# 2007 Chapter 16 Aero

Document Sample

```					     Design of UA Systems

Lesson objective - to review

Basic aerodynamics
relationships
….at levels of fidelity required for pre-
concept and conceptual design of
subsonic UA

Expectations - You will understand how to
apply the basics and to avoid
unnecessary detail

c 2006 LM Corporation                Aerodynamics                   16-1
Design of UA Systems                           Importance

These are the fundamental aerodynamic
relationships needed to define a
subsonic air vehicle for UAS

c 2006 LM Corporation         Aerodynamics                   16-2
Design of UA Systems                                            Overall approach
Parametric design               Overall design issues
- Initial estimates             - Concepts of operation        Today: Aerodynamics
- Engine type                   - Requirements
- Initial engine size
- Initial vehicle size        Integrated Performance
Performance Methods
- Parametric comparisons        - Mission description
- Takeoff
- Model convergence
- Climb
- Requirement convergence
Aerodynamics                                                         - Turn
- Parametric comparisons
- Cfe  CD0                                                         - Accelerate
- CDi                                                               - Cruise
- CLmax – no flaps                                                  - Loiter
- CLmax – flaps                     Trade studies                   - Land
- Trim drag                    -Configuration “Optimization”     - Parametric comparisons
Geometry
Propulsion                                                         - Models
- Size, weight and volume       Weight                               - Fuselage(s)
- Speed and altitude effects     - Weight fractions                  - Nacelle(s)
- Installation effects           - Airframe weight                   - Wings
- Parametric models              - Other weights                     - Tails
- Parametric comparisons         - Weight convergence                - Pods
- Geometry effects               - Weight effects
- Parametric comparisons         - Parametric comparisons

c 2006 LM Corporation               Aerodynamics                                                 16-3
Design of UA Systems                             Aerodynamic definition

Calculations for pre-concept design (exc. estimates as shown)
0: wing incidence angle

Covered here
CL : lift curve slope (clean wing)
CL : lift coefficient = W/qSref = CL
CLt/o : takeoff lift coefficient - estimate
CLd : design lift coefficient
CLmax : maximum lift coefficient (no flaps) – estimate
CD0 : zero lift drag coefficient
CDi : Induced drag coefficient
L/D: lift-to-drag ratio
Tails sized for static stability
Additional calculations required for conceptual design (inc.
calculating estimates per above)
min : minimum drag angle of attack

See Raymer
 max : stall angle of attack (clean and with flaps)
CL flap : lift curve slope (flaps)
CLmin : minimum drag lift coefficient
CDmin : minimum drag coefficient
CLmax flap : maximum lift coefficient (flaps)
Basic stability and control characteristics
Tails sized for control
c 2006 LM Corporation              Aerodynamics                                         16-4
Design of UA Systems                      Discussion subjects

Fundamental aero and notation
2-D aerodynamics (airfoils)
3-D wings (lift)
Lift curve slope
Cruise and loiter lift
Takeoff and landing lift
Maximum lift (stall)
Drag
Zero lift
Reynolds number effects
Mach number effects
Induced drag
Trim
Lift-to-drag ratio
Stability and control
Example problem

c 2006 LM Corporation       Aerodynamics                         16-4a
Design of UA Systems                                         Aerodynamics 101
L = lift
Side view                  V is speed through the air (true air
speed) typically in knots (nm/hr)

    V
M = moment

horizon

 = Flight path angle              D = Drag

W = weight                  Trim force
T = Thrust

Lift (L) - generated primarily by the wing
- Lift vector is defined perpendicular to velocity vector
Drag (D) – Generated by everything exposed to airflow
- Drag vector is defined parallel to velocity vector, two basic components
- Minimum drag - air resistance to basic shape (friction and pressure)
- Drag due to lift (induced drag) - drag that results from creating lift
Thrust - From jet reaction or propeller (Chapter 18)
Trim - Aerodynamic force or moment that keeps pointy end forward
c 2006 LM Corporation                 Aerodynamics                                      16-5
