage in that it prevents fouling
during afterburner operation and the adverse               of the plumbing from the freezing of residual
effect on endurance, the use of the afterburner           fluid at low temperatures. In addition, a large
should be limited to short periods of time.                concentration of alcohol in the mixture can
In addition, there may be limited time for the            provide part of the additional chemical energy
use of the afterburner due to critical heating            required to maintain engine speed. In fact,
of supporting or adjacent structure in the vicin-         the large concentration of alcohol in the in-
ity of the afterburner.                                    jection mixture is a preferred means of adding
   The specific fuel consumption of the basic             additional fuel energy. If the added chemical
engine will increase with the addition of the             energy is included with the water flow, no
afterburner apparatus. The losses incurred by             abrupt changes in governed fuel flow are
the greater fluid friction, nozzle and flame-             necessary and there is less chance of underspeed
holder pressure drop, etc. increase the specific          with fluid injection and overspeed or over-
fuel consumption of the basic engine approxi-             temperature when fluid flow is exhausted. Of
mately 5 to 10 percent.
                                                          course, strict proportions of the mixture are
   The principal advantage of afterburner is the
                                                          necessary. Since most water injection devices
ability to add large amounts of thrust with
relatively small weight penalty.     The applica-         are essentially an unmodulated flow, the use
tion of the afterburner is most common to the             of this device is limited to high engine speed
interceptor, fighter, and high speed type                 and low altitude to prevent the water flow
aircraft.                                                 from quenching combustion.
   The use of wafer injection in the turbojet en-            THE GAS TURBINE-PROPELLER                COM-
gine is another means of thrust augmentation              BINATION.        The turbojet engine utilizes the
which allows the combustion of additional fuel            turbine to extract suflicient power to operate
within engine speed and temperature limits.               the compressor. The remaining exhaust gas
The most usual addition of water injection de-            energy is utilized to provide the high exhaust
vices is to supplement takeoff and climbout               gas velocity and jet thrust. The propulsive
performance, especially at high ambient tem-              efficiency of the turbojet engine is relatively
peratures and high altitudes.        The typical
                                                          low because thrust is produced by creating a
water injection device can produce a 25 to 35
                                                          large velocity change with a relatively small
percent increase in thrust.
   The most usual means of water injection is             mass flow. The gas turbine-propeller combin-
direct flow of the fluid into the combustion              ation is capable of producing higher propulsive
chamber. This is illustrated in figure 2.14.              efficiency in subsonic flight by having the pro-
The addition of the fluid directly into the com-          peller operate on a much greater mass flow.
bustion chamber increases the mass flow and                  The turboprop or propjet powerplant re-
reduces the turbine inlet temperature. The                quires additional turbine stages to continue
drop in temperature reduces the turbine power             expansion in the turbine section and extract
and a greater fuel flow is required to maintain           a very large percent of the exhaust gas energy
engine speed. Thus, the mass flow is increased,           as shaft power. In this sense, the turboprop
more fuel flow is allowed within turbine limits,          is primarily a power producing machine and
and greater, energy is imparted to the exhaust            the jet thrust is a small amount of the output
gases.                                                    propulsive power. Ordinarily, the jet thrust
   The fluid injected into the combustion cham-           of the turboprop accounts for 15 to 25 percent
bers is generally a mixture of water and alco-            of the total thrust output.     Since the turbo-
hol. The water-alcohol        solution has one            prop is primarily a power producing machine,
3~PWbWtlOdWd 3NVldUlV
   08-108-00 SdSMAVN
                                                                                         NAVWEPS Oo-ROT-30
                                                                                     AIRPLANE PERFORMANCE

the turboprop powerplant is rated         by an            engine-propeller combination is operated at a
“equivalent shaft horsepower.”                             constant RPM throughout the major range of
                                                           output power and the principal variables ofcon-
                         T,y                               trol are fuel flow and propeller blade angle.
             ESHP= BHP+325vp
                                                           In the major range of power output, the
where                                                      throttle commands a certain fuel flow and the
    ESHP=equivalent shaft horsepower                       propeller blade angle adjusts to increase the
     EHP= brake horsepower, or shaft horse-                propeller load and remain at the governed
           power applied to the propeller                  speed.
       T,= jet thrust, lbs.                                    The operating limitations of the turboprop
       V=flight velocity, knots, TAS                       powerplant are quite similar in nature to the
       ‘ = propeller efficiency
        1s                                                 operating limitations of the turbojet engine.
                                                           Generally, the turbine temperature limnations
The gas turbine engine is capable of processing            are the most critical items. In addition, over-
large quantities of air and can produce high               speed conditions can produce overstress of the
output power for a given engine size. Thus,                 gearing and propeller as well as overstress of
the principal advantage of the turboprop                    the turbine section.
powerplant is the high specific power output,                   The performance of the turboprop illustrates
high power per engine weight and high power                 the typical advantages of the propeller-engine
per engine size.                                           combination.       Higher propulsive       efficiency
    The gas turbine engine must operate at quite            and high thrust and low speeds provide the
high rotative speed to process large airflows              characteristic of range, endurance, and takeoff
and produce high power. However, high                      performance superior to the turbojet.           As is
rotative speeds are not conducive to high                   typical of all propeller equipped powerplants,
propeller efficiency because of compressibility             the power available is nearly constant with
effects. A large reduction of shaft speed must              speed. Because the power from the jet thrust
be provided in order to match the powerplant                depends on velocity, the power available in-
and the propeller. The reduction gearing must               creases slightly with speed. However, the
provide a propeller shaft speed which can be                thrust available decreases with speed. The
utilized effectively by the propeller and, be-              equivalent shaft horsepower, ESHP, of the
 cause of the high rotative speeds of the turbine,          turboprop is affected by mass ,flow and inlet
 gearing ratios of 6 to 15 may be typical.     The          temperature in fashion similar to that of the
 transmission of large shaft horsepower with                turbojet.    Thus, the ESHP will vary with
 such high gearing involves considerable desi,gn            altitude much like the thrust output of the
 problems to provide good service life. The                 turbojet because the higher altitude produces
 problems of such gearing were one of the                   much lower density and engine mass flow.
 greatest difficulties in the development of                The gas turbine-propeller combination utilizes
 turboprop powerplants.                                     a number of turbine stages to extract shaft
    The governing apparatus for the turboprop               power from the exhaust gases and, as high
 powerplant must account for one additional                 compressor inlet temperatures reduce the fuel
 variable, the propeller blade angle. If the                flow allowable within        turbine temperature
 propeller is governed separately from the tur-              limits, hot days will cause a noticeable loss of
  bine, an interaction can exist between the                output power. Generally, the turboprop is
 engine and propeller governers and various                  just as sensitive, if not more sensitive, to com-
  “hunting,”    overspeed, and overtemperature              pressor inlet air temperature as the turbojet
  conditions are possible. For this reason, the              engine.

                                                                                  NAVWEPS 00-8OT-80
                                                                             AlR,Pl.ANE PERFORMANCE

  The specific fuel consumption of the turbo-       heat and causes the rise of pressure along line
prop powerplant is defined as follows :             CD. The power stroke utilizes the increased
                                                    pressure through the expansion along line DE.
specific fuel consumption=                          Then the exhaust begins by the initial rejection
                          engine fuel flow          along line EB and is completed by the upstroke
                    equivalent shaft horsepower     along line BA.
                c=lbs. per hr.                          The net work produced by the cycle of opera-
                      ESHP                          tion is idealized by the area BCDE on the
                                                    pressure-volume diagram of figure 2.15. Dur-
Typical values for specific fuel consumption, c,    ing the actual rather than ideal cycle of op-
range from 0.5 to 0.8 lbs. per hr. per ESHP.        eration, the intake pressure is lower than the
The variation of specific fuel consumption with     exhaust pressure and the negative work repre-
operating conditions is similar to that of the      sents a pumping loss. The incomplete expan-
turbojet engine. The minimum specific fuel          sion during the power stroke represents a basic
consumption is obtained at relatively high          loss in the operating cycle because of the re-
power setting and high altitudes.       The low     jection of combustion products along line EB.
inlet air temperature reduces the specific fuel     The area EFB represents a basic loss in the
consumption and the lowest values of c are ob-      operating cycle because of the rejection of
tained near altitudes of 25,ooO to 3900 ft.         combustion products along line EB. The area
Thus; the turboprop as well as the turbojet has      EFB represents a certain amount of energy of
a preference for high altitude operation.           the exhaust gases, a part of which can be ex-
THE RECRIPROCATING          ENGINE                   tracted by exhaust turbines as additional shaft
                                                    power to be coupled to the crankshaft (turbo-
   The reciprocating engine is one of the most      compound engine) or to be used in operating a
efficient powerplants used for aircraft power.       supercharger (turbosupercharger).         In addi-
The combination of the reciprocating engine          tion, the exhaust gas energy may be utilized to
and propeller is one of the most efficient means     augment engine cooling flow (ejector exhaust)
of converting the chemical energy of fuel into       and reduce cowl drag.
flying time or distance. Because of the in-             Since the net work produced during the op-
herent high efficiency, the reciprocating engine     erating cycle is represented by the enclosed area
is an important type of aircraft powerplant.         of pressure-volume diagram, the output of the
   OPERATING         CHARACTERISTICS.        The     engine is affected by any factor which influences
function of the typical reciprocating engine in-     this area. The weight of fuel-air mixture will
volves four strokes of the piston to complete        determine the energy released by combustion
one operating cycle. This principal operating        and the weight of charge can be altered by
cycle is illustrated in figure 2.15 by the varia-    altitude,supercharging,etc.     Mixturestrength,
tion of pressure and volume within the cylin-        preignition, spark timing, etc., can affect the
der. The first stroke of the operating cycle is       energy release of a given airflow and alter the
 the downstroke of the piston with the intake        work produced during the operating cycle.
 valve open. This stroke draws in a charge of
                                                         The mechanical work accomplished during
fuel-air mixture along AB of the pressure-
                                                      the power stroke is the result of the gas pres-
volume diagram. The second stroke accom-
plishes compression of the fuel-air mixture           sure sustained on the piston. The linkage of
along line EC. Combustion is initiated by a           the piston to a crankshaft by the connecting
spark ignition apparatus and combustion takes         rod applies torque to the output shaft. During
place in essentially a constant volume. The           this conversion of pressure energy to mechani-
combustion of the fuel-air mixture liberates          cal energy, certain losses are inevitable because
NAVWEPS 00-801-80

       INTAKE     COMPRESSION    COMBUSTION          POWER                    EXHAUST

                                       RECIPROCATING     ENGINE
                                         OPERATING      CYCLE

                                                                 B ------==.f=

                            Figure 2.15. Reciprocating Engines

                                                                                     NAVWEPS 00401-30
                                                                                 AlRPlANE PERFORMANCE

of friction and the mechanical output is less            the power stroke. As such, BMEP is a con-
than the available pressure energy. The power            venient index for a majority of items of recip-
output from the engine will be determined by             rocating engine output, efficiency, and operat-
the magnitude and rate of the power impulses.            ing limitations.
In order to determine the power output of the               The actual power output of any reciptocat-
reciprocating engine, a brake or load device is          ing engine is a direct function of the combina-
attached to the output shaft and the operating           tion of engine torque and rotative speed.
characteristics are determined. Hence, the               Thus, output brake horsepower can be related
term “brake” horsepower, BHP, is used to                 by the combination of BMEP and RPM or
denote the output power of the powerplant.               torque prc~surc and RPM.       No other engine
   From the physical definition of “power” and           instruments can provide this immediate indi-
the particular unit of “horsepower” (1 h.p. =            cation of output power.
33,ooO ft.-lbs. per min.), the brake horsepower             If all other factors are constant, the engine
can be expressed in the following form.                  power output is directly related to the engine
                                                         airflow. Evidence of this fact could be appre-
                 BHP=G                                   ciated from the equation for BHP in terms of
                      TN                                             BHP = @M.W(DXN)
                 BHP= 5255                                                    792,000
                                                         This equation relates that, for a given BMEP,
    BHP= brake horsepower
                                                         the BHP is determined by the product of en-
      T=output torque, ft.-lbs.                          gine RPM, N, and displacement, D. In a
      N=output shaft speed, RPM                          sense, the reciprocating engine could be con-
                                                         sidered primarily as an air pump with the
In this relationship, the output power is ap-
                                                         pump capacity directly affecting the power
preciated as some direct variable of torque, T,
                                                         output. Thus, any engine instrumems which
and RPM. Of course, the output torque is
                                                         relate factors affecting airflow can provide some
some function of the combustion gas pressure
                                                         indirect reflection of engine power. The pres-
during the power stroke. Thus, it is helpful
                                                         sure and temperature of the fuel-air mixture
to consider the mean effective gas pressure
                                                         decide the density of the mixture entering the
during the power stroke, the “brake mean
                                                         cylinder. The carburetor air temperature will
effective pressure” or BMEP.      With use of
                                                         provide the temperature of the inlet air at the
this term, the BHP can be expressed in the
                                                         carburetor. While this carburetor inlet air
following form.
                                                         is not the same temperature as the air in the
           BHP=@MEP)(D)(N)                               cylinder inlet manifold, the carburetor inlet
                        792,m                            temperature provides a stable indication inde-
where                                                    pendent of fuel flow and can be used as a stand-
      BHP= brake horsepower                              ard of performance. Cylinder inlet manifold
     BMEP= brake mean effective pressure, psi            temperature is difficult to determine with the
                                                         same degree of accuracy because of the normal
        D=engine displacement, cu. in.
                                                         variation of fuel-air mixture strength.       The
        N= engine speed, RPM
                                                         inlet manifold pressure provides an additional
The BMEP is not actual pressure within the               indication of the density of airflow entering the
cylinder, but an effective pressure representing         combustion chamber. The manifold absolute
the mean gas load acting on the piston during            pressure, MAP, is affected by the carburetor
 NAVWEPS 00-801-80

 inlet pressure, throttle position, and super-               flame propagation speed, fuel distribution,
 charger or impeller pressure ratio. Of course,              temperature variation,     etc., the maximum
 the throttle is the principal control of mani-              power obtained with a fixed airflow occurs at
 fold pressure and the throttling action controls           fuel-air ratios of approximately 0.07 to 0.08.
 the pressure of the fuel-air mixture delivered              The first graph of figure 2.16 shows the varia-
 to the supercharger inlet.       The pressure re-           tion of output power with fuel-air ratio for a
 ceived by the supercharger is magnified by                 a constant engine airflow, i.e., constant RPM,
 the supercharger in some proportion depend-                MAP, and CAT (carburetor air temperature);
 ing on impeller speed. Then the high pressure              Combustion can be supported by fuel-air ratios
 mixture is delivered to the manifold.                       just greater than .0.04 but the energy released
    Of course, the engine airflow is a function of           is insufficient to overcome pumping losses and
 RPM for two reasons. A higher engine speed                 engine mechanical friction.      Essentially, the
 increases the pumping rate and the volume flow             same result is obtained for the rich fuel-air
 through the engine. Also, with the engine                  ratios just below 0.20. Fuel-air ratios be-
 driven supercharger or impeller, an increase in             tween these limits produce varying amounts of
 engine speed increases the supercharger pres-              output power and the maximum power output
 sure ratio. With the exception of near closed              generally occurs at fuel-air ratios of approxi-
 throttle position, an increase in engine speed             mately 0.07 to 0.08. Thus, this range of fuel-
 will produce an increase in manifold pressure.             air ratios which produces maximum power for
    The many variables affecting the character              a given airflow is termed ,the “best power”
 ,.F the romL.,*r;nn process a:e an I.n~“Lrant
 “1 L..,, c YYU”Cl”Y                                        range. At jo,me lower range of f-ue;-air rariop,
 subject of reciprocating engine operation.                 a maximum of power per fuel-air ratio is ob-
 Uniform mixtures of fuel and air will support              tained and this the “best economy” range.
 combustion between fuel-air ratios of approxi-             The best economy range generally occurs be-
 mately 0.04 and 0.20. The chemically correct               tween fuel-air ratios of 0.05 and 0.07. When
 proportions of air and hydrocarbon fuel would              maximum engine power is required for take-
 be 15 lbs. of air for each lb. of fuel, or a fuel-
                                                            off, fuel-air ratios greater than 0.08 are neces-
 air ratio of 0.067. This chemically correct, or
                                                            sary to suppress detonation.      Hence, fuel-air
 “stoichiometric,”   fuel-air ratio would provide
 the proportions of fuel and air to produce                 ratios of 0.09 to 0.11 are typical during this
maximum release of heat during combustion of                operation.
a grven weight of mixture.          If the fuel-air             The pattern of combustion in the cylinder is
ratio were leaner than stoichiometric, the ex-              best illustrated by the second graph of figure
cess of air and deficiency of fuel would produce            2.16. The normal combustion process begins
lower combustion temperatures and reduced                   by spark ignition toward the end of the com-
heat release for a given weight of charge. If               pression stroke. The electric spark provides
the fuel-air ratio were richer than stoichio-               the beginning of combustion and a flame front
metric, the excess of fuel and deficiency of air            is propagated smoothly through the com-
would produce lower combustion temperatures                 pressed mixture.     Such normal combustion is
and reduced heat release for a given weight of              shown by the plot of cylinder pressure versus
charge.                                                     piston travel. Spark ignition begins a smooth
    The stoichiometric conditions would pro-                rise of cylinder pressure to some peak value
duce maximum heat release for ideal conditions              with subsequent expansion through the power
of combustion and may apply quite closely for               stroke. The variation of pressure with piston
the individual cylinders of the low speed re-               travel must be controlled to achieve the great-
ciprocating engine. Because of the effects of               est net work during the cycle of operation.
                                                                                                                                                  NAVWEPS 00-307-80
                                                                                                                                              AIRPLANE PERFORMANCE

                                                                           BEST                                                    CONSTANT


                              OVERLEAN                                                                              WER-RICH

                                                                        FUEL-AIR              RATIO

          NORMAL COMBUSTION                                                                   DETONATION


                   FLAME PROPAGATION
                                                                                                             BURNJNG                                IGNITION
                                                                                                                                                    FROM HOT SFfYT

                                                                                                        NORMAL CCMBUSTION

                              COMPRESSION STROKE                                                                POWER STROKE
                                                                                 TOP CENTER
                                                                                                                                                                                                 .. .... .... .
  ... ...... ..... ...... ........ ........ ....... ....... ....... ...... ...... ....... ........ ........ ...... ...~

                                                                                                                    RATED                      TAKEOFF
                                                                              CRUISE              1                 POWER          1           POWER              1


                                               ENGINE AIRFLOW, LBS. PER HR.

                                              Figure 2.16. Reciprocating Engine Operation


Obviously, spark ignition timing is an impor-                  Denotation offers the possibility of immedi-
tant factor controlling the initial rise of pres-          ate destruction of the powerplant.      The nor-
sure in the combustion chamber. The ignition               mal combustion process is initiated by the
of the fuel mixture must begin at the proper               spark and beginning of flame front propaga-
time to allow flame front propagation and the              tion     As the flame front is propagated, the
release of heat to build up peak pressure for the          combustion chamber pressure and temperature
power stroke .                                             begin to rise. Under certain conditions of
    The speed of flame front propagation is a              high combustion pressure and temperature,
major factor affecting the power output of the             the mixture ahead of the advancing flame front
reciprocating engine since this factor controls            may suddenly explode with considerable vi-
the rate of heat release and rate of pressure rise         olence and send strong detonation waves
in the combustion chamber. For this reason,                through the combustion chamber. The result
dual ignition is necessary for powerplants of              is depicted by the graph of figure 2.16, whete:a
 high specific power output. Obviously, nor-               sharp, explosive increase in pressure takes place
 mal combustion can be accomplished more                   with a subsequent reduction of the mean pres;
rapidly with the propagation of two flame                  sure during the power stroke. Detonation
fronts rather than one. The two sources of                 produces sharp explosive pressure peaks many
ignition are able to accomplish the combus-                times greater than normal combustion1 Also,
 tion heat release and pressure rise in a shorter          the exploding gases radiate considerable heat
period of time. Fuel-air ratio is another factor           and cause excessive temperatures for many local
 affecting the flame propagation speed in the              parts of the engine. The effects of heavy
combustion chamber. The maximum flame                      detonation are so severe that structural damage
propagation speed occurs near a fuel-air ratio             is the immediate result. Rapid rise of cylinder
of 0.08 and, thus, maximum power output for                head temperature, rapid drop in BMEP, and
a given airflow will tend to occur at this value           loud, expensive noises are evidence of detona-
rather than the stoichiometric value.                      tion.
    Two aberrations of the combustion process                  Detonation is not necessarily confined to. a
are preignition and detonation.       Preignition          period after the beginning of normal flame front
 is simply a premature ignition and flame f&t              propagation.     With extremely low grades of
propagation due to hot spots in the combustion             fuel, detonation can occur before normal igni-
chamber. Various lead and carbon deposits                   tion. In addition, the high temperatures and
and feathered edges on metal surfaces can sup-             pressure caused by preignition will mean that
ply a glow ignition spot and begin a flame                 detonation is usually a corollary of preigniticn.
propagation prior to normal spark ignition.                 Detonation results from a sudden, unstable de-
As shown on the graph of figure 2.16, pre-                  composition of fuel at some critical combina-
ignition     causes a premature          rise of            tion of high temperature and pressure. Thus,
pressure during the piston travel. As a result,             detonation is most likely to occur at any op
preignition combustion pressures and tempera-               erating condition which produces high com-
tures will exceed normal combustion values and              bustion pressures and temperatures. Gener-
are very likely to cause engine damage. Be-                 ally, high engine airflow and fuel-air ratios for
cause of the premature rise of pressure toward              maximum heat release will produce the critical
the end of the compression stroke, the net work             conditions. High engine airflow is common
of the operating cycle is reduced. Preignition              to high MAP and RPM and the engine is most
is evidenced by a rise in cylinder head tempera-            sensitive to CAT and fuel-air ratio in this
ture and drop in BMEP or torque pressure.                   region.

                                                                                         NAVWEPS 00-8OT-80
                                                                                     AIRPLANE PERFORMANCE

    The detonation properties of a fuel are de-             cruise power is the upper limit of power that
  termined by the basic molecular structure of              can be utilized for this operation. Higher air-
  the fuel and the various additives. The fuel              flows and higher power wirhout a change in
 detonation properties are generally specified              fuel-air ratio will intersect the knee of the
  by the antidetonation or antiknock qualities of           detonation envelope.
 an octane rating. Since the antiknock proper-                 The primary factor relating the efficiency of
 ties of a high quality fuel may depend on the              operation of the reciprocating engine is the
 mixture strength, provision must be made                   brake specific fuel consumption, iWE%, or
 in. the rating of fuels. Thus, a fuel grade of             simply c.
 IIS/       would relate a lean mixture antiknock           Brake suecific fuel consumution

 rating of 115 and a rich mixture antiknock                                                   engine fuel flow
 rating of 145. One of the most common opera-                                             = brake horsepower
 tional causes of detonation is fuel contamina-                                  lbs. per hr.
 tion. An extremely small contamination of                                           BHP
 high octane fuel with jet fuel can cause a serious
,decrease in the antiknock rating. Also, the                 Typical minimum values for c range from 0.4
 contamination of a high grade fuel with the                to 0.6 lbs. per hr. per BHP and most aircraft
 next lower grade will cause a noticeable loss of           powerplaots average 0.5. The turbocompound
 antiknock quality.                                         engine is generally the most efficient because
    The fuel metering requirements for an engine            of the power recovery turbines and can ap-
 are illustrated by the third graph of figure 2.16          proach values of c=O.38 to 0.42. It should be
 which is a plot of fuel-air ratio versus engine            noted that the minimum values of specific fuel
 airflow.     The carburetor must provide specific          consumption will be obtained only within the
 fuel-air ratios throughout the range of engine             range of cruise power operation, 30 to 60 per-
 airflow to accommodate certain output power.               cent of the maximum power output.          Gen-
 Most modern engines equipped with auto-                    erally, the conditions of minimum specific fuel
 matic mixture control provide a scheduling of              consumption are achieved with auto-lean or
fuel-air ratio for automatic rich or automatic              manual lean scheduling of fuel-air ratios and
 lean operation. The auto-rich scheduling usu-              high BMEP and low RPM. The low RPM is
ally provides a fuel-air ratio at or near the               the usual requirement to minimize friction
 maximum heat release value for the middle                  horsepower and improve output efficiency.
 range of airflows. However, at high airflows                  The effect of &it&c is to reduce the engine
 a power enrichment must be provided to sup-                airflow and power output and supercharging
press detonation.      The auto-rich schedule gen-          is necessary to maintain high power output
erally will provide an approximate fuel-air                 at high altitude.     Since the basic engine is
ratio of 0.08 which increases to 0.10 or 0.11 at            able to process air only by the basic volume
the airflow for takeoff power. In addition,                 displacement, the function of the supercharger
the low airflow and mixture dilution that oc-               is to compress the inlet air and provide a
                                                            greater weight of air for the engine to process.
curs in the idle power range requires enrich-
                                                            Of course, shaft power is necessary to operate
ment for satisfactory operation.
                                                            the engine driven supercharger and a tempera-
    The schedule of fuel-air ratios with an auto-           ture rise occurs through the supercharger com-
matic lean fuel-air ratio will automatically                pression. The effect of various forms of super-
provide maximum usable economy. If manual                   charging on altitude performance is illustrated
leaning procedures are applicable a lower fuel-             in figure 2.17.
air ratio may be necessary for maximum possi-                  The unsupercharged-or        naturally   aspi-
ble     efficiency. The maximum        continuous           rated-engine    has no means of providing a

                        EFFECT    OF   SUPERCHARGING        ON ALTITUDE


                            LOW SLOWER
                    \        LIMIT MAP                            HIGH SLOWER
               _c U&QJ                                 f-           LIMIT MAf


               Figure 2.17. Fffect of Supercharging on Altitude    Performonce

                                                                                        NAVWEPS OO-ROT-RO
                                                                                     AWIANE  PERFORMANCE

 manifold pressure any greater than the induc-               higher altitude or a lower engine speed would
 tion system inlet pressure. As altitude is                 produce less supercharging and a given MAP
increased with full throttle and a governed                 would require a greater throttle opening.
RPM, the airflow through the engine is                      Generally, the most important critical alti-
reduced and BHP decreases. The first forms of                tudes will be specified for maximum, rated,
 supercharging were of relatively low pressure               and maximum cruise power conditions.
ratio and the added airflow and power could                     A change of the blower to a high speed will
 be handled at full throttle within detonation              provide greater supercharging but will require
limits.     Such a “ground boosted” engine                   more shaft power and incur a greater tempera-
would achieve higher output power at all                    ture rise. Thus, the high blower speed can
 altitudes but an increase in altitude would                 produce an increase in altitude performance
produce a decrease in manifold pressure, air-               within the detonation limitations.        The vari-
flow, and power output.                                     ation of BHP with altitude for the blower at
    More advanced forms of supercharging with               high speed shows an increase in critical alti-
 higher pressure ratios can produce very large               tude and greater BHP than is obtainable in low
 engine airflow.       In fact, the typical case of          blower. Operation below the high blower
 altitude supercharging will produce such high              critical altitude requires some limiting mani-
airflow at low altitude operation that full                 fold pressure to remain within detonation
 throttle operation cannot be utilized within               limits.    It is apparent that the shift to high
detonation limits. Figure 2.17 illustrates this             blower is not required just past low blower
case for a typical two-speed engine driven                  critical altitude but at the point where the
 altitude supercharging installation.        At sea         transition from low blower, full throttle to
level, the limiting manifold pressure produces              high blower, limit hiAP will produce greater
a certain amount of BHP. Full throttle oper-                BHP. Of course, if the blower speed is
ation could produce a higher MAP and BHP                    increased without        reducing the throttle
if detonation were not the problem. In this                 opening, an “overboost” can occur.
case full throttle operation is unavailable                    Since the exhaust gases have considerable
because of detonation limits.        As altitude is         energy, exhaust turbines provide a source of
increased with the supercharger or “blower”                 supercharger power. The turbosupercharger
at low speed, the constant MAP is maintained                (TB.S) allows control of the supercharger
by opening the throttle and the BHP increases               speed and output to very high altitudes with
above the sea level value because of the re-                a variable discharge exhaust turbine (PDT).
duced exhaust back pressure. Opening the                    The turbosupercharger is capable of providing
throttle allows the supercharger inlet to re-               the engine airflow with increasing altitude by
ceive the same inlet pressure and produce the               increasing turbine and supercharger speed.
same MAP. Finally, the increase of altitude                 Critical altitude for the turbosupercharger is
will require full throttle to produce the con-              usually defined by the altitude which produces
stant MAP with low blower and this point is                 the limiting exhaust turbine speed.
termed the “critical altitude” or “full throttle               The minimum specific fuel consumption of
height.”      If altitude is increased beyond the           the supercharged engine is not greatly affected
critical altitude, the engine MAP, airflow, and             by altitudes less than the critical altitude.   At
BHP decrease.                                               the maximum cruise power condition, specific
    The critical altitude with a particular super-          fuel consumption will decrease slightly with
charger installation is specific to a given com-            an increase in altitude up to the critical
bination of MAP and RPM.              Obviously, a          altitude.     Above critical altitude, maximum
lower MAP could be maintained to some                       ,cruise power cannot be maintained but the

specific fuel consumption is not adversely                                heavy detonation or preignition is common to
affected as long as auto-lean or manual lean                              the high airflow at maximum power, the most
power can be used at the cruise power setting.                            likely chance of detonation or preignition is at
   One operating characteristic of the recipro-                           takeoff. In order to suppress detonation or
cating engine is distinctly different from that                           allow greater power for takeoff, water injec-
of the turbojet.     Water vapor in the air will                          tion is often used in the reciprocating engine.
cause a significant reduction in output power of                          At high power’    settings, the injection of the
the reciprocating engine but a negligible loss                            water-alcohol mixture can replace the excess
of thrust for the turbojet engine. This basic                             fuel required to suppress detonation, and de-
difference exists because the reciprocating                               richment provisions can reduce the fuel-air
engine operates with a fixed displacement and                             ratio toward the value for maximum heat re-
all air processed is directly associated with the                         lease. Thus, an increase in power will be ob-
combustion process. If water vapor enters the                             tained by the better fuel-air ratio. In some
induction system of the reciprocating engine,                             instances, a higher manifold pressure can be 1
the amount of air available for combustion is                             utilized to produce additional power. The in-
reduced and, since most carburetors do not                                jection fluid will require proportions of alcohol
distinguish water vapor from air, an enrich-                              and water quite different from the injection
ment of the fuel-air ratio takes place. The                               fluid for jet engine thrust augmentation.
maximum power output at takeoff requires                                  Since derichment of the fuel-air ratio is de-
fuel-air ratios richer than that for maximum                              sired, the anti-detonant injection (AOZ) will
-haezt --A-“-\-   rn               nnr:rLmm.c
                  “W .,, A....A c. b.IIA.cIIIIICIIL .“1111 *-IF-
                         C,I+P-                       . ..I1 La&C                  ,Ir,.Le, :.. -.....^*;*:- L” pC”LuL Ic>luual
                                                                          rr\n+l;n PlC”ll”l111 yu‘ l’ r-^--..-.*--.:J..-l
                                                                          b”IICLIALI                a”c’ L~
place with subsequent loss of power. The                                  fluid from fouling the plumbing.
turbojet operates with such great excess of air                               When the fuel grades are altered during oper-
that the combustion process essentially is                                ation and the engine must be’          operated on a
unaffected and the reduction of air mass flow                             next lower fuel grade, proper account must be
is the principal consideration.   As an example,                          made for the change in the operating limita-
                                                                          tions. This accounting must be made for the
extreme conditions which would produce high
                                                                          maximum power for takeoff and the maximum
specific humidity may cause a 3 percent thrust
                                                                          cruise power since both of these operating con-
loss for a turbojet but a 12 percent loss of BHP                          ditions are near the detonation envelope. In
for a reciprocating engine. Proper accounting                             addition, when the higher grade of fuel again
of the loss due to humidity is essential in the                           becomes available, the higher operating,limits
operation of the reciprocating engine.                                    cannot be used until it is sure chat no contamina-
   OPERATING        LIMITATIONS.         Recipro-                          tion exists from the lower grade fuel remaining
cating engines have achieved a great degree of                            in the tanks.
refinement and development and are one of the                                 Spark plug fouling can provide certain high
most reliable of all types of aircraft power-                             as well as low limits of operating temperatures.
plants. However, reliable operation of the re-                            When excessively low operating temperatures
ciprocating engine is obtained only by strict                             are encountered, rapid carbon fouling of the
adherence to the specific operating limitations.                          plugs will take place. On the other hand,
   The most important operating limitations of                            excessively high operating temperatures will
the reciprocating engine are those provided to                            produce plug fouling from lead bromide de-
ensure that detonation and preignition do not                             posits from the fuel additives.
take place. The pilot must ensure that proper                                 Generally, the limited periods of time at
fuel grades are used that limit MAP, BMEP,                                various high power settings are set to mini-
RPM, CAT, etc., are not exceeded. Since                                   mize the accumulation of high rates of wear
Revised January       1965
                                                                                       NAVWEPS OO-EOT-80
                                                                                   AIRPLANE PERFORMANCE

and fatigue damage. By minimizing             the         disc. In this idealized propeller disc, the pres-
amount of total time spent at high power                  sure difference is uniformly distributed over the
setting, greater overhaul life of the powerplant          disc area but the actual case is rather different
can be achieved. This should not imply that               from this.
the-takeoff rating of the engine should not be               The final velocity of the propeller slipstream,
used. Actually, the use of the full maximum               V,, is achieved some distance behind the pro-
power at takeoff will accumulate less total               peller. Because of the nature of the flow pat-
engine wear than a reduced power setting at               tern produced by the propeller, one half of the
the same RPM because of less time required to             total velocity change is produced as the flow
climb to a given altitude or to accelerate to a           reaches the propeller disc. If the complete
given speed.                                              velocity increase amounts to Za, the flow veloc-
   The most severe rate of wear and fatigue               ity has increased by the amount II at the pro-
damage occurs at high RPM and low MAP.                    peller disc. The propulsive e$icien~, vp, of the
High RPM produces high centrifugal loads                  ideal propeller could be expressed by the fol-
and reciprocating iuertia loads. When the                 lowing relationship:
large reciprocating inertia loads are not cush-
                                                                            output power
ioned by high compression pressures, critical                            ?%I= .
                                                                             mput power
resultant loads can be produced. Thus, op-
erating time at maximum RPM and MAP must                                        TV
be held to a minimum and operation at mari-                              I’
                                                                         ‘ = T(V+a)
mum RPM and low MAP must be avoided.
AIRCRAFT     PROPELLERS                                           v,=propulsive efficiency
                                                                   T=thrust, lbs.
   .The aircraft propeller functions to convert                    V=fligkt velocity, knots
the powerplant shaft horsepower into propul-                       IJ= velocity increment at the
 sive horsepower. The basic principles of pro-                            propeller disc, knots
pulsion apply to the propeller in that thrust is
produced by providing the airstream a mo-                 Since the final velocity, Vs, is the sum of total
mentum change. The propeller achieves high                velocity change 2a and the initial velocity,
propulsive ef?iciency by processing a relatively          V,, the propulsive efliciency rearranges to a
large mass flow of air and imparting a rela-              form identical to that for the turbojet.
tively small velocity change. The momentum                                          2
change created by propeller is shown by the                                 VP’
illustration of figure 2.18.                                                      1+ k
    The action of the propeller can be idealized                                     0
by the assumption that the rotating propeller             So, the same relationship exists as with the
is simply an actuating disc. As shown in fig-             turbojet engine in that high efficiency is de-
ure 2.18, the inflow approaching the propeller            veloped by producing thrust with the highest
disc indicates converging streamlines with an             possible mass flow and smallest necessary
increase in velocity and drop in pressure. The            velocity change.
converging streamlines leaving the propeller                 The actual propeller must be evaluated in a
disc indicate a drop in pressure and increase in          more exact sense to appreciate the effect of
velocity behind the propeller. The pressure               nonuniform disc loading, propeller blade drag
change through the disc results from the distri-          forces, interference flow between blades, etc.
bution of thrust over the area of the propeller           With these differences from the ideal Propeller,

NAVWEPS 00-801-80

            --                   --                          r         PROPELLER   DISC

                 “1    *-                                                                  _ =“,.?*a

            --              --

                                                                       PRESSURE CHANGE
    P;;;lW;;E                                                            THROUGH DISC

                 DISTRIBUTION         OF


                                                      ROTATIONAL FLOW COMPONENT
                                                               mDAT   TIP
                                           ii-       2.18. Rhuiples of Ropellerr

                                                                                        NAVWEPS 00-8OL80
                                                                                    AiRPlANE PERFORMANCE

it is more appropriate to define propeller effi-           angle, and is a function of some proportion of
ciency in the following manner:                            the flight velocity, V, and the velocity due to
                                                           rotation which is mD at the tip. The pro-
          ‘ output propulsive power
                                                           portions of these terms describe the propeller
              mput shaft horsepower                         “advance ratio”, J.

where                                                      where
       vP= propeller efficiency
                                                                J=propeller advance ratio
       T= propeller thrust
       V= flight velocity, knots                               V=flight velocity, ft. per sec.
     BHP= brake horsepower applied to the                       n=propeller rotative speed, revolutions
              propeller                                               per sec.
                                                               D = propeller diameter, ft.
Many di,fferent factors govern the efficiency of
 a propeller. Generally, a large diameter pro-             The propeller blade angle, fi (beta), varies
 peller favors a high propeller efficiency from            throughout the length of the blade but a
 the standpoint of large mass flow. However,               representative value is measured at 75 percent
 a powerful adverse effect on propeller efficiency         of the blade length from the hub.
 is produced by high tip speeds and conipressi-               Note that the difference between the effec-
 bility effects. Of course, small diameter pro-            tive pitch angle, 4, and the blade angle, 8,
pellers favor low tip speeds. In addition, the             determines an effective angle of attack for the
propeller and powerplant must be matched for               propeller blade section. Since the angle of
 compatibility of output and efficiency.                   attack is the principal factor affecting the
    In order to appreciate some of the principal           efficiency of an airfoil section, it is reasonable
factors controlling the efficiency of a given              to make the analogy that the advance ratio, J,
propeller, figure 2.18 Uustrates the distribu-             and blade angle, 8, are the principal factors
 tion of rotative velocity along the rotating              affecting .propeller efficiency. The perform-
propeller blade. These rotative velocities add             ance of a propelleris typified by the chart of
to the local inflow velocities to produce a                figure 2.19 which- illustrates the variation of
variation of resultant velocity and direction              propeller efficiency, ~a, with advance ratio, J,
along the blade. The typical distribution of               for various values of blade angle, 8. The
thrust along the propeller blade is shown with             value of vP for each fl increases with J
the predominating thrust being located on the              until a peak is reached, then decreases. It is
outer portions of the blade. Note that the                 apparent that a fixed pitch propeller may be
propeller producing thrust develops a tip                  selected to provide suitable performance in a
vortex similar to the wing producing lift.                 narrow range of advance ratio but efficiency
Evidence of this vortex can be seen by the con-            would suffer considerably outside this range.
densation phenomenon occurring at this Ioca-                  In order to provide high propeller efficiency
tion under certain atmospheric conditions.                 through a wide range of operation, the pro-
    The component velocities at a given propeller          peller blade angle must be controllable.      The
blade section are shown by the diagram of                  most convenient means of controlling the
figure 2.18. The inflow velocity adds vec-                 propeller is the provision of a constant speed
torially to the velocity due to rotation to pro-           governing apparatus. The constant speed gov-
duce an inclination of the resultant wind with             erning feature is favorable from the standpoint
respect to the planes of rotation.     This incli-         of engine operation in that engine output and
nation is termed + (phi), the effective pitch              efficiency is positively controlled and governed.

The governing of the engine-propeller combi-        a single feathered propeller is a relatively small
nation will allow operation throughout a wide       contribution to the airpfane total drag.
range of power and speed while maintaining             At smaller blade angles near the Rat pitch
efficient operation.                                position, the drag added by the propeller is
   If the envelope of maximum propeller dfi-        very large. AC these small blade angles, the
ciency is available, the propulsive horsepower      propeller windmilling at high RPM can create
available will appear as shown in the second        such a tremendous amount of drag that the
chart of figure 2.19. The propulsive power          airplane may be uncontrollable.        The propel-
available, Pa, is the product of the propeller      ler windmilling at high speed in the low range
efficiency and applied shaft horsepower.            of blade angles can produce an increasein para-
                                                    site drag which may be as great as the parasite
                                                    drag of the basic airplane. An indication of
                                                    this powerful drag is seen by the hclieopter in
                                                    autorotation.    The windmilling      rotor  is ca-
                                                    pable of producing autorotation rates ofdcscent
The propellers used on most large reciprocating     which approach that of a parachute canopy
engines derive peak propeller efficiencies on the   with the identical disc area laading. THUS,
order of s,=O.85 to 0.88. Of course, the peak       the propeller windmilling at high speed and
values are designed to occur at some specific       small blade angle can produce an cffccti+e
design condition.     For example, the selection    drag coefficient of the disc area which compares
of a propel!er for a !ong rasge transport wsuld     with tha~t of a parachute canopy. The drag
require matching of the engine-propeller com-       and yawing moment caused by loss of power
bination for peak efhciency at cruise condjtion.    at high engine-propeller speed is considerable
On the other hand, selection of a propeller for     and the transient yawing displaccmcnt of the
a utility or liaison type airplane would require    aircraft’ may produce critical loads for the
matching of the engine-propeller combination        vertical tail.    For this reason, automatic
to achieve high propulsive power at low speed       feathering may be a necessity rather than a
and high power for good takeoff and climb           luxury.
performance.                                           The large drag which can be produced by
    Several special considerations must be made     the rotating propeller can be utilized to im-
for the application of aircraft propellers. In      prove the stopping performance of the air-
the event of a powerplant malfunction or            plane. Rotation of the propekr blade to
failure, provision must be made to streamline       small positive values or negative values with
the propeller blades and reduce drag so that        applied power can produce large drag or re-
flight may be continued on the remaining op-        verse thrust. Since the thrust capability of the
erating engines. This is accomplished by            propeller is quite high at low speeds, very
feathering the propeller blades which .stops        high deceleration can be provided by reverse
rotation and incurs a minimum of drag for the       thrust alone,
inoperative engine. The necessity for feather-        The qs&zg      limitatiar   of the pmpcllcr are
ing is illustrated in figure 2.19 by the change     closely associated with those of the Rower-
in equivalent parasite area, Af, with propeller     plant. Overspeed conditions are critical be-
                                                    cause of the large centrifugal loads and blade
blade angle, 8, of a typical instaliation.  When
                                                    twisting moments produced by an excessive
the propeller blade angle is in the feathered
                                                    rotative speed. In addition, the propeller
position, the change in parasite drag is at a       blades will have various vibratory modes and
minimum and, in the case of a typical multi-        certain operating limitations may hc necessary
engine aircraft, the added parasite drag from       to prevent exciting resonant conditions.
                                                                                                                                                         NAVWEPS 00-801-80
                                                                                                                                                     AIRPLANE PERFORMANCE
                                                                        ELLER EFFICIENCY

                                                                                               ENVELOPE OF MAXIMUM EFFICIENCY


                                          -I                                       PROPELLER ADVANCE RATIO, J                                                                                 ... ..... .... ... ..
                                                                                   ..                                       ::::::::::::::::::::::::::::::::::::::::::::~~:~~~~~~~~~~~~~~~~~~~~::::::::~:::::::
                                            ........... .-.-................::::::::: ......_.........._..................... ........ ........ ... .. ...... ...... . ....~.~~....................................
                                                                           ::::::::::: ... ..... ...... ..... ..... ..... .1:..
                                                                                   ..                                       .
liiiiiii!lililliiiiiiiliiiii8iiliili::::::::::::::::::::::::::::~~~~~~~~~~~::::::::::::::~~:::::::::::::.... ..... ........ ........ ....... ...... ...... ...... . .
                                                                                                     POWER AVAILABLE
                                                                              \                                         BHP


                                                                                         VELOCITY, KNOTS

                                                                           PROPELLER                DRAG CONTRIBUTION




                                      0                       I5                   30                     45                       60                                        90
                                                                            PROPELLER BLADE ANGLE,P

                                                                 Figure 2.79. Propeller Operation

MAWEPS 00-801-80

                                                           the airspeed corresponding to point A, the
                                                           power or thrust required curves define a par-
                                                            ticular value of thrust or power that must be
   The various items of airplane performance               made available from the powerplant ~to achieve
result from the combination of airplane and                equilibrium.     Some different airspeed such as
powerplant characteristics.    The aerodynamic             that corresponding to point B changes the
characteristics of the airplane generally define           value of thrust or power required to achieve
the power and thrust requirements at various               equilibrium.     Of course, the change of air-
conditions of flight while the powerplant                  speed   to point B also would require a change
characteristics generally define the power and             in angle of attack to maintain a constant lift
thrust available at various conditions of flight.          equal to the airplane weight.       Similarly, to
The matching of the aerodynamic configura-                 establish airspeed and achieve equilibrium at
tion with the powerplant will be accomplished              point C will require a particular angle of attack
to provide maximum performance at the speci-               and powerplant thrust or power. In this case,
fic design condition, e.g., range, endurance,              flight at point C would be in the vicinity of
climb, etc.                                                the minimum flying speed and a major portion
                                                           of the ,thrust or power required would be due
STRAIGHT      AND LEVEL FLlGHT                             to induced drag.
   When the airyJane is in steady, level flight,               The maximum level flight speed for the air-
the condition of equilibrium must prevail.                 plane will be obtained when the power :or
The unaccelerated condition        of flight    is         thrust required equals the maximum power or
achieved with the airplane trimmed for lift                thrust available from the powerplant.         The
equal to weight and the powerplant set for a               minimum level flight airspeed is not usually
thrust to equal the airplane drag. In certain              defined by thrust or power requirement since
conditions of airplane performance it is con-              conditions of, stall or stability and control
venient to consider the airplane requirements              problems generally predominate.
by the thnr$t required (or drag) while in other            CLIMB PERFOLWANCE
cases it is more applicable to consider the
                                                               During climbing flight, the airplane gains
power re@red. Generally, the jet airplane will
                                                           potential energy by virtue of elevation. This
require consideration of the thrust required
                                                           increase in potential energy during a climb is
and the propeller airplane will require consid-
                                                           provided by one, or a combination, of two
eration of the power required. Hence, the
                                                           means: (1) expenditure of propulsive energy
airplane in steady level flight will require lift
                                                           above that required to maintain level flight or
equal to weight and thrust available equal to
                                                           (2) expenditure of airplane kinetic energy, i.e.,
thrust required (drag) or power available equal
                                                           loss of velocity by a zoom. Zooming for alti-
to power required.
                                                           tude is a transient process of trading kinetic
   The variation of power required and thrust
                                                           energy for potential energy and is of considera-
required with velocity is illustrated in figure
                                                           ble importance for airplane configurations
2.20. Each specific curve of power or thrust
                                                           which can operate at very high levels of kinetic
required is valid for a particular aerodynamic
                                                           energy. However, the major portions of climb
configuration at a given weight and altitude.              performance for most airplanes is a near steady
These curves define the power or thrust re-                process in which additional propulsive energy
quired to achieve equilibrium,        Jift-equal-           is converted into potential energy. The funda-
weight, constant altitude flight at various                mental parts of airplane climb performance in-
airspeeds. As shown by the curves of figure                volve a flight condition where the airplane is
2.20, ifit is desired to operate the airplane at           in equilibrium but not at constant altitude.
                                                          NAVWEPS OO-ROT-80
                                                      AIRPLANE PERFORMANCE


                               1    WEIGHT


                                                     -MAXIMUM     LEVEL
                                                          FLIGHT SPEED



                                             -   MAXIMUM LEVEL
                                                  FLIGHT SPEED


               Figure 2.20. Level Right Pedormancc


   The forces acting on the airplane during a             depends on the difference between thrust and
climb are shown by the illustration of figure             drag (T-D),       or excess thrust. Of course,
2.21. When the airplane is in steady flight               when the excess thrust is zero (T-D=0              or
with moderate angle of climb, the vertical                T=D), the inclination of, the flight path is
component of lift is very nearly the same as the          zero-and the airplane is in steady, level flight.
actual lift.     Such climbing flight would exist         When the thrust is greater than the drag, the
with the lift very nearly equal to the weight.            excess thrust will allow a climb angle depend-
The net thrust of the powerplant may be in-               ing on the value of excess thrust.       Also, when
clined relative to the flight path but this effect        the thrust is less than the drag. the deficiency
will be neglectec! for the sake of simplicity.            of thrust will allow an angle ~of descent.
Note that the weight of the aircraft is vertical             The most immediate interest in the climb
but a component of weight will act aft along              angle performance involves obstacle clearance.
the flight path.                                          The maximum angle of climb would occur
    If it is assumed that the aircraft is in a steady     where there exists the greatest difference be-
climb with essentially small inclination of the           tweenthrust available and thrust required, i.e.,
flight path, the summation of forces along the            maximum (T-D).           Figure 2.21 illustrates the
flight path resolves to the following:                    climb angle performance with the curves of
                                                          thrust available and thrust required versus
          Forces forward= Forces aft                      velocity.     The thrust required, or drag, curve
                                                          is nss,~pued be ppw=n*~r;.rP c nc CnmP+-+a!
                                                                                        ..&. “I ““IILL ‘ y
                                                                                y.“- ..I‘                ,
where                                                     airplane configuration which could be powered
     T= thrust available, lbs.                             by either a turbojet or propeller type power-
    D= drag, lbs.                                          plant. The thrust available curves included
    W= weight, lbs.                                        are for a characteristic propeller powerplant
     v=flight    path inclination or angle ,of             and jet powerplant operating at maximum
            climb, degrees (“gamma”)                       output.
                                                              The thrust curves for the representative pro-
This basic relationship neglects some of the               peller aircraft show the typical propeller thrust
factors which may be of importance for air-                which is high at low velocities and decreases
planes of very high climb performance. For                 with an. increase in velocity.       For the pro-
example, a more detailed consideration would               peiler powered airplane, the maximum excess
account for the inclination of thrust from the             thrust and angle of climb will occur at some
flight path, lift not equal to weight, subse-              speed just above the stall speed. Thus, if it
quent change of induced drag, etc. However,                is necessary to clear an obstacle after takeoff,
this basic relationship will define the principal          the propeller powered airplane will attain
factors affecting climb performance. With                  maximum angle of climb at an airspeed con-
this relationship established by the condition
                                                           veniently close to-if        not at-the       takeoff
of equilibrium,     the following    relationship
exists to express the trigonometric sine of the
                                                              The thrust curves for the representative jet
climb angle, y:
                                                           aircraft show the typ~ical turbojet thrust which
                   sin y=-                                 is very nearly constant ~with speed. If the
                                                           thrust available is essentially constant with
   This relationship simply states that, for a             speed, the maximum excess thrust and angle
 given weight airplane, the angle of climb (7)              of climb will occur where the thrust required

                                                                                 NAVWEPS OD-80T-80
                                                                             AIRPLANE PERFORMANCE

                                                                    COMPONENT OF WEIGHT
                                                     w SIN ,--       ALONG FLIGHT PATH

 THRUST      -       -   --           __----                                     AVAILABLE
AVAILABLE                                                                        JET ACFT

                                        VELOCITY, KNOTS
                                                                   l=‘ JET

 AVAILABLE                                                       Pr, POWER REOUIRED
   POWER                                                         POWER AVAILABLE
                                                                   PROP ACFT

                                                     SPEED FOR MAX R.C., JET
                                                     SPEED FOR MAX R.C., PROP

                                        VELOCITY,      KNOTS

                              Figure 2.21. Climb Performance
NAVWEPS 00-801-80

  is at a minimum, (LID),.        Thus, for maxi-           where
  mum steady-state angle of climb, the turbojet                  RC=rate of climb, f.p.-.
  aircraft would be operated at the speed ,for                   P11=power available, h.p.
  (L/D),.     This poses somewhat of a problem                   Pr=power re uired, h.p.
                                                                 W=weight, 1 s  %
  in determining the proper procedure for ob-                    V=true airspeed, knots
  stacle clearance after takeoff. If the obstacle          and
  is a considerable distance from the takeoff                    33,000 is the factor converting horsepower
  point, the problem is essentially that of a long                 to ft-lbs/min
 term gain and steady state conditions will pre-                 101.3isthefactorconvertingknocstof.p.m.
 dominate. That is, acceleration from the take-            The above relationship states that, for a given
 off speed to (L/D),      speed will be favorable          weight airplane, the rate af climb (RC) depends
 because the maximum steady climb angle can                on the difference between the power available
 be attained. However, if the obstacle is a rela-          and the power required (Pd- Pr), or excess
 tively short distance from the takeoff point,             power. Of course, when the excess power is
 the additional distance required to accelerate            zero (Pa-Pr=O       or Pa==PI), the rate of climb
 to (L/D),,    speed may be detrimental and the            is zero and the airplane is in steady level flight.
 resulting situation may prove to be a short               When the power available is greater than the
 term gain problem. In this case, it may prove             power required, the excess power will, allow a
 necessary to begin climb out at or near the take-         rate of climb specific to the magnitude of excess
 off speed or hold the aircraft on the runway              power. Also, when the power available is
for extra speed and a subsequent zoom. The                 less than the power required, the deficiency of
 problem is su&ciently varied that no general              power produces a rate of descent. This rela-
conclusion can be applied to all jer aircraft and          tionship provides the basis for an important
particular procedures are specified for each air-          axiom of flight technique: “For the conditions
craft in the Flight Handbook.                              of steady flight, the power setting is the pri-
    Of greater general interest in climb per-              mary control of rate of climb or descent”.
formance are the factors which affect the rate of             One of the most important items of climb
climb. The vertical velocity of an airplane                performance is the maximum rate of climb.
depends on the flight speed and the inclination            By the previous equation for rate of climb,
of the flight path. In fact, the rate of climb             maximum rate of climb would occur where
is the vertical component of the flight path               there exists the greatest difference between
velocity.    By the diagram of figure 2.21, the            power available and power required, i.e.,
following relationship is developed:                       maximum (Pa- Pr). Figure 2.21 illustrates
                                                           the climb rate performance with the curves of
                  RC- 101.3 V sin y                        power available and power required versus
                                                           velocity.    The power required curve is again a
                                                           representative airplane which could be powered
then                                                       by either a turbojet or propeller type power-
                                                           plant. The power available curves included
       RC=101.3     V
                                                           are for a characteristic propeller powerplant
a&                                                         and jet powerplant operating at maximum
                    2-v                                    output.
       with Pa=%
                                                              The power curves for the representative pro-
       and   Pr=&                                          peller aircraft show a variation of propulsive
                                                           power typical of a reciprocating engine-pro-
                                                           peller combination.      The maximum rate of
                                                           climb for this aircraft will occur at some speed
RevId     J4mwy     1ws
NAVWEPS 06801-80

 near the speed for (L/D&-.       There is no direct          of climb but the airplane must be operated at
 relationship which establishes this situation                some increase of speed to achieve the ,smaller
 since the variation of propeller efficiency is the          peak climb rate (unless the airplane is compres-
 principal factor accounting for the variation                sibility limited).
 of power available with velocity.      In an ideal              The effect of altitude on climb performance
 sense, if the propeller efficiency were constant,            is illustrated by the composite graphs of figure
 maximum rate of climb would occur at the                     2.22. Generally, an increase in altitude will
 speed for minimum power required. How-                       increase the power required and decrease the
ever, in the actual case, the propeller efficiency            power available. Hence, the climb perform-
of the ordinary airplane will produce lower                   ance of an airplane is expected to be greatly
power available at low velocity and cause the                 affected by altitude.    The composite chart of
maximum rate of climb to occur at a speed                     climb performance depicts the variation with
greater than that for minimum power required.                 altitude of the speeds for maximum rate of
   The power curves for the representative. jet              climb, maximum angle of climb, and maximum
aircraft show the near linear variation of power              and minimum level flight airspeeds. As alti-
available with velocity.       The maximum rate              tude is increased, these various speeds finally
of climb for the typical jet airplane will occur             converge at the absolute ceiling of the airplane.
at some speed much higher than that for max-                 At the absolute ceiling, there is no excess of
imum rate of climb of the equivalent propeller               power or thrust and only one speed will allow
powered airplane. In part, this is accounted                 steady level flight.     The variation of rate of
for by the continued increase in power avail-                climb and maximum level flight’ speed’with
able with speed. Note that a 50 percent in-                  altitude for the typical propeller powered air-
increase in thrust by use of an afterburner may              plane give evidence of the effect of supercharg-
cause an increase in rate of climb of approxi-               ing. Distinct aberrations in these curves take
mately 100 percent.                                          place at the supercharger critical altitudes and
   The climb performance of an airplane is                   ~blower shift points.      The curve of time to
affected by many various factors. The con-                   climb is the result of summing.up the incre-
ditions of maximum climb angle or climb rate                 ments of time spent climbing through incre-
occur at specific speeds and variations in speed             ments of altitude. Note that approach to the
will produce variations in climb performance.                absolute ceiling produces tremendous increase
Generally, there is sufficient latitude that small           in the time curve.
variations in speed from the optimum do not                      Specific reference points are established by
produce large changes in climb performance                   these composite curves of climb performance.
and certain operational items may require                    Of course, the absolute ceiling of the airplane
speeds slightly different from the optimum.                  produces zero rate of climb. The serviceceiling
Of course, climb performance would be most                   is specified as the altitude which produces a
critical at high weight, high altitude, or dur-              rate of climb of 100 fpm. The altitude which
ing malfunction of a powerplant.       Then, opti-           produces a rate of climb of 500 fpm is termed
mum climb speeds are necessary. A change                     the combatceiling. Usually, these specific refer-
in airplane weight produces a twofold effect                 ence points are provided for the airplane at
on climb performance. First, the weight, W,                  the combat configuration or a specific design
appears directly in denominator of the equa-                 configuration.
tions for ,both climb angle and climb rate.                      The composite curves of climb performance
In addition, a change in weight will alter the               for the typical turbojet airplane are shown in
drag and power required. Generally, an in-                   figure 2.22. One particular point to note is
crease in weight will reduce the maximum rate                the more rapid decay of climb performance
                                                                              NAVWEPS C&801-80
                                                                          AIRPLANE PERFORMANCE

                   RATE OF,CL!MB_,                           _-

                                                           tiAXlMUM LEVEL FLIGHT SPEED

                                                                HIGH BLOWER CRITICAL ALTITUDE
                                                      FEE0 FOR MA% R c

                                                            LOW BLOWER CRITICAL ALTITUDE

                   = y$y               VELOCITY, KNOTS



                                             \                         MAXIMUM LEVEL
                                                  \                     FLIGHT SPEED

                                                                      -RATE        OF CLIMB
           I         I                   I                  I                          b
                                 VELOCITY, KNOTS

                               POWER OFF DESCENT PERFORMANCE


                                         MINIMUM POWER REP’

               I                VELOCITY, KNOTS
               Figure UP,   Climb ad     Desceni Pedormome

with altitude above the tropopause. This is                 conditions of steady level flight will define
due in great part to the more rapid decay of                various rates of fuel flow throughout the range
engine thrust in the stratosphere.                          of flight speed. The first graph of figure 2.23
   During a power off descent the deficiency of             illustrates a typical variation of fuel flow versus
thrust and power define the angle of descent                velocity.    The specific range can be defined by
and rate of descent. TWO particular points                  the following relationship:
are of interest during a power off descent:
minimum angle of descent and minimum rate                                              nautical miles
                                                                    specific raw=        lbs, of fuel
of descent. The minimum angle of descent
would provide maximum glide distance through
the air. Since no thrust is available from the                                    nautical miles/hr.
power plant, minimum angle of descent would                         pecific range= lbs. of fuel/hr.
be obtained at (L/D)-.       At (L/D),,     the             thus,
deficiency of thrust is a minimum and, as                                                  velocity, knots
shown by figure 2.22, the greatest proportion                       specific range =
                                                                                       fuel flow, lbs. per hr.
between velocity and power required is ob-
tained.    The minimum rate of descent in                   If maximum specific range is desired, the flight
power off flight is obtained at the angle of                condition must provide a maxinium of velocity
attack and airspeed which produce minimum                   fuel flow. This particular point would be
power required. For airplanes of moderate                   located by drawing .a straight line from the
aspect ratio, the speed for minimum rate of                 origin tangent to the curve of fuel flow versus
descent is approximately 75 percent of the                  velocity.
speed for minimum angle of descent                             The general item of range must be clearly
                                                            distinguished from the item of endurance. The
RANGE PERFORMANCE                                           item of range involves consideration of flying
                                                            distance while enduranceinvolves consideration
   The ability of an airplane to convert fuel               of flying time. Thus, it is appropriate to define
energy into flying distance is one of the most              a separate term, “specific endurance.”
important items of airplane performance. The
problem of eficient range operation of an air-                                           flight hours
                                                               specific endurance=
plane appears of two general forms in flying                                               lb. of fuel
operations: (1) to extract the maximum flying
distance from a given fuel load or (2) to fly a                                          flight hours/hr.
specified distance with minimum expenditure                    specific endurance =
                                                                                          lbs. of fuel/hr.
of fuel. An obvious common denominator for                  then,
each of these operating problems is the “spe-                                                       1
cific range, ” nautical miles of flying distance               specific endurance=
                                                                                         fuel flow, lbs. per hr.
per lb. of fuel. Cruise flight for maximum
range cond.itions should be conducted so that               By this definition, the specific endurance is
the airplane obtains maximum specific range                 s&ply the reciprocal of the fuel ~flow. Thus,
throughout the flight.                                      .ifl.maximum endurance is desired, the flight
    GENERAL       RANGE        PERFORMANCE.                 condition ‘ must provide a minimum of fuel
The principal items of range performance can                 flow. This point is readily appreciated as the
be visualized by use of the illustrations of figure          lowest point of the curve of fuel flow versus
2.23. From the characteristics of the aero-                  velocity.  Generally, in subsonic performance,
dynamic configuration and the powerplant, the                the speed at which maximum endurance is

                                                                        NAVWEPS 00-501-50
                                                                    AIRPLANE PERFORMANCE

           I                                          APPLICABLE     FOR A
                                                      PARTICULAR:    WEIGHT
                MAXIMUM                                              ALTITUDE
  FUEL         ENDURANCE                                             CONFIGURATION

                                                LINE FROM ORIGIN
                                               TANGENT TO CURVE

                           VELOCITY,   KNOTS


                                                99% MAXIMUM RANGE

 RANGE                                              APPLICABLE     FOR A PARTICLAR

                           VELOCITY,   KNOTS

                                                  AREA REPRESENTS

                      Figure 2.23. Geneml Range Performance

NAVWEPS oo-80~~80

obtained is approximately 75 percent of the          initial weight of the airplane will require spe-
speed for maximum range.                             cific values of airspeed, altitude,’ and power
    A more exact analysis of range may be ob-        setting to produce the recommended cruise
tained by a plot of specific range versus velocity   condition.    As fuel is consumed and the air-
similar to the second graph of figure 2.23. Of       plane gross weight decreases, the optimum ai,r-
course, the source of these values of specific       speed and power setting may decrease or the
range is derived by the proportion of velocity       optimum altitude may increase. Also, the
and fuel flow from the previous curve of fuel        optimum specific range will increase. The
flow versus velocity.     The maximum specific       pilot must provide the proper cruise control
range of the airplane is at the very peak of the     technique to ensure that the optimum condi-
curve. Maximum endurance point is located            tions are maintained.
by a straight line from the origin tangent to           The final graph of figure 2.23 shows a typical
the curve of specific range versus velocity.         variation of specific range with gross weight
This tangency point defines a maximum of             for some particular cruise operation. At the
(nmi/lb.) per (nmi/hr.) or simply a maximum          beginning of cruise the gross weight is high
of (hrs./lb.).                                       and the specific range is low. As fuel is con-
   While the very peak value of specific range       sumed, and the gross weight reduces, the
would provide maximum range operation, long          specific range increases. .This’ type of curve
range cruise operation is generally recom-           relates the range obtained by the expenditure
mended at some slightly higher airspeed.             of fuel .by the crosshatched area between the
Most long range cruise operation is conducted        gross weights at beginning and end of cruise.
at the flight condition which provides 99 per-       For example, if the airplane begins cruise at
cent of the absolute maximum specific range.         18,500 Jbs. and ends cruise at 13,000 lbs., 5,500
The advantage of such operation is that 1            lbs. of fuel is expended. If the average spe-
percent of range is traded for 3 to 5 percent        cific range were 0.2 nmi/Jb., the total range
higher cruise. velocity.   Since the higher cruise   would be:
speed has a great number of advantages, the
small sacrifice of range is a fair bargain. The               range=(0.2)$         (5,500) lb.
curves of specific range versus velocity are                        = 1,100 nmi.
affected by three principal variables: airplane
gross weight, altitude, and the external aero-          Thus, the total range is dependent on both
dynamic configuration of the airplane. These         the fuel available and the specific range. When
curves are the source of range and endurance         range and economy of operation predominate,
operating data and are included in the per-          the pilot must ensure that the airplane will be
formance section of the flight handbook.             operated at the recommended long range cruise
    “Cruise control” of an airplane implies that     condition.    By this procedure, the airplane
the airplane is operated to maintain the recom-      will be capable of its,maximum design operat-
mended long range cruise condition through-          ing radius or flight distances less than the
out the flight.    Since fuel is consumed during     maximum can be achieved with a maximtim of
cruise, the gross weight of the airplane will        fuel reserve at the destination.
 vary and optimum airspeed, altitude, and               RANGE,      PROPELLER         DRIVEN     AIR-
 power setting can vary, Generally, “cruise          PLANES. The propeller driven airplane com-
 control” means the control of optimum air-          bines the propeller with the reciprocating
 speed, altitude, and power setting to maintain      engine or the gas turbine for propulsive power.
 the 99 percent maximum specific range condi-        In the case of either the reciprocating engine or
 tion. At the beginning of cruise, the high           the gas turbine combination, powerplant fuel
                                                                                            NAVWEPS OS80140
                                                                                        AIRPLANE PERFORMANCE

flow is determined mainly by the shaft poluet                                    v*-    E
put into the propeller rather than thrust. Thus,                                 -4
                                                                                 VI      K
 the powerplant fuel flow could be related di-
 rectly to power required to maintain the air-                                   pr*        *
                                                                                        w* s’
 plane in steady, level flight. This fact allows                                 PC
                                                                                 -=H    WI
 study of the range of the propeller powered                                    SRs    WI
airplane by analysis of the curves of power                                        SRI W,
required versus velocity.                                      where
   Figure 2.24 illustrates a typical curve of                        condition (1) applies to some known condi-
power required versus velocity which, for the                           tion of velocity, power required, and
propeller powered airplane, would be analo-                             specific range for (L/D),., at some basic
gous to the variation of fuel flow versus veloc-                        weight, WI
ity. Maximum endurance condition would be                            condition (2) applies to some new values of
obtained at the point of minimum power re-                              velocity, power required, and specific
quired since this would require the lowest fuel                         range for (L/D),.,     at some different
flow to keep the airplane in steady, level flight.                      weight, WI
Maximum range condition would occur where                      and,
the proportion between velocity and power re-                        V= velocity, knots
quired is greatest and this point is located by                      W= gross weight, Jbs.
a straight line from the origin tangent to the                       Pr=power required, h.p.
curve.                                                              SK= specific range, nmi/lb.
   The maximum range condition is obtained                     Thus a 10 percent increase in gross weight
at maximum lift-drag ratio and it is important                 would create:
to note that (L/D),,         for a given airplane                    a 5 percent increase in velocity
configuration occurs at a particular angle of                        a 15 percent increase in power required
attack and li5t coefficient and is unaffected by                     a 9 percent decrease in specific range
weight or altitude (within           compressibility           when flight is maintained at the optimum con-
limits).    Since approximately 50 percent of                  ditions of (L/D),.,.      The variations of veloc-
the total dra.g a’ (L/D)*
                    t          is induced drag, the            ity and power required must be monitored by
propeller powered airplane which is designed                   the pilot as part of the cruise control to main-
specifically i3r IJong range will have a strong                tain .(L/D),.+      When the airplane fuel weight
preference for rbe thigh aspect rario planform.                is a small part of the gross-weight and the range
   The effect ,df tihe variation of airplane gross             is small, then cruise control procedure can be
weight is illustrated by the second graph of                   simplified to essentially a constant speed and
figure 2.24. ‘  The flight condition of (L/D),.,               power setting throughout cruise. However,
                                                               the long range airplane has a fuel weight which
is achieved a’  t,one-particular value of lift coefIi-
                                                               is a conside’  rable part of the gross weight and
cient for a given airplane configuration.
                                                               cruise control procedure must employ sched-
Hence, a variation of gross weight will alter                  uled airspeed and power changes to maintain
the values of airspeed, power required, and spe-               optimum range conditions.
cific range obtained at (L/D)m.r.         If a given               The effect of altitude on the range of the
configuration ‘ airplane is operated at con-                   propeller powered airplane may be appreciated
stant altitude and the lift coefficient for                     by inspection of the final graph of figure 2.24.
WDL          the following       relationships will             If a given configuration of airplane is operated
awb :                                                           at constant gross weight and the lift coefficient


                                  GENER,AL. RANGE CONDITIONS
                                     PROPELLER   AIRPLANE

        POWER                                                            APPLICABLE   FOR
        REO’                                                             A PARTICULAR
         HP            MAXIMUM                                           -WEIGHT
                       ENDURANCE                                         -ALTITUDE

                                           VELOCITY,    KNOTS

                                      EFFECT    OF GROSS WEIGHT
                                                                     HlGHER   WT.


                                           VELOCITY,    KNOTS

                  A                    EFFECT    OF ALTITUDE
                                                                   AT ALTITUDE
                  t                             SEA    LEVEL


                  I                        VELOCITY,    KNOTS
                       Figure 2.24.   Range Performance, Propeller Aircraft
                                                                                          NAWEPS oo-EOT-80
                                                                                       AWPLANE PERFORMAhlCE

for WD)m.z, change
          a              in altitude will produce           If compressibility     effects are negligible,     any
the following   relationships:                               variation of ~peci)c range with altitude is strictly a
                                                            function of engine-propeller pcrformanCC.
                                                               The airplane equipped with the reciprocating
                                                            engine will experience very little, if any,
                                                            variation of specific range with altitude at low
                                                            altitudes,    There is negligible variation of
                                                            brake specific fuel consumption for values of
where                                                       BHP below the maximum cruise power rating
    condition (I) applies to some known condi-              of the powerplant which is the auto-lean or
       tion of velocity and power required for              manual lean range of engine operation.      Thus,
       W’ ),,,,,z at some original, basic altitude          an increase in altitude will produce a decrease
    condirion (2) applies to some new values of             in specific range only when the increased power
       velocity and power required for (L/D),,              requirement exceeds the maximum cruise power
       at some different altitude                           rating of the powerplants.     One advantage of
and                                                         supercharging is that the cruise power may be
     V= velocity, knots (TAX, of course)                    maintained at high altitude and the airplane
    Pr=power required, h.p.                                 may achieve the range at high altitude with
      o=altitude density ratio (sigma)                      the corresponding increase in TAS. The prin-
Thus, if flight is conducted at 22,000 ft.                  cipal differences in the high altitude cruise and
(o=O.498), the airplane will have:                          low altitude cruise are the true airspeeds and
    a 42 percent higher velocity                            climb fuel requirements.
    a 42 percent higher power required                         The airplane equipped with the turboprop
                                                            powerplant will exhibit a variation of specific
than when operating at sea level. Of course,                range with altitude for two reasons. First,
the greater velocity is a higher TAS since the              the specific fuel consumption (c) of the turbine
airplane at a given weight and lift coefficient             engine improves with the lower inlet tem-
will require the same PAS independent of                    peratures common to high altitudes.          Also,
altitude.    Also, the drag of the airplane at              the low power requirements to achieve opti-
altitude is the same as the drag at sea level but           mum aerodynamic conditions at low altitude
the higher TAS causes a proportionately                     necessitate engine operation at low, inefficient
greater power required. Note chat the same                  output power. The increased power require-
straight line from the origin tangent to the sea            ments at high .altitudes allow the turbine
level power curve also is tangent to the                    powerplant to operate in an efficient output
altitude power curve.                                       range. Thus, while the airplane has no
   The effect of altitude on specific range can be          particular preference for altitude, the power-
appreciated from the previous relationships.                plants prefer the higher altitudes and cause
If a change in altitude causes identical changes            an increase in specific range with altitude.
in velocity and power required, the proportion              Generally, the upper limit of altitude for
of velocity to power required would be un-                  efficient cruise operation is defined by airplane
changed. This fact implies that the specific                gross weight (and power required) or com-
range of the propeller powered airplane would               presslbility effects.
be unaffected by altitude.      In the actual case,            The optimum climb and descent for the
this is true to the extent that powerplant specif-          propeller powered airplane is affected by
ic fuel consumption (c) and propeller efficiency            many different factors and no general, all-
(qp) are the principal factors which could                  inclusive relationship is applicable.       Hand-
cause a variation of specific range with altitude.           book data for the specific airplane and various

operational factors will define operating pro-             On the other hand, since approximately 75
cedures.                                                   percent of the total drag is parasite drag, the
     RANGE, TURBOJET AIRPLANES.             Many           turbojet airplane designed specifically for long
different factors influence the range of the               range has the special requirement for great
 turbojet airplane. In order to simplify the               aerodynamic cleanness.
 analysis of the overall range problem, it is                  The effect of the variation of airplane gross
convenient to separate airplane factors from               weight is illustrated by the second graph
powerplant factors and analyze each item                   of figure 2.25. The flight condition           of
 independently.      An analogy would be the               (mc D1IMI is achieved at one value of lift
study of “horsecart” performance by separat-               coefbcient for a given airplane in subsonic
 ing “cart” performance from “horse” per-                  flight.   Hence, a variation of gross weight will
formance to distinguish the principal factors              alter the values of airspeed, thrust required,
which affect the overall performance.                      and specific range obtained at ,(&/CD)-.        If
     In the case of the turbojet airplane, the             a given configuration is operated at constant
 fuel flow is determined mainly by the thrust              altitude and lift coefficient the following re-~
 rather than power. Thus, the fuel flow could              lationships will apply:
 be most directly related to the thrust required
 to maintain the airplane in steady, level flight.
.This fact allows study of the turbojet powered
 airplane by analysis of the curves of thrust
required versus velocity.       Figure 2.25 illu-
 strates a typical curve of thrust required versus
 velocity which would be (somewhat) analo-                          SR2
 gous to the variation of fuel flow versus veloc-                   SRI          (constant .altitude)
 ity. Maximum endurance condition would                    where
 be obtained at (L/D)-      since this would incur
 the lowest fuel flow to keep the airplane in                    condition (1) applies to some! known condi-
 steady, level flight. Maximum range condition                     tion of velocity, thrust required, and
 would occur where the proportion between                          specific range for (&/CD)-        at some
 velocity and thrust required is greatest and                      basic weight, Wi
 this point is located by a straight line from                   condition (2) applies to some new values of
 the origin tangent to the curve.                                  velocity, thrust required, and specific
     The maximum range is obtained at the aero-                    range for (&/CD)-        at some different
 dynamic condition which produces a maximum                        weight, W,
 proportion between the square root of the                 and
 lift coefficient (CJ and the drag coe&cient                      V= velocity, knots
 (CD), or (&/CD)-.         In subsonic perform-                   W=gross weight, lbs.
 ance, (G/C D>- occurs at a particular value                      Tr= thrust required, lbs.
 angle of attack and lift coefficient and is un-                 .SR= specific range, nmi/lb.
 affected by weight or altitude (within com-               Thus, a 10 percent increase in gross weight
pressibility limits).    At this specific aerody-          would create:
 namic condition, induced drag is approxi-                       a 5 percent increase in velocity
 mately 25 percent of the total drag so the                      a 10 percent increase in thrust required
 turbojet airplane designed for long range does                  a 5 percent decrease in specific range
 not have the strong preference for high aspect            when flight is maintained at the optimum con-
ratio planform like the propeller airplane.                ditions of (&/CD)-.       Since most jet airplanes
                                                                        NAVWEPS 00-8OT-80
                                                                    AIRPLANE PERFORMANCE

                              GENERAL RANGE CONDITIONS

                   MAXIMUM               MAXIMUM
THRUST            ENDURANCE                                  APPLICABLE    FOR
 REO’ D                                                        A PARTICULAR
  LBS                                                         -WEIGHT

                                   VELOCITY,       KNOTS

                              EFFECT OF GROSS WEIGHT



                                EFFECT    OF ALTITUDE


                                           .%A LEVEL
                                           SEA                    AT ALTITUDE

 REP’0                                       /

          7                        VELOCITY.       KNOTS

                   Ftgure P.25. Rangt Performoncr, Jet Aircraft
NAVWEPS 00-801-80

have a fuel weight which is a large part of the            same thrust required must be obtained with a
gross weight, cruise control procedures will be            greater engine RPM.
necessary to account for the changes in opti-                  At this point it is necessary to consider the
mum airspeeds and power settings as fuel is                effect of the operating condition on powerplant
consumed.                                                  performance. An increase in altitude will im-
   The effect of altitude on the range of the              prove powerplant performance in two respects.
turbojet airplane is of great importance be-               First, an increase in altitude when below the
cause no other single item can cause such large            tropopause will provide lower inlet Gr tem-
variations of specific range. If a given con-              peratures which redqce the specific fuel con-
figuration of airplane is operated at constant             sumption (c~). Of course, above the tropo-
gross weight and the lift coefficient for                  pause the specific fuel consumption tends to
(JCL/CDL, a change in altitude will produce                increase. A; low altitude, the engine RPM
the following relationships:                               necessary to produce the required thrust is low
                                                           and, generally, well below the normal rated
       -=     -
              3                                            value. Thus, a second benefit of altifude on
       VI   J .Y*                                          engine performance is due to the increased
        Tr=constant    (neglecting compressibility         RPM required to furnish cruise thrust. An
            effects)                                       increase in engine speed to the normal rated
                                                           value will reduce the specific fu,el consumption.
      -=    - (neglecting factors affecting en-
            3                                                  The increase in specific range with altitude
      JR1 J rJ* gine performance)                          of the turbojet airplane can be attributed to
                                                           these three factors:
                                                                 (1) An increase in altitude will increase the
      condition (I) applies some known condition              proportion of (V/Tr) and provide a greater
        of velocity, thrust required, and specific             TAS for the same TY.
        range for (&QCD),,       at some original,               (2) An increase in altitude in the tropo-
        basic altitude.                                        sphere will produce lower inlet air temperature
      condition (2) applies to some new values of              which reduces the specific.fuel consumption.
        velocity, thrust required, and specific                  (3) An increase in altitude requires in-
        range for (fi/CD)mm at some different                 creasedengine RPM to provide cruise thrust
        altitude.                                              and the specific fuel consumption reduces as
and                                                            normal rated RPM is approached.
                                                           The combined effect of these three factors de-
       V= velocity, knots (TAX, of course)
                                                           fines altitude as the one most important item
       Tr= thrust required, lbs.
                                                           affecting the specific range of the turbojet air-
      JR= specific range, nmi/lb.
        a=altitude density ratio (sigma)                   Pl ane. As an example of this combined’     effect,
                                                           the typical turbojet airplane obtains a specific
Thus, if flight is conducted at 40,000 ft.                 range at 40,ooO ft. which is approximately 150
(u=O.246), the airplane will have:                         percent greater than that obtained at sea leirel.
    a 102 percent higher velocity                          The increased TAS accounts for approxi-
    the same thrust required                               mately two-thirds of this benefit while in-
    a 102 percent higher specific range                    creased engine performance (reduced cJ ,~ac-    ‘
    (even when the beneficial effects of altitude          counts for the other one-third of the benefit.
    on engine performance are neglected)                   For example, at sea level the maximum spe-
                                                           cific range of a turbojet airplane may be 0.1
than when operating at sea level. Of course,               nmi/lb. but at 40,000 ft. the maximum specific
the greater velocity is a higher TAJ and the               range would be approximately 0.25 nmi/lb.
                                                                                       NAVWEPS OO-BOT-RO
                                                                                   AIRPLANE PERFORMANCE

    From the previous analysis, it is apparent             not restrained to a particular altitude, main-
that the cruise altitude of the turbojet should            taining the same lift coeAicient and engine
be as high as possible within compressibility              speed would allow the airplane to climb as the
or thrust limits. Generally, the optimum alti-             gross weight decreases. Since altitude gen-
tude to begin cruise is the highest altitude at            erally produces a beneficial effect on range, the
which the maximum continuous thrust can                    climbing C&SC implies a more efficient flight
provide the optimum aerodynamic conditions.                path.
Of course, the optimum altitude is determined                 The cruising flight of the turbojet airplane
mainly by the gross weight at the begin of                 will begin usually at or above the tropopause
cruise. For the majority of turbojet airplanes             in order to provide optimum range conditions.
this altitude will be at or above the tropopause           If flight is conducted at (a/&)-,       optimum
for normal cruise configurations.                          range will be obtained at specific values of lift
    Most turbojet airplanes which have rran-               coefficient and drag coefficient. When the air-
sonic or moderate supersonic performance will              plane is fixed at these values of CL and C, and
obtain maximum range with a high subsonic                  the TAS is held constant, both lift and drag are
cruise. However, the airplane designed spe-                directly proportional to the density ratio, (T.
cifically for high supersonic performance will             Also, above the tropopause, the thrust is pro-
obtain maximum range with a supersonic                     portional to .J when the TAS and RPM are con-
cruise and subsonic operation will cause low               stant. As a result, a reduction of gross weight
lift-drag ratios, poor inlet and engine perform-           by the expenditure of fuel would allow the
ance and redute the range capability.                      airplane to climb but the airplane would re-
    The cruise control of the turbojet airplane            main in equilibrium because lift, drag, and
is considerably ~different from that of the pro-           thrust all vary in the same fashion. This re-
peller driven airplane. Since the specific range           lationship is illustrated by figure 2.26.
is so greatly affected by altitude, the optimum               The relationship of lift, drag, and thrust is
altitude for begin of cruise should be attained            convenient for, in part, it justifies the condi-
as rapidly as is consistent with climb fuel re-            tion of a constant velocity.     Above the tropo-
quirements. The range-climb program varies                 pause, rhe speed of sound is constant hence a
considerably between airplanes and the per-                constant velocity during the cruise-climb
formance section of the flight handbook will               would produce a constant Mach number. In
specify the appropriate procedure. The de-                 this case, the optimum values of (&,/CD), C,
scent from cruise altitude will employ essen-              and C, do not vary during the climb since the
                                                           Mach number is constant. The specific fuel
tially the same feature, a rapid descent is
                                                           consumption is initially constant above the
necessary to minimize the time at low altitudes
                                                           tropopause but begins to increase at altitudes
where specific’range is low and fuel flow is high
                                                           much above the tropopause. If the specific
for a given engine speed.                                  fuel consumption is assumed to be constant
    During cruise flight of the turbojet airplane,         during the cruise-climb, the following rela-
the decrease of gross weight from expenditure              tionships will apply:
of fuel can result in two types of cruise control.
During a constant altitlrdc C&SC, a reduction in               V, M, CL and C, are constant
gross weight will require a reduction of air-                    62 wz
speed and engine thrust ‘ maintain the opti-
                            to                                   61 w,
mum lift coefhcient of subsonic cruise. While                  FR    02
such a cruise may be necessary to conform to                   FFI   ~1
the flow of traffic, it constitutes a certain in-              JR2-W,     (cruise climb above tropopause,
efficiency of operation. If the airplane were                  x-W9         constant M, c,)
NAVWEPS oo-801-80

where                                                       provide a comparison of the total range avail-
    condition (1) applies to some known condi-              able from a constant altitude or cruise-climb
      tion of weight, fuel flow, and specific
       range at some original basic altitude
       during cruise climb.                                            0.0                     Loo0
    con&&r (2) applies to some new values of                            .I                     1.026
      weight, fuel flow, and specific range at                          .2                     1.057
      some different altitude along a partic-                           .3                     1.92
      ular cruise path.                                                 .4                     1.136
                                                                        .5                     1.182
and                                                                     .6                     1.248
     V= velocity, knots                                                 .7                     1.331
     M = Mach number
                                                             For example, if the cruise fuel weight is 50 per-
     W= gross weight, lbs.
                                                             cent of the gross weight, the climbing cruise
    FF=fuel flow, lbs./hr.
                                                             flight path will provide a range 18.2 percent
    JR= specific range, nmi./lb.
                                                             greater than cruise at constant ,altitude. This
      e=altitude density ratio
                                                             comparison does not include consideration of
Thus, during a cruise-climb flight, a 10 percent             any variation of specific fuel consumption dur-
decrease in gross weight from the consumption                ing cruise or the effects of compressibility in
of fuel would create:                                        defining the optimum aerodynamic conditions
     no change in Mach number or ‘     TAS                   for cruising flight.   However, the comparison
     a 5 percent decrease in EAS                             is generally applicable for aircraft which have
     a 10 percent decrease in C, i.e., higher                subsonic cruise.
        altitude                                                When the airplane has a supersonic cruise for
     a 10 percent decrease in fuel flow                      maximum range, the optimum flight path is
     an 11 percent increase in specific range                generally one of a constant Mach number.
                                                             The optimum flight path is generally-but     not
An important comparison can be made between                 necessarily-a climbing cruise. In this case of
the constant altitude cruise and the cruise-                 subsonic. or supersonic cruise, a Machmeter is
climb with respect to the variation of specific             of principal importance in cruise control of the
range. From the previous relationships, a                    jet airplane.
2 percent reduction in gross weight durmg                       The @ct of wind on nznge is of considerable
                                                            importance in flying operations. Of course,
                                                            a headwind will always reduce range and a
                                                            tailwind will always increase range. The
                                                            selection of a cruise altitude with the most
                                                            favorable (or least unfa:vorable) winds is a rel-
                                                            atively simple matter for the case of the
cruise would create a 1 percent increase in                 propeller powered airplane. Since the range of
specific range in a constant altitude cruise but            the.propeller powered airplane is relatively un-
a 2 percent increase in specific range in a cruise-         affected by altitude, the altitude with the most
climb at constant .Mach number. Thus, a                     favorable winds is selected for range. However,
higher average specific range maintained             the range of the turbojet airplane is greatly
during the expenditure of a given increment of              affected by altitude so the selection of an op-
fuel. If an airplane begins a cruise at optimum             timum altitude will involve considering the
conditions at or above the tropopause with a                wind profile ‘  with the variation of range with
given weight of fuel, the following           data          altitude.    Since the turbojet range increases
                                                                    NAVWEPS 00-801-80
                                                                AIRPLANE PERFORMANCE

                      TURBOJET CRUISE-CLIMB

                                              IF CL AND TAS ARE CONSTANT,
                                              LIFT IS PROPORTIONAL TOE



                                              WEIGHT DECREASES AS FUEL IS

                       EFFECT    OF WIN0    ON RANGE

                                (SPEEDS FOR MAXIMUM
                               GROUNO NAUTICAL ,MlLES
      FUEL                         PER LB. OF FUEL)
     LBS/HR                                   HEADWIND
                I                                 I         /

                                       VELOCITY, KNOTS

                      Figure 2.26.   Range Performance

NAVWEPS 00401-60

 greatly with altitude, the turbojet can tolerate         The specific endurance is simply the reciprocal
 less favorable (or more unfavorable) winds               of the fuel flow, hence maximum endurance
 with increased altitude.                                 conditions would be obtained at the lowest
    In some cases, large values of wind may              fuel flow required to hold the airplane in steady
 cause a significant change in cruise velocity to         level flight. Obviously, minimum fuel flow
 maintain maximum ground nautical miles per               will provide the maximum flying time from a
lb. of fuel. As an example of an extreme con-            given quantity of fuel. Generally, in subsonic
 dition, consider an airplane flying into a head-        performance, the speed at which maximum en-
wind which equals the cruise velocity.     In this       durance is achieved is approximately 75 per-
 case, ““9 increase in velocity would improve            cent of the speed for maximum range.
range.                                                       While many different factors can affect the
    To appreciate the changes in optimum speeds          specific endurance, the most important factors
with various winds, refer to the illustration of         at the control of the pilot are the configuration
figure 2.26. When zero wind conditions exist,            and operating altitude.      Of course, for maxi-
a straight line from the origin tangent to the           mum endurance conditions the airplane must
curve of fuel flow versus velocity will locate            be in the clean configuration and operated at
maximum range conditions.          When a head-          the proper aerodynamic conditions.
wind condition exists, the speed for maximum                 EFFECT OF ALTITUDE              ON ENDUR-
ground range is located by a line tangent drawn          ANCE, PROPELLER DRIVEN AIRPLANES.
from a velocity offset equal to the headwind             Since the fuel flow of the propeller driven air-
velocity.    This will locate maximum range at           plane is proportional to power required, the
some higher velocity and fuel flow. Of course,           propeller powered airplane will achieve maxi-
the range will be less than when at zero wind            mum specific endurance when operated at mini-
conditions but the higher velocity and fuel flow         mum power required. The point of minimum
will minimize the range loss due to the head-            power required is obtained at a specific value
wind.     In a similar sense, a tailwind will re-        of lift coefficient for a particular airplane con-
duce the cruise velocity to maximize the                 figuration and is essentially independent of
benefit of the tailwind.                                 weight or altitude.      However, an increase in
   The procedure of employing different cruise           altitude will increase the value of the minimum
velocities to account for the effects of wind is         power required as illustrated by figure 2.27.
necessary only at extreme values of wind                 If the specific fuel consumption were not in-
velocity.    It is necessary to consider the             fluenced by altitude or engine power, the spe-
change in optimum cruise airspeed when the               cific endurance would be directly proportional
wind velocities exceed 25 percent of the zero            to ji, e.g., the specific endurance at 22,000 ft.
wind cruise velocity.                                    (a=O.498) would be approximately 70 percent
                                                         of the value at sea level. This example is very
ENDURANCE       PERFORMANCE                              nearly the case of the airplane with the recipro-
   The ability of the airplane to convert fuel           cat&g enginesince specific fuel consumption and
energy into flying time is an important factor           propeller efficiency are not directly affected by
in flying operations. The “specific endurance”           altitude.    The obvious conclusion is that
of the airplane is defined as follows:                   maximum endurance of the reciprocating en-
                                                         gine airplane is obtained at the lowest practical
    specific endurance==1                                altitude.
                                                            The variation with altitude of the maximum
                                      1                  endurance of the turboprop airplane requires
    specific endurance=
                          fuel flow, Ibs. per hr.        consideration of powerplant factors in addition
                                                                                         iiEPS Oo-801-80
                                                                                  AIRPLANE PERFORMANCE

                           EFFECT OF ALTlTUOE ON MINIMUM
                                   POWER REO’ D

                                                                     AT ALTITUDE

                                        SEA.LEVEL                        /
                                                                                WEIGHT 8

                                VELOCITY, KNOTS

                          EFFECT OF ALTITUDE ON MINIMUM
                                 THRUST REO’ D

                                     SEA LEVEL                                     AT ALTITUDE
T;;;g                               D
                  MINIMUM THRUST REO’
    LBS                                                                             /’