Design of UA Systems                                                    2D vs 3D wing effects

Wing incidence (i ): measured relative to air vehicle
Zero lift line (ZLL)      thickness (t)   datum, typically a fuselage “waterline” (WL)

Mean thickness (camber) line
Flap deflection angle ()

Velocity (V)
Wing chord  (c)

Wing aerodynamic behavior is generally categorized into 2 dimensional (2D) and
3 dimensional (3D) effects
- 2 D effects are primarily associated with airfoils
- Airfoil contour (shape and camber) and thickness are key drivers
- Thin airfoils are low drag, limited by angle of attack and are structurally inefficient
- Thick airfoils (t/c < 0.2) are aerodynamically/structurally efficient at low speeds
- Airfoils can vary by span location although constant chord and thickness sections
are used to simplify manufacturing
- 3 D effects result from finite span (tip effects) and cross flow
- Lift and drag are affected
- 3D wings are reduced to 2D approximations at a mean aerodynamic chord
c 2006 LM Corporation                          Aerodynamics                                                     16-5aa
Design of UA Systems                                                           Subsonic aero - Lift
L = lift
Side view                                Speed typically represented
by dynamic pressure (q =
V2/2) where  = air density
and/or Mach number
     V
M = moment

p < p0
D = Drag

Lower lift distribution not to scale
p > p0     W = weight             Trim force
Typical lift distribution                                                                     T = Thrust

Lift (L)  linear function of q, angle of attack () and wing area (Sref)
- Usually linearized into coefficient form: CL = L/qSref = CL
- CL determined by airfoil section (2D) and wing (3D) effects
- Airfoil lift characterized by Cl ( 2/rad), Clmax (<1.01.5), Cl0
- 3D effects are losses, optimum distribution is elliptical
- Air density () is function of temperature and pressure
- Both typically defined relative to sea level (e.g. T = T0, p = p0)
- At low subsonic speeds CL  constant, at high subsonic = f(Mach)
c 2006 LM Corporation                                       Aerodynamics                                  16-5a
Design of UA Systems                                                         Aero 101
Subsonic areo - Drag
L = lift
Side view                          Speed is often converted to
dynamic pressure (q = V2/2)
where  = air density
       V
M = moment

Tip            D = Drag
Lower lift distribution not to scale   vortex                                       T = Thrust
Typical lift distribution                  W = weight                 Trim force
Drag (D)  function of q, wetted area (Swet) and lift coefficient (CL)
- Also expressed in coefficient form: CD = D/qSref = CDmin + CDi
- CDmin determined  by shape, surface roughness, wetted area and size
- Sum of all non-lift dependent friction drag components including wing
- Individual components have different form factors (FF) driven by shape
- Major unknown = extent of laminar vs. turbulent boundary layer (BL)
- Advanced designs try to achieve maximum run of laminar BL
- CDi  CL2/Ae where A = Aspect Ratio, e = Oswald efficiency
- e = 1 for elliptical lift distribution = f(A,, t/c,) with definitions to follow
c 2006 LM Corporation                                  Aerodynamics                                    16-5b
Design of UA Systems                                          Drag – cont’d
L = lift
Side view

    V
M = moment

MDD
D = Drag
T = Thrust
W = weight               Trim force
Minimum drag varies with size because of Reynolds number (Rn) effects
- Rn = Vl/ where V = speed, l = characteristic length (chord or
length),  = air viscosity Predicting when laminar flow goes turbulent is an “art”
- Friction drag coefficient (Cf) goes up as l goes down
- Rn also has major impact on % laminar vs. turbulent boundary layer
- High Rn guarantees boundary layer will be turbulent
Minimum drag also varies with Mach (shock induced drag rise) = MDD
- When local M  1, shocks form, drag goes through the roof
- Onset of drag rise determined by sweep and fineness (Lth/Diameter)
c 2006 LM Corporation               Aerodynamics                                   16-5c
Design of UA Systems                                Subsonic 101 - – L/D
Aero aero Drag
L = lift
Side view

    V
M = moment

D = Drag
T = Thrust
W = weight             Trim force
Overall air vehicle performance is determined by the ratio of Lift/Drag (L/D)
- Powered equivalent of glide ratio for sailplane enthusiasts
- For given value of wing loading, lift coefficient (CL) required decreases
with speed  induced drag (CDi) also decreases