                                                                ,’                    WEIGHT 8


                                VELOCITY, KNOTS
                        Figure 2.27. Endurance Performance


to airplane factors. The turboprop power-                   airplane will have a maximum specific endur-
plant prefers operation at low inlet air tem-               ance at 35,ooO ft. which is at least 40 percent
peratures and relatively high power setting to              greater than the maximum value at sea level.
produce low specific fuel consumption.       While          If the turbojet airplane is at low altitude and
an increase in altitude will increase the mini-             it is necessary to hold for a considerable time,
mum power required for the airplane, the                    maximum time in the air will be obtained by
powerplant achieves more efficient operation.               beginning a climb to some optimum altitude
As a result of these differences, maximum en-               dependent upon the fuel quantity available.
durance of the multiengine turboprop airplane               Even though fuel is expended during the climb,
at low altitudes may require shutting down                  the higher altitude will provide greater total
some of the powerplants in order to operate                 endurance. Of course, the use of afterburner
the remaining powerplants at a higher, more                 for the climb would produce a prohibitive re-
efficient power setting.                                    duction in endurance.
    EFFECT OF ALTITUDE            ON ENDUR-                 OFl4X’  TIMUM         RANGE AND         ENDUR-
ANCE, TURBOJET AIRPLANES.                 Since the               ANCE
fuel flow of the turbojet powered airplane is                   There are many conditions of flying oper-
proportional to thrust required, the turbojet               ations in which optimum range or endurance
airplane will achieve maximum specific endur-               conditions are not possible or practical.      In
ance when operated at minimum thrust re-                    many instances, the off-optimum conditions
quired or (L/D),.           In subsonic flight,             result from certain operational requirements
(L/D)m~ occurs at a specific value of lift                  or simplification of operating procedure. In
coefBcient for a given airplane and is essentially          addition, off-optimum performance may be the
independent of weight or altitude.       If a given         result of a powerplant malfunction or failure.
weight an~dconfiguration of airplane is oper-                The most important conditions are discussed
ated at various altitudes, the value of the                 for various airplanes by powerplant type.
minimum thrust required is unaffected by the                   RECIPROCATING             POWERED        AIR-
curves of thrust required versus velocity shown              PLANE. In the majority of cases, the recipro-
in figure 2.27. Hence, it is apparent that the                                                     an
                                                             cating powered airplane is operated at’ engine
aerodynamic configuration has no prefeience                  dictated cruise. Service use will most probably
for altitude (within      compressibility limits)            define some continuous power setting which
and specific endurance is a function only of                 will give good service life and trouble-free
engine performance.                                          operation of the powerplant.     When range or
    The specific fuel consumption of the turbojet            endurance is of no special interest, the simple
 engine is strongly affected by operating RPM                expedient is to operate the powerplant at the
 and altitude.    Generally, the turbojet engine             recommended power setting and accept what-
prefers the operating range near normal rated                ever speed, range, or endurance that results.
engine speed and the low temperatures of the                 While such a procedure greatly simplifies the
 stratosphere to produce low specific fuel con-              matter of cruise control, the practice does not
 sumption.     Thus, increased altitude provides             provide the necessary knowledge required for
 the favorable lower inlet air temperature and               operating a high performance, long range
requires a greater engine speed to provide the               airplane.
 thrust required at (L/D)-.          The typical                The failure of an engine on the multiengine
 turbojet airplane experiences an increase in                reciprocating powered airplane has interesting
 specific endurance with altitude with the peak              ramifications.   The first problem appearing is
 values occurring at or near the tropopausc.                 to produce sufficient power from the remaining
For example, a typical single-engine turbojet                engines to keep the airplane airborne. The
                                                                                        NAVWEPS OO-ROT-RO
                                                                                    AtRPLANE PERFORMANCE

 problem will be most .critical if the airplane is             TURBOPROP          POWERED        AIRPLANE.
  at high altitude, high gross weight, and with             The turbine engine has the preference for
  gaps and gear extended. Lower altitude,                   relatively high power settings and high alti-
  jettisoning of weight items, and cleaning up              tudes to provide low specific fuel consumption.
  the airplane will reduce the power required for           Thus, the off-optimum conditions of range or
 flight. Of course, the propeller on the in-                endurance can be concerned with altitudes
  operative engine must be feathered or the                 less than the optimum.        Altitudes less than
 power required may exceed that available from              the optimum can reduce the range but the
 the remaining operating powerplants.                       loss can be minimized on the multiengine
     The effect on range is much dependent on               airplane by shutting down some powerplants
 the airplane configuration.      When the pro-             and operating the remaining powerplants at a
  peller on the’  inoperative engine is feathered,          higher, more efficient output.        In this case
 the added drag is at a minimum, but there is               the change of range is confined to the variation
 added the trim drag ,required to balance                   of specific fuel consumption with altitude.
  the unsymmetrical power. When both these                     Essentially the same situation exists in the
 sources of added drag are accounted for, the              case of engine failure when cruising at optimum
 (L/D)-      ,is reduced but not by significant             altitude.    If the propeller on the inoperative
 amounts. Generally, if the specific fuel con-              engine is feathered, the loss of range will be
 sumption and propeller efficiency do not deteri-          confined to the change in specific fuel con-
 orate, the maximum specific range is not greatly           sumption from the reduced cruise altitude.      If
 reduced. On the twin-engine airplane the                   a critical power situation exists due to engine
 power required must .be furnished by the one              failure, a reduction in altitude provides im-
 remaining engine and this. usually requires               mediate benefit because of the reduction of
 more than the,maximum cruise-rating of the                power required and the increase in power
 powerplant.i As a result the powerplant can-              available from the power plants. In addition,
 not be operated in the auto-lean or manual                the jettisoning of expendable weight items
 lean, power range and the specific ,fuel con-             will improve performance and, of course, the
 sumption increasesgreatly!      Thus, noticeable          clean configuration provides minimum parasite
 loss of range must be anticipated when one                drag.
 engine fails on the twin-engine airplane. The                 Maximum specific endurance of the turbo-
failure of oneengine on the four (or more)                 prop airplane does not vary as greatly with
engine airpla,W may allow the required, power              altitude as the turbojet airplane. While each
to be,develo,ped:by.the three remaining power-             configuration has its own particular operating
plants operating in an economical power range.             requirements, low altitude endurance of the
If the airplane is clean, at low altitude, and             turboprop airplane requires special considera-
 low gross weight, ,the failure of one engine is           tion. The single-engine turboprop will gen-
not likely to cause a, loss of range. However,             eraBy experience an increase in specific endur-
then loss. of ‘ two engines is likely ‘ cause a
                                       to                  ance with an increase in altitude from sea level.
considerable loss of range.                                However, if the airplane is at low altitude and
    When engine failure produces a critical                must hold or endure for a period of time, the
power or range situation, improved perform-                decision to begin a climb or hold the existing
ance is possible with- theairplane in ;the clean           altitude will depend on the quantity of fuel
configuration at low altitude.        Also, jetti-         available. The decision depends primarily on
soning of expendable weight items will reduce              the climb fuel,requirements and the variation of
the power required and improve the specific                specific endurance with altitude.      A somewhat
range.                                                     similar problem exists with the multiengine
                                                                                         NAVWEPS OO-EOT-80
                                                                                     AIRPLANE PERFORMANCE

turboprop airplane but additional factors are              number, cruise-climb, or whatever the appro-
available to influence the specific endurance at           priate technique) will result in a loss of range
low altitude.     In other words, low altitude             capability.
endurance can be improved by shutting down                    The failure of an engine during the optimum
some powerplants and operating the remaining               cruise of a multiengine turbojet airplane will
powerplants at higher, more efbcient power                 cause a noticeable loss of range. Since the
setting. Many operational factors could decide             optimum cruise of the turbojet is generally a
whether such procedure would be a suitable                 thrust-limited cruise, the loss of part of the
technique.                                                 total thrust means that the airplane must
   TURBOJET POWERED AIRPLANE.                  In-         descend to a lower altitude.      For example, if a
creasing altitude has a powerful effect on both            twin-engine jet begins an optimum cruise at
the range and endurance of the turbojet air-               35,000 ft. (e=O.31) and one powerplant fails,
plane. As a result of this powerful effect, the            the airplane must descend to a lower altitude
typical turbojet airplane will achieve maxi-               so that the operative engine can provide the
mum specific endurance at or near the tropo-               cruise thrust. The resulting altitude would be
pause. Also, the maximum specific range will               approximately 16,030 ft. (~=0.61).         Thus, the
be obtained at even higher altitudes since the             airplane will experience a loss of the range
peak specific range generally occurs at the                remaining at the point of engine failure and
highest altitude at which the normal rating of             loss could be accounted for by the reduced
the engine can sustain the optimum aero-                   velocity (TM) and the increase in specific fuel
dynamic conditions.      At low altitude cruise            consumption (c~) from the higher ambient air
conditions, the engine speed necessary to sus-             temperature. In the case of the example air-
tain optimum aerodynamic conditions is very                plane, engine failure would cause a 30 to 40
low and the specific fuel consumption is rela-             percent loss of range from the point of engine
tively poor. Thus, at low altitude, the air-               failure. Of course, the jettisoning of expend-
plane prefers the low speeds to obtain                     able weight items would allow higher altitude
(&/CD)-        but the powerplant prefers the              and would increase the specific range.
higher speeds common to higher engine effi-                    Maximum endurance in the turbojet air-
ciency. The compromise results in maximum                  plane varies with altitude but the variation is
specific range at flight speeds well above the             due to the changes in ‘    fuel flow necessary to
optimum aerodynamic conditions.       In a sense,          provide the thrust required at (I./D),...        The
low altitude cruise conditions are engine                   low inlet air temperature of the tropopause
dictated.                                                  and the greater engine speed reduce the specific
   Altitude is the one most important factor               fuel consumption to a minimum.         If the single-
affecting the specific range of the turbojet               engine turbojet airplane is at low altitude
airplane. Any operation below the optimum                  and must hold or endure for a period of time,
altitude will have a noticeable effect on the               a climb should begin to take advantage of the
range capability     and proper consideration              higher specific endurance at higher altitude.
must be given to the loss of range. In addi-                The altitude to which to climb will be deter-
tion, turbojet airplanes designed specifically for          mined by the quantity of fuel remaining. In
long range will have a large percent of the                 the case of the multiengine turbojet at low
gross weight as fuel. The large changes in                  altitude, some slightly      different procedure
gross weight during cruise will require partic-             may be utilized.   If all powerplants are oper-
ular methods of cruise control to extract the               ating, it is desirable to climb to a higher
maximum flight range. A variation from the                  altitude which is a function of the remaining
optimum flight path of cruise (constant Mach                fuel quantity.   An alternative at low altitude
NAVWEPS oo-80mo

would be to provide the endurance thrust with      the airplane were at a 60’ bank and lift were
some engine(s) shut down and the remaining         not provided to produce the exact load factor
engine(s) operating at a more efficient power      of 2.0, the aircraft would be accelerating in the
output.     This technique would cause a mmi-      vertical direction as well as the horizontal di-
mum loss of endurance if at low altitude.    The   rection and the turn would not be steady.
feasibility of such a procedure is dependent       Also, any sideforce on the aircraft due to
on many operational factors.                       sideslip, etc., would place the resultant aero-
   In all cases, the airplane should be in the     dynamic force out of the plane of symmetry
cleanest possible external configuration because   perpendicular to the lateral axis and the turn
the specific endurance is directly proportional    would not be coordinated.
to the (L/D).                                          As a consequence of the increase lift re-
MANEUVERING          PERFORMANCE ,...s’ .i :.,cyz’ quired to produce the steady turn in a bank,
                                                  ’ihe induced drag is increased above that in-
   When the airplane is’ turning flight, the
                                                   curred by steady, wing level, lift-equal-weight
airplane is not in static equilibrium for there
                                                   flight.    In a sense, the increased lift required
must be developed the unbalance of force to
produce the acceleration of the turn. During       in a steady turn will increase the total drag or
a steady coordinated turn, the lift is inclined    power required in the same manner as increased
to produce a horizontal component of force to       gross weight in level flight.        The curves of
                                                   figure 2.28 illustrate the general effect of turn-
equal the centrifugal force of the turn. In
                                                   ing flight on the total thrust and power re-
addition, the steady turn is achieved by pro-
                                                   quired. Of course, the change in thrust re-
ducing a vertical component of lift which is
                                                   quired at any given speed is due to the change
equal to the weight of the airplane. Figure
                                                    in induced drag and the magnitude of change
2.28 illustrates the forces which act on the
                                                    depends on the value of induced drag in level
airplane in a steady, coordinated turn.
                                                   flight and the angle of bank in .turning flight.
   For the case of the steady, coordinatedturn,
                                                    Since the induced drag generally varies as the
the vertical component oft lift must equal the
                                                    square of C,, the following data provide an
weight of the aircraft so that there will be no
                                                   illustration of the effect of various degrees of
acceleration in the vertical direction.      This
                                                    bank :
requirement leads to the following relation-
                                                                               Load factor, Pcrccnt incrcaw in
                      *=- L                                                         n       induced drag from
                                                                                               lcvcl flight
                      BE-- 1
                          cos q5
                      n=sec $6
       rz= load factor or “G”
      L=lift,   lbs.
      W= weight, Ibs.                              Since the, induced drag predominates at low
       += bank angle, degrees (phi)                speeds, steep turns at low speeds can produce
From this relationship it is apparent that the             significant increases in thrust or power required
steady, coordinated turn requires specific values          to maintain altitude.     Thus, steep turns must
of load factor, n, at various angles of bank, 6.           be avoided after takeoff, during approach, and
For example, a bank angle of 60’ requires a                especially during a critical power situation
load factor of 2.0 (cos 60’=0.5 or set 60’=2.0)            from failure or malfunction of a powerplant.
to provide the steady, coordinated turn. If                The greatly increased induced drag is just as
                                                         NAVWEPS 00-801-80
                                                     AIRPLANE PERFORMANCE

            CENTRIFUGAL      FORCE

        I         I       TURNING     FLIGHT&

        I                     VELOCITY,     KNOTS

                                    LEVEL   FLIGHT

                          VELOCITY,   KNOTS

            Figure 2.28. Effect of Turning Flight

important-if    not more important-as         the         If the airplane were to hold the same angle of
increased stall speed in turning flight.    It is         bank at 500 knots (TAS), the turn radius
important also that any turn be well coordi-              would quadruple (r=22,200 ft.) and the turn
nated to prevent the increased drag attendant             rate would be one-half the original value
to a sideslip.                                            (ROT=2.19 deg. per sec.).
   TURNING      PERFORMANCE.          The hori-              Values of turn radius and turn rate versus
zontal component of lift will equal the centrif-          velocity are shown in figure 2.29 for various
ugal force of steady, turning flight.  This fact          angles of bank and the corresponding load
allows development of the following relation-             factors. The conditions are for the steady,
ships of turning performance:                             coordinated turn at constant altitude but the
                                                          results are applicable for climbing or descend-
turn radius                                               ing flight when the angle of climb or descent
                                                          is relatively small. While the effect of alti-
                     r= 11.26 tan 6
                                                          tude on turning performance is not immediately
                                                          apparent from these curves, the principal effect
      r= turn radius, ft.
                                                          must be appreciated as an increased true air-
    I’ velocity, knots (TAX)
                                                          speed (TAX) for a given equivalent airspeed
     ti = bank angle, degrees
ttrrn rate                                                   TACTICAL PERFORMANCE.                  Many tac-
                 ROT= 1,091 tan rb                        tical maneuvers require the use of the maxi-
                              V                           mum turning capability of the airplane. The
where                                                     maximum turning capability of an airplane will
    ROT=rate of turn, degrees per sec.                    be defined by three factors:
      $= bank angle, degrees                                     (1) Maximum lift capability. The combi-
      v=velocity,  knots, TAS                                nation of maximum lift coefIicient, C,,=,
These relationships define the turn radius, I,               and wing loading, W/S, will define the
and rate of turn, ROT, as functions of the two               ability of the airplane to develop aero-
principal variables: bank angle, +, and velocity,            dynamically the load factors of maneuvering
I’ (TAX).    Thus, when the airplane is flown                flight.
in the steady, coordinated turn at specific                      (2) Optrating ftrcngth limits will define the
values of bank angle and velocity, the turn                  upper limits of maneuvering load factors
rate and turn radius are fixed and independent               which will not damage the primary struc-
of the airplane type. As an example, an air-                 ture of the airplane. These limits must not
plane in a steady, coordinated turn at a bank                be exceeded in normal operations because of
angle of 45’ and a velocity of 250 knots (TAS)               the possibility      of structural damage or
would have the following turn performance:                   failure.
                                                                 (3) Thwt or power limits will define the
                                                             ability of the airplane to turn at constant
                                                             altitude.   The limiting condition would al-
                                                             low increased load factor and induced drag
       = 5,550 ft.                                           until the drag equals the maximum thrust
and                                                          available from the powerplant.        Such a case
                                                             would produce the maximum turning capa-
                           250                               bility for maintaining constant altitude.
                                                             The first illustration of figure 2.30 shows
                      -4.37 deg. per sec.                 how the aerodynamic and structural limits

NAVWEPS 00-801-80

define the maximum turning performance.                     and it produces the minimum turn radius
The acrodynomic limir describes the minimum                 within aerodynamic and structural limitations.
turn   radius available to the airplane when                At speeds less than the maneuver speed, the
operated at C,,,,.     When the airplane is at the          limit load factor is not available aerodynami-
stall speed in level flight, all the lift is neces-         cally and turning performance is aerody-
sary to sustain the aircraft in flight and none             namically limited.    At speeds greater than
is available to produce a steady turn. Hence,               the maneuver speed, CL- and maximum
the turn radius at the stall speed is infinite.             aerodynamic load factor are not available and
As speed is increased above the stall speed, the            turning performance is structurally limited.
airplane at C,,, is able to develop lift greater            When the stall speed and limit load factor
than weight and produce a finite turn radius.               are known for a particular configuration, the
For example, at a speed twice the stall speed,              maneuver speed is related by the following
the airplane at CL,,,,=is able to develop a load            expression:
factor of four and utilize a bank angle of 75.5’
(cos 75.~~ = 0.25). Continued increase in                   where
speed increases the load factor and bank angle                  V,=maneuver speed, knots
which is available aerodynamically but, be-                     V.=stall speed, knots
cause of the increase in velocity and the basic                 n limit = limit load factor
effect on turn radius, the turn radius approaches
 an absolute minimum value. When C,,, is                    For example, an airplane with a limit load
 unaffected by velocity, the aerodynamic mini-              factor of 4.0 would have a maneuver speed
mum turn radius approaches this absolute                    which is twice the stall speed.
value which is a function of C,,,,,,,, W/S, and 6.              The aerodynamic limit line of the first
 Actually, the one common denominator of                     illustration of figure 2.30 is typical of an air-
aerodynamic turning performance is the wing                 plane with a CL, which is invariant with
level stall speed.                                          speed. While this is applicable for the ma-
    The aerodynamic limit of turn radius requires            jority of subsonic airplanes, considerable differ-
 that the increased velocity be utilized to pro-            ence would be typical of the transonic or
 duce increasing load factors and greater angles            supersonic airplane at altitude.        Compressi-
 of bank. Obviously, very high speeds will                  bility effects and changes in longitudinal
 require very high load factors and the absolute            control power may produce a maximum avail-
 aerodynamic minimum turn radius will require               able CL which varies with velocity and an
 an infinite load factor. Increasing speed above            aerodynamic turn radius which is not an
 the stall speed will eventually produce the                 absolute minimum at the maximum of velocity.
 limit load factor and continued increase in                    The second illustration of figure 2.30 describes
 speed above this point will require that load              the constant altitude turning          performance
 factor and bank angle be limited to prevent                of an airplane. When an airplane is at high
 structural damage. When the load factor and                ,altitude, the turning performance at the high
 bank angle are held constant at the structural             speed end of the flight speed range is more
 limit, the turn radius varies as the square of             usually thrust limited rather than structurally
 the velocity and increases rapidly above the               limited.     In flight at constant altitude, the
 aerodynamic limit.      The intersection of ‘ the          thrust must equal the drag to maintain equilib-
 aerodynamic limit and structural limit lines               rium and, thus, the constant altitude turn
 is the ‘   *maneuver speed.” The maneuver                  radius is infinite at the maximum level flight
 speed is the minimum speed necessary to                    speed. Any bank or turn at maximum level
 develop aerodynamically the limit load factor              flight speed would incur additional drag and
                                                                  NAVWEPS 00-801-80
                                                              AIRPLANE PERFORMANCE

                       EFFECT OF AERODYNAMIC AND


                                                            ABSOLUTE MINIMUM

             A--                       I                          t
                          VELOCITY, KNOTS (TAS)

         L             CONSTANT ALTITUDE TURNING

                       BANK ANGLE

RADIUS                                     THRUST OR

                           VELOCITY, KNOTS (TAS)
                     figure 2.30. Maneuvering Performance


cause the airplane to descend. However, as                    speed or minimum flying speed, e.g., 15 per-
speed is reduced below the maximum level                      cent above the stall speed.
flight speed, parasite drag reduces and allows                   (2) The accclcration during the takeoff or
increased load factors and bank angles and                    landing roll. The acceleration experienced
reduced radius of turn, i.e., decreased parasite              by any object varies directly with the un-
drag allows increased induced drag to accom-                  balance of force and inversely as the mass of
modate turns within the maximum thrust                        the object.
available. Thus, the considerations of con-                      (3) The takeoff or landing roll distance is
stant altitude will increase the minimum turn                 a function of both the acceleration and
radius above the aerodynamic limit and define                 velocity.
a particular airspeed for minimum turn radius.             In the actual case, the takeoff and landing dis-
    Each of the three limiting factors (aero-              tance is related to velocity and acceleration in
dynamic, structural, and power) may combine                a .very complex fashion. The main source of
to define the turning performance of an air-               the complexity is that the forces acting on the
                                                           airplane during the takeoff or landing roll are
Pl ane. Generally, aerodynamic and structural             “difficult to define wit,h simple relationships.
limits predominate at low altitude while aero-
dynamic and power limits predominate at high               Since the acceleration is a function of these
                                                           forces, the acceleration is difficult to define in
altitude.   The knowledge of this turning per-
                                                           a simple fashion and it is a principal variable
formance is particularly necessary for effective
                                                           affecting distance. However, some simplifica-
operation of fighter and interceptor types of
                                                           tion can be made to study the basic relatiomhip
                                                           of acceleration, velocity, and distance While
TAKEOFF AND LANDING PERFORMANCE                            the acceleration is not necessarily constant or
   The majority of pilot caused airplane acci-             uniform throughout the takeoff or landing
dents occur during the takeoff and landing                 roll, the assumption of uniformly acceler-
phase of flight.     Because of this fact, the             ated motion will facilitate study of the princi-
Naval Aviator must be familiar with all the                pal variables. affecting takeoff and landing
many variables which influence the takeoff and             distance.
                                                              From basic physics, the relationship of
landing performance of an airplane and must
                                                           velocity, acceleration, and distance for uni-
strive for exacting, professional techniques of
                                                          formly accelerated motion is defined by the
operation during these phases of flight.
                                                           following equation:
   Takeoff and landing performance is a con-
dition of accelerated motion, For instance,                                      s=g
during takeoff the airplane starts at zero veloc-         where
ity and accelerates to the takeoff velocity to                  S= acceleration distance, ft.
become airborne. During landing, the air-                      V= final velocity, ft. per sec., after accel-
plane touches down at the landing speed and                           erating uniformly from zero velocity
decelerates (or accelerates negatively) to the                  a= acceleration, ft. per sec.*
zero velocity of the stop. In fact, the landing           This equation ‘  could relate the takeoff distance
performance could be considered as a takeoff              in terms of the takeoff velocity and acceleration
in reverse for purposes of study. In either               when the airplane is accelerated uniformly
case, takeoff or landing, the airplane is ac-             from zero velocity to the final takeoff velocity.
celerated between zero velocity and the takeoff           Also, this expression could relate the landing
or landing velocity.   The important factors of           distance in terms of the landing velocity and
takeoff or landing performance are:                       deceleration when the airplane is accelerated
      (1) The takeoff or landing velocity which           (negatively) from the landing velocity to a
   will generally be a function of the stall              complete stop. It is important to note that
    NAVWEPS 00-801-80
NAVWEPS 00-801-80

the distance varies directly as the square of the   the runway requirements. The minimum take-
velocity and inversely as the acceleration.         off distance is obtained by takeoff at some
   As an example of this relationship, assume       minimum safe velocity which allows sufficient
that during takeoff an airplane is, accelerated     margin above stall and provides satisfactory
uniformly from zero velocity to a takeoff           control and initial rate of climb. Generally,
velocity of 150 knots (253.5 ft. per sec.) with     the takeoff speed is some fixed percentage of
an acceleration of 6.434 ft. per sec.* (or, 0.2g,   the stall speed or minimum control speed for
since g=32.17 ft. per sec.*). The takeoff           the airplane in the takeoff configuration.      As
distance would be:                                  such, the takeoff will be accomplished at some
                                                    particular value of lift coefficient and angle of
                                                    attack. Depending on the airplane character-
                                                    istics, the takeoff speed will be anywhere from
                  = (253.5)*                        1.05 to 1.25 times the stall speed or minimum
                    (2)(6.434)                      control speed. If the takeoff speed is specified
                  =5,ooo ft.                        as 1.10 times the stall speed, the takeoff lift
                                                    coefficient is 82.6 percent of CL- and the angle
 If the acceleration during takeoff were reduced    of attack and lift coeticient for takeoff are
10 percent, the takeoff distance would increase     fixed values independent of weight, altitude,
 11.1 percent; if the takeoff velocity were         wind, etc. Hence, an angle of attack indicator
increased 10 percent, the takeoff distance          can be a valuable aid during takeoff.
would increase 21 percent. These relation-             To obtain minimum takeoff distance at the
ships point to the fact that proper accounting      specified takeoff velocity, the forces which act
must be made of altitude, temperature, gross        on the aircraft must provide the maximum
weight, wind, etc. because any item affecting       acceleration during the takeoff roll. The
acceleration or takeoff velocity will have a        various forces acting on the aircraft may or
definite effect on takeoff distance.                may not be at the control of the pilot and
    If an airplane were to land at a velocity of    various techniques may be necessary in certain
150 knots and be decelerated uniformly to a         airplanes to maintain takeoff acceleration at
stop with the same acceleration of 0.2g, the        the highest value.
landing stop distance would be 5,000 ft.               Figure 2.32 illustrates the various forces
However, the case is not necessarily that an        which act on the aircraft during takeoff roll.
aircraft may have identical takeoff and landing     The powerplant thrust is the principal force to
performance but the principle illustrated is that   provide the acceleration and, for minimum
distance is a function of velocity and accelera-    takeoff ,distance, the output thrust should be
tion. As before, a 10 percent lower accelera-       at a maximum.       Lift and drag are produced as
tion increases stop distance Il.1 percent, and a    soon as the airplane has speed and the values
10 percent higher landing speed increases           of lift and drag depend on the angle of attack
landing distance 21 percent.
                                                    and dynamic .pressure. Rolling friction results
    The general relationship of velocity, accel-
                                                    when there is a normal force on the wheels
eration, and distance for uniformly accelerated
                                                    and the friction force is the product of the
motion is illustrated by figure 2.31. In this
illustration., acceleration distance is shown as    normal force and the coefficient of rolling
a function of velocity for various values of        friction.   The normal force pressing the wheels
acceleration.                                       against the runway surface is the net of weight
    TAKEOFF       PERFORMANCE.         The mini-    and lift while the rolling friction coefficient is
mum takeoff distance is of primary interest in      a function of the tire type and runway surface
the operation of any aircraft because it defines    texture.
                                                                                     NAVWEPS 00-801-80
                                                                                 AIRPLANE PERFORMANCE

  The acceleration of the airplane at any                    The total retarding for& on the aircraft is
instant during takeoff roll is a function of the          the sum of drag and rolling friction (D+F)
net accelerating force and the airplane mass.             and, for the majority of configurations, this
From Newton’ second law of motion:                        sum is nearly Constant or changes only slightly
                                                          during the takeoff roll. The net accelerating
or                                                        force is then the difference between the power-
                                                          plant thrust and the total retarding force,
      a=acceleration,~fr. per set                                         Fn=T-D-F
     Fn- net accelerating force,
     W=weight, lbs.                                       The variation of the net accelerating force
      g? gravitational accelerat                          throughout the takeoff roll is shown in figure
        =32.17 ft. per sec.*                              2.32. The typical propeller airplane demon-
     M= mass, slugb                                       strates a net accelerating force which decreases
                                                          with velocity and the resulting acceleration is
        = WE
                                                          initially high but decreases throughout the
The riet aicelerating fdrce on ‘    the airplane,         takeoff roll. The typical jet airplane demon-
F,, is the net of thiust, T, drag, D, and rolling         strates a net accelerating force which is essen-
friction, F. Thus, the acceleration -at any               tially constant throughout the takeoff roll.
instant during takeoff roll is:                           As a result, the takeoff performance of the
                                                          typical turbojet airpiane will compare closely
               a=&T-D-F)                                  with the case for uniformly accelerated motion.
                                                             The pilot technique required to achieve peak
Figure 2.32 illustrates the typical variation of          acceleration throughout takeoff roll can vary
the various fbrces acting on the aircraft                 considerably between airplane configurations.
throughout the takeoff roll: If ‘ is assumed
                                    it                    In some instances, maximum acceleration will
that the aircraft is at essentially constant              be obtained by allowing the airplane to remain
angle of attack during takeoff roll, CL and Co            in the three-point attitude throughout the roll
are constant and the forces of lift and drag              until the airplane simply reaches lift-equal-to-
vary as the square of the speed. For the case             weight and flies off the ground. Other air-
of uniformly     accelerated motion, distance             planes may require the three-point attitude
along the takeoff roll is proportional also to            until the takeoff speed is reached then rotation
the square bf the velocity hence velocity                 to the takeoff angle of attack to become air-
squared and distance can be used almost synon-            borne. Still other configurations may require
omously. Thus, lift and drag will vary lint               partial or complete rotation to the takeoff
arly with dyriamic pressure (4) or P from                 angle of attack prior to reaching the takeoff
the point of beginning takeoff roll.      As the          speed. In this case, the procedure may be
rolling friction coefficient -is esscnti&y un-            necessary to provide a smaller retarding force
affected by velocity, the rolling ftiction will           (D+F)     to achieve peak acceleration. When-
vary as the normal force on the wheels. At                ever any form of pitch rotation is necessary the
zero velocity, the normal force on the wheels             pilot must provide the proper angle of attack
is equal to the airplane weight but, at takeoff           since an excessive angle of attack will cause
velocity, the lift is equal to the weight and             excessive drag and hinder (or possibly pre-
the normal force is zero. Hence, rolling fric-            clude) a successful takeoff. Also, irisufficient
tion decreases linearly with 4 or Vz from the              rotation may provide added rolling resistance
beginning of takeoff roll and reaches zero at              or require that the airplane accelerate to some
the point of takeoff.                                      excessive speed prior to becoming airborne.
                                                                                     Revised January   1965
NAVWEPS O&601-80
                    FORCES ACTING ON THE AIRPLANE                                 DURING
                                TAKEOFF ROLL


                           ,-THRUST       (PROPELLER),           T           ,/
                                      THRUST         (JETI,T         /

                                                      /’     \

                (T-D-F)                         /                                           1
             ACCELERATING                 /’                                                           CONSTANT
                  FORCE                       (T;&F)                                                       a    1
              (PROPELLER)-        ,
                                      I         ’

           INNING                  WHICH IS ESSENTIALLY                                         POINT OFF
                                PROPORTIONAL TO DISTANCE                                        TAKEOFF
                                IN UNIFORMLY ACCELERATED
          ROLL                            MOTION

                 Figure 2.32.   Forces Acting       on the Airplane                During   Takeoff Roll

                                                                                         NAVWEPS 00401-80
                                                                                     AIRPLANE PERFORMANCE

In this sense, an angle of attack indicator is           mass to accelerate, and (3) increased retarding
especially useful for night or instrument takeoff        force (D+F).      If the gross weight increases,
conditions as well as. the ordinary day VFR              a greater speed is necessary to produce the
takeoff conditions.    Acceleration errors of the        greater lift to get the airplane airborne at the
attitude gyro usually preclude accurate pitch            takeoff lift coefficient. The relationship of
rotation under these conditions.                         takeoff speed and gross weight would be as
   FACTORS AFFECTING            TAKEOFF PER-             follows:
FORMANCE.         In addition to the important
factors of proper technique, many other vari-
ables affect the takeoff performance of an air-
plane. Any item which alters the takeoff                     where
velocity or acceleration during takeoff roll will                VI= takeoff velocity corresponding         to
affect the takeoff distance. In order to evalu-                         some original weight, Wi
ate the effect of the many variables, the prin-                  V2= takeoff velocity corresponding         to
cipal relationships of uniformly accelerated                            some different weight, W,
motion,will be assumed and consideration will
 be given to those effects due to any nonuni-                Thus, a given airplane in the takeoff configura-
formity of acceleration during the process of                tion at a given gross weight will have a specific
 takeoff. Generally, in the case of uniformly                takeoff speed (EAS or CAS) which is invariant
accelerated motion, distance varies directly                 with altitude, temperature, wind, etc. because
with the square of the takeoff velocity and in-              a certain value of 4 is necessary to provide lift
 versely as the takeoff acceleration.                        equal to weight at the takeoff CL. As an ex-
                                                             ample of the effect of a change in gross weight
                                                             a 21 percent increase in takeoff weight will
                                                             require a 10 percent increase in takeoff speed to
where                                                         support the greater weight.
     S= distance                                                 A change in gross weight will change the
     V= velocity,                                            net accelerating force, Fn, and change the
     a= acceleration                                         mass, M, which is being accelerated. If the
  ;’ con&&‘ (I)   applies to some known takeoff              airplane has a relatively high thrust-to-weight
       distance, Si, which was common to                      ratio, the change in the net accelerating force
       some original takeoff velocity, Vi, and                is slight and the principal effect on accelera-
       acceleration, ai.                                      tion is due to the change in mass.
     condition (2) applies to some new takeoff                   To evaluate the effect of gross weight on
       distance, Sa, which is the result of some
                                                              takeoff distance, the following relationship
       different value of takeoff velocity, Vs, or
                                                              are used :
       acceleration, aa.
                                                                    the effect of weight on takeoff velocity is
With xhis basic relationship, the effect of the
many variables on takeoff ‘        distance can be
   The effect of gross weight on takeoff distance is
                                                                  if the change in net accelerating force~is
large and proper consideration of this item
                                                                  neglected, the effect of weight on accelera-
must be made in predicting takeoff distance.
                                                                  tion is
Increased gross weight can be considered to
produce a threefold effect on takeoff perform-
 ance: (1) increased takeoff velocity, (2) greater
NAVWEPS 00-801-80

    the effect of these items on takeoff dis-                  the effect of a headwind is to reduce the
    tance is                                                   takeoff ground velocity by the amount of
                                                               the headwind velocity, VW

                                                               the effect of wind      on acceleration    is
                  g+?)x(Z)                                     negligible,

                     J-2 - a
                     -= WY2
                     J-1 ( W )
                                                               the effect of these items on takeoff distance
         (ut 1eaJt this effect because weight will             is
         alter the net accelerating force)
This result approximates the e5ect of gross
weight on takeoff distance for airplanes with
relatively high thrust-to-weight    ratios. In
effect, the takeoff distance will vary at least
as the square of the gross weight.      For ex-
ample, a 10 percent increase ,in takeoff gross
weight would cause:
    a 5 percent increase in takeoff velocity                   where
    at least a, 9 percent decrease in acceleration                  Xi= zero wind takeoff distance
    at least a 21 percent increase in takeoff                       Sa=takeoff distance into the head-
    distance                                                            wind
                                                                   V,= headwind velocity
For the airplane with a high thrust-to-weight
ratio, the increase in takeoff distance would                      VI= takeoff ground velocity with zero
be approximately 21 to 22 percent but, for                              wind, or, simply, the take05
the airplane with a relatively low thrust-to-                           airspeed
*eight ratio, the increase in takeoff distance
                                                           As a .result of this relationship, a headwind
would be approximately 25 to 30 percent.
                                                           wh,ich is 10 percent of the takeoff airspeed will
Such a powerful effect requires proper con-
                                                           reduce the takeoff distance 19 percent. How-
sideration of gross weight in predicting takeoff
                                                           ever, a tailwind (or negative headwind) which
                                                           is 10 percent of the take05 airspeed will in-
   The effect of wind on takeoff distance is large
                                                           crease the takeoff distance 21 percent. In the
and proper consideration also must be provided
                                                           case where the headwind velocity is 50 percent
when predicting takeoff distance. The effect
                                                           of the takeoff speed, the takeoff distance would
of a headwind is to allow the airplane to reach
the takeoff velocity at a lower ground velocity            be approximately 25 percent of the zero wind
while the effect of a tailwind is to require the           takeoff distance (75 percent reduction).
airplane to achieve a greater ground velocity                 The e5ect of wind on landing distance is
to attain the takeoff velocity.     The effect of          identical to the effect on takeoff distance.
the wind on acceleration is relatively small               Figure 2.33 illustrates the general dfect of
and, for the most part, can be neglected. To               wind by the percent change in takeoff or land-
evaluate the effect of wind on takeoff distance,           ing distance as a function of the ratio of wind
the following relationships are used:                      velocity to takeoff or landing speed.
                                                                                 NAVWEPS 00-801-80
                                                                             AIRPLANE PEkFORMANCE

Figure 2.33.   Approximate   Effect   of Wind     Velocity   on Takeoff or Landing Distance


    The cffcct of nrnzuay slope on takeoff distance          “feel” of    the airplane but will produce an un-
is due to the component of weight along the                  desirable   increase in takeoff distance. Assum-
inclined path of the airplane. A runway                      ing that      the acceleration is essentially un-
slope of 1 percent would provide a force com-                affected,    the takeoff distance varies as the
ponent along the path of the airplane which is               square of    the takeoff velocity,
1 percent of the gross weight.         Of course, an
upslope would contribute a retarding force                                        s*
                                                                                 -=    vz.2
component while a downslope would contri-                                        J-1 0 v,
bute an accelerating force component. For
the case of the upslope, the retarding force                 Thus, 10 percent excess airspeed would increase
component adds to drag and rolling friction to               the takeoff distance 21 percent. In most criti-
reduce the net accelerating force. Ordinarily,               cal takeoff conditions, such an increase in
a 1 percent runway slope can cause a 2’ 4       tO           takeoff distance would be prohibitive and the
percent change in takeoff distance depending                 pilot must adhere to the recommended takeoff
on rhe airplane characrerisrics. The airplane                speeds.
with the high thrust-to-weight ratio is least                   The effect of prcs~wc   altitude and ambient
affected while the airplane with the low thrust-             rcmpcraturc is to define primarily the density
to-weight ratio is most affected because the                 altitude and its effect on takeoff performance.
slope force component causes a relatively                    While subsequent corrections are appropriate
greater change in the net accelerating force.                for the effect of temperature on certain items
    The effect of runway slope must be consid-               of powerplant performance, density altitude
ered when predicting the takeoff distance but                defines certain effects on takeoff performance.
the effect is usually minor for the ordinary run-            An increase in density altitude can produce a
way slopes and airplanes with moderate                       two-fold effect on takeoff performance: (I) in-
thrust-to-weight ratios. In fact, runway slope               creased takeoff velocity and (2) decreased
considerations are of great significance only                thrust and reduced net accelerating force. If
when the runway slope is large and the airplane              a given weight and configuration of airplane is
has an intrinsic low acceleration, i.e., low                 taken to altitude above standard sea level, the
 thrust-to-weight ratio. In the ordinary case,
                                                             airplane will still require the same dynamic
 the selection of the takeoff runway will favor
                                                             pressure to become airborne at the takeoff lift
 the direction with an upslope and headwind
rather than the direction with a downslope                   coefficient. Thus, the airplane at altitude will
 and tailwind.                                               take 05 at the same equivalent airspeed (EAS)
     The effect of propertakeoff t&city is important         as at sea level, but because of the reduced
 when runway lengths and takeoff distances are               density, the true airspeed (TAS) will be
 critical.   The takeoff speeds specified in the             greater. From basic aerodynamics, the rela-
 flight handbook are generally the minimum                   tionship between true airspeed and equivalent
 safe speeds at which the airplane can become                 airspeed is as follows:
 airborne. Any attempt to take 05 below the
                                                                                  TAS   1
 recommended speed may mean that the air-
 craft may stall, be difficult to control, or have
 very low initial rate of climb. In some cases,              where
 an excessive angle of attack may not allow                      TAS= true airspeed
  the airplane to climb out of ground effect. On                 EAS= equivalent airspeed
  the other hand, an excessive airspeed at takeoff                 n=altitude density ratio
 may improve the initial rare of climb and                          0 = Plpo
                                                                                                   NAVWEPS 00-805-80
                                                                                               AIRPLANE PERFORMANCE

   The effect of density altitude on powerplant                    combined effects would be approximated
thrust depends much on the type of power-                          for the case of the airplane with high in-
plant. An increase in altitude above standard                      trinsic acceleration by the following:
sea level will bring an immediate decrease in
power output for the unsupercharged or ground                                      g=(gyx(~)
boosted reciprocating engine or the turbojet
and turboprop engines. However, an increase
in altitude above standard sea level will not                                      g=(i)x(;)
cause a decrease in power output for the super-
charged reciprocating engine until the altitude                                    s2 12
                                                                                   -=    -
exceeds the critical altitude.   For those power-                                  J-1 0 a
plants which experience a decay in thrust with                     where
an increase in altitude, the effect on the net
                                                                       S,= standard sea level takeoff distance
accelerating force and acceleration can be ap-
                                                                       Ja= takeoff distance at altitude
proximated by assuming a direct variation
                                                                         o=altitude density ratio
with density. Actually, this assumed vari-
ation would closely approximate the effect on                 As a result of these relationships, it should.
airplanes with high thrust-to-weight       ratios.         be appreciated that density altitude will affect
This relationship would be as follows:                     takeoff performance in a fashion depending
                   a2 Fm P
                  -=-=-En                                  much on the powerplant type. The effect of
                  al Frill PO                              density altitude on takeoff distance can be
where                                                      appreciated by the following comparison:
     ai, Fn, = acceleration and net accelerating
                  force corresponding to sea level
     aa, Fn, = acceleration and net accelerating
                  force corresponding to altitude
              ~=altitude density ratio                                                                      P

In order to evaluate the effect of these items on
takeoff distance, the following relationships
are used :
     if an increase in altitude does not alter ac-
     celeration, the principal effect would be
     due to the greater TAS                                                                                 drirude
                                                                               --                       -- --

                ;=(g,yxe)                                  sealevel....
                                                                                    1 .0?.98
                                                           Z,cmfC.....              I ..c605   1.125             6.05 12.5    19.9
                                                           ,,mfi.....               I L.wls     1.191            9.28 19.5    30.1
                -=- 1                                      4.@JJfc.....             L. 126      1.264           12.6 26.4     40.6
                $1 (T                                      5.Ccnft.....             L.
                                                                                    1 1605      1.347           16.05 34.7      52.3
                                                           6.-xafC.....             I1.1965     1.431           19.65 0.1      65.8
    Si=standard sea level takeoff distance                                     -                        -                     -
    St= takeoff distance at altitude
     o-altitude density ratio                                 From the previous table, some approximate
                                                           rules of thumb may be derived to illustrated
    if an increase in altitude reduces accelera-           the differences between the various airplane
    tion in addition to the increase in TAS, the           types. A 1,ooo-ft. increase in density altitude

NAVWEPS 00-801-80
will cause these approximate increases in                           (2) Gross weight.
takeoff distance:                                                   (3) Temperature--an additional correc-
     3% percent for the supercharged recipro-                    tion for nonstandard temperatures to ac-
        cating airplane when below critical                      count for the thrust loss associated with
         altitude                                                high compressor inlet air temperature.
     7 percent for the turbojet with high thtust-                For this correction the ambient tempera-
         to-weight ratio                                         ture at the runway conditions is appro-
     10 percent for the turbojet with low                        priate rather than the ambient temperature
        thrust-to-weight ratio                                   at some distant location.
These approximate relationships show the                            (4) Wind.
turbojet airplane to be much more sensitive to              In addition, corrections are necessary to ac-
density altitude than the reciprocating powered             count for runway slope, engine power defi-
airplane, This is an important fact which                   ciencies, etc.
must be appreciated by pilots in transition                    LANDING        PERFORMANCE.          In many
from propeller type to jet type airplanes.                   cases, the landing distance of an airplane will
Proper accounting of pressure altitude (field               define the runway requirements for flying
elevation is a poor substitute) and temperature             operations. This is particularly the case of
is mandatory for accurate prediction of takeoff                           jet
                                                            high speed ‘ airplanes at low altitudes where
roll distance.                                              landing distance is the problem rather than
   The most critical conditions of takeoff                  takeoff performance. The minimum landing
performance are the result of somecombination               distance is obtained by landing at some mini-
of high gross weight, altitude, temperature                 mum safe velocity which allows sufficient mar-
and unfavorable wind. In a11 cases, ir be-                  gin above stall and provides satisfactory, con-
hooves the pilot to make an accurate prcdic-                trol and capability for waveoff       Generally,
tion of takeoff’ distance from the performance              the landing speed is some fixed percentage of
data of the Flight Handboo& regardless of the               the stall speed or minimum control speed for
runway available, and to strive for.2 polished,             the airplane in the landing configuration.    As
                                                            such, the landing will be accomplished at
professional takeoff technique.
                                                            some particuIar value of ~lift coefficient and
   In the prediction of takeoff distance from
                                                            angle of attack. The exact value of CL and
the handbook data, the following primary
                                                            P for landing will depend on the airplane
considerations must be given:                               characteristics but, once defined, the values are
   Reciprocating poweredairplane                            independent of weight, altitude, wind, etc.
        (1) Pressure altitude and temperature-              Thus, an angle of attack indicator can be a
     to define the effect of density altitude on            valuable aid during approach and landing.
     distance.                                                 To obtain minimum landing distance at the
        (2) Gross weight-a     large effect on dis-         specified landing velocity, the forces which
     tance.                                                 act on the airplane must provide maximum
        (3) Specific humidity-to     correct cake-          deceleration (or negative.acceIeration) during
     off distance for the power loss associated             the landing roll. The various forces actin~g.
     with water vapor.                                      on the airplane during the landing roll may
        (4) Wind-a large effect due to the wind             require various techniques to maintain landing
     or wind component along the runway.                    deceleration at the peak value.
   Turbine poweredairplane                                     Figure 2.34 illustrates the forces acting on
        (I) Pressure altitude and temperature-               the aircraft during landing roll. The power-
     to define the effect of density altitude.              plant thnrJt should be a minimum positive
                                                                                    NAVWEPS OO-EOT-RO
                                                                                AtRPtANE PERFORMANCE

 value, or, if reverse thrust is available, a maxi-       Figure 2.34 illustrates the typical variation
mum negative value for minimum landing dis-           of the various forces acting on the aircraft
tance. Lift and drag are produced as long as           throughout the landing roll.      If it is assumed
the airplane has speed and the values of lift         that the aircraft is at essentially constant angle
 and drag depend on dynamic pressure and               of attack from the point of touchdown, CL and
angle of attack. Braking friction results when        CD are constant and the forces of lift and drag
there is a normal force on the braking wheel          vary as the square of the velocity.       Thus, lift
surfaces and the friction force is the product of     and drag will decrease linearly with 4 or V’
the normal force and the coe&cient of braking         from the point of touchdown.         If the braking
friction.    The normal force on the braking          coefficient is maintained at the maximum
surfaces is some part of the net of weight and        value, this maximum value of coefficient of
lift, i.e., some other part of this net may be        friction is essentially constant with speed and
distributed to wheels which have no brakes.           the braking friction force will vary as the
The maximum coefficient of braking friction is        normal force on the braking surfaces. As the
primarily a function of the runway surface con-       airplane nears a complete stop, the velocity
dition (dry, wet, icy, etc.) and rather inde-         and lift approach zero and the normal force on
pendent of the type of tire for ordinary condi-       the wheels approaches the weight of the air-
tions (dry, hard surface runway).         However,    plane. At this point, the braking friction
the operating coefficient of braking friction is      force is at a maximum.         Immediately after
controlled by the pilot by the use of brakes.         touchdown, the lift: is quite large and the
    The acceleration of the airplane during the       normal force on the wheels is small. As a re-
landing roll is negative (deceleration) and will      sult, the braking friction force is small. A
be considered to be in that sense. At any in-         common error at this point is to apply exces-
stant during the landing roll the acceleration        sive brake pressure without sufficient normal
is a function of the net retarding force and the      force on the wheels. This may develop a skid
airplane mass. From Newton’ second law of
                                  s                   with a locked wheel and cause the tire to blow
motion:                                               out so suddenly that judicious use of the brakes
                                                      is necessary.
                   B = Fr/M                              The coefficient of braking friction can reach
or                                                    peak values of 0.8 but ordinarily values near
                                                      0.5 are typical for the dry hard surface runway.
                   a=g 0+/W)                          Of course, a slick, icy runway can reduce the
where                                                 maximum braking friction coefficient to values
                                                      as low as 0.2 or 0.1: If the entire weight of
      a= acceleration, ft. per seca (negative)
                                                      the airplane were the normal force on the brak-
     Fr=net retarding force, lbs.
                                                      ing surfaces, a coefficient of braking friction of
      g= gravitational acceleration, ft. per sec.’
     W=weight,     lbs.                               0.5 would produce a deceleration of %g, 16.1 ft.
     M= mass, slugs                                   per sec.a Most airplanes in ground effect
                                                      rarely produce lift-drag ratios lower than 3 or
       = Wig
                                                      4. If the lift of the airplane were equal to the
The net retarding force on the airplane, Fr, is       weight, an L/D = 4 would produce a decelera-
the net of drag, D, braking friction, F, and          tion of xg, 8 ft. per sec.* By this comparison
thrust, T. Thus, the acceleration (negative)          it should be apparent that friction braking
at any instant during the landing roll is :
                                                      offers the possibility of greater deceleration
                                                      than airplane aerodynamic braking.          To this
                d=$ (Df F--T)
                                                      end, the majority of airplanes operating from
NAVWEPS 00-801-80
                           FORCES ACTING ON THE AIRPLANE
                                DURING LAUDING ROLL


                       DRAG + BRAKING

             POINT                                                                 FINAL
          OF LANDING                                                               STOP

                   Figure 2.34.   Forces Acting   on Airplane   During   Landing    Roll

                                                                                      NAVWEPS 00-ROT-80
                                                                                  AIRPLANE PERFORMANCE

dry hard surface runways will require particular           sufficient to cause deceleration of the airplane
techniques to obtain minimum landing dis-                  it can be used in deference to the brakes in the
tance. Generally, the technique involves low-              early stages of the landing roll, i.e., brakes
ering the nose wheel to the runway and retract-            and tires suffer from continuous, hard use but
ing the flaps to increase the normal force on              airplane aerodynamic drag is free and does not 1
the braking surfaces. While the airplane drag              wear out with use. The use of aerodynamic
is reduced, the greater normal force can pro-              drag is applicable only for deceleration to 60
vide greater braking friction force to com-                ot 70 percent of the touchdown speed. At
pensate for the reduced drag and the net retard-           speeds less than 60 to 70 percent of the touch-
ing force is increased.                                    down speed, aerodynamic drag is so slight as
    The technique necessary for minimum land-              to be of little use and braking must be utilized
ing distance can be altered~ to some extent in             to produce continued deceleration of the
certain situations.    For example, low aspect             airplane.
ratio airplanes with high longitudinal control                Powerplant thrust is not illustrated on
power can create very high drag at the high                figure 2.34 for there are so many possible
speeds immediate to landing touchdown.          If         variations.    Since the objective during the
the landing gear configuration or flap or                  landing toll is to decelerate, the powerplant
incidence setting precludes a large reduction              thrust should be the smallest possible positive
of CL, the normal force on the braking surfaces            value or largest possible negative value. In
and braking friction force capability are rela-            the case of the turbojet aircraft, the idle
tively small. Thus, in the initial high speed              thrust of the engine is nearly constant with
part of the landing roll, maximum deceleration             speed throughout the landing roll. The idle
would be obtained by creating the greatest                 thrust is of significant magnitude on cold days 1
possible aerodynamic drag. By the time the                 because of the low compressor inlet air temper-
aircraft has slowed to 70 or 80 percent of the             ature and low density altitude.         Unfortu-
touchdown speed, aerodynamic drag decays                   nately, such atmospheric conditions usually
 but braking action will then be effective.                have the corollary of poor braking action be-
                                                           cause of ice or water on the runway. The
Some form of this technique may be necessary
                                                           thrust from a windmilling propeller with the
 to achieve minimum distance for some con-
                                                           engine at idle can produce large negative thrust
 figurations when the coefficient of braking               early in the landing roll but the negative force
 friction is low (wet, icy runway) and the                 decreases with speed. The .large negative
 braking friction force capability is reduced              thrust at high speed is valuable in adding to
 relative to airplane aerodynamic drag.                    drag and braking friction to increase the net
     A distinction should be made between the              retarding force.
 techniques for minimum landing distance and                   Various devices can be utilized to provide
 an ordinary landing roll with considerable                 greater deceleration-of the airplane or to mini-
 excess runway .available. Minimum landing                 mize the wear and teat on tires and brakes.
 distance will be obtained from the landing                ‘The drag parachute can provide a large retatd-
  speed by creating a continuous peak decelera-             ing force at high 4 and greatly increase the de-
  tion of the airplane. This condition usually              celeration during the initial phase of landing
  requites extensive use of the brakes for maxi-            toll.   It should be noted that the contribution
 mum deceleration. On the other hand, an                    of the drag chute is important only during the
  ordinary landing roll with considerable excess            high speed portion of the landing roll. For
  runway may allow extensive use of aero-                   maximum effectiveness, the drag chute must be
  dynamic drag to minimize wear and tear on                 deployed immediately after the airplane is in
  the tires and brakes. If aerodynamic drag is              contact with the runway. Reverse thrust of
                                                                                      Revised January   1965

propellers is obtained by rotating the blade
angle well below the low pitch stop and
applying engine power. The action is to ex-        where
tract a large amount of momentum from the              Si = landing distance resulting from certain
airstream and thereby create negative thrust.                  values of landing velocity, Vi, and
The magnitude of the reverse thrust from pro-                  acceleration, 6zi
pellets is very large, especially in the case of       S2=landing distance resulting from some
the turboprop where a very large shaft power                   different values of landing velocity,
can be fed into the propeller. In the case of                  V2, or acceleration, a2
reverse propeller thrust, maximum effective-
ness is achieved by use immediately after the      With this relationship, the effect of the many
airplane is in contact with the runway.     The    variables on landing distance can be apptoxi-
reverse thrust capability is greatest at the       mated.
high speed and, obviously, any delay in pro-          The effect of gross wclght on landing distance
ducing deceleration allows runway to pass by       is one of the principal items determining the
at a rapid rate. Reverse thrust of turbojet        landing distance of an airplane        One effect
 engines will usually employ some form of          of an increased gross weight is that the airplane
 vanes, buckets, or clamshells in the exhaust to   will require a greater speed to support the
turn or direct the exhaust gases forward.          airplane at the landing angle of attack
Whenever the exit velocity is less than the in-    and lift coefficient. The relationship of land-
 let velocity (or negative), a negative momen-     ing speed and gross weight would be as
 tum change occurs and negative thrust is          follows:
produced. The reverse jet thrust is valuable
and effective but it should not be compared
with the reverse thrust capability of a com-
 parable propeller powerplant which has the        where
 high intrinsic thrust at low velocities.     As        Vi=landing     velocity corresponding to
 with the propeller reverse thrust, jet reverse                 some original weight, W,
 thrust must be applied immediately after               Vs = landing velocity corresponding to
 ground contact for maximum effectiveness in                    some different weight, W,
 reducing landing distance.                        Thus, a given airplane in the landing con-
    FACTORS AFFECTING LANDING              PER-    figuration at a given gross weight will have a
 FORMANCE.         In addition to the important    specific landing speed (MS ot CAS) which is
factors of proper technique, many other vari-      invariant with altitude, temperature, wind,
 ables affect the landing performance of an air-   etc., because a certain value of 4 is necessary
 plane. Any item which alters the landing          to provide lifr equal to weight at the landing
 velocity or deceleration during landing toll      C,. As an example of the effect of a change in
 will affect the landing distance. As with         gross weight, a 21 percent increase in landing
 takeoff performance, the relationships of uni-    weight will require a 10 percent increase in
 formly accelerated motion will be assumed         landing speed to support the greater weight.
applicable for studying the principal effects on      When minimum landing distances are con-
 landing distance. The case of uniformly ac-       sidered, braking friction forces predominate
 celerated motion defines landing distance as      during the landing toll and, for the majority
 varying directly as the square of the landing     of airplane configurations, braking friction is
velocity and inversely as the acceleration dur-    the main source of deceleration. In this case,
 ing landing toll.                                 an increase in gross weight provides a greater

normal force and increased braking friction                 braking friction will bring both airplanes to
force to cope with the increased mass. Also,                a stop in the same distance. The heavier ait-
the higher landing speed at the same CL and                 plane will have the gteater mass to decelerate
CD produce an average drag which increased in               but the greater normal force will provide a
the same proportion as the increased weight.                greater retarding friction force. As a result,
Thus, increased gross weight causes like in-                both airplanes would have identical accelera-
creasesin the sum of drag plus braking friction             tion and identical stop distances from a given
and the acceleration is essentially unaffected.             velocity.      However, the heavier airplane
   To evaluate the effect of gross weight on                would have a greater kinetic energy to be dis-
landing distance, the following relationships               sipated by the brakes and the principal differ-
are used:                                                   ence between the two airplanes as they reach
     the effect of weight on landing velocity is            a stop would be that the heavier airplane
                                                            would have the hotter brakes. Therefore,
                                                            one of the factors of braking performance is the
                                                            ability of the brakes to dissipate energy with-
                                                            out developing excessive temperatures and
     if the net retarding force increases in the            losing effectiveness.
     same proportion as the .weight, the accel-                To appreciate the effectiveness of modern
     eration is unaffected.
                                                            brakes, a 30,000-lb. aircraft landing at 175
     the effect of these items on landing dis-              knots has a kinetic energy of 41 million ft.-lbs.
     tance is,                                              at the instant of touchdown.       In a minimum
                                                            distance landing, the brakes must dissipate
                                                            most of this kinetic energy and sach brake must
                                                            absotb an input power of approximately 1,200
or                                                          h.p. for 25 seconds. Such requirements for
                     $2 w*                                  brakes are extreme but the example serves to
                     s,=w,                                  illustrate the ptoblems of brakes for high
                                                            performance airplanes.
In effect, the minimum landing distance will                    While a 10 percent increase in landing
vary directly as the gross weight.          For ex-         weight causes:
ample, a 10 percent increase in gross weight                       a 5 percent higher landing speed
at landing would cause:                                            a 10 percent greater landing distance,
       a 5 percent increase in landing velocity             it also produces a 21 percent increase in the
       a 10 percent increase in landing distance            kinetic energy of the airplane to be dissipated
    A contingency of the previous analysis is the            during the landing roll.     Hence, high landing
relationship between weight and braking ftic-               weights may approach the energy dissipating
tion force. The maximum coefficient of brak-
                                                             capability of the brakes.
ing friction is relatively independent of the
                                                                The s&t of wind on landing distance is large
usual range of normal forces and rolling speeds,
                                                             and deserves proper consideration when pre-
e.g., a 10 percent increase in normal force would
create a like 10 percent increase in braking                 dicting landing distance. Since the airplane
friction force. Consider the case of two air-                will land at a particular airspeed independent
planes of the same type and c.g. position but                of the wind, the principal effect of wind on
of ~diffetent gross weights.      If these two air-          landing distance is due to the change in the
planes are rolling along the runway at some                  ground velocity at which the airplane touches
speed at which aerodynamic forces are negli-                 down. The effect of wind on acceleration
gible, the use of the maximum coefficient of                 duting the landing distance is identical to the
                                                                                     NAVWEPS OO-ROLRO
                                                                                 AIRPlANE PERFORMANCE

effect on takeoff distance and is approximated                              TAS 1
by the following relationship:                                              E-33=5
                  ..-.=13 v 2
                  $2                                         TAS= true airspeed
                  Sl c 1                                     EAS= equivalent airspeed
where                                                          a=altitude density ratio
     Si= zero wind landing distance                      Since the airplane lands at altitude with the
     Sa=landing distance into a headwind                 same weight and dynamic pressure, the drag
    I’ = headwind velocity                               and braking friction throughout the landing
     Vi=landing    ground velocity with zero             toll have the same values as at sea level. As
          wind or, simply, the landing airspeed          long as the condition is within the capability
                                                         of the brakes, the net retarding force is un-
As a result of this relationship, a headwind
                                                         changed and the acceleration is the same as
which is 10 percent of the landing airspeed will
                                                         with the landing at sea level.
reduce the landing distance 19 percent but a
                                                            To evaluate the effect of density altitude on
tailwind (or ‘   negative headwind) which is 10
                                                         landing distance, the following relationships
percent of the landing speed will increase the
                                                         are used :
landing distance 21 percent. Figure 2.33 illus-
                                                              since an increase in altitude does not alter
trates this general effect.
                                                              acceleration, the effect would be due to
    The effect of ranway slope on landing distance            the greater TAS
 is due to the component of weight along the
inclined path of the airplane. The relation-
ship is identical to the case of takeoff per-
formance but the magnitude of the effect is
 not as great. While account must be made
for the effect, the ordinary values of runway
 slope do not contribute a large effect on landing            where
 distance. For this reason, the selection of the                  S1= standard sea level landing      dis-
 landing runway will ordinarily favor the direc-                          tance
 tion with a downslope and’        headwind rather                Sa=Ianding distance at altitude
 than an upslope and tailwind.                                     c=altitude density ratio
    The effect of pressurealtitude and ambient tem-
 perature is to define density altitude and its effect     From this relationship, the minimum land-
 on landing performance. An increase in dens-            ing distance at 5,OCOft. (u=O.8617) would be
 ity altitude will increase the landing velocity         16 percent greater than the minimum landing
  but will not alter the net retarding force. If         distance at sea level. The approximate increase
  a given weight and configuration of airplane           in landing distance with altitude is approxi-
 is taken to altitude above standard sea level,          mately 3% percent for each 1,ooO ft. of altitude.
 the airplane will still require the same 4 to           Proper accounting of density altitude is neces-
 provide lift equal to weight at the landing C,.         sary to accurately predict landing distance.
  Thus, the airplane at altitude will land at the           The effect of proper landing velocity is impor-
  same equivalent airspeed (EAS) as at sea level         tant when runway lengths and landing dis-
  but, because of the reduced density, the true          tances are critical. The landing speeds specified
  airspeed (TM) will be greater. The relation-           in the flight handbook ate generally the mini-
  ship between true airspeed and equivalent air-         mum safe speeds at which the airplane can be
  speed is as follows:                                   landed. Any attempt to land at below the

specified speed may mean that the airplane may           brakes. In all cases, it is necessary to make an
stall, be difhcult to control, or develop high           accurate prediction of minimum landing dis-
rates of descent. On the other hand, an exces-           tance to compare with the available runway.
sive speed at landing may improve the control-           A polished, professional landing technique is
lability (especially in crosswinds) but will             necessary because the landing phase of flight
cause an undesirable increase in landing dis-            accounts for more pilot caused aircraft acci-
tance. The principal effect of excess landing            dents than any other single phase of flight.
speed is described by:                                      In the prediction of minimum landing dis-
                                                         tance from the handbook data, the following
                  -=    v2
                        - *                              considerations must be given:
                  h    0VI                                    (1) Pressure altitude and temperature-to
Thus, a 10 percent excess landing speed would               define the effect of density altitude.
cause a 21 percent increase in landing distance.              (2)’ Gross weight-which       define the CAS
The excess speed places a greater working load              or EAS for landing.
on the brakes because of the additional kinetic               (3) Wind-a      large effect due to wind or
energy to be dissipated. Also, the additional               wind component along the runway.
speed causes increased drag and lift in the nor-              (4) Runway slope-a relatively small cor-
mal ground attitude and the increased lift will             rection for ordinary values of runway slope.
reduce the normal force on the braking sur-                 IMPORTANCE          OF HANDBOOK            PER-
faces. The acceleration during this range of             FORMANCE DATA.             The performance sec-
speed immediately after touchdown may suffer             tion or supplement of the flight handbook con-
and it will be more likely that a tire can be            tains all the operating data for the airplane.
blown out from braking at this point. As a               For example, all data specific to takeoff, climb,
result, 10 percent excess landing speed will             range, endurance, descent and landing are in-
cause at JUJ; 21 percent greater landing dis-            cluded in this section. The ordinary use of
tance.                                                   these data in flying operations is mandatory
   The most critical conditions of landing per-          and great knowledge and familiarity of the air-
formance are the result of some combination of           plane can be gained through study of this
high gross weight, density altitude, and un-             material.    A complete familiarity      of an air-
favorable wind. These conditions produce the                    s
                                                         plane’ characteristics can be obtained only
greatest landing distance and provide critical           through extensive analysis and study of the
levels of energy dissipation required of the             handbook data.

                                                                                 NAVWEPS 00-801-80
                                                                           HIGH SPEED AERODYNAMICS

                                         Chapter 3
                        HIGH SPEED AERODYNAMICS

    Developments in aircraft and powerplants           GENERAL     CONCEPTS   AND      SUPERSONIC
 have produced high performance airplanes                           FLOW  PATTERNS
with capabilities for very high speed flight.
The study of aerodynamics at these very high           NATURE    OF COMPRESSIBILITY
flight speeds has many significant differences
from the study of classical low speed aero-               At low flight speeds the study of aero-
dynamics. Therefore, it is quite necessary             dynamics is greatly simplified by the fact
that the Naval Aviator be familiar with the            that air may experience relatively       small
nature of high speed airflow and the charac-           changes in pressure with only negligible
teristics   of high    performance    airplane         changes in density. This airflow is termed
configurations.                                                     since the air may undergo changes
  NAVWEPS 00-601-60

  in pressure without apparent changes in den-                     directions. Evidence of this “pressure warn-
  sity. Such a condition of airflow is analogous                   ing’ ’ is seeii in the typical subsonic flow
  to the flow of water, hydraulic fluid, or any                    pattern of figure 3.1 where there is upwash
  other incompressible fluid. However, at high                    and flow direction change well ahead of the
  flight speeds the pressure changes that take                    leading edge. If the object is travelling at
  place are quite large and significant changes                   some ,speed above the speed of sound the air-
  in air density occur. The study of airflow at                   flow ahead of the object will not be influenced
  high speeds must account for these changes                      by the pressure field on the object since pres-
1 in air density and must consider that the                       -sure disturbances cannot. be propagated ahead
1 air is compressible and that there will be                       of the object. Thus, as the flight speed nears
   “compressibility effects.”                                     the speed of sound a compression wave will
      A factor of great importance in the study of                form at the leading edge and all changes in
  high speed airflow is the speed of sound.                       velocity and pressure will take place quite
  The speed of sound is the rate at which small                   sharply and suddenly. The airflow, ahead of
  pressure disturbances will       be propagated                  the object is not influenced until the air par-
  through the air and this propagation speed                       ticles are suddenly forced out .of the way by
  is solely a function of air temperature. The                     the concentrated pressure wave set up by the
  accompanying table illustrates the variation                    object. Evidence of this phenomenon is seen
  of the speed of sound in the standard                            in the typical supersonic flow pattern of
  atmosphere.                                                      figure 3.1.
 TABLE 3-I.   V.r;afIm < T<
                                                                      The analogy of surface waves on the water
              Altitude   in the                                   may help clarify these phenomena. Since a
                                                                   surface wave is simply the propagation of a
                                                                   pressure disturbance, a ship moving at a speed
                                                                   much less than the wave speed will not form
                                  D F.       - c.       K?uI,      a “bow wave.”                    s
                                                                                       As the. ship’ speed nears
                                     59.0        15.0     661.7
                                     41.1         5.1     650.3    the wave pro$agation speed the bow wave
                                     23.3      -4.8       6%.6     will form and become stronger as speed is
                                       5.5    -14.7       6X6.7
                                  --12.,      --24.6      614.6
                                                                   increased beyond the wave speed.
                                  --30.2      -34.5       602.2       At this point it should become apparent
                                  -48.0       -44.4       589.6    that all compressibility effects depend upon
                                  -65.8       --w.3       516.6
                                  -69.7       -56.5       573:s    the relationship of airspeed to the speed of
                                  -69.1       -56.5       573.8    sound. The term used to describe this rela-
                                  -69.7       -56.5       573.8
                                                                   tionship is the Mach number, M, and this
                                                                   term is the ratio of the true airspeed to the
    As an object moves through the air mass,                        speed of sound.
 velocity and pressure changes occur which                                                  ,-I
 create pressure disturbances in the airflow sur-
 rounding the object. Of course, these pressure                   where
 disturbances are propagated through the air                          M=Mach number
 at the speed of sound. If the object is travel-                      V= true airspeed, knots
 ling at low speed the pressure disturbances are                       d= speed of sound, knots
 propagated ahead of the object and the airflow                          =a&
 immediately ahead of the object is influenced                        aO=speed of sound at standard sea level
 by the pressure field on the object. Actually,                                  conditions, 661 knots
 these pressure disturbances are transmitted in                         e= temperature ratio
 all directions and extend indefinitely in all                            = T/T,

 Revised January         1965
                                                              NAVWEPS OD-8OT-80
                                                        HIGH SPEED AERODYNAMICS


                        OF LEADING EDGE



Figure 3.1.   Comparison   of Subsonic and Supersonic Now Patterns


    It is important to note that compressibility        exist in both compressible and incompressible
effects are not limited to flight speeds at and         cases.
above the speed of sound. Since any aircraft                The example of subsonic incompressible flow
will have some aerodynamic shape and will               is simplified by the fact that the density of
be developing lift there will be local flow             flow is constant throughout the tube. Thus,
velocities on the surfaces which arc greater            as the flow approaches a constriction and the
than the flight speed. Thus, an aircraft can            streamlines converge, velocity increases and
experience compressibility       effects at flight      static pressure decreases. In other words, a
speeds well below the speed of sound. Since             convergence of the tube requires an increasing
there is the possibility of having both subsonic        velocity to accommodate the continuity of
and supersonic flows existing on the aircraft           flow. Also, as the subsonic incompressible
it is convenient to define certain regimes of           flow enters a diverging section of the tube,
flight.    These regimes are defined approxi-           velocity decreases and static pressure increases
mately as follows:                                       but density remains unchanged. The behavior
       Subsonic-Mach numbers below 0.75                  of subsonic incompressible flow is that a con-
       Transonic-Mach     numbers from 0.75 to          vergence causes expansion (decreasing pressure)
          1.20                                           while a divergence causes compression (in-
       Supersonic-Mach     numbers from 1.20 to          creasing pressure).
          5.00                                              The example of supersonic compressible flow
       Hypersonic-Mach     numbers above 5.00            is complicated by the fact that the variations
While the flight Mach numbers used to define             of flow density are related to the changes
these regimes of flight are quite approximate,           in velocity and static pressure. The behavior
it is important to appreciate the types of flow          of supersonic compressible flow is that a con-
existing in each area. In the subsonic regime            vergence causes compression while a divergence
it is most likely that pure subsonic airflow             causes expansion. Thus, as the supersonic
exists on all parts of the aircraft.        In the       compressible flow approaches a constriction
transonic regime it is very probable that flow           and the streamlines converge, velocity dc-
on the aircraft components may be partly sub-            creases and static pressure increases. Con-
sonic and partly supersonic. The supersonic              tinuity of mass flow is maintained by the
and hypersonic’ flight regimes will provide              increase in flow density which accompanies the
definite supersonic flow velocities on all parts         decrease in velocity.     As the supersonic com-
of the aircraft.    Of course, in supersonic flight      pressible flow enters a diverging section of the
 there will be some portions of the boundary              tube, velocity increases, static pressure de-
layer which are subsonic but the predominating            creases, and density decreases to accommodate
flow is still supersonic.                                 the condition of continuity.
     The principal differences between subsonic              The previous comparison points out three 1
 and supersonic flow are due to the cmprrs-               significant differences between supersonic corn- 1
 Jibi&      of the supersonic flow.      Thus, any        pressible and subsonic incompressible flow.
change of velocity or pressure of a supersonic
                                                                (a) Compressible flow includes the addi-
flow will produce a related change of density
                                                             tional variable of flow density.
 which must be considered and accounted for.
 Figure 3.2 provides a comparison of incom-                     (b) Convergence of flow causes expansion
 pressible and compressible flow through a                   of incompressible flow but compression of
 closed tube. Of course, the condition of con-               compressible flow.
 tinuity must exist in the flow through the                     (c) Divergence of flow causes compression
 closed tube; the mass flow at any station along             of incompressible flow but expansion of
 the tube is constant. This qualification must               compressible flow.
Revised January   1965
                                                                                                            NAVWEPS OD-8OT-80
                                                                                                      HIGH SPEEO AERODYNAMICS


       ---                     --                                            //------
       ---                    --          --_-__--                                          ------
        __--__-----                                                               -------
      ----                          ---                  ---_
                                                                                   ---                        -----
                                             --        ---_

                              INCREASING VELOCITY                            DECREASING VELOCITY
                              DECREASING PRESSURE                            INCREASING PRESSURE
                               CONSTANT DENSITY                                CONSTANT DENSITY


                                          CONVERGING                                     DIVERGING

                              DECREASING VELOCITY                            INCREASING VELOCITY
                              INCREASING PRESSURE                            DECREASING PRESSURE
                                          DENSITY                             DECREASING DENSITY

 figure            3.2.   Comparison of Compressible                and lncomprossible          Flow Through a Closed Tube


                            OBLIQUE SHOCK WAVE-,

                          SUPERSONIC FLOW INTO A CORNER

                               SERfES OFOBLIOUE SHOCK WAVES


                          Figure 3.3. Oblique Shock Wave Formotion

                                                                               NAVWEPS OD-807-80
                                                                         HIGH SPEED AERODkNAMlCS

‘           SUPERSONIC FLOW PATTERNS                 will form on each surface of the wedge and the
                                                      inclination of the shock wave will be a func-
    When supersonic flow is clearly established,
 all changes in velocity, pressure, density, flow     tion of the free stream Mach number and the
 direction, etc., take place quite suddenly and      wedge angle. As the free stream Mach number
                                                      increases, the shock wave angle decreases; as
 in relatively confined areas. The areas of flows
                                                      the wedge angle increases the shock wave
change are generally distinct and the phenom-
 ena are referred to as “wave” formations. All       angle increases, and, if the wedge angle is in-
compression waves occur suddenly and are             creased to some critical amount, the shock
wasteful of energy. Hence, the compression           wave will detach from the leading edge of the
                                                     wedge. It is important to note that detach-
waves are distinguished by the sudden “shock”
                                                     ment of the shock wave will produce sub$onic
type of behavior. All expansion waves are not
so sudden in their occurrence and are not waste-     flow immediately after the central portion of
ful of energy like the compression shock waves.      the shock wave. Figure 3.4 illustrates these
Various types of waves can occur in supersonic       typical flow patterns and the effect of Mach
flow and the nature of the wave formed depends       number and wedge angle.
upon the airstream and the shape of the object           The previous flow across a wedge in a
causing the flow change. Essentially, there          supersonic airstream would allow flow in ;UU
are three fundamental types of waves formed          dimensions. If a cone were placed in a super-
in supersonic flow: (1) the oblip shock wave         sonic airstream the airflow would occur in
(compression), (2) the normal shock wave             three dimensions and there would be some
(compression), (3) the expansion wave (no            noticeable differences in flow characteristics.
shock).                                              Three-dimensional flow for the same Mach
    OBLIQUE SHOCK WAVE.               Consider the   number and flow direction change would pro-
case where a supersonic airstream is turned          duce a weaker shock wave with less change in
into the preceding airflow.       Such would be      pressure and density. Also, this conical wave
the case of a supersonic flow “into a comer”         formation allows changes in airflow that con-
as shown in figure 3.3. A supersonic airstream       tinue to occur past the wave front and the
passing through the oblique shock wave will          wave strength varies with distance away from
                                                     the surface. Figure 3.5 depicts the typical
experience these changes:
                                                     three-dimensional flow past a cone.
       (1) The airstream is slowed down; the
                                                         Oblique shock waves can be reflected like
    velocity and Mach number behind the wave
                                                     any pressure wave and this effect is shown in
    are reduced but the flow is still supersonic
                                                     figure 3.5. This reflection appears logical and
       (2) The flow direction is changed to flow     necessary since the original wave changes the
    along the surface
                                                     flow direction toward the wall and the reflected
       (3) The static pressure of the airstrea:m
                                                      wave creates the subsequent flow change to
    behind the wave is increased
                                                     cause the flow to remain parallel to the wall
       (4) The density of the airstream behind
                                                     surface. This reflection phenomenon places
    the wave is increased
       (5) Some of the available energy of the       definite restrictions on the size of a model in a
    airstream (indicated by the sum of dynamic       wind tunnel since a wave reflected back to the
    and static pressure) is dissipated and turned    model would cause a pressure distribution not
    into unavailable heat energy. Hence, the         typical of free flight.
    shock wave is wasteful of energy.                    NORMAL        SHOCK WAVE.         If a blunt-
    A typical case of oblique shock wave forma-      nosed object is placed in a supersonic airstream
tion is that of a wedge pointed into a super-        the shock wave which is formed will be de-
sonic airstream. The oblique shock wave              tached from the leading edge. This detached

                                                           M = 3.0

                                                        M = 3.0           \


                 Figure 3.4. Shock Waves Formed by Various Wedge Shapes

                                                              NAVWEPS 00-BOT-80
                                                        HIGH SPEED AERODYNAMICS

                      CONE IN SUPERSONIC FLOW

                   CONICAL WAVE

                     REF:LECTED OBLIOUE WAVES

           MODEL IN WIND
        TUNNEL WITH wows
         REFL\Cmg    FROM

Figure 3.5.   Three Dimensional   and Reflected   Shock Waves

                                      209                       Revised Januaty I%5

                                        OBLlOuE SHOCK

                                                     ,SHOCK WAVE

                          Figure 3.6. Normal ShockWave   Formation
                                                                                      NAVWEPS OD-EOT-80
                                                                                HIGH SPEED AERODYNAMICS

wave also occurs when a wedge or cone angle                    Mach number ahead of the wave is 1.25,
exceeds some critical value. Whenever the                      the Mach number of the flow behind the
shock wave forms perpendicular to the up-                      wave is approximately 0.80.
stream flow, the shock wave is termed a                            (2) The airflow direction immediately
“normal” shock wave and the flow immediately                   behind the wave is unchanged.
behind the wave is subsonic. Any relatively                        (3) The static pressure of the airstream
blunt object in a supersonic airstream will form               behind the wave is increased greatly.
a normal shock wave immediately ahead of the                       (4) The density of the airstream behind
leading edge slowing the airstream to subsonic                 the wave is increased greatly.
SO the airstream may feel the presence of the                      (5) The energy of the airstream (indi-
blunt nose and flow around it. Once past the                   cated by total pressure-dynamic plus static)
blunt nose the airstream may remain subsonic                   is greatly reduced. The normal shock wave
or accelerate back to supersonic depending on                  is very wasteful of energy.
the shape of the nose and the Mach number of                   EXPANSION WAVE.            If a supersonic air-
the free stream.                                           stream were turned away from the preceding
    In addition to the formation of normal                 flow an expansion wave would form. The
shock waves described above, this same type                flow “around a corner” shown in figure 3.7
of wave may be formed in an entirely different             will not cause sharp, sudden changes in the
manner when there is no object in the super-               airflow except at the corner itself and thus is
sonic airstream. It is particular that whenever            not actually a “shock” wave. A supersonic
a supersonic airscream is slowed to subsonic               airstream passing through an expansion wave
without a change in direction a normal shock               will experience these changes:
wave will form as a boundary between the                           (1) The airstream is accelerated; the ve-
supersonic and subsonic regions. This is an                    locity and Mach number behind the wave
important fact since aircraft usually encounter                are greater.
some “compressibility effects” before the flight                   (2) The flow direction is changed to
speed is sonic. Figure 3.6 illustrates the man-                flow along the surface-provided        separa-
ner in which an airfoil at high subsonic speeds                 tion does not occur.
has local flow velocities which are supersonic.                    (3) The static pressure of the airstream
As the local supersonic flow moves aft, a                      behind the wave is decreased.
normal shock wave forms slowing the flow                            (4) The density of -the airstream behind
to subsonic. The transition of flow from                        the wave is decreased.
subsonic to supersonic is smooth and is not                        (5) Since the flow changes in a rather
accompanied by shock waves if the transition                   gradual manner there is no “shock” and
 is made gradually with a smooth surface. The                   no loss of energy in the airstream. The
 transition of flow from supersonic to subsonic
                                                                expansion wave does not dissipate air-
without      direction change always forms a
                                                                stream energy.
 normal shock wave.
     A supersonic airstream passing through a                   The expansion wave in three dimensions is
 normal shock wave will experience these                   a slightly different case and the principal
 changes:                                                   difference is the tendency for the static pres-
        (1) The airstream is slowed to subsonic;            sure to continue to increase past the wave.
     the local Mach number behind the wave is                   The following table is provided to summa-
     approximately equal to the reciprocal of the           rize the characteristics of the three principal
     Mach number ahead of the wave-e.g.,        if          wave forms encountered with supersonic flow.

NAVWEPS 00-807-80

                              EXPANSION WAVE,

                     SUPERSONIC FLOW
                     AROUND A CORNER

                            SERIES OF EXPANSION WAVES7

                    SUPERSONIC FLOW
                 AROUND A SMOOTti CORNER

                           Figure 3.7.   Expansion Wove   Formation

                                                                                                       NAVWEPS 00-8OT-80
                                                                                                 HIGH SPEED AERODYNAMICS

                                               TABLE 3-P. Suprnonk Wave Charactwiltks

Typeof wave formation                Oblique shock wave                     Normal shock wave.         Expansion wwc.

                                                                                                                     ‘ //
                                                                                                          -       ,/$y
                                _-                                     _-                         __
Flow direction change.               “Flow   into a corner,”                No change.                 “Flow around a corner,”
                                       turned into preceding                                             turned away from pre-
                                       flow.                                                             ceding flow.
                                                                       __                         -.
Efkct cm velociry and Mach           Decreased but still      supcr-                                   Increased to higher super-
  number.                              sonic.                                                            sonic.
                                                                       __                         -.
Effect on static pressure and        Increase.           :.                 Great increase,            DeCrWSe.
                                                                       __                         -.
                                     DKICaSe                                Great decrease             No change (no shock).

                                                                       -                          -

SECTIONS       IN   SUPERSONIC                 FLOW                            Parts (c) and (d) of figure 3.8 show the
                                                                            wave pattern and resulting pressure distribu-
   In order to appreciate the effect of these                               tion for a double wedge airfoil at zero lift.
various wave forms on the aerodynamic char-                                 The airstream moving over the surface passes
acteristics in supersonic flow, inspect figure 3.8.                         through an oblique shock, an expansion wave,
Parts (a) and (b) show the wave pattern and                                 and another oblique shock. The resulting
resulting pressure distribution for a thin flat                             pressure distribution on the surfaces produces
plate at a positive angle of attack. The air-                               no net lift, but the increased pressure on the
stream moving over the upper surface passes                                 forward half of the chord along with the de-
through an expansion wave at the leading edge                               creased pressure on the aft half of the chord
and then an oblique shock wave at the trailing                              produces a “wave” drag. This wave drag is
edge. Thus, a uniform suction pressure exists
                                                                            caused by the components of pressure forces
over the upper surface. The airstream moving                                which are parallel to the free scream direction.
underneath the flat plate passes through an
                                                                            The wave drag is in addition to the drag due
oblique shock wave at the leading edge then an
                                                                            to friction, separatien, lift, etc., and can be
expansion wave at the trailing edge. This pro-
duces a uniform positive pressure on the under-                             a very considerable part of the total drag at
side of the section. This distribution of pres-                             high supersonic speeds.
sure on the surface will produce a net lift and                                Parts (e) and (f) of figure 3.8 illustrate the
incur a subsequent drag due co lift from the in-                            wave pattern and resulting pressure distribu-
clination of the resultant lift from a perpen-                              tion for the double wedge airfoil at a small
dicular co the free stream.                                                 positive angle of attack. The net pressure

NAVWEPS 00-8oT-80

                                                       NOTE: CENTER OF PRESSURE
                                                             IS AT 50% CHORD

                                                       vb        FLAT PLATE PRESSURE DISTRIBUTION
                                                                         NO NET LIFT BUT
                                                                         HAVE “WAVE DRAG”

                    AT ZERO LIFT                       0d        REDOUBLEWEDGE PRESSURE
                                                                 DISTRIBUTION AT ZERO LIFT

                                                                             DRAG DUE TO LIFT

                                                                             L-WAVE DRAG

                                                       0 f        DOUBLEWEDGEPRESSURE
                                                                DISTRIBUTION AT POSITIVE LIFT

                                                       0    b     CONVENTIONAL BLUNT NOSE

               Figure 3.8. Typical Supersonic Flow Patterns and Distribution of Pressure

                                                                                      NAWEPS 00-80T-80
                                                                                HIGH SPEED AERODYNAMICS

 distribution produces an inclined lift with                  will be located approximately at the SO per-
drag due to lift which is in addition to the                  cent chord position.  As this contrasts with
wave drag at zero lift.      Part (g) of figure 3.8           the subsonic location for the aerodynamic
 shows the wave pattern for a circular arc air-               center of the 23 percent chord position, sig-
foil. After the airflow traverses the oblique                 nificant changes in aerodynamic trim and
shock wave at the leading edge, the airflow                   stability may be encountered in transonic
undergoes a gradual but continual expansion                   flight.
until the trailing edge shock wave is en-
countered. Part (h) of figure 3.8 illustrates
the wave pattern on a conventional blunt nose
                                                                     CONFIGURATION        EFFECTS
airfoil in supersonic flow. When the nose is
blunt the wave must detach and become a                     TRANSONIC      AND SUPERSONIC PLIGHT
normal shock wave immediately ahead of the
leading edge. Of course, this wave form                          Any object in subsonic flight which has some
produces an area of subsonic airflow at the                  finite thickness or is producing lift will have
leading edge with very high pressure and                     local velocities on the surface which are
density behind the detached wave.                            greater than the free stream velocity.      Hence,
    The drawings of figure 3.8 illustrate the                compressibility    effects can be expected to
typical patterns of supersonic flow and point                occur at flight speeds less than the speed of
out these facts concerning aerodynamic surfaces              sound. The transonic regime of flight pro-
in two dimensional supersonic flow:                          vides the opportunity for mixed subsonic and
       (1) All changes in velocity, pressure,                supersonic flow and. accounts for the first 1
    density and flow direction will take place               significant effects of compressibility.
   quite suddenly through the various. wave                      Consider a conventional airfoil shape as
   forms. The shape of the object and the                    shown in figure 3.9. If this airfoil is at a
   required flow ,direction change dictate the               flight Mach number of 0.50 and a slight posi-
    type and strength of the wave formed.                    tive angle of attack, the maximum local
       (2) As always, lift results from the distri-          velocity on the surface will be greater than
    bution of pressure on a surface and is the net           the flight speed but most likely less than
    force perpendicular to the free stream direc-            sonic speed. Assume that an increase in
    tion. Any component of the lift in a direc-              flight Mach number to 0.72 would produce
    tion parallel to the windstream will be                 lfrst cvidmc of local son@flow. This condition
    drag due to lift.                                        of flight would be the highest flight speed
       (3) In supersonic flight, the zero lift drag          possible without supersonic flow and would
    of an airfoil of some finite thickness will              be termed the “critical Mach number.” Thus,
    include a “wave drag.” The thickness of                 critical Mach number is the bouodary between
    the airfoil will have an extremely powerful              subsonic and transonic flight and is an im-
    effect on this wave drag since the wave drag             portant ~point of reference for all compressi- 1
    varies as the square of the thickness ratio-             bility effects encountered in transonic flight.
    if the thickness is reduced 50 percent, the              By delinition, critical Mach number is the
   wave drag is reduced 73 percent. The lead-                “free stream Mach number which produces
   ing edges of supersonic shapes must be sharp              6rst evidence of local sonic flow.”     Therefore,
   or the wave formed at the leading edge will               shock waves, buffet, airflow separation, etc.,
    be a strong detached shock wave.                         take place above critical Mach number.
       (4) Once the flow on the airfoil is super-                As critical Mach number is exceeded an
   sonic, the aerodynamic center of the surface              area of ~uprrronic airflow is created and a normal
                                                                                        Revised January   1965

                                                        MAXIMUM LOCALVELOCITY
                                                          IS LESS THAN SONIC

                                                              MAXIMUM LOCAL VELOCITY
                                                                   EOUALTO SONIC

                          M =.72
                 (CRITICAL MACH NUMB

                                 NORMAL SHOCK WAVE
                                                              POSSIBLE SEPARATION

                                                                         NORMAL SHOCK

                                                  \\I              NORMAL SHOCK

                                                          NORMAL SHOCK

                          Figure 3.9.   Transonic Flow Patterns (sheet 1 of 2)

                                                      NAVWEPS OD-801-80
                                                HIGN SPEED AEQODYNAMICJ

                                       WING IN TRANSONIC   FLOW

                 I   M = .700  a= +2O CL= ,370
                           NO SHOCK WAVES

                         M-.800  a=+2O   CL=.442
                     SHOCK FORMATION IS APPARENT           AT
                       25 TO 30 % CHORD POSITION

                         M=.075   a=+20 CL=.450
                      AFT   PORTION     OF WING PLAPJFORM

Figure 3.9. Transonic Flow Patterns (sheet 2 of 2)

 shock wave forms as the boundary between                value all oblique portions of the waves incline
 the supersonic flow and the subsonic flow on            more greatly and the detached normal shock
 the aft portion of the airfoil surface. The             portion of the bow wave moves closer to the
 acceleration of the airflow from subsonic to            leading edge.
 supersonic is smooth and unaccompanied by                  Of course, all components of the aircraft
 shock waves if the surface is smooth and the            are affected by compressibility in a manner
 transition gradual. However, the transition              somewhat similar to that of basic airfoil.
of airflow from supersonic to subsonic is                The tail, fuselage, nacelles, canopy, etc. and
always accompanied by a shock wave and,                  the efkct of the interference between the
when there is no change in direction of the              various surfaces of the aircraft must be
airflow, the wave form is a normal shock                 considered.
wave.                                                       FORCE DIVERGENCE.            The airflow sepa-
    Recall that one of the principal effects of          ration induced by shock wave formation can
th,e normal shock wave is to produce a large             create significant variations in the aerody-
increase in the static pressure of the airstream         namic force coefficients. When the free stream
behind the wave. If the shock wave is                    speed is greater than critical Mach number some
strong, the boundary layer may not have                  typical effects on an airfoil section are as
sufficient kinetic energy to withstand the               follows :
large, adverse pressure gradient and separation                (1) An increase in the section drag coeffi-
will occur. At speeds only slightly beyond                  cient for a given section lift coe5cient.
critical Mach number the shock wave formed                     (2) A decrease in section lift coefficient
is not strong enough to cause spearation or                 for a given section angle of attack.
any noticeable change in the aerodynamic                       (3) A change in section pitching moment
force coefficients. However, an increase in                 coe5cient.
speed above critical Mach number sufhcient               A reference point is usually taken by a plot
to form a strong shock wave can cause sepa-              of drag coe5cient versus Mach number for
ration of the boundary layer and produce                 a constant lift coefficient. Such a graph is
sudden changes in the aerodynamic force                  shown in figure 3.10. The Mach number
coefficients. Such a flow condition is shown             which produces a sharp change in the drag
in figure 3.9 by the flow pattern for M=O.n.             coe5cient is termed the “force divergence”
Notice that a further increase in Mach number            Mach number and, for most airfoils, usually
to 0.82 can enlarge the supersonic area on the           exceeds the critical Mach number at least 5
upper surface and form an additional area of             to 10 percent. This condition is also referred
supersonic flow and normal shock wave on the             to as the “drag divergence” or “drag rise.”
lower surface.                                              PHENOMENA        OF TRANSONIC FLIGHT.
    As the flight speed approaches the speed of          Associated with the “drag rise” are buffet,
sound the areas of supersonic flow enlarge and           trim and stability changes, and a decrease
 the shock waves move nearer the trailing                in control surface effectiveness. Conventional
edge. The boundary layer may remain sepa-                aileron, rudder, and elevator surfaces sub
rated or may reattach depending much upon                jetted to this high frequency buffet may
 the airfoil shape and angle of attack. When             “buzz,” and changes in hinge moments may
the flight speed exceeds the speed of sound              produce undesirable control forces. Of course,
 the “bow” wave forms at the leading edge and            if the buffet is quite severe and prolonged,
this typical flow pattern is illustrated in              structural damage may occur if this operation
figure 3.9 by the drawing for M= 1.05. If the            is in violation of operating limitations.   When
speed is increased to some higher supersonic             airflow separation occurs on the wing due to
                                                                                  NAVWEPS OO-EOT-80
                                                                            HIGH SPEED AERODYNAMICS

                                                 FORCE DIVERGENCE
                CD                                 MACH NUMBER
               DRAG                      CRITICAL
           COEFFICIENT                 MACH NUMBER.

                                                          I                   I          c
                                                        0.5                   1.0
                                              ht,MACH         NUMBER

                               Figure 3ilO.   Compressibility Drag Rise

shock wave formation, there will be a loss of            downwash change can contribute to “pitch
lift and subsequent loss of downwash aft of              up.”
the affected area. If the wings shock unevenly               Since most of the dificulties of transonic
due to physical shape differences or sideslip,           flight are associated with shock wave induced
a rolling moment will be created in the                  flow separation, any means of delaying or
direction of the initial loss of lift and con-           alleviating the shock induced separation will
tribute to control difficulty (“wing drop”).             improve the aerodynamic characteristics. An
If the shock induced separation occurs sym-              aircraft conhguration may utilize thin surfaces
metrically near the wing root, a decrease in             of low aspect ratio with sweepback to delay
downwash behind this area is a corollary of              and reduce the magnitude of transonic force
the loss of lift.  A decrease in downwash on             divergence. In addition, various methods of
the horizontal tail will create a diving moment          boundary layer control, high lift devices,
and the aircraft will “tuck under.” If these             vortex generators, etc., may be applied to
conditions occur on a swept wing. planform,              improve transonic characteristics. For exam-
the wing center of pressure shift contributes            ple, the application of vortex generators to a
to the trim change-root       shock first moves          surface can produce higher local surface veloci-
the wing center of pressure aft and adds to the          ties and increase the kinetic energy of the
diving moment; shock formation at the wing               boundary layer. Thus, a more severe pressure
tips first moves the center of pressure forward          gradient (stronger shock wave) will be neces-
and the resulting climbing moment and tail               sary to produce airflow separation.
 NAVWEPS 00-801-80

      Once the configuration of a transonic air-            can be quite weak, the pressure waves can be
  craft is fixed, the pilot must respect the effect         of sufficient magnitude to create an audible
  of angle of attack and altitude. The local flow           disturbance. Thus, “sonic booms” will be a
1 velocities on any upper surface increase with an          simple consequence of supersonic flight.
  increase in angle of attack. Hence, local sonic              The aircraft powerplant: for supersonic flight
  flow and subsequent shock wave formation                  must be of relatively high thrust output.
  can occur at lower free stream Mach numbers.              Also, in many cases it may be necessary to
  A pilot must appreciate this reduction of force           provide the air breathing powerplant with
  divergence Mach number with lift coefficient              special inlet configurations which will slow
  since maneuvers at high speed may produce                 the airflow to subsonic prior to reaching the
  compressibility effects which may not be en-              compressor face or combustion chamber. Aero-
  countered in unaccelerated flight.      The effect        dynamic heating of supersonic flight can pro-
  of altitude is important since the magnitude              vide critical inlet temperatures for the gas
  of any force or moment change due to com-                 turbine engine as well as critical structural
  pressibility will depend upon the dynamic                 temperatures.
  pressure of the airstream.       Compressibility             The density variations in airflow may be
  effects encountered at high altitude and low              shown by certain optical techniques. Schlieren
  dynamic pressure may be of little consequence             photographs and shadowgraphs can define the
  in the operation of a transonic aircraft. How-            various wave patterns and their effect on the
  ever, the same compressibility         effects en-        airflow.    The Schlieren photographs presented
  countered at low altitudes and high dynamic               in figure 3.11 define the flow conditions on an
  pressures will create greater trim changes,               aircraft in supersonic flight.                    I
  heavier buffet, etc., and perhaps transonic
  flight restrictions which are of principal inter-         TRANSONIC AND SUPERSONIC CONFIGU-
  est only to low altitude.                                    RATIONS
  While many of the particular effects of super-               Aircraft configurations developed for high
  sonic flight will be presented in the detail of           speed flight will have significant differences in
  later discussion, many general effects may be             shape and planform when compared with air-
  anticipated.     The airplane configuration must          craft designed for low speed flight.      One of
  have aerodynamic shapes which will have low               the outstanding differences will be in the
   drag in compressible flow. Generally, this will          selection of airfoil profiles for transonic or
   require airfoil sections of low thickness ratio          supersonic flight.
   and sharp leading edges and body shapes of                   AIRFOIL    SECTIONS. It should be ob-
   high fineness ratio to minimize the supersonic           vious that airfoils for high speed subsonic
   wave drag. Because of the aft movement of the            flight should have high critical Mach num-
   aerodynamic center with supersonic flow, the             bers since critical Mach number defines the
   increase in static longitudinal stability will           lower limit for shock wave formation and
   demand effective, powerful control surfaces to           subsequent force divergence. An additional
    achieve adequate controllability      for super-        complication     to airfoil selection in this
    sonic maneuvering.                                      speed range is that the airfoil should have
      As a corollary of supersonic flight the shock         a high maximum lift coefficient and sufficient
   wave formation on the airplane may create                thickness to allow application of high lift
   special problems outside the immediate vicinity          devices. Otherwise an excessive wing area
    of the airplane surfaces. While the shock               would be required to provide maneuverability
    waves a great distance away from the airplane            and reasonable takeoff and landing speeds.
                                                                NAVWEPS DG-RDT-RD
                                                          HIGH SPEED AERODYNAMICS

                      FE!4 MODEL AT VARIOUS
                          MACH NUMBERS
                           a-O0  pee

        M* 1.2                                         W 1.6

Figure 3.11. Schliemn Photographs of Supersonic Flight (sheet 1 of 2)

Figure 3.7 1. Schlieren Photographs of Supersonic Flight (sheet 2 of 2)
                                                                                NAVWEPS 00-801-80
                                                                          HIGH SPEED AERODYNAMICS

However, if high speed flight is the primary            Figure 3.13 shows the flow patterns for
consideration, the airfoil must be chosen to         two basic supersonic airfoil sections and pro-
have. the highest practical critical Mach            vides the approximate equations for lift,drag,
number.                                              and lift curve slope. Since the wave drag is
    Critical Mach number has been defined as         the only factor of difference between -the two
the flight Mach number which produces first          airfoil sections, notice the configuration fac-
evidence of local sonic flow. Thus, the air-         tors which affect the wave drag. For the
foil shape and lift coe&ient-which       determine   same thickness ratio, the circular arc airfoil
the pressure and velocity distribution-will          would have a larger wedge angle formed
have a profound effect on critical Mach number.      between the upper and lower surfaces at the
Conventional, low speed airfoil shapes have          leading edge. At the same flight Mach num-
relatively poor compressibility characteristics      ber the larger angle at the leading edge would
because of the high local velocities near the        form the stronger shock wave at the nose and
leading edge. These high local velocities are        cause a greater pressure change on the circular
inevitable if both the maximum thickness and         arc airfoil.   This same principle applies when
camber are well forward on the chord. An             investigating the effect of airfoil thickness.
improvement of the compressibility character-        Notice that the wave drag coefficients for
istics can be obtained by moving the points of       both airfoils vary as the SQUARE of the
maximum camber and thickness aft on the              thickness ratio, e.g., if the thickness ratio
chord. This would distribute the pressure and        were doubled, the wave drag coefhcient would
velocity more evenly along the chord and             he four times as great. If the thickness were
produce a lower peak velocity for the same           increased, the airflow at the leading edge will
lift coefficient. Fortunately, the airfoil shape     experience a greater change in direction and
 to provide extensive lamiaar flow and low           a stronger shock wave will be formed. This
profile drag in low speed, subsonic flight will      powerful variation of wave drag with thick-
provide a pressure distribution which is favor-      ness ratio necessitates the use of very thin air-
 able for high speed flight.          Figure 3.12    foils with sharp leading edges for supersonic
illustrates    the pressure distributions      and   flight.   An additional consideration is that
 variation of critical Mach number with lift         thin airfoil sections favor the use of low aspect
coefficient for a conventional low speed airfoil     ratios and high taper to obtain lightweight
and a high speed section.                            structures and preserve stiffness and rigidity.
    In order to obtain a high critical Mach              The parameter JMz-l          appears in the
 number from an airfoil at some low lift              denominator of each of the equations for the
 coefficient the section must have:                   aerodynamic coefficients and indicates a de-
       (u) Low thickness ratio. The point of         crease in each of these coefficients with an
    maximum thickness should be aft to smooth         increase in Mach number. Essentially, this
    the pressure distribution.                       means that any aerodynamic surface becomes
       (6) Low camber. The mean camber line          less sensitive to changes in angle of attack at
    should be shaped to help minimize the            higher Mach numbers. The decrease in lift
    local velocity peaks.                            curve slope with Mach number has tremendous
In addition, the higher the required lift            implications in the stability and control of
 coefficient the lower the critical Mach number       high speed aircraft.   The vertical tail becomes
 and more camber is required of the airfoil.          less sensitive to angles of sideslip and the
 If supersonic flight is a possibility the thick-     directional stability of the aircraft will deteri-
ness ratio and leading edge radius must be            orate with Mach number. The horizontal
 small to decrease wave drag.                         tail of the airplane experiences the same

                                              SAME Cl                 LOW PEAK FOR



                                                                    HIGH SPEED SECTION
                                                                     (LAMINAR FLOW)

                                                     SECTION LIFT COEFFICIENT

                          Figure 3.72. High speed Section Characteristics

                                                                      NAVWEPS 00-BOT-80
                                                                HIGH SPEED AERODYNAMICS

    DOUBLE WEDGE SECTION                            CIRCULAR    ARC SECTION






          ( +/c ) = AIRFOIL THICKNESS    RATIO

             a      2 ANGLE OF ATTACK (IN RADIANS)

            M    = MACH NUMBER

   Figure 3.73. Approximate   Equations for Supersonic Section Characteristics


 general effect and contributes less damping to                 In addition to the delay of the onset of com-
 longitudinal pitching oscillations.     These ef-          pressibility effects, sweepback will reduce the
 fects can become so significant at high Mach               magnitude of the changes in force coefficients
 numbers that the aircraft might require com-               due to compressibility.      Since’the component
 plete synthetic stabilization.                             of velocity perpendicular to the leading edge is
     PLANFORM EFFECTS. The development                      less than the free stream velocity, the magni-
 of surfaces for high speed involves considera-             tude of all pressure forces on the wing will be
 tion of many items in addition to the airfoil              reduced (approximately by the square of the
 sections. Taper, aspect ratio, and sweepback               cosine of the sweep angle). Since compressi-
 can produce major effects on the aerodynamic               bility force divergence occurs due to changes in
 characteristics of a surface in high speed flight.         pressure distribution, the use of sweepback will
 Sweepback produces an unusual effect on the                 “soften” the force divergence. This effect is
  high speed characteristics of a surface and has            illustrated by the graph of figure 3.14 which
  basis in a very fundamental concept of aero-              shows the typical variation of drag coeiIicient
  dynamics. A grossly simplified method of                  with Mach number for various sweepback
  visualizing the effect of sweepback is shown in            angles. The straight wing shown begins drag
  figure 3.14. The swept wing shown has the                 rise at M=O.lO, reaches a peak near M=l.O,
  streamwise velocity broken down to a com-                  and begins a continual drop past M= 1.0. Note
  ponent of velocity perpendicular to the leading            that the use of sweepback then deh+y~the drag
  edge and a component parallel to the leading               rise to some~higher Mach number and wdms
  edge. The component of speed perpendicular                 the magnitude of the drag rise.
  to the leading edge is less than the               In view of the preceding discussion, sweep-
  speed (by the cosine of the sweep angle) and               back will have the following principal ad-
  it is this velocity component which determines             vantages :
  the magnitude of the pressure distribution.                       (1) Sweepback will delay the onset of all
      The component of speed parallel to the lead-               compressibility effects. Critical Mach num-
  ing edge could be visualized as moving across                  ber and force divergence Mach number will
  constant sections and; in doing so, does not                   increase since the velocity component affect-
  contribute to the pressure distribution on the                 ing the pressure distribution is less than the
   swept wing. Hence, sweep of a surface pro-                    free stream velocity. Also, the peak of drag
   duces a beneficial e&ct ‘ high speed flight                   rise is delayed to some higher supersonic
   since higher flight speeds may be obtained be-                 speed-approximately     the speed which pro-
   fore components of speed perpendicular to the                  duces sonic flow perpendicular to the leading
   leading edge produce critical conditions on the                edge. Various sweeps applied to wings of
   wing. This is one of the most important ad-                   .moderate aspect ratio will produce these
   vantage of sweep since there is an increase in                approximate effects in transonic flight:
   critical Mach number, force divergence Mach
   number, and the Mach number at which the
   drag rise will peak. In other words, sweep will
   delay the onset of compressibility effects.                              angle(k)
      Generally, the effect of wing sweep will
   apply to either sweep back or sweep forward.
   While the swept forward wing has been used
1 in rare instances, the aeroelastic instability of
   such a wing creates such a problem that sweep
   back is more practical for ordinary applica-
 Revised Jaanuar~ 1965
                                                                            NAVWEPS 00-80T-80
                                                                      HIGH SPEED AERODYNAMICS

                                                                       VELOCITY COhlPONENT
                                                                       PARALLEL TO LEADING
                                         FREE STREAM
                          /                                    \

        SWEEP ANGLE,     11

                                                                       VELOCITY COMPONENT
                                                                       PERPENDICULAR TO
                                                                       LEADING EDGE


              0                  I.0                         2.0                    3.0
                                       MACH NUMBER, M

                                                  IlC.IT t            ,STRAIGHT

                  MACH NUMBER, M                                   MACH NUMBER, M

                       Figure 3.14. General Effects of Sweepbock

                EFFECT       OF SWEEPBACK       ON LOW SPEED LIFT           CURVE

         COEFFICIENT                                                                 SWEPT

                                       ANGLE   OF ATTACK,O

                    EFFECT   OF SWEEPBACK       ON YAW AND ROLL            MOMENTS    /

                                                                           YAW MOMENT

                     SWEPT WING AT                                      SWEPT WING IN A
                      ZERO SIDESLIP                                  SIDESLIP TO THE RIGHT

                       SWEPT    WING                                    SWEPT WING IN A
                     IN LEVEL   FLIGHT                                  S IDESLIP TOWARD
                                                                         THE DOWN WING

                       Figure 3.15.   Aerodynamic         Effects Due to Sweepbach

                                                                                       NAVWEPS 00-801-80
                                                                                 HIGH SPEED AERODYNAMICS

     (2) Sweepback will reduce the magnitude                     (1) The wing lift curve slope is reduced
  of change in the aerodynamic force coeffi-                 for a given aspect ratio. This is illustrated
  cients due to compressibility.  Any change                 by the lift curve comparison of figure 3.15
  in drag, lift, or moment coefbcients will be               for the straight and swept wing.             Any
  reduced by the use of sweepback. Various                   reduction of lift curve slope implies the
  sweep angles applied to wings of moderate                  wing is less sensitive to changes in angle of
  aspect ratio will produce these approximate                attack. This is a beneficial effect only when
  effects in transonic flight.                               the effect of gusts and turbulence is con-
                                                             sidered. Since the swept wing has the
                                                             lower lift curve slope it will be less sensitive
                                                             to gusts and experience less “bump” due
                                                             to gust for a given aspect ratio and wing
                                                  -_         loading. This is a consideration particular
    00...............................             0           to the aircraft whose structural design shows
    150..............         ................    5           a predominating effect of the gust load
    M”..............................             15           spectrum, e.g., transport, cargo, and patrol
    45’                                          35
    600..............................            60          types.
                                                  -              (2) “Divergence” of a surface is an aero-
These advantages of drag reduction and preser-                elastic problem which can occur at high
vation of the transonic maximum lift coefficient              dynamic pressures. Combined bending and
are illustrated in figure 3.14.                               twisting deflections interact with aerody-
                                                              namic forces to produce sudden failure of
    Thus, the use of sweepback on a transonic                 the surface at high speeds. Sweep forward
aircraft will reduce and delay the drag rise and              will aggravate this situation by “leading”
preserve the maneuverability of the aircraft                  the wing into the windstream and tends to
in transonic flight. It should be noted that a                lower the divergence speed. On the other
small amount of sweepback produces very                       hand, sweepback tends to stabilize the
little benefit. If sweepback is to be used at all,            surface by “trailing” and tends to raise the
at least 30’ to 33’ must be used to produce any               divergence speed. By this tendency, sweep-
significant benefit. Also note from figure 3.14               back may be beneficial in preventing di-
that the amount of sweepback required to                      vergence within the anticipated speed range.
d&y drag rise in supersonic flight is very large,                 (3) Sweepback contributes slightly to the
e.g., more than 60° necessary at M=2.0.        By             static directional-or   weathercock-stability
comparison of the drag curves at high Mach                     of an aircraft.    This effect may be appre-
numbers it will be appreciated that extremely
                                                               ciated by inspection of hgure 3.13 which
high (and possibly impractical) sweepback is                   shows the swept wing in a yaw or sideslip.
necessary to delay drag rise and that the lowest               The wing into the wind has less sweep and
drag is abtained with zero sweepback. There-
                                                               a slight increase in drag; the wing away
fore, the planform of a wing designed to operate
                                                               from the wind has more sweep and less
continuously at high Mach numbers will tend
to be very thin, low aspect ratio, and unswept.                drag. The net effect of these force changes is
An immediate conclusion is that sweepback is                   to produce a yawing moment tending to
a device of greatest application in the regime of              retarn the nose into the relative wind.
transonic flight.                                              This directional stability contribution        is
     A few of the less significant advantages of               usually small and of importance in tailless
 sweepback are as follows:                                     aircraft only.

                                                                                         Revised January   l%S
                                                                                                NAVWEPS 00-801-80
                                                                                          HIGH SPEED AERODYNAMICS

       (4) Sweepback contributes to lateral sta-            arated. The combined effect of taper and
    bility in rhe same sense as dihedral. When              sweep present a considerable problem of tip
   the swept wing aircraft is placed in a side-             stall and this is illustrated by the flow pat-
   slip, the wing into the wind experiences an              terns of figure 3.16. Design for high speed
    increase in lift since the sweep is less and            performance may dictate high sweepback,
    the wing away from the wind produces less               while structural efficiency may demand a
   lift since rhe sweep is greater. As shown in             highly tapered planform. When such is the
   figure 3.15, the swept wing aircraft in a                case, the wing may require extensive aero-
   sideslip experiences lift changes and a sub-             dynamic tailoring to provide a suitable stall
   sequent rolling moment which tends to                    pattern and a lift distribution at cruise condi-
   right the aircraft.      This lateral stability          tion which reduces drag due to lift. Wash-
   conrribution depends on the sweepback and                out of the tip, variation of section camber
   the lift coefficient of the wing. A highly               throughout span, flow fences, slats, leading
   swept wing operating at high lift coeflicient            edge extension, etc., are typical devices used
   usually experiences such an excess of this               to modify the stall pattern and minimize
   lateral stability contribution that adequate             drag due to lift at cruise condition.
   controllability may be a significant problem.               (2) As shown by the lift curve of figure
   As shown, the swept wing has certain im-                 3.15 the use of sweepback will reduce the lift
portant advantages. However, the use of                     curve slope and the subsonic maximum lift
sweepback produces certain inevitable disad-                coefficient. It is important to note this
vantages which are important from the stand-                case is definitely subsonic since sweepback
point of both airplane design and flight oper-              may be used to improve the transonic ma-
ations. The most important of these disad-                  neuvering capability.     Various sweep angles
vantages are as follows:                                    applied to wings of moderate aspect ratio
       (1) When sweepback is combined with                  produce these approximate effects on the
   taper there is an extremely powerful tendency            subsonic lift characteristics:
   for the wing to stall tip first. This pattern
   of stall is very undesirable since there would
   be little stall warning, a serious reduction                 Angle
                                                            sweep (A):
   in lateral control effectiveness, and the for-               O”.................................          0
   ward shift of the center of pressure would                     w................................          4
   contribute to a nose up moment (“pitch up”                     300.                                      14
   or “stick force lightening”).      Taper has its               450..........                             30
                                                                  M)Q................................       yl
   own effect of producing higher local lift
   coefhcients toward the tip and one of the                The reduction of the low speed maximum
   effects of sweepback is very similar.        All         lift coefficient (which is in addition to that
   outboard wing sections are affected by the               lost due to tip stall) has very important
   upwash of the preceding inboard sections                 implications in design. If wing loading is
   and the lift distribution resulting from sweep-          not reduced, stall speeds increase and sub-
   back alone is similar to that of high taper.             sonic maneuverability decreases. On the
       An additional effect is the tendency to              other hand, if wing loading is reduced, the
   develop a strong spanwise flow of the bound-             increase in wing surface area may reduce
   ary layer toward the tip when the wing is at             the anticipated benefit of sweepback in the
   high lift coefficients. This spanwise flow               transonic flight regime. Since the require-
   produces a relatively low energy boundary                ments of performance predominate, certain
   layer near the tip which can be easily sep-              increases of stall speeds, takeoff speeds,


                                SPANWISE LIFT O~STR~BUT~ON
         WC                         TIP STALL TENDENCY
        26                          OF UNMOOIFIEO WING
        g::        1.0    - - - -                                    -    I.0
        Ot+   ,s
        t ” 3
        it                               WING MODIFIED BY
        zi                              WASHOUT, CAMBER,
        OCJ                           SECTION VARIATION, ETC.
        v)          0 f                                             ! 0
                     ROOT                                          TIP

                                       TYPICAL STALLSEQUENCE

             SPANWISE FLOW OF
              BOUNDARY LAYER

                                                           STALL AREA

                   Figure 3.16. Stall Characteristics of Tapered Swept Wing

                                                                   NAVWEPS 00-8OT-80
                                                             HIGH SPEED AERODYNAMICS

                                             STRAIGHT WING OF SAME
                                             AREA, ASPEC&ATIO,  AN0


                           WING BENDING PRODUCES
-/TIP                               ROTATION


   TIP VIEW                                    TRAILING EDGE VIEW

              figure 3.17. Structurd Complications Due to Sweephk


 and landing speeds usually will be accepted.                 marginal control during crosswind takeoff
 While the reduction of lift curve slope may                  and landing where the aircraft must move in
 be an advantage for gust considerations,                     a controlled sideslip. Therefore, it is not
 the reduced sensitivity to changes in angle                  unusual to find swept wing aircraft with
 of attack has certain undesirable effects in                 negative dihedral and lateral control de-
 subsonic flight.       The reduced wing lift                 vices designed principally to meet cross wind
 curve slope tends to increase maximum lift                   takeoff and landing requirements.
 angles of attack and complicate the problem                      (5) The structural complexity and aero-
 of landing gear design and cockpit visi-                     elastic problems created by sweepback are of
 bility.    Also, the lower lift curve slope                  great importance. First, there is the effect
 would reduce the contribution to stability                   shown in figure 3.17 that swept wing has a
 of a given tail surface area.                                greater structural span than a straight wing
    (3) The use of sweepback will reduce                      of the same area and aspect ratio. This effect
 the effectiveness of trailing edge control                    increases wing structural      weight since
 surfaces and high lift devices. A typical                    greater bending and shear material must be
 example of this effect is the application of                 distributed in the wing to produce the same
 a single slotted flap over the inboard 60                    design strength. An additional problem is
 percent span to both a straight wing and a                   created near the wing root and “carry-
 wing with 35” sweepback. The flap applied                     through” structure due to the large twisting
 to the straight wing produces an increase                    loads and the tendency of the bending stress
 in maximum lift coefficient of approxi-                      distribution to concentrate toward the trail-
 mately 50 percent. The same type flap                         ing edge. Also shown in figure 3.17 is the
 applied to the swept wing produces an                         influence of wing deflection on the spanwise
 increase in maximum lift coefficient of                      lift distribution.   Wing bending produces
 approximately 20 percent. To produce some                    tip rotation which tends to unload the tip
 reasonable maximum lift coefficient one a                    and move the center of pressure forward.
 swept wing may require unsweeping the                        Thus, the same effect which tends to allay
 flap hinge line, application of leading edge                 divergence can make an undesirable contri-
 high lift devices such as slots or slats, and                bution to longitudinal stability.
 possibly boundary layer control.                             EFFECT OF ASPECT RATIO AND TIP
    (4) As described previously, sweepback                 SHAPE. In addition to wing sweep, plan-
 contributes to lateral stability by producing             form properties such as aspect ratio, and tip
 stable rolling moments with sideslip. The                 shape, can produce significant effects on the
 lateral stability contribution of sweepback               aerodynamic characteristics at high speeds.
 varies with the amount of wing sweepback                  There is no particular effect of aspect ratio on
 and wing lift coefficient-large       sweepback           critical Mach number at high or medium
 and high lift coefficients producing large                aspect ratios. The aspect ratio must be less
 contribution to lateral stability.    While sta-          than four or five to produce any apparent
 bility is desirable, any excess of stability will         change in critical Mach number. This effect
 reduce controllability.    For the majority of            is shown for a typical 9 percent thick sym-
 airplane configurations, high lateral sta-                metrical airfoil in the graph of figure 3.18.
 bility is neither necessary nor desirable, but            Note that very low aspect ratios are required
 adequate control in roll is absolutely neces-             to cause a significant increase in critical Mach
 sary for good flying qualities. An excess of              number. Very low aspect ratios create the
 lateral stability from sweepback can aggra-               extremes of three dimensional flow and sub-
 vate “Dutch roll” problems and produce                    sequent increase in free stream speed to create
                                                                                         NAVWEPS 00-801-80
                                                                                   HIGH SPEED AERODYNAMICS

                            APPROXIMATE  VARIATION   OF CRITICAL
                            MACH NUMBER WITH ASPECT RATIO FOR
                            A 9% THICK AIRFOIL   SECTION

  MACH      .85-
  MCR      .80-

            .75 -
            .7od        I           1   1    I             1    9    I
                   01       2   3   4   5    6      7      8    9   IO   II   I2
                                    ASPECT        RATIO,       AR

                                                        MACH CONES FORMED AT
                                                        TIPS OF RECTANGULAR
                                                        WING IN SUPERSONIC  FLOW


           AT THE TIP OF THE

                                                               Y-        MACH CONE

                                    VORTEX CREATED WITHIN
                                    THE MACH CONE AT THE TIP
                                    OF THE RECTANGULAR  WING

                   WING WITH TIPS
                   “RAKED” OUTSIDE
                   THE TIP CONES

                             Figure 3.18. Generd        Pknform Effects


local sonic flow. Actually, the extremely                 supersonic drag due to lift is a function of the
low aspect ratios required to produce high                section and angle of attack while the subsonic
critical Mach number are not too practical.               induced drag is a function of lift coefficient
Generally, the advantage of low aspect ratio              and aspect ratio. This comparison makes it
must be combined with sweepback and high                  obvious that supersonic flight does not demand
speed airfoil sections.                                   the use of high aspect ratio planforms typical
   The thin rectangular wing in supersonic                of low speed aircraft.      In fact, low aspect
flow illustrates several important facts. AS              ratios and high taper are favorable from the
shown in figure 3.18, Mach cones form at the              standpoint of structural considerations if very
tips of the rectangular wing and affect t~he              thin sections are used to minimize wave drag.
pressure distribution on the area within the                 If sweepback is applied to the supersonic
cone. The vortex develops within the tip                  wing, the pressure distribution will be affected
cone due to the pressure differenti,al and the            by the location of the Mach cone with respect
resulting average pressure on the area within             to the leading edge. Figure 3.19 illustrates the
thecone is approximately one-half the pressure            pressure distribution for the delta wing plan-
between the cones. Three-dimensional flow                 form in supersonic flight with the leading edge
on the wing is then confined to the area within           behind or ahead of the Mach cone. When the
the tip cones, while the area between the                 leading edge is behind the Mach cone the com-
cones experiences pure two-dimensional flow.              ponents of velocity perpendicular to the leading
    It is important to realize that the three-            edge are still subsonic even though the free
dimensional flow on the rectangular wing in               stream flow is supersonic and the resulting
supersonic flight differs greatly from that of            pressure distribution will greatly resemble the
subsonic flight.    A wing of finite aspect ratio         subsonic pressure distribution for such a plan-
in subsonic flight experiences a three-dimen-             form. Tailoring the leading edge shape and
sional flow which includes the tip vortices,              camber can minimize the components of the
downwash behind the wing, upwash ahead of                 high leading edge suction pressure which are
the wing, and local induced velocities along              inclined in the drag direction and the drag due
the span. Recall that the local induced veloc-            to lift can be reduced. If the leading edge
ities along the span of the wing would incline            is ahead of the h4ach cone, the flow over this
the section lift aft relative to the free stream          area will correspond to the two-dimensional
and result in “induced drag.” Such a flow                 supersonic flow and produce constant pressure
condition cannot be directly correlated with              for that portion of the surface between the
the wing in supersonic flow, ~ The flow pattern           leading edge and the Mach cone.
for the rectangular wing of figure 3.18 dem-                 CONTROL SURFACES. The design of con-
onstrates that the three-dimensional flow is              trol surfaces for transonic and supersonic flight
confined to the tip, and pure two-dimensional             involves many important considerations. This
flow exists on the wing area between the tip              fact is illustrated by the typical transonic and
cones. If the wing tips were to be “raked”                supersonic flow patterns of figure 3.19. Trail-
 outside the tip cones, the entire wing flow              ing edge control surfaces can be affected ad-
would correspond to the two-dimensional (or               versely by the shock waves formed in flight
 section) conditions.                                     above critical Mach number. If the airflow
    Therefore, for the wing in supersonic flow,           is separated by the shock wave the resulting
no upwash exists ahead of the wing, three-                buffet of the control surface can be very objec-
dimensional effects are confined to the tip               tionable. In addition to the buffet of the sur-
cones, and no local induced velocities occur              face, the change in the pressure distribution due
along the span between the tip cones. The                 to separation and the shock wave location can
                                                                   NAVWEPS 00-801-60
                                                             HIGH SPEED AERODYNAMICS
                      DELTA    WING   PLANFORM


        MACH CONE                            MACH CONE

                         CONTFOL SURFACE
                          FLOW PATTERNS

                        SONIC FLOW ON
                        G EDGE CONTROLS




             Figure 3.19. Planform Effects and Control Surfaces

create very large changes in control surface               just above the speed of sound only slight modi-
hinge moments. Such large changes in hinge                 fications to ordinary subsonic inlet design pro-
moments create very undesirable control forces             duce satisfactory performance. However, at
and present the need for an “irreversible” con-            supersonic flight speeds, the inlet design must
trol system. An irreversible control. system               slow the air with the weakest possible series-or
would employ powerful hydraulic or electric                combination of shock waves to minimize en-
actuators to move the surfaces upon control by             ergy losses and temperature rise. Figure 3.20
the pilot and the airloads developed on the                illustrates some of the various forms of super-
surface could not feed back to the pilot. Of               sonic inlets or “diffusers.”
course, suitable control forces would be syn-                  One of the least complicated types of inlet
thesized by bungees, “4” springs, bobweights,              is the simple normal shock type diffuser. This
etc.                                                       type of inlet employs a single normal shock
   Transonic and supersonic flight can cause a             wave at the inlet with a subsequent internal
noticeable reduction in the effectiveness of               subsonic compression. At low supersonic Mach J
trailing edge control surfaces. The deflection             numbers the strength of the normal shock wave
of a trailing edge control surface at low sub-             is not too great and this type of inlet is quite
sonic speeds alters the pressure distribution on           practical.    At higher supersonic Mach num-
the fixed portion as well as the movable portion           bers, the single normal shock wave is very
of the surface. This is true to the extent that a          strong and causes a great reduction in the total
l-degree deflection of a 40 percent chord eleva-           pressure recovered by the inlet. In addition,
tor produces a lift change very nearly the                  it is necessary to consider that the wasted 1
equivalent of a l-degree change in stabilizer               energy of the airstream will appear as an addi-
setting. However, if supersonic flow exists on              tional undesirable rise in temperature of the
the surface, a deflection of the trailing edge              captured inlet airflow.
control surface cannot influence the pressure                  If the supersonic’airstream can be captured,
distribution in the supersonic area ahead of the           the shock wave formations tiill be swallowed
movable control surface. This is especially                and a gradual contraction will reduce the speed
true in high supersonic flight where supersonic            to just above sonic. Subsequent diverging flow 1
flow exists over the entire chord and the change           section can then produce the normal shock
in pressure distribution is limited to the area of         wave which slows the airstream to subsonic.
the control surface. The reduction in effective-           Further expansion continues to slow the air to
ness of the trailing edge control surface at tran-         lower subsonic speeds. This is the convergent-
sonic and supersonic speeds necessitates the use           divergent type inlet shown in figure 3.20. If
of an all movable surface. Application of the              the initial contraction is too extreme for the
all movable control surface to the horizontal              inlet Mach number, the shock wave formation
tail is most usual since the increase in longi-            will not be swallowed and will move out in
tudinal stability in supersonic flight requires a          front of the inlet. The external location of the
high degree of control effectiveness to achieve            normal shock wave will produce subsonic flow
required controllability   for supersonic maneu-           immediately at the inlet. Since the airstream
vering.                                                    is suddenly slowed to subsonic through the
   SUPERSONIC         ENGINE      INLETS.      Air         strong normal shock a greater loss of airstream
which enters the compressor section of a jet               energy wiIl occur.
engine or the combustion chamber of a ramlet                   Another form of diffuser employs an external
usually must be slowed to subsonic velocity.               oblique shock wave which slows the super-
This process must be accomplished with the                 sonic airstream before the normal shock occurs.
least possible waste of energy. At flight speeds           Ideally, the supersonic airstream could be

Revised January   1965
                                                                       NAVWEPS 00-8OT-80
                                                                 HIGH SPEED AERODYNAMICS


  SINGLEOBLIOUE SHOCK                                         IPLE OBLIOUE SHOCK

                                                  NORMAL SHOCK WAVE

   NEAR DESIGN RANGE                                 BELOW DESIGN RANGE

                      EFFECT OF DIFFUSER DESIGN AND

   .90    -
   .BO    -
   .70    -
   .60    -
.50 -             -
   .40    -
   .30    -
   .20    -
    .I0   7
0          I
           I          1.5              2.5              3.5
          1.0                  2.0            3.0                 4.0
                                      MACH NUhl6ER

                Figure 3.20.   Various Types of Supersonic Mets


 slowed gradually through a series of very            airplane are developed, the most likely general
 weak oblique shock waves to a speed just             configuration properties will beas follows:
 above sonic velocity.       Then the subsequent             (1) The wing will be of low aspect ratio,
 normal shock to subsonic could be quite weak.            have noticeable taper, and have sweepback
 Such a combination of the weakest possible               depending on the design speed range. The
 waves would result in the least waste of energy          wing sections will be of low thickness ratio
 and the highest pressure recovery. The ef-               and require sharp leading edges.
 ficiency of various types of diffusers is shown             (2) The fmelagc and naceller will be of
 in figure 3.20 and illustrates this principle.           high fineness ratio (long and slender). The
    An obvious complication of the supersonic             supersonic pressure distribution may create
 inlet is that the optimum shape is variable with         significant lift and drag and require con-
 inlet flow direction and Mach number. In                 sideration of the stability contribution of
 other words, to derive highest efficiency and            these surfaces.
 stability of operation, the geometry of the                 (3) The t&Z surfaces will be similar to
 inlet would be different at each Mach number             the wing-low     aspect ratio, tapered, swept
 and angle of attack of flight.    A typical super-       and of thin section with sharp leading edge.
 sonic military aircraft may experience large             The controls will be fully powered and ir-
 variations in angle of attack, sideslip angle,           reversible with all movable surfaces the
 and flight Mach number during normal oper-               most likely configuration.
 ation. These large variations in inlet flow                 (4) In order to reduce interference drag
 conditions create certain important design               in transonic and supersonic flight, the gross
 considerations.                                          cross section of the aircraft may be “area
       (1) The inlet should provide the highest           ruled” to approach that of some optimum
    practical efficiency. The ratio of recovered          high speed shape.
    total pressure to airstream total pressure is         One of the most important qualities of high
    an appropriate measure of this efficiency.        speed configurations will be the low speed
       (2) The inlet should match the demands         flight characteristics.    The low aspect ratio
    of the powerplant for airflow. The airflow        swept wing planform has the characteristic
    captured by the inlet should match that           of high induced drag at low flight speeds.
    necessary for engine operation.                   Steep turns, excessively low airspeeds, and
       (3) Operation of the inlet at flight condi-    steep, power-off approaches can then produce
    tions other than the design condition should      extremely high rates of descent during landing.
    not cause a noticeable loss of efficiency or      Sweepback and low aspect ratio can cause
    excess drag. The operation of the inlet                                   of
                                                      severe deterioration ‘ handling qualities at
    should be stable and not allow “buzz”             speeds below those recommended for takeoff
    conditions (an oscillation of shock location      and landing. On the other hand, thin, swept
    possible during off-design operation).            wings at high wing loading will have rela-
In order to develop a good, stable inlet design,      tively high landing speeds. Any excess of
the performance at the design condition may           this basically high airspeed can create an im-
be compromised. A large variation of inlet            possible requirement of brakes, tires, and arrest
flow conditions may require special geometric         ing gear. These characteristics require that
features for the inlet surfaces or a completely       the pilot account for the variation of optimum
variable geometry inlet design,                       speeds with weight changes and adhere to the
    SUPERSONIC CONFIGURATIONS.                When    procedures and techniques outlined in the
all the various components of the supersonic          flight handbook.
                                                                                             NAVWEPS Do-Sd-eD
                                                                                    “,G”    SPEED AERODYNAMICS

                                 EFFECT OF SPEED AND ALTITUDE
                                    ON AERODYNAMIC  HEATING

                                                     SEA LEVEL

                                      RAM    TEMPERATURE

Z                                                                                  STAGNATION
w                                                                                 TEMPERATURE
                                                                                      IN THE

         0,              --I
              0                500          1000           1500         2000      2500            3000
                                            TRUE     AIRSPEED,       KNOTS

                                      APPROXIMATE    EFFECT OF TEMPERATURE
                                 ON TENSILE   ULTIMATE  STRENGTH, l/2 HR, EXPOSURE







                   30-                                          ,-ALUMINUM

                   20-                                              ALLOY


                    Or          I
                         0     100    200   300     400    500    600    700   SO0 900     ~000
                                               TEMPERATURE,              “F

                                     Figure 3.21. Aerodynamic Heating


 AERODYNAMIC          HEATING                              Higher temperatures produce definite reduc-
                                                           tions in the strength of aluminum alloy and
     When air flows over any aerodynamic surface
                                                           require the use of titanium alloys, stainless
  certain reductions in velocity occur with cor-
                                                           steels, etc., at very high temperatures. Con-
  responding increases in temperature.        The
                                                           tinued exposure at elevated temperatures effects
  greatest reduction in velocity and increase in
                                                           further reductions of strength and magnifies the
  temperature will occur at the various stagna-
                                                           problems of “creep” failure and structural
  tion points on the aircraft. Of course, similar
  changes occur at other points on the aircraft
                                                              The turbojet engine is adversely affected by
  but these temperatures can be related to the
                                                           high compressor inlet air temperatures. Since
  ram temperature rise at the stagnation point.
                                                           the thrust output of the turbojet is some func-
  While subsonic flight does not produce temper-
                                                           tion of the fuel flow, high compressor inlet air
  atures of any real concern, supersonic flight
                                                           temperatures reduce the fuel flow that can be
  can produce temperatures high enough to be
                                                           used within      turbine operating temperature
  of major importance to the airframe and power-
                                                           limits.    The reduction in performance of the
  plant structure. The graph of figure 3.21 il-
                                                           turbojet engines with high compressor inlet
1 lustrates the variation of ram temperature rise
                                                           air temperatures requires that the inlet design
  with airspeed in the standard atmosphere.
                                                           produce the highest practical efficiency and
  The ram temperature rise is independent of
                                                           minimize the temperature rise of the air
  altitude and is a function of true .airspeed.
                                                           delivered to the compressor face.
  Actual temperatures would be the sum of the
                                                              High flight speeds and compressible flow
  temperature rife and the ambient air temper-
                                                           dictate airplane configurations which are much
  ature. ~Thus, low altitude flight at high Mach
  numbers will produce the highest temperatures.           different from the ordinary subsonic airplane.
     In addition to the effect on the crew member          To achieve safe and efficient operation, the pilot
  environment,     aerodynamic heating creates             of the modern, high speed aircraft must under-
  special problems for the airplane structure              stand and appreciate the advantages and dis-
  and the powerplant.       The effect of tempera-         advantages of the configuration. A knowledge
  ture on the short time strength of three typical         of high speed aerodynamics will contribute
  structural materials is shown in figure 3.21.            greatly to this understanding.

  Revised January   1965
                                                                                  NAVWEPS 00-80T-80
                                                                               STABILITY AND CONTROL

                                          Chapter         4

                           STABILITY AND CONTROL

   An aircraft must have satisfactory handling          flight which provide the most critical require-
qualities in addition to adequate performance.          ments of stability and control and these condi-
‘lYhe aircraft must have adequate stability to          tions must be understood and respected to
maintain a uniform flight condition and recover         accomplish safe and efficient operation of the
from the various disturbing influences. It is           aircraft.
necessary to provide sufficient stability to                            DEFINITIONS
minimize the workload of the pilot. Also, the
                                                        STATIC   STABILITY
aircraft must have proper response to the
controls so that it may achieve the inherent              An aircraft is in a state of equilibrium when
performance. There are certain conditions of            the sum of all forces and all moments is equal

                        POSITIVE   STATIC      STABILITY

                            TENDENCY TO RETURN
                              TO EOUILIBRIUM

                             TENDENCY TO CONTINUE
                          IN/DISPLACEMENT DIRECTION

                         NEGATIVE    STATIC        STABILITY

                            EOulLlBRlUM        ENCOUNTERED
                          AT ANY POINT         OF DISPLACEMENT



                           Figure 4.1.    Static   Stability
                                                                                          NAVWEPS 00-802-80
                                                                                       STABILITY ,AND CONTROL

to zero. When an aircraft is in equilibrium,                  aircraft from some trimmed angle of attack.
there are no accelerations and the aircraft                   If the aerodynamic pitching moments created
continues in a steady condition of flight.         If         by this displacement tend to return the air-
the equilibrium is disturbed by a gust or deflec-             craft to the equilibrium angle of attack the
tion of the controls, the aircraft will experi-               aircraft   has positive   static longitudinal
ence acceleration due to unbalance of moment                  stability.
or force.
    The static stability of a system is defined by            DYNAMIC      STABILITY
the initial tendency to return to equilibrium
conditions following some disturbance from                        While static stability is concerned with the
equilibrium.      If an object is disturbed from              tendency of a displaced body to return to
equilibrium and has the tendency to return                    equilibrium, dynamic stability is defined by
to equilibrium, positive .rtatic Jtability exists.            the resulting motion with time. If an object is
If the object has a tendency to continue in the               disturbed from equilibrium, the time history
direction of disturbance, negative static stability           of the resulting motion indicates the dynamic
or static instability exists. An intermediate                 stability of the system. In general, the system
                                                              will demonstrate positive dynamic stability
condition could occur where an object dis-
placed from equilibrium remains in equilibrium                if the amplitude of motion decreases with
                                                              time. The various condirions of possible
in the displaced position.      If the object subject
                                                              dynamic behavior are illustrated by the time
to a disturbance has neither the tendency to
                                                              history diagrams of figure 4.2.
return nor the tendency to continue in the dis-
placement direction, ncutrnl Jtatic stability ex-                 The nonoscillatory modes shown in figure
ists. These three categories of static stability              4.2 depict the time histories possible without
are illustrated in figure 4.1. The ball in a                  cyclic motion. If the system is given an initial
 trough illustrates the condition of positive                 disturbance and the motion simply subsides
static stability.    If the ball is displaced from            without oscillation, the mode is termed “sub-
equilibrium at the bottom of the trough, the                  sidence” or “deadbeat return.” Such a motion
initial tendency of the ball is to return to the               indicates positive static stability by the tend-
 equilibrium condition.       The ball may roll                ency to return to equilibrium and positive dy-
back and forth through the point of equilib-                  namic stability since the amplitude decreases
rium but displacement to either side creates                  with time. Chart B illustrates the mode of
the initial tendency to return. The ball on a                  “divergence” by a noncyclic increase of ampli-
hill illustrates the condition of static insta-               tude with time. The initial tendency to con-
bility.     Displacement from equilibrium at the              tinue in the displacement direction is evidence
hilltop brings about the tendency for greater                 of static instability and the increasing ampli-
displacement. The ball on a flat, level surface               tude is proof of dynamic instability.      Chart C
                                                               illustrates the mode of pure neutral stability.
illustrates the condition of neutral static sta-
                                                              If the original disturbance creates a displace-
 bility.    The ball encounters a new equilibrium
                                                              ment which remains constant thereafter, the
at any point of displacement and has neither
                                                              lack of tendency for motion and the constant
stable nor unstable tendencies.                               amplitude indicate neutral static and neutral
    The term “static” is applied to this form of              dynamic stability.
stability since the resulting motion is not                        The oscillatory modes of figure 4.2 depict the
considered. Only the tendency to return to                     time histories possible with cyclic motion.
eqmlibrtum conditions is considered in static                 One feature common to each of these modes is
 stability.    The static longitudinal stability of           that positive static stability is demonstrated in
 an aircraft is appreciated by displacing the                  the cyclic motion by tendency to return to
                               NON-OSCILLATORY                 MODES

                 (OR DEAD BEAT        RETURN)

     5        (POSITIVE   STATIC)                                                 (NEGATIVE     STATIC)
     0        (POSITIVE   DYNAMIC)                                                (NEGATIVE     DYNAMIC)

                                                                  (NEUTRAL    STATIC)
                                                                  (NEUTRAL    DYNAMlc)

                                       OSCILLATORY         h


                          (POSITIVE    STATIC)       ;
                          (POSITIVE    DYNAMIC)
                                                                             (POSITIVE    STATIC)
                                                                             (NEUTRAL      DYNAMIC)

                                                                              (P0slTl~E     STATIC)
                                                                              (NEGATIVE     DYNAMIC)

                                      Figure 4.2. Dynamic Sfabihty

                                                                                         NAVWEPS OO-ROT-80
                                                                                      STABILITY AND CONTROL

 quilibrium     conditions.    However, the dy-                 In any system, the existence of static sta-
 namic behavior may be stable, neutral, or un-               bility does not necessarily guarantee the
 stable. Chart D illustrates the mode of a                   existence of dynamic stability.      However,
 damped oscillation where the amplitude de-                  the existence of dynamic stability implies
creaseswith time. The reduction of amplitude                 the existence of static stability.
 with time indicates there is resistance to mo-                 Any aircraft must demonstrate the required
 tion and that energy is being dissipated. The               degrees of static and dynamic stability.       If
dissipation of energy-or “damping’-is    ‘      nec-         the aircraft were allowed to have static in-
essary to provide positive dynamic stability.                stability with a rapid rate of divergence, the
If there is no damping in the system, the mode               aircraft would be very difficult-if not impos-
of chart E is the result, an undamped oscilla-               sible-to fly. The degree of difficulty would
tion. Without damping, the oscillation con-                  compare closely with learning to ride a uni-
 tinues with no reduction of amplitude with                  cycle. In addition, positive dynamic stability
 time. While such an oscillation indicates posi-             is mandatory in certain areas to preclude
 tive static stability, neutral dynamic stability            objectionable continued oscillations of the
exists. Positive damping is necessary to elimi-              aircraft.
nate the continued oscillation. As an example,
an automobile with worn shock absorbers (or                  TRIM    AND    CONTROLLABILITY
 “dampers”) lacks sufficient dynamic stability
                                                                 An aircraft is said to be trimmed if all
and the continued oscillatory motion is neither
                                                             moments in pitch, roll, and yaw are equal to
pleasant nor conducive to safe operation. In
                                                             zero. The establishment of equilibrium at
the same sense, the aircraft must have sufficient
                                                             various conditions of flight is the function of
damping to, rapidly dissipate any oscillatory
motion which would affect the operation of                   the controls and may be accomplished by
the aircraft. When natural aerodynamic damp-                 pilot effort, trim tabs, or bias of a surface
ing cannot be obtained, a synthetic damping                  actuator.
must be furnished to provide the necessary                      The term “controllability”       refers to the
positive dynamic stability.                                  ability of the aircraft to respond to control
                                                             surface displacement and achieve the desired
    Chart F of figure 4.2 illustrates the mode of
 a divergent oscillation.     This motion is stat-           condition of flight. Adequate controllability
                                                             must be available to perform takeoff and
ically stable since it tends to return to the
                                                             landing and accomplish the various maneuvers
equilibrium position.       However, each subse-
                                                             in flight. An important contradiction exists
quent return to equilibrium is with increasing.
                                                             between stability and controllability         since
velocity such that amplitude continues to
                                                             adequate controllability    does not necessarily
increase with time.         Thus, dynamic insta-
bility exists. The divergent oscillation occurs              exist with adequate stability.     In fact, a high
when energy is supplied to the motion rather                 degree of stability tends to reduce the controlla-
than dissipated by positive damping.            The          bility of the aircraft.    The general relation-
                                                             ship between static stability and controlla-
most outstanding illustration of the divergent
                                                             bility is illustrated by figure 4.3.
oscillation occurs with the short period pitch-
                                                                Figure 4.3 illustrates various degrees of
ing oscillation of an aircraft.      If a pilot un-          static stability by a ball placed on various
knowingly supplies control functions which                   surfaces. Positive static stability is shown by
are near the natural frequency of the airplane               the ball in a trough; if the ball is displaced
in pitch, energy is added to the system, nega-               from equilibrium at the bottom of the trough,
tive damping exists, and the “pilot induced                  there is an initial tendency to return to equilib-
oscillation” results.                                        rium. If it is desired to “control” the ball

                                   POSITIVE STATIC

                                                                   CREASED POSIT,VE
                                                                    TIC STABILITY

                            NEUTRAL STATIC STABILITY

                                 STATIC STABILITY

                        Figure 4.3. Stability     and Control/ability

                                                                                     NAVWEPS DD-8OT-80
                                                                                  STABILITY AND CONTROL

and maintain it in the displaced position, a              &ease the angle of attack, the aircraft would
force must be supplied in rhe direction of                be trimmed at the higher angle of attack by
displacement co balance the inherent tendency             a push force to keep the aircraft from con-
to return to equilibrium.        This same stable         tinuing in the displacement direction.     Such
tendency in an aircraft resists displacement              control force reversal would evidence the aii-
from trim by pilot effort on the controls or              plane instability; the pilot would be supply-
atmospheric disturbances.                                 ing the stability by his attempt to maintain
    The effect of increased stability on con-             the equilibrium.   An unstable aircraft can be
trollabilicy    is illustrated by rhe ball in a           flown if the instability is slight with a low
 steeper trough. A greater force is required to           rate of divergence. Quick reactions coupled
 “control” the ball to the same lateral dis-              with effective controls can allow the pilot to
 placement when the stability is increased.               cope with some degree of static instability.
 In this manner, a large degree of stability tends        Since such flight would require constant at-
to make the aircraft less controllable.         It is     tention by the pilot, slight instability can be
necessary to achieve the proper balance be-               tolerated only in airships, helicopters, and
 tween stability and tontrollability     during rhe       certain minor motions of the airplane. How-
 design of an aircraft because the ~ppcr limits           ever, the airplane in high speed flight will
of stability arc set by the lower 1imitJ of controlla-    react rapidly to any disturbances and any in-
bility.                                                   stability would create unsafe conditions. Thus,
    The effect of reduced stability on .controlla-        it is necessary to provide some positive static
bility is illustrated by the ball on a flat surface.      stability  to the major aircraft degrees of
When neutral static stability exists, the ball            freedom.
may be displaced from equilibrium and there
is no stable tendency to return. A new point              AIRPLANE     REFERENCE AXES
of equilibrium is obtained and no force is
required to maintain the displacement.            As         In order to visualize the forces and moments
the static stability approaches zero, controlla-          on the aircraft; it is necessary to establish a
 bility increases to infinity and the only resist-        set of mutually perpendicular reference axes
ance to displacement is a resistance to the               originating at the center of gravity.      Figure
motion of displacement-damping.             For this      4.4 illustrates a conventional right hand axis
reason, the lower Limits of stability may be Set          system. The longitudinal or X axis is located
by the upper limits of controllability.       If the      in a plane of symmetry and is given a positive
stability of the aircraft is too low, control             direction pointing into the wind. A moment
deflections may create exaggerated displace-              about this axis is a rolling moment, L, and the
ments of the aircraft.                                    positive direction for a positive rolling moment
    The effect of static instability. on controlla-       utilizes the right hand rule. The vertical or 2
bility is illustrated by the ball on a hill.       If     axis also is in a plane of symmetry and is estab-
                                                          lished positive downward.        A moment about
the ball is displaced from equilibrium at the
                                                          the vertical axis is a yawing moment, N, and a
top of the hill, the initial tendency is for the
                                                          positive yawing moment would yaw the air-
ball td continue in the displaced direction.              craft co the right (right hand rule).         The
In order to “control”~the ball to some lateral            lateral or Y axis is perpendicular to the plane
displacement, a force must be applied oppo&               of symmetry and is given a positive direction
to the direction of displacement. This effect             out the right side of the aircraft. A moment
would be appreciated during flight of an un-              about the lateral axis is a pitching moment, M,
stable aircraft by an unstable “feel” of the air-         and a positive pitching moment is in the nose-
craft. If the controls were deflected co in-              up dlrection.
 NAVWEPS 00-8OT-80

                                                                              CENTER OF
                                                                              ..-.. ,.-..      _

                                                                             VERTICAL   AXIS

                                  Figure 4.4. Airplane Rekre&e Axes

LONGITUDINAL        STABILITY     AND                     and magnitude.        Neutral static longitudinal
  CONTROL                                                 stability usually defines the lower limit of
                                                          airplane stability since it ‘ the boundary
STATIC LONGITUDINAL             STABILITY                 between stability and instability.           The air-
                                                          plane with neutral static stability’ may be
    GENERAL CONSIDERATIONS.               An air-         excessively responsive to controls and the
craft will exhibit positive static Iongitudinal           aircraft has no tendency to return to trim fol-
stability if it tends to return to the trim angle         lowing a disturbance.          The airplane with
of attack when displaced by a gust or control             negative sradc longitudinal         stability is in-
movement. The aircraft which is unstable will             herently divergent from any intended trim
continue to pitch in the disturbed direction              condition.     If it is at all possible to fly the
until the displacement is resisted by opposing             aircraft, the aircraft. cannot be trimmed and
control forces. If the aircraft is neutrally              illogical control forces and deflections are rc-
stable, it tends to remain at any displacement            quired to provide equilibrium with a change
to which it is disturbed. It is most necessary            of attitude and airspeed.
to provide an airplane with positive staric                   Since static longitudinal stability depends
longitudinal stability.    The stable airplane is         upon the relationship of angle of attack and
safe and easy to fly since the airplane seeks and         pitching moments, it is necessary to study the
tends to maintain a trimmed condition of                  pitching moment contribution of each com-
flight.   It also follows that control deflec-            ponent of the aircraft.       In a manner similar
tions and control “feel” are logical in direction         to all other aerodynamic forces, the pitching
                                                                                           NAVWE,PS OO-ROT-80
                                                                                        STABILITY AND CONTROL

moment about the lateral axis is studied in                    B of figure 4.5 provides comparison of the
the coefficient form.                                          stable and unstable conditions.       Positive sta-
                                                               bility is indicated by the curve with negative
                 M = C,qS(MAC)                                 slope. Neutral static stability would be the
or                                                             result if the curve had zero slope. If neutral
                            M                                  stability exists, the airplane could be dis-
                   &=    qS(MAC)                               turbed to some higher or lower lift coefficient
where                                                          without change in pitching moment coefficient.
    M=pitching     moment about the c.g., ft.-                 Such a condition would indicate that the air-
        lbs., positive if in a nose-up direction               plane would have no tendency to return to
    q= dynamic pressure, psf                                   some original equilibrium and would not hold
    S= wing area, sq. ft.                                      trim. An airplane which demonstrates a posi-
    MAC=mean aerodynamic chord, ft.                            tive slope of the C, versus C, curve would be
    C,= pitching moment coefficient                            unstable. If the unstable airplane were subject
                                                               to any disturbance from equilibrium at the
 The pitching moment coefficients contributed                  trim point, the changes in pitching moment
 by all the various components of the aircraft                 would only magnify the disturbance. When
 are summed up and plotted versus lift coeffi-                 the unstable airplane is disturbed to some
 cient. Study of this plot of C, versus C,                     higher CL, a positive change in C, occurs which
 will relate the static longitudinal         stability         would illustrate a tendency for continued,
 of the airplane.                                              greater displacement. When the unstable air-
     Graph A of figure 4.5 illustrates the variation           plane is disturbed to some lower C,,, a negative
  of pitching moment coefficient, C,, with lift                change in C, takes place which tends to create
  coefficient, C,, for an airplane with positive               continued displacement.
  static longitudinal     stability.     Evidence of               Ordinarily, the static longitudinal stability
  static stability is shown by the tendency to re-             of a conventional airplane configuration does
,t,urn to equilibrium-or         “trim”-    upon dis-          not vary with lift coefficient. In other words,
.,placement. The airplane described by graph A                 the slope of C, versus CL does not change with
 is in trim or equilibrium when C,=O and, if the               CL. However, if the airplane has sweepback,
‘airplane is disturbed to some different C,, the               large contribution of power effects to stability,
 pitching moment change tends to return the                    or significant changes in downwash at the
 aircraft to the.point of trim. If the airplane                horizontal tail, noticeable changes in static
 ‘were disturbed to some higher C, (point Y), a                stability can occur at high lift coefficients.
 negative or nose-down pitching moment is de-                  This condition is illustrated by graph C of
 veloped which tends to decrease angle of attack               figure 4.5. The curve of C, versus CL of this
 back to the trim point. If the airplane were                  illustration shows a good stable slope at low
disturbed to some lower C,, (point X), a posi-                 values of CL. Increasing CL effects a slight
 tive, or nose-up pitching moment is developed
                                                               decrease in the negative slope hence a decrease
 which tends to increase the angle of attack
                                                               in stability occurs. With continued increase
 back to the trim point. Thus, positive static
 longitudinal stability is indicated by a negative             in C,, the slope becomes zero and neutral
 slope of C, versus C,, i.e., positive stability is            stability exists. Eventually, the slope be-
 evidenced by a decrease in CM with an increase                comes positive and the airplane becomes un-
 in C,.                                                        stable or “pitch-up”      results. Thus, at any
    The degree of static longitudinal stability is             lift coefficient, the static stability of the air-
 indicated by the slope of the curve of pitching               pl.ane is depicted by the slope of the curve of
 moment coefficient with lift coefficient. Graph               CM versus CL.

                                                                    LIFT COEFFICIENT


              CM----                                                        CL

                                   LESS STABLE        -NEUTRAL

                        Figure 4.5. Airphmc Static Longitudinal Stability

                                                                                      NAVWEPS OO-BOT-BO
                                                                                   STABILITY AND CONTROL

   CONTRIBUTION       OF THE COMPONENT                    not vary with C, since all changes in lift would
SURFACES. The net pitching moment about                   take place at the c.g. In this case, the wing
the lateral axis is due to the contribution of            contribution to stability would be neutral.
each of the component surfaces acting in their            When the c.g. is located behind the a.c. the
appropriate flow fields. By study of the con-             wing contribution i,s unstable and the curve
tribution of each component the effect of each            of C, versus CL for the wing alone would have
component on the static stability may be ap-              a positive slope.
preciated. It is necessary to recall that the                 Since the wing is the predominating aero-
pitching moment coefficient is defined as:                dynamic surface of an airplane, any change in
                                                          the wing contribution       may produce a sig-
                        M                                 nificant change in the airplane stability.    This
                ‘ =qS(MAC)                                fact would be most apparent in the case of the
                                                          flying wing or tailless airplane where the wing
Thus, any pitching moment coefficient-re-                 contribution determines the airplane stability.
gardless of source-has the common denomi-                 In order for the wing to achieve stability, the
nator of dynamic pressure, q, wing area, S, and           c.g. must be ahead of the a.c. Also, the wing
wing mean aerodynamic chord, MAC. This                    must have a positive pitching moment about
common denominator is applied to the pitch-                the aerodynamic center to achieve trim at
ing moments contributed by the fuselage and               positive lift coefficients. The first chart of
nacelles, horizontal tail, and power effects              figure 4.7 illustrates that the wing which is
as well as pitching moments contributed by                stable will trim at a negative lift coefficient if
the wing.                                                 the C,,, is negative. If the stable wing has a
   WING.      The contribution of the wing to             positive C,,, it will then trim at a useful posi-
stability depends primarily on the location               tive CL. The only means available to achieve
of the aerodynamic center with respect to the             trim at a positive CL with a wing which has a
airplane center of gravity.       Generally, the          negative C,,, is an unstable c.g. position aft of
aerodynamic center-or a.c.-is defined as the              the ax. As a result, the tailless aircraft
point on the wing mean aerodynamic chord                  cannot utilize high lift devices which incur
where the wing pitching moment coefficient                any significant changes in C,,,.
does not vary with lift coefficient. All changes              WhiIe the trim lift coefficient may be altered
in lift coefficient effectively take place at the          by a change in c.g. position, the resulting
wing aerodynamic center. Thus, if the wing                 change in stability is undesirable and is unsat-
experiences some change in lift coefficient, the           isfactory as a primary means of control.      The
pitching moment created will be a direct                  variation of trim CL by deflection of control
function of the relative location of the a.c. and         surfaces is usually more effective and is less
c.g.                                                       inviting of disaster. The early attempts at
   Since stability is evidenced by the develop-           manned flight led to this conclusion.
ment of restoring moments, the c.g. must be                   When the aircraft is operating in subsonic
forward of the a.c. for the wing to contribute
                                                          flight, the a.c. of the wing remains fixed at the
to positive static longitudinal stability.     As
                                                           25 percent chord station. When the aircraft
shown in figure 4.6, a change in lift aft of the
                                                           is flown in supersonic flight, the ax. of the
c,g. produces a stable restoring moment de-
pendent npon the lever arm between the a.c.                wing will approach the 50 percent chord sta-
and c.g. In this case, the wing contribution               tion. Such a large variation in the location
would be stable and the curve of CM versus CL             of the a.c. can produce large changes in the
for the wing alone would have a negative slope.           wing contribution and greatly alter the air-
If the c.g. were located at the a.c., C, would            plane longitudinal stability.     The second chart
NAVWEPS 00-801-80

                        t    CHANGE    IN LIFT

                            ~AERODYNAMIC               CENTER
                            CENTER    OF GRAVITY


                              Figure 4.6. Wing     Contribution

                                                                NAVWEPS 00-BOT-80
                                                             STABILITY AND CONTROL


CM                                            .ICl-2A-rI\,C C~              e
                                                                 I IDIIETAIPI

     I       STABLE, NEGATIVE f&AC

   ) =3=Ez.,.
  +                                            CL

                                 SUBSONIC -


Figure 4.7. Effect of CM~~ C. G. Position and Mach Nimber


of figure 4.7 illustrates the change of wing             nacelles deserves consideration in several in-
contribution possible between subsonic and               stances. Body upwash and variation of local
supersonic flight.     The large increase in static      Mach number can influence the wing lift while
stability in supersonic flight can incur high            lift carryover and downwash can effect the fu-
trim drag or require great control effectiveness         selage and nacelles forces and moments.
to prevent reduction in maneuverability.                      HORIZONTAL        TAIL.    The horizontal tail
     FUSELAGE AND NACELLES.                In most       usually provides the greatest stabilizing influ-
cases, the contribution of the fuselage and              ence of all the components of the airplane. To
nacelles is destabilizing.    A symmetrical body         appreciate the contribution of the horizontal
of revolution in the flow field of a perfect fluid       tail to stability, inspect figure 4.9. If the air-
develops an unstable pitching moment when                plane is given a change in angle of attack, a
given an angle of attack. In fact, an increase           change in tail lift will occur at the aerody-
in angle of attack produces an increase in the           namic center of the tail. An increase in lift
unstable pitching moment without the devel-              at the horizontal tail produces a negative
opment of lift.     Figure 4.8 illustrates the pres-     moment about the airplane c.g. and tends to
sure distribution which creates this unstable            return the airplane to the trim condition.
moment on the body of revolution.            In the      While the contribution of the horizontal tail
 actual case of real subsonic flow essentially           to stability is large, the -magnitude of the
the same effect is produced. An increase in              contribution is dependent upon the change in
 angle of attack causes an increase in the                tail lift and the lever arm of the surface. It is
 unstable pitching moment but a negligible                obvious that the horizontal tail will produce a
 increase in lift.                                        stabilizing effect only when the surface is aft
      An additional factor for consideration is the       of the c.g. For this reason it would be inap-
 influence of the induced flow field of the wing.         propriate to refer to the forward surface of a
 As illustrated in figure 4.8, the upwash ahead           canard (tail&St) configuration as a horizontal
 of the wing increases the destabilizing influence        “stabilizer.”    In a logical sense, the horizontal
 from the portions of the fuselage and nacelles           “stabilizer” must be aft of the c.g. and-
  ahead of the wing.       The downwash behind            generally speaking-the farther aft, the greater
 the wing reduces the destabilizing influence             the contribution to stability.
 from the portions of the fuselage and nacelles               Many factors influence the change in tail
 aft of the wing.      Hence, the location of the         lift which occurs with a change in airplane
 fuselage and nacelles relative to the wing is            angle of attack. The area of the horizontal
  important in determining the contribution to            tail has the obvious effect that a large surface
  stability.                                              would generate a large change in lift.         In a
      The body of revolution in supersonic flow           similar manner, the change in tail lift would
  can develop lift of a magnitude which cannot            depend on the slope of the lift curve for the
  be neglected. When the body of revolution in            horizontal tail.      Thus, aspect ratio, taper,
  supersonic flow is given an angle of attack, a          sweepback, and Mach number would deter-
  pressure distribution typical of figure 4.8 is the      mine the sensitivity of the surface to changes
  result. Since the center of pressure is well             in angle of attack. It should be appreciated
  forward, the body contributes a destabilizing            that the flow at the horizontal tail is not of
  influence. AS is usual with supersonic con-              the same flow direction or dynamic pressure as
   figurations, the fuselage and nacelles may be           the free stream. Due to the wing wake, fuse-
   quite large in comparison with the wing area            lage boundary layer, and power effects, the q
   and the contribution to stability may be large.         at the horizontal tail may be greatfy different
   Interaction between the wing and fuselage and           from the 4 of the free stream. In most in-
                                                           NAVWEPS oo-BDT-BD
                                                        STABILITY AND CONTROL




        Figure 4.8.    Body or Nacelle Contribution


                          -.                                       CHANGE IN LIFT
                                                                 ON HORIZONTAL TAlL

                                                                      OF HORIZONTAL TAIL

                                                                   DOWNWASH AT

                        FUSELAGE CROSS FLOW
                        SEPARATION VORTICES

                        Figure 4.9.   Contribution   of Tail and Downwash Effects

                                                                                      NAVWEPS OO-BOT-80
                                                                                   STABILITY AND CONTROL

stances, the 4 at the tail is usually less and this      stabilizing so that the complete configuration
reduces the efficiency of the tail.                      will exhibit positive static stability at the
    When the airplane is given a change in angle         anticipated c.g. locations. In addition, the tail
of attack, the horizontal tail does not expe-            and wing incidence must be set to provide a
rience the same change in angle of attack as             trim lift coefficient near the design condition.
the wing. Because of the increase in down-                   When the configuration of the airplane is
wash behind, the wing, the horizontal tail will          fixed, a variation of c.g. position can cause
experience a smaller change in angle of attack,          large changes in the static stability.      In the
e.g., if a 10" change in wing angle of attack            conventional airplane configuration, the large
causes a 4O increase in downwash at the hori-            changes in stability with c.g. variation are
zontal tail, the horizontal tail experiences             primarily due to the large changes in the wing
only a 6’ change in angle of attack. In this             contribution.     If the incidence of all surfaces
manner, the downwash at the horizontal tail              remains fixed, the effect of c.g. position on
reduces the contribution to stability.          Any      static longitudinal stability is typified by the
factor which alters the rate of change of down-          second chart of figure 4.10. As the cg. is
wash at the horizontal tail will directly affect         gradually moved aft, the airplane static sta-
the tail contribution and airplane stability.            bility’ decreases, then becomes neutral then
    Power effects can alter the downwash at the          unstable., The c.g. position which produces
horizontal tail and affect the tail contribution.        zero ,slope and neutral static stability is re-
Also, the ~downwash at the tail is affected by           ferred to aspthe ~“neutral point.” The neutral
the lift distribution on the wing and the flow           point may be imagined as the effective aerody-
condition ,on the fuselage. The low aspect               namic center of the entire airplane configura-
ratio airplane requires large angles of attack           ration, i.e., with the c.g. at this position, all
to achieve high ,lift coefficients and this posi-        changes in net lift effectively occur at this
tions the fuselage at high angles of attack.             point and no change in pitching moment
The change in the wing downwash can be                   results. The neutral point defines the most
accompanied by crossflow separation vortices             aft c.g. position without static instability.
on the fuselage. It is possible that the net                 POWER EFFECTS. The effects of power may
effect obviates or destabilizes the contribu-
                                                         cause significant changes in trim lift coefficient
tion of the horizontal tail and produces air-
                                                         and static. longitudinal stability.      Since the
plane instability.
    POWER-OFF STABILITY.            When the in-         contribution to stability is evaluated by the
trinsic stability of a configuration is of interest,     change in moment coefficients, power effects
power effects are neglected and the stability            will be most significant when the airplane
 is considered by a buildup of the contributing~          operates at high power and low airspeeds such
components. Figure 4.10 illustrates a typical             as the power approach or waveoff condition.
 buildup of the components of a conventional                 The effects of power are considered in two
airplane configuration.       If the c.g. is arbi-        main categories. First, there are the direct
 trarily set at 30 percent MAC, the contribu-             effects resulting from the forces created by the
 tion of the wing alone is destabilizing as indi-         propulsion unit. Next, there are the indirect
cated by the positive slope of CM versus C,.              effects of the slipstream and other associated
 The combination of the wing and fuselage                 flow which alter the forces and moments of the
 increases the instability.      The contribution         aerodynamic surfaces. The direct effects of
 of the tail alone is highly stabilizing from             power are illustrated in figure 4.11. The ver-
 the large negative slope of the curve. The               tical location of the thrust line defines one of
  contribution of the tail must be sufficiently           the direct contributions to stability.       If the

                                         TYPICAL     GUILD-UP 0F tzci~m~ENTs

             CM                                                 ,-WING+ FUSELAGE

                                                                                WING ONLY/.

                            C.G. @ 30%      MAC

                                               EFFECT     OF C.G.    WsITION

            CM                                                           50%    MAC

                                                                         40%    MAC (NEUTRAL pOlNn

                          Figure 4.10.   Stability   Build-up   and Effect of C.G. Positim
                                                                                    NAVWEPS 00-BOT-80
                                                                                 STABILITY ,AND CONTROL

thrust line is below the c.g., thrust produces a         slipstream creates a normal force at the plane
positive or noseup moment and the effect is de-          of the propeller similar to a wing creating lift
stabilizing.   On the other hand, if the thrust          by deflecting an airstream. As this normal
line is ,located above the c.g., a negative              force will increase with an increase in airplane
moment is created and the effect is stabilizing.         angle of attack, the effect will be destabilizing
   A propeller or inlet duct located ahead of            when the propeller is ahead of the cg. The
the c.g. contributes a destabilizing effect. As          magnitude of the unstable contribution de-
shown in figure 4.11, a rotating propeller in-           pends on the distance from the c.g. to the
clined to the windstream causes a deflection             propeller and is largest at high power and low
of the airflow. The momentum change of the               dynamic pressure. The normal force created

                         EFFECT    OF VERTICAL     LOCATION   OF THRUST      LINE

                   d     DESTABILIZING

                                   DESTABILIZING      INCRE
                                       IN NORMAL     FORCE

                                  DESTABILIZING   INCREASE
                                   IN DUCT INLET NORMAL

                                  Figure 4.11. Direct Power Effects
                                                   NAVWEPS GO-BOT-BO
                                                STABILITY AND CONTROL

                   MOMENTS AFFECTED BY

                                           -DYNAMIC PRESSURE
                                            AT TAIL AFFECTED
                                            BY SLIPSTREAM


                            FLOW INDUCED BY
                              JET EXHAUST

                             DOWNWASH AT TAIL

Figure 4.12.   Indirect   Power Effects.


at the inlet of a jet engine contributes a similar      static stability at high power, high CL, and
destabilizing effect when the inlet is ahead            low 4. It is generally true that any airplane
of the c,g. As with the propeller, the magni-           will experience the lowest level of static longi-
tude of the stability contribution is largest at        tudinal stability under these conditions. Be-
high thrust and low flight speed.                       cause of the greater magnitude of both direct
    The indirect effects of power are of greatest       and indirect power effects, the propeller pow-
concern in the propeller powered airplane               ered airplane usually experiences a greater
rather than the jet powered airplane.            As     effect than the jet powered airplane.
shown in figure 4.12, the propeller powered                 An additional effect on stability can be from
airplane creates slipstream velocities on the           the extension of high lift devices. The high
various surfaces which are different from the           lift devices tend to increase downwash at the
flow field typical of power-off flight.       Since     tail and reduce the dynamic pressure at the tail,
the various wing, nacelle, and fuselage surfaces        both of which are destabilizing.         However,
are partly or wholly immersed in this slip-             the high lift devices may prevent an unstable
stream, the contribution of these components            contribution of the wing at high CL. While
to stability can be quite different from the            the effect of high lift devices depends on the
power-off flight condition.       Ordinarily,   the     airplane configuration, the usual effect is de-
change of fuselage and nacelle contribution             stabilizing.     Hence, the airplane may experi-
with power is relatively small. The added               ence the most critical forward neutral point
lift on the portion of the wing immersed in              during the power approach or waveoff. Dur-
the slipstream requires that the airplane oper-         ing these conditions of flight the static stability
ate at a lower angle of attack to produce the           is usually the weakest and particular attention
same effective lift coefficienr. Generally, this        must be given to precise control of the air-
reduction in angle of attack to effect the same         plane. The power-on neutral point may set
CL reduces the tail contribution to stability.          the most aft limit of c.g. position.
However, the increase in dynamic pressure at                CONTROL FORCE STABILITY.             The static
the tail tends to increase the effectiveness of         longitudinal stability of an airplane is defined
the tail and may be a stabilizing effect. The            by the tendency to return to equilibrium upon
magnitude of this contribution         due to the       displacement. In otherwords, the stable air-
slipstream velocity on the tail will depend on          plane will resist displacement from the trim or
the c.g. position and trim lift coefficient.            equilibrium.      The control forces of the air-
    The deflection of the slipstream by the nor-        plane should reflect the stability of the air-
mal force at the propeller tends to increase the        plane and provide suitable reference for precise
downwash at the horizontal tail and reduce              control of the airplane.
 the contribution to stability.    Essentially the          The effect of elevator deflection on pitching
 same destabilizing effect is produced by the           moments is illustrated by the first graph of
flow induced at the exhaust of the jet power-           figure 4.13. If the elevators of the airplane are
plant.     Ordinarily, the induced flow at the           fixed at zero deflection, the resulting line of
 horizontal tail of a jet airplane is slight and is                     s
                                                         CM versus C’ for 0’ depicts the static stability
 destabilizing when the jet passes underneath           and trim lift coefficient. If the elevators are
the horizontal tail.      The magnitude of the          fixed at a deflection of 10” up, the airplane
 indirect power effects on stability tends to be         static stability is unchanged but the trim lift
 greatest at high Cr, high power, and low flight         coefficient is increased. A change in elevator
 speeds.                                                 or stabilizer position does not alter the tail
    The combined direct and indirect power               contribution to stability but the change in
 effects contribute to a general reduction of            pitching moment will alter the lift coeflicient
                                                                                          NAVWEPS 00-SOT-80
                                                                                       STABILITY AND CONTROL

                              EFFECT       OF ELEVATOR           DEFLECTION

                                  nre, CCTl,-..,

                                                                          TRIM   FOR

                CG@20%        MAC

                  TRIM        C, VERSUS        ELEVATOR          DEFLECTION

            A          TRIM       AIRSPEED     VS ELEVATOR            DEFLECTION

ii                                                          ’        X~SLE
oz                                                                                              t
                                    /                    ~RSPEED
2                             /
2    DOWN               /

                            Figure 4.13.     Longitudinal       Control


at which equilibrium will occur. As the ele-                 tail is subject to an increase in angle of attack
vator is fixed in various positions, equilibrium             and the elevators tend to float up, the change
(or trim) will occur at various lift coefficients            in lift on the tail is less than if the elevators
and the trim CL can be correlated with elevator              remain fixed and the tail contribution           to
deflection as in the second graph of figure 4.13.            stability is reduced. Thus, the “stick-free”
   When the c,g. position of the airplane is                 stability of an airplane is usually less than the
fixed, each elevator position corresponds to a               stick-fixed stability.    A typical reduction of
particular trim lift coefficient. AS the c.g. is             stability by free elevators is shown in figure
moved aft the slope of this line decreases and               4.14(A) where the airplane. stick-free demon-
the decrease in stability is evident by a given              strates a reduction of the slope of CM versus Cs.
control displacement causing a greater change                While aerodynamic balance may be provided
in trim lift coefficient. This is evidence that              tu reduce control forces, proper balance of the
decreasing stability causes increased controlla-             surfaces will reduce floating and prevent great
bility and, of course, increasing stability de-              differences between stick-fixed and stick-free
creases controllability.      If the c.g. is moved           stability.   The greatest floating tendency oc-
aft until the line of trim CL versus elevator de-            curs when the surface is at a high angle of
flection has zero slope, neutral static stability            attack hence the greatest difference between
is obtained and the “stick-fixed” neutral point              stick-fixed and stick-free stability occurs when
is determined.                                               the airplane is at high angle of attack.
   Since each value of lift coefhcient corresponds              If the controls are fully powered and actu-
to a particular value of dynamic pressure re-                ated by an irreversible mechanism, the sur-
quired to support an airplane in level flight,               faces are not free to float and there is no differ-
uim airspeed can be correlated with elevator                 ace between the stick-fixed and stick-free
deflection as in the third graph of figure 4.13.             static stability.
If the c.g. location is ahead of the stick-fixed                The control forces in a conventional air-
neutral point and control position is directly               plane are made up of two components. First,
related to surface deflection, the airplane will             the basic stick-free stability of the airplane
give evidence of stick podion mbility.            In         contributes an incremem of force which is
other words, the airplane will require the                   independent of airspeed.. Next, there. is an
stick to be moved aft to increase the angle                  increment of force dependent on the trim tab
of attack and trim at a lower airspeed and to                setting which varies with-the dynamic pres-
 be moved forward to decrease the angle of                   sure or the square of ‘      equivalent airspeed.
 attack and trim at a higher airspeed. To be                 Figure 4.14(B) indicates the variation of
 sure, it is desirable to have an airplane demon-            stick force with airspeed and illustrates the
strate this feature. If the airplane were to                 effect of tab setting on stick force. In order
have stick position instability,       the airplane          te trim the airplane at point (1) a certain
would require the stick to be moved aft to trim              amount of up elevator is required and zero
at a higher airspeed or to be moved forward to               stick force is obtained~ with’the nse of the tab.
trim at a lower airspeed.                                    To trim the airplane for higher speeds corre-
    There may be slight differences in the static            sponding to points (2) and (3) less and less
longitudinal      stability if the elevators are             nose-up tab is required. Note that when the
allowed to float free. If the elevators are                  airplane is properly trimmed, a push force is
allowed to float free as in “hands-off” flight,              required to increase airspeed and a pull force
the elevators may have a tendency to “float”                 is required to decrease airspeed. In this man-
or streamline when the horizontal tail is given              ner, the airplane would indicate positive stick
a change in angle of attack. If the hot&ma1                  force stability with a stable “feel” for air-
                                                                            NAVWEPS 00-BOT-80
                                                                         STABILITY AND CONTROL

                           STICK -FIXED

     a,,,   I,
                                                               TAB   FORCE INCREMENT

                     INCREMENT                                             EQUIVALENT

                     CG AT 20% MAC         I

                            CG POSITION

                     p-z;                                      ,/’EQUlV
                       10% MAC


,o                                                                                      T
-                                                                                       D

                                               FRICTION FORC

                             Figure 4.74. Control Force Stability
 NAVWEPS 00-801-80

 speed, If the airplane were given a large nose        the pitch motion which adds to the restoring
 down tab setting the pull force would in-             moment from the basic static stability.         The
 crease with airspeed. This fact points out the        principal source of this additional pitching
 possibility of “feel” as not being a true indi-       moment is illustrated in figure 4.15.
 cation of airplane static stability.                      During a pull-up the airplane is subject to
     If the c.g. of the airplane were varied while     an angular rotation about the lateral axis and
 maintaining trim at a constant airspeed, the          the horizontal tail will experience a component
 effect of c.g. position on stick force stability      of wind due to the pitching velocity.           The
 could be appreciated. As illustrated in figure        vector addition of this component velocity to
 4,14(C), moving the c,g. aft decreases the            the flight velocity provides a change in angle
 slope of the line of stick force through the          of attack for the tail and the change in lift on
 trim speed. Thus, decreasing stick force              the tail creates a pitching moment resisting
 stability is evident in that smaller stick forces     the pitching motion.        Since the pitching mo-
 are necessary to displace the airplane from           ment opposes the pitching motion but is due
 the trim speed. When the stick force gradient         to the pitching motion, the effect is a damping
 (or slope) becomes zero, the c.g. is at the           in pitch. Of course, the other components of
 stick-free neutral point and neutral stability        the airplane may develop resisting moments
 exists. If the c.g. is aft of the stick-free          and contribute to pitch damping but the
 neutral point, stick force instability         will   horizontal tail is usually the largest contri-
 exist, e.g. the airplane will require a push           bution. The added pitching moment from
 force at a lower speed or a pull force at a higher    pitch damping will effect a higher stability
 speed. It should be noted that the stick force         in maneuvers than is apparent in steady flight.
 gradient is low at low airspeeds and when             From this consideration, the neutral point for
 the airplane is at low speeds, high power,            maneuvering flight will be aft of the neutral
 and a c.g. position near the aft limit, the            point for unaccelerated flight and in most cases
  “feel” for airspeed will be weak.                    will not be a critical item. If the airplane
     Control system friction can create very un-        demonstrates static stability in unaccelerated
 desirable effects on control forces. Figure            flight, it will most surely demonstrate stability
  4.14(D) illustrates that the control force            in maneuvering flight.
  versus airspeed is a band rather than a line.             The most direct appreciation of the ma-
  A wide friction force band can completely             neuvering stability of an airplane is obtained
  mask the stick force stability when the stick         from a plot of stick force versus load factor
  force stability is low. Modern flight control         such as shown in figure 4.15. The airplane
  systems require precise maintenance to mini-          with positive maneuvering stability should
  mize the friction force band and preserve             demonstrate a steady increase in stick force
  proper feel to the airplane.                          with increase in load factor or “G”.           The
     MANEUVERING           STABILITY.     When an       maneuvering stick force gradient-or           stick
 airplane is subject to a normal acceleration,         force per G-must be positive but should be
  the flight path is curved and the airplane is         of the proper magnitude.           The stick force
  subject to a pitching velocity.       Because of      gradient must not be excessively high or the
  the pitching velocity in maneuvering flight,          airplane will be difficult and tiring to maneuver.
  the longitudinal stability of the airplane is         Also, the stick force gradient must not be too
  slightly greater than in steady flight condi-         low or the airplane may be overstressed in-
  tions. When an airplane is subject to a pitch-        advertently when light control forces exist.
1 ing velocity at a given lift coefficient, the air-    A maneuvering stick force gradient of 3 to 8
  plane develops a pitching moment resisting            lbs. per G is satisfactory for most fighter and
                                                                       NAVWEPS 00-801-80
                                                                    STABILITY AND CONTROL

                             CHANGE IN TAIL LIFT

                                                             RELATIVE WIND
                                                         FROM ANGULAR ROTATION
                               CHANGE IN TAIL ANGLE OF
                               ATTACK DUE TO PITCHING

  !!I 30

  ;    20                                MANEUVERING STICK
  ::                                       FORCE GRADIENT

  g    IO

            I   2       3      4     5     6       7        8
                               LOAD FACTOR, n
                                  (OR G)

  % MAC         /

                                                   LOAD FACTOR

                    Figure 4.15. Maneuvering Stability

NAVWEPS 00-8’X-60

attack airplanes. A large patrol or transport           leading edge (unshielded) or partway to the
type airplane would ordinarily show a much              leading edge (shielded). Aerodynamic balance
higher maneuvering stick force gradient be-             can be achieved by the provision of- a hinge
cause of the lower limit load factor.                   line aft of the control surface leading edge.
   When the airplane has high static stability,         The resulting overhang of surface area ahead
the maneuvering stability will be high and              of the hinge line will provide a degree of
a high stick force gradient will result. A               balance depending on the amount of overhang.
possibility exists that the forward c.g. limit          Another variation of aerodynamic balance is
could be set to prevent an excessively high             an internal balance surface ahead of the hinge
maneuvering stick force gradient.         As the         line which is contained within ,the surface.
c.g. is moved aft, the stick force gradient de-         A flexible seal is usually incorporated to in-
creases with decreasing maneuvering stability           crease the effectiveness of the balance area.
and the lower limit of stick force gradient             Even the bevelling of the trailing edge..of the
may be reached.                                         control surface is effective also as a balancing
    The pitch damping of the airplane is obvi-           technique. The choice of the type of aerody-
 ously related to air density. At high altitudes,        namic balance will depend on many factors
the high true airspeed reduces the change in             such as required degree of balance, simplicity,
tail angle of attack for a given pitching velocity       drag, etc.
and reduces the pitch damping. Thus, a de-                   Many devices can be added to a control
crease in maneuvering stick force stability can          system to modify or tailor the stick force
be expected with increased altitude.                     stability to desired levels. If a spring is added
    TAILORING       CONTROL FORCES.           The        to the control system as shown in figure 4.16,
 control forces should reflect the stability of          it will tend to center the stick and provide a
 the airplane but, at the same time, should be           force increment depending on stick displace-
 of a tolerable magnitude. The design of the             ment. When the control system has a fixed
 surfaces and control system may employ an                gearing between stick position and surface
 infinite variety of techniques to provide satis-        deflection, the centering spring will provide a
factory control forces.                                  contribution to stick force stability according
    Aerodynamic balance must be thought of in            to stick position.    The contribution to stick
two different senses. First, the control surface         force stability will be largest at low flight
 must be balanced to reduce hinge moments due             speeds where relatively large control deflec-
 to changes in angle of attack. This is necessary         tions are required. The contribution will be
 to reduce the floating tendency of the surface           smallest at high airspeed because of the smaller
which reduces the stick-free stability.     Next,        control deflections required. Thus, .the stick
 aerodynamic balance can reduce the hinge                centering bungee will increase the airspeed
moments due to deflection of the control sur-             and maneuvering stick force stability but the
face. Generally, it is difficult to obtain a high        contribution decreases at high airspeeds. A
 degree of deflection balance without incurring           variation of this device would be a spring
 a large overbalance of the surface for changes           stiffness which would be controlled to vary
 in angle of attack.                                      with dynamic pressure, 4. In this case, the
    Some of the types of aerodynamic balance              contribution   of the spring to stick force
 are illustrated in figure 4.16. Thesimple horn           stability would, not diminish with. speed.
 type balance employs a concentrated balance                 A “downspring” added to a control system
 area located ahead of the hinge line. The                is~a means ~of increasing airspeed stick force
 balance area may extend completely to the                stability without a change in airplane static

                                                                         NAVWEPS 00-8OT-80
                                                                      STABILITY AND CONTROL

                 TYPES     OF   AERODYNAMIC       BALANCE
                                                 INTERNAL BALANCE
                                           <I           XlBLESE&
                                                 WITH FL’


                                                 ---‘   “1G EDGE BEVEL -,

               EFFECT     LaF STICK      CENTERING      SPRING

                                    TICK CENTERING
                                    RING OR BUNGEE

    PULL                   FORCE INCREMENTADDED
                                 BY SPRING
E                                                                 e
                                \                  AIRSPEED

                                LOAD FACTOR

                        figure 4.16. loiloring   Control forces
NAVWEPS 00-801-80

                                         EFFECT   OF DOWNSPRING

                               u         P*RELO+DED       SPRING



                                        EFFECT    OF BOBWEIGHT





                                                                    FORCE INCREMENT
                                                                     BY BOBWEIGHT

                                                  LOAD    FACTOR

                                   Figure 4.77. Tailoring Control Forces

                                                                                 NAVWEPS 00-EOT-80
                                                                              STABILITY AND CONTROL

stability.    As shown in figure 4.17, a down-           Various control surface tab devices can be
spring consists of a long preloaded spring at-        utilized to modify control forces. Since the de-
tached to the control system which tends to           flection of a tab is so powerful in creating hinge
rotate the elevators down. The effect of the          moments on a control surface, the possible
downspring is to contribute an increment of           application of tab devices is almost without
pull force independent of control deflection or       limit,    The basic trim tab arrangement is
airspeed. When rhe downspring is added to             shown in figure 4.18 where a variable linkage
the control system of an airplane and the air-        connects the tab and the control surface. Ex-
plane is retrimmed for the original speed, the        tension or contraction of this linkage will de-
airspeed stick force gradient is increased and        flect the tab relative to the control surface and
there is a stronger feel for airspeed. The down-      create a certain change in hinge mon~ent coef-
spring would provide an “ersatz” improve-             ficient. The use of the trim tab will allow the
ment to an airplane deficient in airspeed stick       pilot to reduce the hinge moment to zero and
force stability,     Since the force increment from   trim the control forces to zero for a given flight
the downspring is unaffected by stick position        condition. Of course, the trim tab should have
or normal acceleration, the maneuvering stick         adequate effectiveness so that control forces
force stability would be unchanged.                   can be trimmed out throughout the flight speed
    The bobweight is an effective device for im-      range.
proving stick force stability.         As shown in        The lagging tab arrangement shown in figure
figure 4.17, the bobweight consists of an eccen-      4.18 employs a linkage between the fixed sur-
tric mass attached to the control system              face and the tab surface. The geometry is
which-in       unaccelerated flight--contributes      such that upward deflection of the control
an increment of pull force identical to the           surface displaces the tab down relative to the
downspring.        In fact, a bobweight added to      control surface. Such relative displacement
the control system of an airplane produces an          of the tab will aid in deflection of the control
effect identical to the downspring.        The bob-   surface and thus reduce the hinge moments due
weight will increase the airspeed stick force         to deflection. An obvious advantage of this
gradient and increase the feel for airspeed.          device is the reduction of deflection hinge
    A bobweighr will have an effect on the            moments without a change in aerodynamic
maneuvering stick force gradient since the bob-        balance.
weight mass is subjected to the same accelera-            The leading tab arrangement shown in figure
tion as the airplane. Thus, the bobweight will        4.18 also employs a linkage between the fixed
provide an increment of stick force in direct         surface and the tab surface. However, the
proportion to the maneuvering acceleration of         geometry of the linkage is such that upward
the airplane. Because of the linear contribu-          deflection of the control surface displaces the
tion of the bobweight, the bobweight can be            tab up relative to the control surface. This
applted to Increase the maneuvering stick force       relationship serves to increase the control sur-
stability if the basic airplane has too low a         face hinge moments due to deflection of the
value or develops a decreasing gradient at high        surface.
lift coefficients.                                        The servo tad shown in figure 4.18 utilizes a
    The example of the bobweight is useful to         horn which has no direct connection to the
point out the effect of the control system dis-       control surface and is free to pivot about the
 tributed masses. All carrier aircraft must have       hinge axis. However, a linkage connects this
the control system mass balanced to prevent            free horn to the tab surface. Thus, the control
 undesirable control forces from the longi-            system simply deflects the tab and the resulting
 tudinal accelerations during catapult launching.      hinge moments deflect the control surface.

                           TRIM TAB

                                   VARIABLE LINKAGE

                           LAGGING TAB

                          LEAOING TAB

                           SERVO    TAB
                                            HORN FREE TO
                                            PIVOT ON HINGE 13X6

                           SPRING TAB

                                                  ON HINGE AXIS

                                                        FIXED TO SURFACE

                         SPRING LLADED      TAB

                                        ROTATES TAB UP

                        Figure 4.18. Various Tab Devices

                                                                                        NAVWEPS OtWOT-80
                                                                                     STABILITY AND CONTROL

 Since the only control forces are those of the              stability.    Ati airplane with high static longi-
  tab, this device makes possible the deflection             tudinal stability will exhibit great resistance
  of large surfaces with relatively small control            to displacement from equilibrium.           Hence,
 forces.                                                     the most critical conditions of controllability
     A variation of the basic servo tab layout is            will occur when the airplane has high sta-
  the sprirzg tab arrangement of figure 4.18.                bility, i.e., the lower limits of controllability
  When the control horn is connected to the                  will set the upper limits of stability.
 control surface by springs, the function of the                 There are three principal conditions of
 tab is to provide a given portion of the required           fli~ght which provide the critical requirements
 control forces. The spring tab arrangement                  of longitudinal       control power.     Any one
 can then function as a boost to reduce control              or combination of these conditions can de-
 forces. The servo tab and spring tab are                    termine the longitudinal control power and
 usually applied to large or high speed subsonic             set a limit to forward c.g. position.
 airplanes to provide tolerable stick forces.                    MANEUVERING             CONTROL REQUIRE-
    The spring Zoadcdtab of figure 4.18 cotisists            MENT.       The airplane should have sufficient
 of a free tab preloaded with a spring which                 longitudinal control power to attain the maxi-
 furnishes a constant moment about the tab                   mum usable lift coefficient or limit load factor
 hinge line. When the airplane is at zero air-               during maneuvers. As shown in figure 4.19,
 speed, the tab is rotated up to the limit of                forward movement of the c.g. increases the
 deflection. As airspeed is increased, the aero-             longiturjinal     stability   of an airplane and
dynamic hinge moment on the tab will finally                 requires larger control deflections to produce
equal the spring torque and the tab will begin              changes in trim lift coefficient.          For the
 to streamline. The effect of this arrangement               example shown, the maximum effective de-
 is to provide a constant hinge moment to the                flection of the elevator is not capable of trim-
control system and contribute a constant push                                      at
                                                             ing the airplane ‘ C,,,, for c.g. positions
force requirement at speeds above the preload               ahead of 18 percent MAC.
speed. Thus, the spring loaded tab can im-                       This particular control requirement can be
prove the stick force gradient in a manner                  most critical for an airplane in supersonic
similar to the downspring.         Generally, the            flight.    Supersonic flight is usually accom-
spring loaded tab may be more desirable                     panied by large increases in static longltu-
because of greater effectiveness and the lack of            dinal stability and a reduction in the effective-
undesirable control forces during ground                    ness of control surfaces. In order to cope with
operation.                                                  these trends, powerful all-movable surfaces
    The various tab devices have almost un-                 must be used to attain limit load factor or
limited possibilities for tailoring control forces.         maximum usable C, in supersonic flight. This
However, these devices must receive proper                  requirement is so important that once satis-
care and maintenance in order to function                   fied, the supersonic configuration usually has
properly. In addition, much care must be                    sufficient longitudinal control power for all
taken to ensure that no slop or play exists in              other conditions of flight.
the joints and fittings, otherwise destructive                  TAKEOFF        CONTROL        REQUIREMENT.
flutter may occur.                                          At takeoff, the airplane must have sufficient
                                                            control power to assume the takeoff attitude
LONGITUDINAL        CONTROL                                 prior to reaching takeoff speed. Generally,
                                                            for airplanes with tricycle landing gears, it
  To be satisfactory, an airplane must have                 is desirable to have at least sufficient control
adequate controllability as well as adequate                power to attain the takeoff attitude at 80
NAVWEPS 00-80’1-80

                                     MAXIMUM                                                MOST FORWARD
                            DEFLECTION                                                  CG FOR MANEUVERING

              DOWN                                    POSITION



                                               TAKE     OFF CONTROL

                                                                          REDUCED DOWNWASH
                                                                          DUE TO GROUND EFFECT

           . .:,.,. ‘ ,;,,.,,>:~~,‘ y::, ,: :“ J.:;:‘ : :.,
                    ,:::.;,y ::..‘ i;,:,‘ ,/.: ‘ j:~!,.:
                                       ;. ~..                               .
                                                  i... .,-:~, :,., :.:, :, .‘
                                                            -, :,.:        :~’
                                                LANDING        CONTROL

                                      Figure 4.19. Longitudinal           Control   Requirements

                                                                                        NAVWEPS 00-BOT-80
                                                                                     STABILITY AND CONTROL

percent of the stall speed for propeller air-               flaps are fully extended, and power is set at
planes or 90 percent of the stall speed for jet             idle. This configuration will provide the
airplanes. This feat must be accomplished on                most stable condition which is most demand-
a smooth runway at all normal service takeoff               ing of controllability.    The full deflection of
loading conditions.                                         flaps usually provides the greatest wing diving
   Figure 4.19 illustrates the principal forces             moment and idle power will produce the most
acting on an airplane during takeoff toll.                  critical (least) dynamic pressure at the hoti-
When the airplane is in the three point attitude            zontal tail.
at some speed less than the stall speed, the                   The landing control requirement has one
wing lift will be less than the weight of the               particular difference from the maneuvering
airplane. As the elevators must be capable                  control requirement of free flight.        As the
of rotating to the takeoff attitude, the critical           airplane approaches the ground surface, there
condition will be with zero load on the nose                will be a change in the three-dimensional flow
wheel and the net of lift and weight supported              of the airplane due to ground effect. A wing in
on the main gear. Rolling friction resulting                proximity to the ground plane will experience
from the normal force on the main gear creates              a decrease in tip vortices and downwash at
an adverse nose down moment.          Also, the             a given lift coefficient. The decrease in down-
center of gravity ahead of the main gear                    wash at the tail tends to increase the static
contributes a nose down moment and this                     stability and produce a nosedown moment from
consideration could decide the most aft loca-               the reduction in download on the tail. Thus,
tion of the main landing gear during design.                the airplane just off the runway surface will
The wing may contribute a large nose down                   requite additional control deflection to trim
moment when flaps are deflected but this                    at a given lift coefficient and the landing con-
effect may be countered by a slight increase                trol requirement may be critical in the design
in downwash at the tail.       To balance these             of longitudinal control power.
nose down moments, the horizontal              tail             As an example of ground effect, a typical
should be capable of producing sufficient nose              propeller powered airplane may requite as
up moment to attam the takeoff attitude. at                 much as 15” more up elevator to trim at CL-
the specified speeds.                                       in ground effect than in free flight away from
   The propeller airplane at takeoff power may              the ground plane. Because of this effect, many
induce considerable slipstream velocity at the              aitplaneshavesufIicientcontrolpowertoachieve
horizontal tail which can provide an increase               full stall out of ground effect but do not have
in the e&iency       of the surface. The jet                the ability to achieve full stall when in close
airplane does not experience a similar magni-               proximity to the ground.
tude of this effect since the induced velocities                In some cases the effectiveness of the control
from the jet are relatively small compared                  surface is adversely affected by the use of trim
to the slipstream velocities from a propeller.              tabs. If trim tabs are used to excess in ttim-
   LANDING      CONTROL REQUIREMENT                         ming stick forces, the effectiveness of the
 At landing, the airplane must have suthcient               elevator.may be reduced to hinder landing or
control power to ensure adequate control at                 takeoff control.
specified landing speeds. Adequate landing                     Each of the three principal conditions re-
control is usually assured if the elevators are             quiting adequate longitudinal control are ctit-
capable of holding the airplane just off the                ical for high static stability.    If the forward
runway at 105 percent of the stall speed. Of                c.g. limit is exceeded, the airplane may en-
course, the most critical requirement will exist            counter a deficiency of controllability     in any
 when the c.g. is in the most forward position,             of these conditions.     Thus, the forward c.g.
                                                                                NAVWEPS DD-801-80
                                                                             STABILITY AND CONTROL

limit is set by the minimum permissible con-             (4) The displacement or deflection of the
 trollability   while the aft c.g. limit is set by       elevator when the stick-free condition is
 the minimum permissible stability.                      considered.
LONGITUDINAL            DYNAMIC       STABILITY.         The longitudinal dynamic stability of an
    All previous considerations of longitudinal      airplane generally consists of three basic modes
stability have been concerned with the initial       (or manners) of oscillation.    While the longi-
tendency of the airplane to return to equilib-       tudinal motion of the airplane may consist of a
rium when subjected to a disturbance. The            combination of these modes, the characteristics
considerations of longitudinal       dynamic sta-    of each mode are sufficiently distinct that each
bility ate concerned with time history response      oscillatory tendency may be studied separately.
of the airplane to these disturbances, i.e., the         The first mode of dynamic longitudinal sta-
variation of displacement amplitude with time        bility consists of a very long period oscillation
following a disturbance. From previous deli-         referred to as the phagoid. The phugoid or long
nition, dynamic stability will exist when the        period oscillation involves noticeable vatia-
amplitude of motion decreases with time and          tions in pitch attitude, altitude, and airspeed
dynamic instability will exist if the amplitude      but nearly constant angle of attack. Such an
increases with time.                                 oscillation of the airplane could be considered
    Of course, the airplane must demonstrate         as a gradual interchange of potential and
positive dynamic stability for the major longi-      kinetic energy about some equilibrium airspeed
tudinal motions.       In addition, the airplane     and altitude. Figure 4.20 illustrates the char-
must demonstrate a certain degree of longitu-        acteristic motion of the phugoid.
dinal stability by reducing the amplitude of             The period of oscillation in the phugoid is
motion at a certain rate. The requited degree        quite large, typical values being from 20 to 100
of dynamic stability is usually specified by         seconds. Since the pitching rate is quite low
the time necessary for the amplitude to reduce       and only negligible changes in angle of attack
to one-half the original value-the         time to   take place, damping of the phugoid is weak and
damp to half-amplitude.                              possibly negative. However, such weak or
    The airplane in free flight has six degrees of   negative damping does not necessarily have any
freedom: rotation in roll, pitch, and yaw and        great consequence. Since the period of oscilla-
translation in the horizontal, vertical, and         tion is so great, the pilot is easily able to
lateral directions. In the case of longitudinal      counteract the oscillatory tendency by very
dynamic stability, the degrees of freedom can        slight and unnoticed control movements. In
be limited to pitch rotation, vertical and           most cases, the necessary corrections ate so
horizontal translation.      Since the airplane is   slight that the pilot may be completely un-
usually symmetrical from port to starboard,          aware of the oscillatory tendency.
there will be no necessity for consideration of          Due to the nature of the phugoid, it is not
coupling between longitudinal         and lateral-   necessary to make any specific aerodynamic
directional motions. Thus, the principal vari-       provisions to contend with the oscillation.
ables in the longitudinal motion of an airplane      The inherent long period of the oscillation al-
will be:                                             lows study to be directed to more important
   (1) The pitch attitude of the airplane.           oscillatory tendencies. Similarly, the diffet-
    (2) The angle of attack (which will differ       ences between the stick-fixed and stick-free
    from the pitch attitude by the inclination of    phugoid are not of great importance.
    the flight- path).                                   The secondmodeof longitudinal dynamic sta-
    (3) The flight velocity.                          bility is a relatively short period motion that

                                              IST     MODE     OR PHUGOID

                                        ANGLE         OF ATTACK AT EACH
                                        INS%;          ,,“L&blSG$~,lGH~                        &

    5                                                             PERIOD
                                                               LoNG ------I

                            2ND       MODE OR SHORT              PERIOD   OSCILLATION

                    MOTION            OCCURS AT ESSENTIALLY               CONSTANT          SPEED

                                 L    TIME TO DAMP TO
                                      HALF AMPLITUDE

                                              Lb--                                                 TIME

                -6.HORT              PERIOD      -

                                     UNSTABLE         OSCILLATION

                                 Figure 4.20.        Longiitudinal   Dynamic   Sttxbility

                                                                                        NAVWEPS 00-BOT-80
                                                                                     STABILITY AND CONTROL

can be assumed to take place with negligible               control system is greatly magnified. In addi-
changes in velocity. The second mode consists              tion, response lag of the controls may add to
of a pitching oscillation during which the air-            the problem of attempting to forceably damp
plane is being restored to equilibrium by the              the oscillation. In this case, should an oscilla-
static stability and the amplitude of oscillation          tion appear, the best rule is to release the con-
decreased by pitch damping. The typical mo-                trols as the airplane stick-free will demonstrate
tion is of relatively high frequency with a                the necessary damping, Even an attempt to
period of oscillation on the order of 6.5 to 5             fix the controls when the airplane is oscillating
seconds.                                                   may result in a small unstable input into the
    For the conventional subsonic airplane, the            control system which can reinforce the oscilla-
second mode stick-fixed is characterized by                tion to produce failing flight loads. Because
heavy damping with a time to damp to half                  of the very short period of the oscillation, the
amplitude of approximately 0.5 seconds. IJsu-              amplitude of an unstable oscillation can reach
ally, if the airplane has static stability stick-          dangerous proportions in an extremely short
fixed, the pitch damping contributed by the                period of time.
horizontal tail will assume sufficient dynamic                  The third mode occurs in the elevator free case
stability for the short period oscillation. How-           and is usually a very short period oscillation.
ever, the second mode stick-free has the possi-            The motion is essentially one of the elevator
bility of weak damping or unstable oscilla-                 flapping about the hinge line and, in most
tions. This is the case where static stability             cases, the oscillation has very heavy damping.
does not automatically imply adequate dy-                  A typical flapping mode may have a period of
namic stability.     The second mode stick-free is         0.3 to 1.5 seconds and a time to damp to half-
essentially a coupling of motion between the                amplitude of approximately 0.1 second.
airplane short period pitching motion and ele-                  Of all the modes of longitudinal dynamic
vator in rotation about the hinge line. Ex-                 stability, the second mode or porpoising oscil-
treme care must be taken in the design of the               lation is of greatest importance.        The por-
control surfaces to ensure dynamic stability for            poising oscillation has the possibility          of
 this mode. The elevators must be statically                damaging flight loads and can be adversely
 balanced about the hinge line and aerodynamic              affected by pilot response lag. It should be
 balance must be within certain limits. Control             remembered that when stick-free the airplane
system friction must be minimized as it con-                will demonstrate the necessary damping.
tributes to the oscillatory tendency. If insta-                 The problems of dynamic stability are acute
 bility were to exist in the second mode, “por-             under certain conditions of flight. Low static
 poising” of the airplane would result with                 stability generally increases the period (de-
 possibility of structural damage. An oscilla-              creases frequency) of the short period oscil-
 tion at high dynamic pressures with large                  lations and increases the time to damp to half-
 changes in angle of attack could produce severe            amplitude.     High altitude-and     consequently
 flight loads.                                               low density-reduces the aerodynamic damp-
     The second mode has relatively short periods            ing. Also, high Mach numbers of supersonic
 that correspond closely with the normal pilot               flight produce a decay of aerodynamic damping.
 response lag time, e.g., 1 or 2 seconds or less.
 There is the possibility that an attempt to                MODERN      CONTROL       SYSTEMS
 forceably damp an oscillation may actually re-
 inforce the oscillation and produce instability.             In order to accomplish the stability and
 This is particularly true in the case of powered           control objectives, various configurations of
 controls where a small input energy into the               control systems are necessary. Generally, the

 type of flight control system is decided by the            by the actuator and none of the hinge moments
 size and flight speed range of the airplane.               are fed back through the controls. In such
    The conventional control system consists of             a control system, the control position decides
 direct mechanical linkages from the controls               the deflection of the control surfaces regardless
 to the control surfaces. For the subsonic                  of the airloads and hinge moments. Since the
 airplane, the principal means of producing                 power-operated control system has zero feed-
 proper control forces utilize aerodynamic bal-             back, control feel must be synthesized other-
 ance and various tab, spring, and bobweight                wise an infinite boost would exist.
 devices. Balance and tab devices are capable                  The advantages of the power-operated COR-
 of reducing control forces and will allow the              trol system are most apparent in transonic and
 use of the conventional control system on large            supersonic flight. In transonic flight, none of
airplanes to relatively high subsonic speeds.               the erratic hinge moments are fed back to the
    When the airplane with a conventional                  pilot.    Thus, no unusual or erratic control
control system is operated at transonic speeds,            forces,will be encountered in transonic flight.
 the great changes in the character of flow                 Supersonic flight generally requires the use of
can produce great aberrations in control sur-              an all-movable horizontal surface to achieve
face hinge moments and the contribution of                  the necessary control effectiveness. Such con-
tab devices. Shock wave formation and                       trol surfaces must then be actuated and posi-
separation of flow at transonic speeds will                tively positioned by an irreversible device.
limit the use of the conventional control                      The most important item of an artificial feel
system to subsonic speeds.                                 system is the stick-centering spring or bungee.
   The power-boostedcontrol system employs a               The bungee develops a stick force in proportion
‘mechanical actuator in parallel with the                   to stick displacement and thus provides feel
mechanical linkages of a conventional control              for airspeed and maneuvers. A bobweight
system. The principle of operation is to pro-              may be included in the feel system to develop
vide a fixed, percentage of the required control           a steady positive maneuvering stick force
forces thus reducing control forces at high                gradient which is independent of airspeed for
speeds. The power-boosted control system                   ordinary maneuvers.
requires a hydraulic actuator with a control                   The gearing between the stick position and
valve which supplies boost force in fixed                  control surface deflection is not necessarily a
proportion to control force. Thus, the pilot               linear relationship.     The majority of powered
is given an advantage by the boost ratio to                control systems will employ a nonlinear gear-
assist in deflecting the control surface, e.g.,            ing such that relatively greater stick deflection
with a boost ratio of 14, the actuator provides            per surface deflection will occur at the neutral
14 lbs. of force for each 1 lb. of stick force.            stick position.      This sort of gearing is to
   The power-boosted control system has the                advantage for airplanes which operate at flight
obvious advantage of reducing control forces               conditions of high dynamic pressure. Since
at high speeds. However, at transonic speeds,              the airplane at high 4 is very sensitive to small
the changes in control forces due to shock                 deflections of the control surface, the nonlinear
waves and separation still take place but to a             gearing provides higher stick force stability
lesser degree. The “feedback” of hinge                     with less sensitive control movements than
moments is reduced but the aberrations in                  the ‘ system with a linear gearing. Figure 4.21
stick forces may still exist.                              illustrates a typical linear and nonlinear control
   The power-opsrdted, irreversible control system         system gearing.
consists of mechanical actuators controlled                    The second chart of figure 4.21 illustrates
by the pilot. The control surface is deflected             the typical control system stick force variation
                                                                            NAVWEPS 00-ROT-80
                                                                         STABILITY AND CONTROL
                           CONTROL SYSTEM GEARING

                                CONTROL SYSTEM STICK FORCE

                                                               STICK FORCE LBS.




       LEADING      EDGE DOWN                            LEADING EDGE UP

     25O      200         I50        100      50                    50      I00

                      Figure 4.27. Longitudinal Control System

 with control surface deflection. While it is               moments which tend to restore the airplane
 desirable to have a strong centering of the                to equilibrium.
 stick near the neutral position, the amount of                DEFINITIONS.       The axis system of an air-
 force required to create an initial displacement           plane will define a positive yawing moment,
 must be reasonable. If the control system                  N, as a moment about the vertical axis which
 “break-out” forces are too high, precise control           tends to rotate the nose to the right.     As in
 of’the airplane at high speeds is diflicult.    As         other aerodynamic considerations, it is con-
 the solid friction of the control system con-              venient to consider yawing moments in the
 tributes to the break-out forces, proper mainte-           coefficient form so that static stability can be
 nance of the control system is essential. Any              evaluated independent of weight, altitude,
 increase in control system friction can create             speed, etc. The yawing moment, N, is de-
 unusual and undesirable control forces.                    fined in the coefficient form by the following
    The trim of the powered control system is               equation:
essentially any device to produce zero control                                 N = C,qSb
force for a given control surface deflection.               or
One system may trim off bungee force at a
given stick position while another system may                                   C,=N
trim by returning the stick to neutral position.
    Flight at high supersonic Mach numbers
might require a great variety of devices in the                  N=yawing     moment, ft.-lbs;
longitudinal control system. The deteriora-                          positive to the right
tion of pitch damping with Mach-number may                        q= dynamic pressure, psf
require that dynamic stability be obtained                        S=wing area, sq. ft.
synthetically by pitch dampers in the control                     b=wing span, ft.
system. The response of the airplane to                          C,=yawing     moment coefficient, positive
longitudinal control may be adversely affected                       to the right
by flight at high dynamic pressures. In such
conditions of flight stick forces must be ade-           The yawing moment coefficient, C,, is based on
quate to prevent an induced oscillation.      Stick      the wing dimensions $ and 6 as the wing is the
                                                         characteristic surface of the airplane.
forces must relate the transients of flight as
                                                            The yaw angle of an airplane relates the dis-
well as the steady state conditions.       Such a
                                                         placement of the airplane centerline from some
contribution to control system forces may be
                                                         reference azimuth. and is assigned the short-
provided by a pitching acceleration bobweight
                                                        ,hand notation I& (psi). A positive yaw angle
and a control system viscous damper.
                                                         occurs when the nose of the airplane is dis-
DIRECTIONAL       STABILITY    AND    CONTiOL            placed to the right of the azimuth direction.
                                                         The definition of sideslip angle involves a sig-
DIRECTIONAL       STABILITY                              nificant difference. Sides&p angle relates the
   The directional stability of an airplane is           displacement of the airplane centerline from
essentially the “weathercock”     stability and          the relative wind rather than some reference
involves moments about the vertical axis and             azimuth., Sideslip angle is’ provided the short-
their relationship with yaw or sideslip angle.           hand notation p (beta) and is positive when
An airplane which has static directional sta-            ihe rela&e wind is displaced to the right of
bility would tend to return to an equilibrium            the,airplane centerline. Figure 4.22 illustrates
when subjected to some disturbance from equi-            the definitions of sideslip and yaw angles.
librium.    Evidence of static directional sta-             The sideslip angle, 8, is essentially the di-
bility would be the development of yawing                rectional angle of attack of the airplane and
                                                                                  NAVWEPS 00-ROT-80
                                                                               STABILITY AND CONTROL

is the primary reference in lateral stability as          Static directional stability must be in evi-
well as directional stability considerations.         dence for all the critical conditions of flight.
The yaw angle, #, is a primary reference for          Generally, good directional stability is a ftm-
wind tunnel tests and time history motion of          damental quality directly affecting the pilots’
an airplane. From the definitions there is no         impression of an airplane.
direct relationship between @ and # for an                CONTRIBUTION           OF THE AIRPLANE
airplane in free flight, e.g., an airplane flown      COMPONENTS.            The static directional sta-
through a 360° turn has yawed 360” but side-          bility of the airplane is a result of contribution
slip may have been zero throughout the entire         of each of the various airplane components.
turn. Since the airplane has no directional           While the contribution of each component is
sense, static directional stability of the air-       somewhat dependent upon and related to other
plane is appreciated by response to sideslip.         components, it is necessary to study each
   The static directional stability of an airplane    component separately.
can be illustrated by a graph of yawing moment            The vertical tail is the primary source of
coe&cient, C., versus sideslip angle, 8, such as      directional stability      for the airplane. As
shown in figure 4.22. When the airplane is            shown in figure 4.23, when the airplane is in
subject to a positive sideslip angle, static direc-   a sideslip the vertical tail will experience a
tional stability will be evident if a positive        change in angle of attack. The change in
yawing moment coefficient results.           Thus,    lift-or    side force-on the vertical tail creates
when the relative wind comes from the right           a yawing moment about the center of gravity
(+p), a yawing moment to the right (+C.)              which tends to yaw the airplane into the
should be created which tends to weathercock          relative wind. The magnitude of the vertical
the airplane and return the nose into the wind.       tail contribution to static directional stability
Static directional stability will exist when the      then depends on the change in tail lift and the
curve of C,, versus fi has a positive slope and the   tail moment arm. Obviously, the tail moment
degree of stability will be a function of.the         arm is a powerful factor but essentially dic-
slope of this curve. If the curve has zero slope,     tated by the major configuration properties of
there is no tendency to return to equilibrium         the airplane.
and neutral static directional stability exists.          When the location of the vertical tail is set,,
When the curve of C. versus /3 has a negative         the contribution of the surface to directional
slope, the yawing moments developed by side-          stability depends on its ability to produce
slip tend to diverge rather than restore and          changes in lift-or     side force-with  changes in
static directional instability exists.                sideslip. The surface area of the vertical tail
   The final chart of figure 4.22 illustrates the     is a powerful factor with the contribution of
fact that the instantaneous slope of the curve of     the vertical tail being a direct function of the
C,, versus @ will describe the static directional     area. When all other possibilities are ex-
stability of the airplane. At small angles of         hausted, the required directional stability may
sideslip a strong positive slope depicts strong       be obtained by increases in tail area. How-
directional stability.    Large angles of sideslip    ever, increased surface area has the obvious
produce zero slope and neutral stability.        At   disadvantage of increased drag.
very high sideslip the negative slope of the              The lift curve slope of the vertical tail
curve indicates directional instability.       This   relates how sensitive the surface is to changes
decay of directional stability with increased         in angle of attack. While it is desirable to
sideslip is not an unusual condition. However,        have a high lift curve slope for the vertical
directional instability should not occur at the       surface, a high aspect ratio surface is not
angles of sideslip of ordinary flight conditions.     necessarily practical or desirable. The stall

                                                                                    +N,YAWlNG       MOMENT

                        YAWING MOMENT


                                                                                    SIDESLLANGLE,      p

                             Figure 4.22.       Static    Directional   Stability

                                                                                 NAVWEPS OO-ROLRO
                                                                              STARIUTY AND CONTROL

angle of the surface must be sufficiently great      greater aerodynamic force and, generally, a
to prevent stall and subsequent loss of effec-       continued destabilizing influence.
tiveness at ordinary sideslip angles. The high          Figure 4.23 illustrates a typical buildup of
Mach numbers of supersonic flight produces a         the directional stability of an airplane by
decrease in lift curve slope with the consequent     separating the contribution of the fuselage
reduction in tail contribution to stability.    In   and tail. As shown by the graph of C. versus
order to have sufficient directional stability at    6, the contribution of the fuselage is de-
high Mach numbers, the typical supersonic            stabilizing but the instability       decreases at
configuration will exhibit relatively        large   large sideslip angles. Tbe contribution of the
vertical tail surfaces.                              vertical tail alone is highly stabilizing up to
   The flow field in which the vertical tail         the point where the surface begins to stall.
operates is affected by the othei components         The contribution of the vertical tail must be
of the airplane as well as powe; effects. The        large enough so that the complete airplane
dynamic pressure at the vertical tail could          (wing-fuselage-tail combination) exhibits the
depend on the slipstream of a propeller or the       required degree of stability.
boundary layer of the fuselage. Also, the               The dorsal fin has a powerful effect on pre-
local flow direction at the vertical tail is in-     serving the directional stability at large angles
fluenced by the wing wake, fuselage crossflow,       of sideslip wliich would produce stall of the
induced flow of the horizontal tail, or the          vertical tail. The addition of a dorsal fin to
direction of slipstream from a propeller. Each       the airplane will allay the decay of directional
of these factors must be considered as possibly      stability at high sideslip in two ways. The
affecting the contribution of the vertical tail      least obvious but most important effect is a
to directional stability.                            large increase in the fuselage stability at large
   The contribution of the wing tb %tatic direc-     sideslip angles. In addition, the effective
tional stability is tisually small: The swept        aspect rario of the vertical tail is reduced
wing provides a stable contribution’ depending       which increases the stall angle for the surface.
on the amount of sweepback but the contribu-         By this twofold effect, the addition of the
tion is relatively weak when compared with           dorsal fin is a v     useful’ device.
other components.                    :.                 Poluer effects on static directional stability
    The contribution of the fuselage nacelles        are similar to the power effects on static
is of primary importance since these compo-          longitudinal stability.    The direct effects are
nents furnish rhe greatest destabilizing in-         confined to the normal force at the propeller
fluence. The contribution of the fuselage and        plane or the jet inlet and, of course, are de-
nacelles is similar to the longitudinal case         stabilizing when the propeller or inlet is
with the exception that there is no large in-        located ahead of the c.g. The indirect effects
fluence of the induced flow field of the wing.       of power induced velocities and flow dirkccion
The subsonic center of pressure of the fuselage      changes at the vertical tail are quite significant
will be located at or forward of the quarter-        for the propeller driven airplane and can pro-
length point and, since the airplane c.g. is         duce large directional trim changes. As in
usually considerably aft of this point, the
                                                     the lontitudinal case, the indirect effects are
fuselage contribution     will be destabilizing.
                                                     negligible for the jet powered airplane.
However, at large angles of sideslip the large
destabilizing contribution of the fuselage di-          The contribution of the direct and indirect
minishes which is some relief to the problem         power effects to static directional stability is
of maintaining directional stability at large        greatest for the propeller powered airplane
displacements. The supersonic pressure,. dis-        and usually slight for the jet powered airplane.
tribution on the body provides a relatively          In either case, the general effect of power is
NAVWEPS oO-801-80

                           CONTRIBUTION         OF VERTICALTAIL

                                                                                               CHANGE IN
                                                                                                TAIL LIFT

                                      TYPICAL DIRECTIONAL         STABILITY

                                                                               AIRPLANE WITH
                                                                                 DORSAL FIN
                                                            STALL              ,-ADDED

                  Figure 4.23.   Contribution    of Components    to Directional   Stability

                                                                     NAVWEPS Oe8OT-80
                                                                  STABILITY AND CONTROL

                 DIRECTIONAL    STABILITY

t                                         RUDDER-FIXED


                                                             RUDDER   FLOAT

                                                    -e            ANGLE
                     SIDESLIP   ANGLE,    p

        EFFECT        OF ANGLE    OF ATTACK

                                         HIGH ANGLE
                                         OF ATTACK
                     SIDESLIP   ANGLE,    fla

                 EFFECT   OF MACH NUMBER

                     SIDESLIP   ANGLE,    p

     Figure 4.24. Factors Affecting       Direcfional Stability


destabilizing and the greatest contribution            because of increase in the fuselage boundary
will occur at high power and low dynamic               layer at the vertical tail location. The decay of
pressure as during a waveoff.                          dir&ctional stability with angle of attack is
    As in the case of longitudinal static stability,   most significant for the low aspect ratjo air-
freeing the controls will reduce the effective-        plane with sweepback since this configuration
 ness of the tail and alter the stability.    While    requires such high angles of attack to achieve
 the rudder must be balanced to reduce control         high lifr coefficients. Such decay in directional
pedal forces, the rudder will tend to float or         stability can have a profound effect on the re-
 streamline and reduce the contribution of the         sponse of the airplane to adverse yaw and spin
vertical tail to static directional stability. The     characteristics.
floating tendency is greatest at large angles of          High Mach ntrmbersof supersonic flight reduce
sideslip where large angles of attack for the          the contribution of the vertical tail to direc-
 vertical tail tend to decrease aerodynamic bal-       tional stability because of the reduction of lift
 ante. Figure 4.24 illustrates the difference be-      cnrve slope with Mach number. The third
 tween rudder-fixed and rudder-free static di-         chart of figure 4.24 illustrates the typical decay
rectional stability.                                   of directional stability with Mach number. To
    CRITICAL CONDITIONS.            The most criti-    produce the required directional stability at
cal conditions of,staric directional stability are     high Mach numbers, a viziy large vertical tail
usually the combination of several separate            area may be necessary. Ventral fins may be
effects. The combination which produces the            added as an additional contribution to direc-
most critical condition is much dependent upon         tional stability but landing clearance require-
the type and mission of the airplane. In addi-         ments may limir their size or require the fins to
tion, there exists a coupling of lateral and di-       be retractable.
rectional effects such that the required degree           Hence, the most critical demands of static
of static directional stability may be deter-          directional stability will occur from some
mined by some of these coupled conditions.             combination of the following effects:
    Center of gravity position has a relatively              (1) high angle of sideslip
negligible effect on static directional stability.           (2) high power at low airspeed
The usual range of c.g. position on any air-                 (3) high angle of attack
plane is set by the Jinits of long&d&a/ stability            (4) high Mach number
and control.      Within this limiting range of        The propeller powered airplane may have such
c.g. position, no significant changes take place       considerable power effects that the critical
in the contribution of the vertical tail, fuselage,    conditions may occur at low speed while the
nacelles, etc. Hence, the static directional           effect of high Mach numbers may produce the
stability is essentially unaffected by the varia-      critical conditions for the typical supersonic
tion of c.g. position within the longitudinal          airplane. In addition, the coupling of lateral
limits.                                                and directional effects may require prescribed
    When the airplane is at a high angle of a$tack     degrees of directional stability.
a decrease in static directional stability can be
anticipated. As shown by the second chart of           DIRECTIONAL       CONTROL
figure 4.24, a high angle of attack reduces the           In addition to directional stability, the air-
stable slope of the curve of C,, versus 8, The         plane must have adequate directional control
decrease in static directional stability is due in     to coordinate turns, balance power effects,
great part to the reduction in the contribution        create sideslip, balance unsymmetrical power,
of the vertica1 tail. At high angles of attack,        etc. The principal source of directional con-
the effectiveness of the vertical tail is reduced      trol is the rudder and the rudder must be
                                                                                         NAVWEPS 00-SOT-80
                                                                                      STABIUTY AND CONTROL

capable of producing sufhcient yawing moment                have a stable rudder pedal feel through the
for the critical conditions of flight.                      available range of sideslip.
   The effect of rudder deflection is to produce                 DIRECTIONAL         CONTROL        REQUIRE-
a yawing moment coefficient according to                    MENTS.         The control power of the rudder
control deflection and produce equilibrium at                must be adequate to contend with the many
some angle of sideslip. For small deflections                unsymmetrical conditions of flight.         Gener-
of the rudder, there is no change in stability               ally, there are five conditions of flight which
but a change in equilibrium.           Figure 4.25           provide the most criticalrequirements        of di-
shows the effect of rudder deflection on yawing             rectional control power. The type and mission
moment coefficient curves with the change in                 of the airplane will decide which of these
equilibrium sideslip angle.                                  conditions is most important.
    If the airplane exhibits static directional                  ADVERSE YAW.          When an airplane is
stability with rudder lixed, each angle of side-             rolled into a turn yawing moments are pro-
slip requires a particular deflection of the                 duced which require rudder deflection to main-
rudder to achieve equilibrium.          Rudder-free          tain zero sideslip, i.e., coordinate the turn.
directional stability will exist when the float              The usual source of adverse yawing moment is
angle of the rudder is less than the rudder                  illustrated in figure 4.26. When the airplane
deflection required for equilibrium.      However            shown is subject to a roll to the left, the down-
at high angles of sideslip, the floating tend-               going port wing will experience a new relative
ency of the rudder increases. This is illus-                 wind and an increase in angle of attack. The
trated by the second chart of figure 4.25 where              inclination of the lift vector produces a com-
 the line of rudder float angle shows a sharp                ponent force forward on the downgoing wing.
 increase at large values of sideslip. If the                The upgoing starboard wing has its lift in-
floating angle of the rudder catches up with                 clined with a component force aft. The re-
the required rudder angle, the, rudder pedal                 sulting yawing moment due to rolling motion
force will decrease to zero and rudder lock will             is in a direction opposite to the roll and is
                                                             hence “adverse yaw.” The yaw due to roll is
occur. Sideslip angles beyond this point pro-
                                                             primarily a function of the wing lift coefficient
duce a floating angle greater than the required
                                                             and is greatest at high C,.
rudder deflection and the rudder tends to float
                                                                 In addition to the yaw due to rolling motion
to the limit of deflection.                                  there will be a yawing moment contribution
    Rudder lock is accompanied by a reversal of              due to control surface deflection. Conventional
pedal force and rudder-free instability        will          ailerons usually contribute an adverse yaw
exist. The dorsal fin is a useful addition in                while spoilers may contribute a favorable or
 this case since it will improve the directional              “proverse” yaw. The high wing airplane
 stability at high angles of sideslip. The re-               with a large vertical tail may encounter an
sulting increase in stability requires larger                influence from inboard ailerons. Such a con-
 deflections of the rudder to achieve equilibrium            figuration may induce flow directions at the
at high sideslip and the tendency for rudder                 vertical tail to cause proverse yaw.
lock is reduced.                                                 Since adverse yaw will be greatest at high
    Rudder-free directional stability is appre-              C, and full deflection of the ailerons, coordi-
ciated by the pilot as the rudder pedal force to             nating steep turns at low speed may produce
 maintain a given sideslip. If the rudder pedal              a critical requirement for rudder control power.
 force gradient is too low near zero sideslip, it                SPIN RECOVERY.        In the majority of air-
 will be difficult to maintain zero sideslip dur-             planes, the rudder is the principal control for
 ing various maneuvers. The airplane should                   spin recovery. Powerful control of sideslip at
NAVWEPS 00-807-80
                            EFFECT OF RUDDER DEFLECTION            ON
                               EOlJlLlSRlUM SIDESLIP ANGLE

                                                       RUDDER DEFLECTION

                                   RUDDER LOCK.

                                RUDDER DEFLECTION

                                                                               FLOAT ANGLE

                        /                      SIDESLIP ANGLE, p                  +

                            EFFECT DF RUDDER           LOCK   ON PEDAL         FORCE

                                                                              RUDDER LOCK
                                                                  DORSAL FIN ADDED
                                Figure 4.25.    Directional   Control

                                                                                     NAVWEPS 00-8OT-30
                                                                                 STABILITY AND CONTROL

                     ADVERSE        YAW DUE TO ROLL

                      ,IRPLANE.IN      ROLL TO LEFT


       PORT WING

                                              \FOR   SAKE OF CLARITY.                     /


            YAWING    MOMENT        DUE TO ASYMMETRICAL                THRUST

            FROM ASYMMETRICAL                                    /

        I                                                                            w
        I                EQUIVALENT       AIRSPEED,        KNOTS
                Figure 4.26.   Requirements    for Directional       Control


high angles of attack is required to effect re-            speed of the airplane in the lightest practical
covery during a spin. Since the effectiveness              takeoff configuration.     This will provide ade-
of the vertical tail is reduced at large angles of         quate directional control for the remaining
attack, the directional control power neces-               conditions of flight.
sary for spin recovery may produce a critical                 Once defined, the minimum directional con-
requirement of rudder power.                               trol speed is not a function of weight, altitude,
   SLIPSTREAM ROTATION.             A critical di-         etc., but is simply the equivalent airspeed (or
rectional control requirement may exist when               dynamic pressure). to produce a required yaw-
the propeller powered airplane is at high                  ing moment with the maximum rudder deflec-
power and low airspeed. As shown in figure                 tion. If the airplane is operated in the critical
4.26, the single rotation propeller induces                unbalance of power below the minimum con
a slipstream swirl which causes a change in                trol speed, the airplane will yaw uncontrolla-
flow direction at the vertical tail. The rudder            bly into the inoperative engine. In order to
must furnish sufficient control power to balance           regain directional control below the minimum
this condition and achieve zero sideslip.                  speed certain alternatives exist: reduce power
   CROSSWIND TAKEOFF AND LANDING.                          on the operating engines or sacrifice altitude
Since the airplane must make a true path down              for airspeed. Neither alternative is satisfac-
the runway, a crosswind during takeoff or                  tory if the airplane is in a marginal condition
landing will require that the airplane be.con-             of powered flight so due respect must be given
trolled in a sideslip. The rudder must have                to the minimum control speed.
sufficient control power to create the required                Due to the side force on the vertical tail, a
sideslip for the expected crosswinds.                      slight bank is necessary to prevent turning
   ASYMMETRICAL           POWER.      The design           flight at zero sideslip. The inoperative engine
of a multiengine airplane must account for the             will be raised and the inclined wing lift will
possibility of an engine failure at low airspeed.          provide a component of force to balance the 1
The unbalance of thrust from a condition of                 side force on the tail.
unsymmetrical power produces a yawing mo-                      In each of the critical conditions of required
ment dependent upon the thrust unbalance                   directional control, high directional stability
and the lever arm of the force. The deflection             is desirable as it will reduce the displacement
of the rudder will create a side force on the tail         of the aircraft from any disturbing influence.
and contribute a yawing moment to balance                  Of course, directional control must he sufficient
the yawing moment due to the unbalance of                  to attain zero sideslip. The critical control
thrust. Since the yawing moment coefficient                requirement for the multiengine airplane is
from the unbalance of thrust will be greatest              the condition of asymmetrical power since
at low speed, the critical requirement will be             spinning is not common to this type of airplane.
at a low speed with the one critical engine                The single engine propeller airplane may have
out and the remaining engines at maximum                   either the spin recovery or the slipstream rota-
power.     Figure 4.26 compares the yawing                 tion as a critical design condition. The single
moment coeflicient for maximum rudder deflec-              engine jet airplane may have a variety of
tion with the yawing moment coefficient for                critical items but the spin recovery require-
the unbalance of thrust. The intersection of               ment usually predominates.
the two lines,determines the minimum speed
for directional control, i.e., the lowest speed              LATERAL     STABILITY    AND   CONTROL
at which the rudder control moment can equal
the moment of unbalanced thrust, It is usually             LATERAL     STABILITY
specified that the minimum directional control               The static lateral stability of an airplane
 speed be no greater than 1.2 times the stall              involves consideration of rolling moments due
Revised January   1965
                                                                                        NAVWEPS 00-8OT-80
                                                                                     STABILITY AND COI’

to sideslip. If an airplane has favorable rolling          moment coefficient results. Thus, when the
moment due to sideslip, a lateral displacement             relative wind comes from the right (+-a>,
from wing level flight produces sideslip and               a rolling moment to the left (-Cl> should be
the sideslip creates rolling moments tending               created which tends to roll the airplane to
to return the airplane to wing level flight.               the left. Lateral stability will exist when
By this action, static lateral stability will be           the curve of C1 versus p has a negative slope
evident. Of course, a sideslip will produce                and the degree of stability will be a function
yawing moments depending on the nature of                  of the slope of this curve. If the slope of the
the static directional stability but the consid-           curve is zero, neutral lateral stability exists;
rations of static lateral stability will involve           if the slope is positive lateral instability is
only the ‘ relationship of rolling moments and             present.
sideslip.                                                     It is desirable to have lateral stability or
   DEFINITIONS.        The axis system of an               favorable roll due to sideslip. However, the
airplane defines a positive rolling, L, as a               required magnitude of lateral stability is deter-
moment about the longitudinal        axis which            mined by many factors. Excessive roll due to
tends to rotate the right wing down. As in                 sideslip complicates crosswind takeoff and
other aerodynamic considerations, it is con-               landing and may lead to undesirable oscil-
venient to consider rolling moments in the                 latory coupling with the directional motion of
coefficient form so that lateral stability can             the airplane. In addition, a high lateral sta-
be evaluated independent of weight, altitude,              bility may combine with adverse yaw to hinder
speeds, etc. The rolling moment, L, is defined             rolling performance. Generally, favorable han-
in the coeflicient form by the following equa-             dling qualities are obtained with a relatively
tion :                                                     light-or    weak positive-lateral     stability.
                     L=C,qSb                                  CONTRIBUTION          OF THE AIRPLANE
or                          *                              COMPONENTS.           In order to appreciate the
                      +I                                   development of lateral stability in an airplane,
                          0                                each of the contribution components must be
                                                           inspected. Of course, there will be interference
    L=rolling     moment, ft.-lbs., positive to            between the components which will alter the
         the right                                         contribution to stability of each component on
    4 = dynamic pressure, psf.                             the airplane.
    S=wing area, sq. ft.                                       The principal surface contributing         to the
     b = wingspan, ft.                                     lateral stability of an airplane is the wing. The
    C,=rolling     moment coeflicient, positive            effect of the geometric dihedral of a wing is a
         to the right                                      powerful contribution to lateral stability.        As
                                                           shown in figure 4.28, a wing with dihedral will
   The angle of sideslip, 8, has been defined
                                                           develop stable rolling moments with sideslip.
previously as the angle between the airplane
                                                           If the relative wind comes from the side, the
centerline and the relative wind and is positive
when the relative wind is to the right of the              wing into the wind is subject to an increase in
centerline.                                                angle of attack and develops an increase in lift.
   The static lateral stability of an airplane can         The wing away from the wind. is subject to a
be illustrated by a graph of rolling moment                decrease in angle of attack and develops a de-
coefficient, Cl, versus sideslip angle, 8, such            crease in lift. The changes in lift effect a rolling
as shown in figure 4.27. When the airplane                 moment tending to raise the windward wing
is subject to a positive sideslip angle, lateral           hence dihedral contributes a stable roll due to
stability will be evident if a negative rolling             sideslip.

              RELATIVE WIND
                                                             +L,   ROLLING MOMENT

                                         ROLLING MOMENT COEFFICIENT

                                                                          UNSTABLE 7,

                                                                          SIDESLIP   ANGLE, /3

                         TABLE ROLL DUE
                          TO SIDESLIP


                          Figure 4.27.    Static   Lateral    Stability

                                                                           NAVWEPS CID-8OT-80
                                                                        STABILITY AND CONTROL

                                 EFFECT OF DlilEDRAL
                 EFFECTIVE      INCREASE     IN

--SE                                                                          IN
                                                  LIFT DUE TO SIDESLIP

                               EFFECT OF SWEEPBACK


                         CONTRIBUTION      OF VERTICAL TAIL

                                     SIDESLIP CONTRIBUTES
                                        ROLLING MOMENT

       Figure 4.28.   Contribution   of Components   to Lateral   Stability


      Since wing dihedral is so powerful in pro-          there is no wing lift to change. Thus, the
ducing lateral stability it is taken as a common          dihedral effect due to sweepback is zero at zero
denominator of the lateral stability contribu-            lift and increases directly with wing lift
tion of all other components. Generally, the              coefficient. When the demands of high speed
contribution of wing position, flaps, power,              flight require a large amount of sweepback, the
etc., is expressed as an equivalent amount of             resulting configuration may have an excessive-
 “effective dihedral” or “dihedral effect.”               ly high dihedral effect at low speeds (high CL)
     The contribution of the fadage alone is              while the dihedral effect may be satisfactory
usually quite small depending on the location             in normal flight (low or medium C,).
of the resultant aerodynamic side force on the                The vertical tail of modern configurations
fuselage. However, the effect of the wing-                can provide a sign&ant-and,          at times, un-
fuselage-tail combination is significant since            desirable-contribution     to the effective dihe-
the vertical placement of the wing on the fuse-           dral. If the vertical tail is large, the side force
lage can greatly affect the stability of the com-         produced by sideslip may produce a noticeable
bination.      A wing located at the mid wing             rolling moment as well as the important yaw-
position will generally exhibit a dihedral effect         ing moment contribution.         Such an effect is
no different from that of the wing alone. A               usually small for the conventional airplane
low wing location on the fuselage may con-                configuration but the modern high speed
tribute an effect equivalent to 3’ or 4’ of nega-         airplane configuration induces this effect to a
tive dihedral while a high wing location may              great magnitude. It is difficult then to obtain
contribute a positive dihedral of 2’ or 3’ The            a large vertical tail contribution to directional
magnitude of dihedral effect contributed by               stability without incurring an additional con-
vertical position of the wing is large and may            tribution to dihedral effect.
necessitate a noticeable dihedral angle for the               The amount of effective dihedral necessary
low wing configuration.                                   to produce satisfactory flying qualities varies
     The contribution of wccpback to dihedral ef-         greatly with the type and purpose of the air-
fect is important because of the nature of the            plane. Generally, the effective dihedral should
contribution.      As shown in figure 4.28, the           not be too great since high roll due to side-
swept wing in a sideslip has the wing into                slip can create certain problems. Excessive
wind operating with an effective decrease in              dihedral effect can lead to “Dutch roll,”
sweepback while the wing out of the wind                  difficult rudder coordination in rolling maneu-
is operating with an effective increase in                vers, or place extreme demands for lateral
sweepback. If the wing is at a positive lift              control power during crosswind takeoff and
coefficient, the wing into the wind has less              landing.     Of course, the effective dihedral
sweep and an increase in lift and the wing out            should not be negative during the predominat-
of the wind has more sweep and a decrease in              ing conditions of flight, e.g., cruise, high
lift.     In this manner the swept back wing              speed, etc. If the airplane demonstrates satis-
would contribute a positive dihedral effect and           factory dihedral effect for these conditions of
the swept forward wing would contribute a                 flight, certain exceptions can be considered
negative dihedral effect.                                 when the airplane is in the takeoff and landing
    The unusual nature of the contribution of             configuration.    Since the effects of flaps and
sweepback to dihedral effect is that the con-             power are destablizing and reduce the dihedral
tribution is proportional       to the wing lift          effect, a certain amount of negative dihedral
coefficient as well as the angle of sweepback.            effect may be possible due to these sources.
It should be clear that the swept wing at zero                The deflection of flaps causes the inboard
lift will provide no roll due to sideslip since           sections of the wing to become relatively more
                                                                                        NAVWEPS, OO-ROT-80
                                                                                    STABILITY AND CONTROL

effective and these sections have a small                         (2) Yawing moment due to sideslip or
spanwise moment arm. Therefore, the changes                    static directional stability.
in wing lift due to sideslip occur closer in-                     (3) Yawing moment due to rolling veloc-
board and the dihedral effect is reduced. The                  ity or the adverse (or proverse) yaw.
effect of power on dihedral effect is negligible                  (4) Rolling moment due to yawing ve-
for the jet airplane but considerable for the                  locity-a    cross effect similar to (3). If the
propeller driven airplane. The propeller slip-                 aircraft has a yawing motion to the right,
stream at high power and low airspeed makes                    the left wing will move forward faster and
the inboard wing sections much more effective                  momentarily develop more lift than the
and reduces the dihedral effect. The reduction                 right and cause a rolling moment to the
in dihedral effect is most critical when the                   right.
flap and power effects are combined, e.g., the                    (3) Aerodynamic side force due to side-
propeller driven airplane in the power approach                slip.
or waveoff.                                                       (6) Rolling moment due to rolling ve-
   With certain exceptions during the condi-                   locity or damping in roll.
tions of landing and takeoff, the dihedral                        (7) Yawing moment due yawing velocity
effect or lateral stability should be positive                 or damping in yaw.
but light. The problems created by excessive                      (8) The moments of inertia of the air-
dihedral effect are considerable and difficult                 plane about the roll and yaw axes.
to contend with.       Lateral stability will be            The complex interaction of these effects pro-
evident to a pilot by stick forces and displace-            duces three possible types of motion of the
ments required to maintain sideslip. Positive               airplane: (a) a directional        divergence, (b)
stick force stability will be evident by stick              a spiral divergence, and (c) an oscillatory
forces required in the direction of the controlled          mode termed Dutch roll.
sideslip.                                                       Directional divergence is a condition which
                                                            cannot be tolerated. If the reaction to a small
LATERAL     DYNAMIC       EFFECTS                           initial sideslip is such as to create moments
   Previous discussion has separated the lateral            which tend to increase the sideslip, directional
and directional response of the airplane to                 divergence will exist. The sideslip would in-
sideslip. This separation is convenient for                 crease until the airplane is broadside to the
detailed study of each the airplane static                  wind or structural failure occurs. Of course,
lateral stability and the airplane static direc-            increasing the static directional stability re-
tional stability.   However, when the airplane              duces the tendency for directional divergence.
in free flight is placed in a sideslip, the lateral             Spiral divergencewill exist when the static
and directional response will be coupled, i.e.,             directional stability is very large when com-
simultaneously the airplane produces rolling                pared with the dihedral effect. The character
moment due to sideslip and yawing moment                    of spiral divergence is by no means violent,
due to sideslip. Thus, the lateral dynamic
                                                            The airplane, when disturbed from the equilib-
motion of the airplane in free flight must
                                                            rium of level flight, begins a slow spiral which
consider the coupling or interaction of the
lateral and directional effects.                            gradually increases to a spiral dive. When a
   The principal effects which determine the                small sideslip is introduced, the strong direc-
lateral dynamic characteristics of an airplane              tional stability tends to restore the nose into
are :                                                       the wind while the relatively weak dihedral
      (1) Rolling moment due to sideslip or                 effect lags in restoring the airplane laterally,
   dihedral effect (lateral stability).                     In the usual case, the rate of divergence in the

spiral motion is so gradual that the pilot can            The contribution of sweepback to the lateral
control the tendency without difficulty.               dynamics of an airplane is significant. Since
   Dutch roll is a coupled lateral-directional         the dihedral effect from sweepback is a function
oscillation which is usually dynamically stable        of lift coefficient, the dynamic characteristics
but is objectionable because of the oscillatory        may vary throughout the flight speed range.
nature. The damping of this oscillatory mode           When the swept wing airplane is at low C,, the
may be weak or strong depending on the prop-           dihedral effect is small and the spiral tendency
erties of the airplane. The response of the air-       may be apparent. When the swept wing air-
plane to a disturbance from equilibrium is a           plane is at high C,, the dihedral effect is in-
combined rolling-yawing oscillation in which           creased and the Dutch Roll oscillatory tendency
the rolling motion is phased to precede the            is increased.
yawing motion. Such a motion is quite unde-               An additional oscillatory mode is possible
sirable because of the great havoc it would            in the lateral dynamic effects with the rudder
create with a bomb, rocket, or gun platform.           free and the mode is termed a “snaking” oscil-
   Generally, Dutch roll will occur when the           lation.   This yawing oscillation is greatly
dihedral effect is large when compared to static       affected by the aerodynamic balance of the
directional stability.     Unfortunately,    Dutch     rudder and requires careful consideration in
roll will exist for relative magnitudes of dihe-       design to prevent light or unstable damping
dral effect and static directional stability be-       of the oscillation.
tween the limiting conditions for directional
divergence and spiral divergence. When the             CONTROL      IN ROLL
dihedral effect is large in comparison with
static directional stability,     the Dutch roll           The lateral control of an airplane is ac-
motion has weak damping and is objectionable.           complished by producing differential lift on
When the static directional stability is strong         the wings. The rolling, moment created by
in comparison with the dihedral effect, the             the differential lift can be used to accelerate
Dutch roll motion has such heavy damping                the airplane to some rolling motion or control
that it is not objectionable. However, these            the airplane in a sideslip by opposing dihedral
qualities tend toward spiral divergence.                effect. The differential lift for control in
    The choice is then the least of three evils.        roll is usually obtained by some type of ailerons
Directional divergence cannot be tolerated,             or spoilers.
Dutch roll is objectionable, and spiral diver-             ROLLING MOTION OF AN AIRPLANE.
gence is tolerable if the rate of divergence is       / When an airplane is given a rolling motion in
low. For this reason the dihedral effect should         flight, the wing tips move in a helical path
be no more than that required for satisfactory          through the air. As shown in figure 4.29, a
lateral stability.   If the static directional sta-     rolling velocity to the right gives the right
bility is made adequate to prevent objection-           wing tip a downward velocity component and
able Dutch roll, this will automatically be             the left wing tip an upward velocity com-
sufficient to prevent directional divergence,           ponent. By inspection of the motion of the
Since the more important handling qualities             left wing tip, the velocity of the tip due to
are a result of high static directional stability       roll combines with the airplane flight path
and minimum necessary dihedral effect, most             velocity to define the resultants motion. The
airplanes demonstrate a mild spiral tendency.           resulting angle between the flight path vector
As previously mentioned, a weak spiral tend-            and the resultant path of the tip is the helix
ency is of little concern to the pilot and cer-         angle of roll. From the trigonometry of small
 tainly preferable to Dutch roll.                       angles, the helix angle of roll can be defined as:
                                                                                       NAVWEPS 00-6OT-60
                                                                                    STABILITY AND CONTROL

                                                            If the airplane is unrestrained and sideslip is
        Roll helix angle=&;     (radians)
                                                            allowed, the affect of the directional stability
where                                                       and dihedral effect can be appreciated. The
                                                            conventional airplane will develop adverse
     p=rate of roll, radians per second
                                                            yawing moments due to aileron deflection and
     6=wing    span, ft.                                    rolling motio6.    Adverse yaw tends to produce
                                                            yawing displacements and sideslip but this is
    V=airplane    flight velocity,   ft. per sec.           resisted by the directional stability of the air-
                                                            plane. If adverse yaw produces sideslip, di-
and, one radian=S7.3 degrees
                                                            hedral effect creates a rolling moment opposing
Generally, the maximum values of rVobtained                 the roll and tends to reduce the roll rate. The
                                                            typical transient motions (A) and (B) of the
by control in roll are approximately   0.1 to 0.07.         time history diagram of figure 4.29 show that
The helix angle of roll, $i,   is, actually a com-          high directional stability with low dihedral
                                                            effect is the preferable combination.      Such a
mon denominator of rolling performance.                     combination provides an airplane which has
    The deflection of the lateral control surfaces          no extreme requirement of coordinating aileron
creates the differential lift and the rolling               and rudder in order to achieve satisfactory
moment to accelerate the airplane in roll. The              rolling performance. While the coupled mo-
roll rate increases until an equal and opposite             tion of the airplane in roll is important,
moment is created by the resistance to rolling              further discussion of lateral control will be
motion or “damping in roll.”          The second             directed to pure uncoupled rolling performance.
illustration of figure 4.29 defines the source                  ROLLING PERFORMANCE.             The required
of the damping in roll. When the airplane                   rolling performance of an airplane is generally
is given a rolling velocity to the right, the
downgoing wing experiences an increase in                   specified as certain necessary values of the roll 1
angle of attack due to the helix angle of roll.             helix angle, &I$   However,     in certain condi-
Of course, the upgoing wing experiences a
decrease in angle of attack. In flight at angles            tions of flight, it may be more appropriate to
of attack less than that for maximum lift, the              specify minimum times for the airplane to
downgoing wing experiences an increase in                   accelerate through a given angle of roll.
lift and the upgoing wing experiences a de-                 Usually, the maximum value of 2% should be
crease in lift and a rolling moment is developed
which opposes the rolling motion. Thus, the                 on the order of 0.10. Of course, fighters and
steady state rolling motion occurs when the                 attack airplanes have a more specific require-
damping moment equals the control moment.                   ment for high rolling performance and 0.09
    The response of the airplane to aileron deflec-         may be considered a minimum necessary 2v.  Pb
tion is shown by the time history diagram of
figure 4.29. When the airplane is restrained                Patrol, transport, and bomberairplaneshaveless
                                                            requirement for high rolling performance and a
so that pure rolling motion is obtained, the
initial response to an aileron deflection is a              Pb
                                                            2-V of 0.07 may be adequate for these types.
steady increase in roll rate. As the roll rate                The ailerons or spoilers must be powerful
increases so does the damping moment and the                                                Pb
roll     acceleration   decreases. Finally,    the          enough to provide the required rV’ While
damping moment approaches the control mo-                   the size and effectiveness of the lateral control
ment and a steady state roll rate is achieved.              devices is important, consideration must be
                                                                                          Revised January   1965

                              HELIX      ANGLE OF ROLL

                                                                          IP VELOCITY,$

                                                     RCUING VELOCITY, P

                                         TIP VELOCITY WE       TO ROLL

                                                                           ( RADIANS 1
                              DAMPING        IN ROLL


                            AIRPLANE      RESPONSE TO AILERON        DEFLECTION

                        PIRPLANE RESTRAINED
                        TO ROLLING MOTION ONLY

                                         ------(A)                   HIGH DlRECTlCNAL STABILITY
                                                                     m   DIHEDRAL EFFECT
                                      AIRPLANE UNRESTRAINED
                               \      AND FREE TO SIDESLIP
                                    \    (RUDDER FIXED)  ( B ) LOW DIRECTIONAL STABIUTY
                                          .---A                HIGH MHEDRAL EFFECT

                            TIME,    SECONDS

                                    Figure 4.29. Rolling Performance

                                                                                      NAVWEPS OO-BOT-BO
                                                                                   STABILIJY AND CONTROL

given to the airplane size. For geometrically              the critical speed, with some limited amount
similar airplanes, a certain deflection of the             of force applied by the pilot (usually the limit
                                                           of lateral force is assumed to be 30 lbs.), the
ailerons will produce a fixed value of I!!. mde-
                                                           ailerons cannot be held at full deflection, ~~Pb
pendent of the airplane size. However, the
roll rate of the geometrically similar airplanes           drops, and rate of roll decreases. In this exam-
at a given speed will vary inversely with the              ple, the rolling performance at high speeds is
span, b.                                                   limited by the ability of the pilot to maintain
                                                           full deflection of the controls. In an effort to
                                                           reduce the aileron hinge moments and control
              Pb -                                         forces, extensive application is made of aerody-
                                                           namic balance and various tab devices. How-
               p=(constant)       7                        ever, 100 percent aerodynamic balance is not
                              (       )                    always feasible or practical but a sufficient
Thus, the smaller airplane will have an ad-                value of Pb must be maintained at high speeds.
vantage in roll rate or in time to accelerate                         ZV
through a prescribed angle of roll. For ex-                    Rather than developing an extensive weight
ample, a one-half scale airplane will develop              lifting   program mandatory for all Naval
twice the rate of roll of the full scale airplane.         Aviators, mechanical assistance in lateral con-
This relationship points to the favor of the               trol can be provided.       If a power boost is
small, short span airplane for achieving high              provided for the lateral control system, the
roll performance.                                          rolling performance of the airplane may be
   An important variable affecting the rate of             extended to higher speeds since pilot effort
roll is the true airspeed or flight velocity, V.           will not be a limiting factor. The effect of a
If a certain deflection of the ailerons creates a          power boost is denoted by the dashed line
                     Pb                                    extensions of figure 4.30. A full powered,
specific value of -7 the rate of roll varies               irreversible lateral control system is common
directly with the true airspeed. Thus, if the              for high speed airplanes. In the power oper-
roll helix angle is held constant, the rate of             ated system there is no immediate limit to the
roll at a particular true airspeed will not be             deflection of the control surfaces and none of
affected by altitude.    The linear variation of           the aberrations in hinge moments due to com-
roll rate with airspeed points out the fact that           pressibility are fed back to the pilot. Control
high roll rates will require high airspeeds.               forces are provided by the stick centering
The low roll rates at low airspeeds are simply             lateral bungee or spring.
a consequence of the low flight speed and this                  A problem particular to the high speed is
condition may provide a critical lateral con-              due to the interaction of aerodynamic forces
trol requirement for satisfactory handling                 and the elastic deflections of the wing in
qualities.                                                 torsion.     The deflection of ailerons creates
   Figure 4.30 illustrates the typical rolling             twisting moments on the wing which can cause
paformance of a low speed airplane. When                   significant torsional deflections of the wing.
the ailerons are at full deflection, the maximum            At the low dynamic pressures of low flight
roll helix angle is obtained. The rate of roll             speeds, the twisting moments and twisting
increases linearly with speed until the control             deflections are too small to be of importance.
forces increase to limit of pilot effort and full           However, at high dynamic pressures, the
 control deflection cannot be maintained. Past              deflection of an aileron creates significant

NAVWEPS 00-807-80

              ^,                                                    ,/           <EiECT
                                                              0                           OF ADDED
             O/SEC.                                                                       BOOST

                                                                         V. KNOTS

              ROLL .lD

                                                                         V, KNOTS



                                         SPEED CORRESPONDING
                                       TO LIMIT OF PILOT EFFORT
                                    TO MAINTAIN MAXIMUM   DEFLECTION

         (3                     A
         3                1.0
         0           5                                                   ELASTIC     WING


                                    Figure 4.30.    Control       in Roll

                                                                                   NAVWEPS OO-UOT-80
                                                                                STABILITY AND CONTROL

  twisting deflections which reduce the effec-         trolled in a sideslip to accomplish crosswind
 tiveness of the aileron, e.g., downward deflec-       takeoff and landing. The lateral control dur-
 tion of an aileron creates a nose down twist of       ing crosswind takeoff and landing is a par-
 the wing which reduces the rolling moment             ticular problem when the dihedral effect is
 due to aileron deflection. At very high speeds,       high. Since the sweepback contributes a large
 the torsional deflection of the wing may be           dihedral effect at high lift coefficients, the
 so great than a rolling moment is created             problem is most important for the airplane
 opposite to the direction controlled and “aile-       with considerable sweepback. The limiting
 ron reversal” occurs. Prior to the speed for          crosswind components must be given due re-
 aileron reversal, a serious loss of roll helix        spect especially when the airplane is at low
 angle may be encountered. The effect of this          gross weight. At low gross weight the speci-
 aeroelastic phenomenon on rolling perform-            fied takeoff and landing speeds will be low and
 ance is illustrated in figure 4.30.                   the controlled angle of sideslip will be largest
    To counter the undesirable inceractiuo be-         for a given crosswind velocity.
 tween aerodynamic forces and wing torsional
 deflections, the trailing edge ailerons may be
                                                        MISCELLANEOUS         STABILITY    PROBLEMS
 moved inboard to reduce the portion of the
 span subjected to twisting         moments.      Of      There are several general problems of flying
 course, the short span, highly tapered wing           which involve certain principles of stability as
 planform is favorable for providing relatively        well as specific areas of longitudinal, direc-
 high stiffness. In addition, various configura-       tional and lateral stability.    Various condi-
tions of spoilers may be capabIe of producing          tions of flight will exist in which certain
 the required rolling performance without the          problems of stability (or instability)   are un-
 development of large twisting moments.                avoidable for some reason or another. any
    CRITICAL REQUIREMENTS,              The critical   of the following items deserve consideration
 conditions for requiring adequate lateral con-        because of the possible unsafe condition of flight
 trol power may occur at either high speed or          and the contribution to an aircraft accident.
 low speed depending on the airplane configura-
 tion and intended use. In transonic and super-
sonic flight, compressibility      effects tend to     LANDING      GEAR CONFIGURATIONS
reduce the effectiveness of lateral control de-            There are three general configurations for the
 vices to produce required roll helix angles.          aircraft landing gear: the tricycle, bicycle, and
These effects are most significant when com-           “conventional”      tail wheel arrangement. At
bined with a loss of control effectiveness due to      low rolling speeds where the airplane aerody-
 aeroelastic effects. Airplanes designed for           namic forces are negligible, the “control-fixed”
high speed flight must maintain suflicient             static stability of each of these configurations
lateral control effectiveness at the design dive       is determined by the side force characteristics
speed and this is usually the predominating            of the tires and is not a significant problem.
requirement.                                               The instability which allows ground loops
    During landing and takeoff, the airplane           in an aircraft with a conventional tail wheel
must have adequate lateral control power to            landing gear is quite basic and can be appre-
contend with the ordinary conditions of flight.        ciated from the illustration of figure 4.31. Cen-
The lateral controls must be capable of achiev-        trifugal force produced by a turn must be
ing required roll helix angles and acceleration        balanced and the aircraft placed in equilibrium.
through prescribed roll dispIacements. Also,           The greatest side force is produced at the main
the airplane must be capable of being con-             wheels but to achieve equilibrium with the

                                                            TAIL WHEEL


                                                          SIDE FORCE ON
                                                          MAIN WHEELS
                                                      CENTRIFUGAL        FORCE

                                        \\                   CONFIGURATION

                                                                  NOSE WHEEL
                                                                  SIDE FORCE

                                                 CENTRIFUGAL         FORCE

                                                     BICYCLE    CONFIGURATION


                        Figure 4.31.   Landing Gear Configurations
                                                                                  NAVWEPS DD-BDT-80
                                                                               STABILITY AND CONTROL

   center of gravity aft of the main wheels a bal-       The bicycle configuration of landing gear
   ancing load on the tail wheel must be produced      has stability characteristics more like the
   toward the center of turn. When the tail            automobile.     If directional control is ac-
   wheel is free to swivel, the equilibrium of the     complished with the front wheels operated
   turn requires a control force opposite to the       by power controls, no stability problem exists
  direction of turn-i.e..     control force insta-    at low speeds. A problem can exist when the
  bility.   The inherent stability problem exists     airplane is at high speeds because of a distribu-
  because the center of gravity is aft of the point   tion of normal force being different from the
  where the main side forces are developed. This      ordinary static weight distribution.       If the
  condition is analogous to the case of static        airplane is held onto the runway at speeds
  longitudinal    stability  with the center of       well above the normal takeoff and landing
  gravity aft of the neutral point.                   speeds, the front wheels carry a greater than
      The conventional tail wheel configuration       ordinary amount of normal force and a tend-
  has this basic instability or ground loop tend-     ency for instability exists. However, at these
  ency which must be stabilized by the pilot.         same high speeds the rudder is quite powerful
  At high rolling speeds where aerodynamic            and the condition is usually well within
  forces are significant, the aerodynamic direc-      control.
  tional stability of the airplane resists the           The basically stable nature of the tricycle
  ground looping tendency. The most likely            and bicycle landing gear configurations is best
  times for a ground loop exist when rolling          appreciated by the ease of control and ground
  speeds  are not high enough to provide a con-       maneuvering of the airplane. Operation of
 tribution of the aerodyhamic forces. When the        a conventional tail wheel configuration after
 tail wheel is free to swivel or when the normal      considerable experience with tricycle cohfigu-
 force on the tail wheel is small, lack of pilot      rations requires careful consideration af the
 attention can allow the ground loop to take          stability that must be furnished by the pilot
 place.                                               during ground maneuvering.
     The tricycle landing gear configuration has      SPINS AND      PROBLEMS      OP SPIN
 an inherent stability d,ue to the relative posi-     RECOVERY
 tion of the main wheels and the center of               The motion of an airplane in a spin can
 gravity.      Centrifugal force produced by a        involve many complex aerodynamic and in-
turn is balanced by the side force on the main        ertia forces and moments. However, there are
 wheels and a side force on the nose wheel in         certain fundamental relationships regarding
 the direction of turn. Note that the freeing         spins and spin recoveries with which all
 the nose wheel to swivel produces moments            aviators should be familiar.     The spin differs
 which bring the aircraft out of the turn. Thus,      from a spiral dive in that the spin always
the tricycle configuration has a basic stability      involves flight at high angle of attack while given evidence by control displace-          the spiral dive involves a spiral motion of
ment and a wheel side force in the direction          the airplane at relatively low angle of attack.
                                                         The stall characteristics and stability of
of turn. Because of the contrast in stability,
                                                      the airplane at high lift coefficients are im-
the tricycle configuration is much less difficult
                                                      portant in the initial tendencies of the airplane.
to maneuver than the tail wheel configuration         As previously mentioned, it is desirable to
and does not provide an inherent ground loop          have the wing initiate stall at the root first
tendency. However, a steerable nose wheel             rather than tip first.     Such a stall pattern
is usually necessary to provide satisfactory          prevents the undesirable rolling moments at
maneuvering capabilities.                             high lift coeGients, provides suitable stall
                                                                                NAVWEPS OO-BOY-BO
                                                                             STABIUTY AND CoMml

 warning, and preserves lateral control effec-       damping in roll is generally referred to as
 tiveness at high angles of attack. Also, the         “autorotation.”
 airplane must maintain positive static longi-           When the conventional airplane is stalk4
 tudinal stability at high lift coe&ients and        and some rolling-yawing       displacement takes
 should demonstrate satisfactory stall recovery      place, the resulting autotiotation rolling mo-
 characteristics.                                    ments and yawing moments start the airplane
    In order to visualize the principal effects of   into a self-sustaining rolling-yawing     motion.
 an airplane entering a spin, suppose the air-       The autorotation rolling and yawing tenden-
plane is subjected to the rolling and yawing         cies of the airplane at high angles of attack
 velocities shown in figure 4.32. The yawing         are the principal prospin moments of the
velocity to the right tends to produce higher        conventional airplane configuration and these
 local velocities on the left wing than on the       tendencies accelerate the airplane into the
 right wing.      The rolling velocity tends to      spin until some limiting        condition exists.
 increase the angle of attack for the downgoing      The stabilized spin is not necessaray a simple
 right wing (a,) and. decrease the angle of          steady vertical spiral but may involve some
 attack for the upgoing left wing (al).        At    coupled unsteady oscillatory motion.
 airplane angles of attack below the stall this          An important characteristic of the mote
 relationship produces roll due to yaw, damping      conventional airplane configuration is that the
 in roll, etc., and some related motion of the       spin shows a predominating contribution of
 airplane in unstalled flight.      However, at      the autorotation     tendency. Generally, the
 angles of attack above the stall, important         conventional configuration has a spin motion
changes take place in the aerodynamic char-          which is primarily rolling with moderate yaw.
 acteristics.                                        High directional stability is favorable since it
    Figure 4.32 illustrates the aerodynamic          will limit or minimize the yaw displacement
characteristics typical of a conventional air-       of the spinning airplane.
plane configuration, i.e., moderate or high             The fundamental requirement of the spin is
aspect ratio and little-if      any-sweepback.       that the airplane be placed at an excessive
Ifs this airplane is provided a rolling displace-    angle of attack to produce the autorotation
ment when at some angle of attack above              rolling and yawing tendencies. Generally
the stall, the upgoing wing experiences a            speaking, the conventional airplane must be
decrease in angle of attack with a correspond-       stalled .before a spin can take place. This
ing increase in C, and decrease in C,,. In other     relationship establishes a fundamental p&r-
words, the upgoing wing becomes less stalled.        ciple of recovery-the     airplane must be un-
Similarly, the downgoing wing experiences            stalled by decreasing the wing angle of attack.
an increase in angle of attack with a corre-         The most dfective procedure for the conven-
sponding decrease in CL and increase in CD. Es-      tional configuration is to use opposite rudder
sentially, the downgoing wing becomes more           to stop the sideslip, then lower the angle of
stalled. Thus, the rolling motion is aided           attack with the elevators. With sufficient
rather than resisted and a yawing moment is          rudder power this procedure will produce a
produced in the direction of roll. At angles         positive recovery with a minimum loss of
of attack below stall the rolling motion is          altitude.    Care should be taken during pullout
resisted by damping in roll and adverse yaw          from the ensuing dive to prevent excessive
is usually present. At angles of attack above        angle of attack and entry into another spin.
the stall, the damping in roll is negative and          It should be appreciated that a spin is always
a rolling motion produces a rolling moment           a possible corollary of a stall and the self-
in the direction of the roll.      This negative     sustaining motion of a spin will take place at


                                    AERODYNAMIC CHARACTERISTICS TYPICAL OF
                                         A CONVENTIONAL CONFIGURATION


                  I         0, ANGLE OF ATTACK                  QL     OR

                          TYPICAL    Q’ H “lU”
                                         . ..I,.”
                                    co NFIGURATION
                                                                       A    CD


                         a, ANGLE OF ATTACK                     OL     aR
                                    Figure 4.32.      Spin Characteristics

                                                                                    NAWWEPS DO-BOT-BO
                                                                                 STABILITY AND CONTROL

 excessive angles of attack. Of course, a low            attack is capable of producing pro-spin mo-
 speed airplane could be: designed to be spin-           ments of considerable magnitude which con-
 proof by making it stallproof.        By limiting       tribute to the self-sustaining nature of the
 the amount of control deflection, the airplane           spin. Also, the large distributed mass of the
 may not have the longitudinal control power             fuselage in rolling-yawing rotation contributes
to trim to maximum lift angle of attack. Such            to inertia moments which flatten the spin and
 a provision may be possible for certain light           place the aircraft at extreme angles of attack.
 planes and commercial aircraft but would                   The spin recovery of the modern high speed
 create an unrealistic and impractical limita-           airplane involves principles which are similar
 tion on the utility of a military airplane.             to those of the spin recovery of the conven-
    The modern high speed airplane configura-            tional airplane. However, the nature of the
 tion is typified by low aspect ratio, swept wing         spin for the modern configuration may involve
planforms with relatively large yaw and pitch            specific differences in technique necessary to
 inertia. The aerodynamic characteristics of             reduce the sideslip and angle of attack. The
 such a configuration are shown in figure 4.32.          use of opposite rudder to control the sideslip
The lift curve (C, versus U) is quite shallow at         and effect recovery will depend on the effective-
high angles of attack and maximum lift is not            ness of the rudder when the airplane is in the
clearly defined. When this type of airplane is           spin. At high positive angles of attack and
provided a rolling motion at high angles of              high sideslip the rudder effectiveness may be
attack, relatively small changes in C, take              reduced and additional anti-spin moments must
place. When this effect is combined with the             be provided for rapid recovery. The deflection
relatively short span of this type airplane, it is       of ailerons into the spin reduces the autorota-
apparent that the wing autorotation contribu-            tion rolling moment and can produce adverse
tion will be quite weak and will not be a pre-           yaw to aid the rudder yawing moment in
dominating pro-spin moment. The relatively               effecting recovery.
large changes in drag coefficient with rolling              There may be many other specific differences
motion imply .a predominance of yaw for the              in the technique necessary to effect spin re-
spin of the high speed airplane configuration.          covery . The effectiveness of the rudder during
    Actually, various other factors contribute           recovery may be altered by the position of
to the predominating yaw tendency for the               elevators or horizontal tail. Generally, full
spin of the modern airplane configuration.              aft stick may be necessary during the initial
The static directional stability deteriorates at        phase of recovery to increase the effectiveness
high angles of attack and may be so weak that           of the rudder. The use of power during the
extemely large yaw displacements result. In             spin recovery of a propeller powered airplane
certain instances, very high angles of attack           may or may not aid recovery depending on the
may bring such a decay in directional stability         specific airplane and the particular nature of
that a “slice” or extreme yaw displacement              the slipstream effects. The use of power during
takes place before a true spin is apparent. At          the spin recovery of a jet powered airplane
these high angles of attack, the adverse yaw            induces no significant or helpful flow but does
due to roll and aileron deflection can be very          offer the possibility of a severe compressor
strong and create large yaw displacements of            stall and adverse gyroscopic moments. Since
                                                        the airplane is at high angle of attack and
the airplane prior to realizing a stall.
                                                        sideslip, the flow at the inlet may be very
    The aircraft with the relatively large, long        poor and the staI1 limits considerably reduced.
fuselage can exhibit a significant moment con-          These items serve to point out possible dif-
tribution from the fuselage alone. The cross            ferences in technique required for various con-
flow pattern on the fuselage at high angles of          figurations.    The spin recovery specific for


                                         v                                PITCH-UP


                                                                          SEPARATION OR
                                                                          STALLTIP FIRST

                                                   RD SHIFT OF VORTEX

               INCREASE IN LOCAL
               DDWNWAM AT TAIL

                                                              :   :

                                FUSELAGE CROSS-
                               FLOW SEPARATION
                              VORTICES INCREASE
                           LOCAL DOWNWASH AT TAIL

                                   Figure 4.33. Pitch-up
                                                                                 NAWEPS DD-EDT-89
                                                                              STABILITY AND CQNROL

each airplane is outlined in the pilot’ hand-
                                       s             the wing flow field where higher relative
book and it is impcrativc that the specific tech-    downwash exists. Thus, a decrease in stability
nique be followed for successful recovery.           would take place.
                                                        Certain changes in the flow field behind the
PITCH-UP                                             wing at high angles of attack can produce large
                                                     changes in the tail contribution to stability.
    The term of “pitch-up” generally applies to      If the wing tips stall first, the vortices shift in-
the static longitudinal instability encountered      board and increase the local downwash at the
by certain configurations at high angle of           tail for a given airplane C,. Also, the fusel~age
attack. The condition of pitch-up is illustrated     at high angle of attack can produce strong
by the graph of CM versus C, in figure 4.33.         cross flow separation vortices which increase
Positive static longitudinal stability is evident    the local downwash for a horizontal tail placed
at low values of Cs by the negative slope of the     above the fuselage. Either one or a combiua-
curve. At higher values of Cs the curve changes      tion of these downwash influences may provide
to a positive slope and large positive pitching      a large unstable contribution of the horizontal
moments are developed. This sort of in-              tail.
stability implies that an increase in angle of          The pitch-up instability is usually conlined
attack produces nose up moments which tend           to the high angle of attack range and may be
to bring about further increases in angle of         a consequence of a configuration that otherwise
attack hence the term “pitch-up” is applied.         has very desirable flying qualities. In such a
    There are several items which may con-           case it would be necessary to provide some
tribute to a pitch-up tendency.        Sweepback      automatic control function to prevent entry
of the wing planform can contribute unstable         into the pitch-up range or to provide synthetic
moments when separation or stall occurs at            stability for the condition. Since the pitch-up
the tips first. The combination of sweepback          is usually a strong instability with a high1
and taper alters the lift distribution to produce    rate of divergence, most pilots would not be
high local lift coefficients and low energy          capable of contending with the condition. At
boundary layer near the tip. Thus, the tip            high 4, pitch-up would be of great danger in
stall is an inherent tendency of such a plan-         that structural failure could easily result. At
form. In addition, if high local lift coefficients   low q, failing flight loads may not result but
exist near the tip, the tendency will be to incur     the strong instability may preclude a successful
the shock induced separation first in these          recovery from the ensuing motion of the, air-
areas. Generally, the wing will contribute           plane.
to pitch-up only when there is large sweepback.
    Of course, the wing is not the only item con-    EFFFCTS OF HIGH        MACH NUMBFB
tributing to the longitudinal stability of the
airplane. Another item important as a source            Certain stability problems are particular to
of pitch-up is the downwash at the horizontal        supersonic flight. While most of the problem
 tail. The contribution of the tail to stability     areas have been treated in particular in previous
depends on the change in tail lift when the air-     discussion, it is worthwhile      to review the
 plane is given a change in angle of attack.         effects of supersonic flight on the various items
 Since the downwash at the tail reduces the          of stability.
 change in angle of attack at the tail, any in-         The static longitudinal stability of an air-
 crease in downwash at the tail is destabilizing.    plane increases during the transition from sub-
 For certain low aspect ratio airplane configura-    sonic to supersonic flight.    Usually the prin-
 tions, an increase in airplane angle of attack      cipal source of the change in stability is due to
 may physically locate the horizontal tail in        the shift of the wing aerodynamic center with
NAVWEPS oo-s01-80

Mach number. As a corollary of this increase                 deflection when subject to load, the tendency
in stability is a decrease in controllability   and          may be to lower the contribution to static
an increase in trim drag.                                    stability and reduce the damping contribution.
    The static directional stability of an air-              Thus, the problem of adequate stability of the
plane decreases with Mach number in super-                   various airplane motions is aggravated.
sonic flight. The influence of the fuselage and
the decrease in vertical tail lift curve slope               PILOT   INDUCED     OSCILLATIONS
 bring about this condition.
   The dynamic stability       of the airplane                  The pilot may purposely induce various
generally deteriorates with Mach number in                   motions to the airplane by the action of the
supersonic flight.    Since a large part of the              controls.     In additron, certain undesirable
damping depends on the tail surfaces, the                    motions may occur due to inadvertent action
decrease in lift curve slope with Mach number                on the controls.      The most important con-
will account in part for the decrease in damp                dition exists with the short period longitu-
ing. Of course, all principal motions of the                 dinal motion of the airplane where pilot-
aircraft must have satisfactory damping and                  control system response lag can produce an
if the damping is not available aerodynami-                  unstable oscillation.     The coupling possible
cally it must be provided synthetically to                   in the pilot-control     system-airplane combi-
obtain satisfactory flying qualities. For many               nation is most certainly capable of producing
high speed configurations the pitch and yaw                  damaging flight loads and loss of control of
dampers, flight stabilization       systems, etc.,           the airplane.
are basic necessities rather than luxuries.                     When the normal human response lag and
    Generally, flight at high Mach number will               control system lag are coupled with the air-
cake place at high altitude hence the effect of              plane motion, inadvertent control reactions
high altitude must be separated for study.                   by the pilot may furnish a negative damping
All of the basic aerodynamic damping is due                  to the oscillatory motion and dynamic in-
to moments created by pitching, rolling, or                  stability exists. Since the short period motion
yawing motion of the aircraft. These moments                 is of relatively high frequency, the amplitude
are derived from the changes in angles of                    of the pitching oscillation can reach dangerous
attack on the tail surfaces with             angular         proportions in an unbelievably short time.
rotation (see fig. 4.15). The very high true                 When the pilot induced oscillation is en-
 airspeeds common to high altitude flight                    countered, the most effective solution is an
 reduce the angle of attack changes and reduce               immediate release of the controls.      Any at-
 the aerodynamic damping. In fact, the aero-                 tempt to forcibly damp the oscillation simply
 dynamic damping is proportional             to &            continues the excitation and amplifies the
 similar to the proportion of true airspeed to               oscillation.    Freeing the controls removes
 equivalent airspeed. Thus, at the altitude of               the unstable (but inadvertent) excitation and
 4O,C00 ft., the aerodynamic damping would                   allows the airplane to recover by virtue of
 be reduced to one-half the sea level value and              its inherent dynamic stability.
 at the altitude of 100,000 ft. the aerodynamic                  The pilot induced oscillation is most likely
 damping would be reduced to one-tenth the                    under certain conditions, Most obvious is the
 sea level value.                                             case of the pilot unfamiliar with the “feel”
    High dynamic pressures (high $I can be                    of the airplane and likely to overcontrol or
 common to flight at high Mach number and                     have excessive response lag. High speed flight
 adverse aeroelastic effects may be encountered.              at low. altitude (high 4) is most likely to
 If the aircraft surfaces, encounter significant              provide low stick-force gradients and periods
                                                                                      NAVWEPS OO-SOT-80
                                                                                   STABILITY AND CONTROL

of oscillation which coincide with the pilot-              and pitch inertia and each inertia is a measure
control system response lag. Also, the high 4              of the resistance to rolling, yawing, or pitching
flight condition provides the aerodynamic                  acceleration of the airplane. The long,slender,
capability for failing flight loads during the             high-density fuselage with short, thin wings
oscillation.                                               produces a roll inertia which is quite small in
    If a pilot induced oscillation is encountered          comparison to the pitch and yaw inertia.
the pilot must rely on the inherent dynamic                These characteristics are typical of the modern
stability of the airplane and immediately                  airplane configuration. The more conventional
release the controls. If the unstable excitation           low speed airplane may have a wingspan
is continued, dangerous oscillation amplitudes             greater than the fuselage length. This type of
will develop in a very short time.                         configuration produces a relatively large roll
                                                           inertia. A comparison of these configurations
ROLL COUPLING                                              is shown in figure 4.34.
                                                               Inertia coupling can be illustrated by con-
   The appearance of “inertia coupling” prob-              sidering the mass of the airplane to be con-
lems in modern airplanes was the natural result            centrated in two elements, one representing the
of the progressive change in aerodynamic and               mass ahead of the c.g. and one representing the
inertia characteristics to meet the demands of             mass behind the c.g. There are two principal
high speed flight.     Inertia coupling problems           axis systems to consider: (1) the aerodynamic,
were unexpected only when dynamic stability                or wind axis is through the c.g. in the relative
analyses did not adequately account for the                wind direction, and (2) the inertia axis is
rapid changes in aerodynamic and inertia                   through the c.g. in the direction of the two
characteristics of airplane configurations. The            element masses. This axis system is illus-
The term of “intertia coupling” is somewhat                trated in figure 4.34.
misleading because the complete problem is                     If the airplane shown in figure 4.34 were in
one of aerodynamic as well as inertia coupling.            some flight condition where the inertia axis
   “Coupling” results when some disturbance                and the aerodynamic axis are alined, no inertia
about one airplane axis causes a disturbance               coupling would result from rolling motion.
about another axis. An example of uncoupled                However, if the inertia axis is inclined to the
motion is the disturbance provided an airplane             aerodynamic axis, rotation about the aero-
when subjected to an elevator deflection. The              dynamic axis will create centrifugal forces and
resulting motion is restricted to pitching                 cause a pitching moment. In this case, a
motion without disturbance in yaw or roll.                 rolling motion of the aircraft induces a pitch-
An example of, coupled motion could be the                 ing moment through the action of inertia
disturbance provided an airplane when sub-                 forces. This is “inertia coupling” and is
jected to rudder deflection. The ensuing mo-               illustrated by part B of figure 4.34.
tion can be some combination of yawing and                     When the airplane is rotated about the
rolling motion. Hence, the rolling motion is               inertia axis no inertia coupling will exist but
coupled with the yawing motion to define the               aerodynamic coupling will be present. Part
resulting motion.       This sort of interaction           C of figure 4.34 shows the airplane after rolling
results from aerodynamic characteristics and is            90” about the inertia axis. The inclination
termed “aerodynamic coupling.”                             which was initially the angle of attack (a) is
   A separate type of coupling results from the            now the angle of sideslip (-6).         Also the
inertia characteristics of the airplane conligura-         original zero sideslip has now become zero
tion. The inertia characteristics of the com-              angle of attack. The sideslip induced by this
plete airplane can be divided into the roll, yaw,          90° displacement will affect the roll rate

                                                              cc      >             -I


                                            0 A

                               MASS                                          MOTION


           OF ATTACK.

                               fh        SIDEFORCE


                                                                   u pgq    ROLL

                                         Figure 4.34.     Roll Coupling
                                                                                         NAVWEPS 00-8OT-80
                                                                                      STABILITY AND CONTROL

depending on the nature of the dihedral effect              pitch frequency and yaw frequency. Gen-
of the airplane.                                            erally, the greater the static longitudinal and
   It should be noted that initial inclination of           directional stability, the higher will be the
the inertia axis above the aerodynamic axis                 coupled pitch-yaw frequency. When the air-
will cause the inertia couple to provide adverse            plane is subject to roiling motion, the inertia
yaw with rolling motion.        If the inertia axis         couple disturbs the airplane in pitch and yaw
 were initially inclined below the aerodynamic              with each roll revolution and provides a dis-
axis (as may happen at high 4 or negative load               turbing forcing function.’ If the airplane is
factors), the roll induced inertia couple would             rolled at a rate equal to the coupled pitch-yaw
provide proverse yaw. Thus, roll coupling                   frequency, the oscillatory motion will either
may present a problem at both positive and                  diverge or stabilize at some maximum ampli-
negative inclination of the inertia axis depend-            tude depending on the airplane characteristics.
ing on the exact aerodynamic and inertia                        The longitudinal stability of the typical high
characteristics of the configuration.                        speed configuration is much greater than the
   As a result of the aerodynamic and inertia               directional stability and results in a pitch fre-
coupling, rolling motion can induce a great                 quency higher than the yaw frequency. In-
variety of longitudinal, directional, and lateral           creasing the directional stability by increasing
forces and moments. The actual motion of                    the vertical tail area, addition of ventral hns,
the airplane is a result of a complex combina-              or use of stabilization systems will increase the
tion of the aerodynamic and inertia coupling.               coupled pitch-yaw frequency and raise the roll
Actually, all airplanes exhibit aerodynamic                 rate at which a possible divergent condition
and inertia coupling but of varying degrees.                could exist. Increasing directional stability
The roll coupling causes no problem when the                 by the addition of ventral fins rather than by
moments resulting from the inertia couple are               addition to the vertical tail has an advantage
easily counteracted by the aerodynamic re-                  of not contributing to the positive dihedral
storing moments. The very short span, high                  effect at low or negative angles of attack.
speed modern aircraft has the capability for                High dihedral effect makes higher roll rates
the high roll rates which cause large magni-                more easily attainable in roll motion where
tudes of the inertia couple. The low aspect                 proverse yaw occurs.
ratio planform and flight at high Mach number                   Since the uncoupled yawing frequency is
allow large inclination of the inertia axis with            lower than the pitching frequency, a divergent
respect to the aerodynamic axis and also add                condition would lirst reach critical proportions
to the magnitude of the inertia couple. In                  in yaw, closely followed by pitch. Of course,
addition, the aerodynamic restoring moments                 whether the airplane motion becomes divergent
deteriorate as a result of high Mach number                 directionally or longitudinally      is of academic
and angle of attack and can create the most                 interest only.
serious roll coupling conditions.                              There is one additional type of coupling
   Since the roll coupling induces pitching and             problem that is referred to as “autorotative
yawing motion, the longitudinal and direc-                  rolling.”    A rolling airplane which has a high
tional stability is important in determining the            positive dihedral effect may reach a large pro-
overall characteristics of the coupled motion.              verse sideslip as a result of the inertia couple and
A stable airplane, when disturbed in pitch and              the rolling moment due to sideslip may exceed
yaw, will return to equilibrium after a series              that available from lateral control.         In such
of oscillations.   For each flight condition, the           a case it would not be possible to stop the air-
airplane will have a coupled pitch-yaw fte-                 plane from rolling although lateral control
quency between the uncoupled and separate                   was held full against the roll direction.       The
                                                                                    NAVWEPS DD-EOT-80
                                                                                 STABMTY AND CONTROL

 design features which result in a large positive        The first four items can be effected,only during
 dihedral effect are high sweepback, high wing           design or by design changes. Some roll per-
 position, or large, high vertical tail, When            formance restriction is inevitable since all of
 the inertia axis is inclined below the aero-            the desirable characteristics are difficult to
 dynamic axis at low or negative angles of               obtain without serious compromise elsewhere
 attack, the roll induced inertia couple results         in the airplane design. The typical high
 in proverse yaw.                                        speed airplane will have some sort of roll pet-
    Depending on the flight condition where the          formance limitation provided by flight restric-
roll coupling problem exists, four basic types           tions or automatic control devices to prevent
 of airplane behavior are possible:                      reaching some critical condition from which
       (1) Coupled motion stable but unacceptabk.        recovery is impossible. Any roll restriction
    In this case the motion is stable but proves         provided an airplane must be regarded as a
    unacceptable because of poor damping of the          principal flight operating limitation since the
    motion. Poor damping would make it                   more severe motions can cause complete loss
    dificult to track a target or the initial am-        of control and structural failure.
    plitudes of the motion may be great enough
    to cause structural failure of loss of control.      HELICOPTER      STABILITY    AND CONTROL
       (2) Coupled motion stable and acceptable.
    The behavior of the airplane is stable and               In discussing many of the problems of sta-
    adequately damped to allow acceptable                 bility and control that occur in high speed
    target tracking.     The amplitudes of motion         airplanes, one might be prone to believe that
    are too slight to result in structural failure        the slow flying helicopter does not have any
    or loss of control.                                   such problems. Unfortunately,      this is not
       (3) Coupledmotion divergentand unacceptable.       the case. Flying qualities that would be con-
    The rate of divergence is too rapid for the           sidered totally unsatisfactory by fixed-wing
    pilot to recognize the condition and recover          standards ate normal for helicopters. Heli-
    prior’ to structural failure or complete loss         copter pilots are living evidence that an un-
    of control.                                                                 .:
                                                          stable aircraft ca. k‘ controlled.   Also, they
       (4) Coupled.motion divergent but acceptable.      are evidence ~a. control without stability
    For such a condition the rate of divergence          requires constant attention and results in con-
    is quite slow and considerable roll displace-        siderable pilot fatigue.
    ment is necessary to produce a critical ampli-           “Inertia coupling” problems are relatively
    tude. The condition can be recognized                new to fixed-wing aircraft but a similar effect
    easily in time to take corrective action.            in the helicopter rotor has resulted in some
    There are available various means to cope            of its most important characteristics.      This
with the problem of roll coupling.          The fol-     aerodynamic-dynamic coupling effect is so im-
lowing items can be applied to control the               portant that it must be considered in discussing
problem of roll coupling:                                both stability and control.      The helicopter
       (ZZ) Increase directional stability.              derives both longitudinal and lateral control
       (b) Reduce dihedral effect.                       by tilting the main rotor and thus producing
       (c) M’ mnmze t h e mc 1‘mation of the inertia     a pltchmg or rolling moment as indicated in
    axis at norma