- Minimum drag, however, increases               Major drivers
- Maximum L/D occurs when CDi = CDmin or              Wing aspect ratio (A)
- CL(L/Dmax) = sqrt[CDminAe]                      Wing thickness ratio (t/c)
- For given CDmin, A and e  one CL for L/Dmax        Wing sweep ()
- And for given W/Sref  one V for L/Dmax          Wing taper ratio ()

c 2006 LM Corporation               Aerodynamics                                16-5d
Design of UA Systems                                                                            Aspect Ratio

www.is.northropgrumman.com.gallery.usaf.jpg
www.is.northropgrumman.com.gallery.usaf.jpg

AR = b2/Sref

www.nasa.dfrc.gov.B52.jpg

www.nasa.dfrc.gov.SR71..jpg
AR = 8.6
AR = 1.7                       Vmax  550 KTAS                         AR = 25
Vmax  2000 KTAS                        M 0.9                          Vmax  350 KTAS

c 2006 LM Corporation                           Air vehicle geometry                                                           16-5e
Design of UA Systems                                                                              Wing sweep

www.is.northropgrumman.com.gallery.usaf.jpg
www.is.northropgrumman.com.gallery.usaf.jpg

AR = b2/Sref

www.nasa.dfrc.gov.B52.jpg

www.nasa.dfrc.gov.SR71..jpg
LE Sweep = 40
LE Sweep = 60                    Vmax  550 KTAS                       LE Sweep = 10
Vmax  2000 KTAS                         M 0.9                         Vmax  350 KTAS

c 2006 LM Corporation                           Air vehicle geometry                                                           16-5f
Design of UA Systems                                                                         Wing thickness ratio (t/c)

www.nasa.dfrc.gov.B70jpg                                 www.nasa.dfrc.gov.NB52.jpg
t/c  16%
AR = 14
Vmax  250 KTAS

t/c  2.5%
AR = 1.75                                                      t/c  199.5%
Vmax  1700 KTAS                                                      AR = 8.6
Vmax  550 KTAS                                       UAV history.air war college.jones.03.97

Raw data sources - Roskam, Janes All the World’s Aircraft and unbublished sources

c 2006 LM Corporation                                     Air vehicle geometry                                                                                      16-5g
Design of UA Systems                                                                                  Wing taper ratio vs. e
www.nasa.dfrc.gov.F106.jpg
www.nasa.dfrc.gov.Altair..jpg

 = 0.4
Lockheed Martin,.Paris Airshow 2005

=0                                         = 0.23
=1

Data: Courtesy of Greg Costa, Air Vehicle Directorate, Air Force Research Labs

www.grumman.net/gallery/N28732.jpg

www.nasa.dfrc.gov.HyperIII.jpg

=1

Efficiency varies with  and  (regardless of camber) but by different amounts
c 2006 LM Corporation                                         Air vehicle geometry                                                                      16-5h
Design of UA Systems                     Mean aerodynamic chord (mac)

Nominal chord location used to represent and/or resolve
overall aerodynamic forces at a single location
• Often generated graphically (chart follows) but simple to
calculate from fundamental geometry1
mac (length) = (2/3)Cr[1++2]/[1+] BL = “Butt line”
 = taper ratio = Ct/Cr           BL0 = centerline
FS = “Fuselage Station”
Cr = root chord                   FS0 = tip of forebody
Ct = tip chord)
BL mac location (Ymac) = (b/6)[(1+2)/(1+)]
b = span
 = taper ratio
FS mac location (Xmac) = YmacTan LE
Particularly important for estimating weight and balance
• Relative position of center of gravity (c.g) to aerodynamic
center (a.c.) determines stability
1   For simple trapezoidal wing. For more complex planforms see Roskam
c 2006 LM Corporation           Aerodynamics                                   16-6
Design of UA Systems                                     Trim vs. stability

Positive static stability
c.g. forward of a.c.
     V

horizon

Note: the aerodynamic center is for
W = weight           Trim      T = Thrust

Mean aerodynamic chord (mac)

Aerodynamic center (a.c.)
Moment () = constant
Section a.c. located  25% mac1
1 Aircraft a.c. depends on configuration but
= center of
typically ranges from 20% to 40% mac with                           gravity
unswept, high AR a.c.  25% mac
c 2006 LM Corporation                  Aerodynamics                                    16-6a
Design of UA Systems                                  Negative static stability

c.g. aft of a.c.
     V

horizon

T = Thrust
W = weight

Mean aerodynamic chord (mac)

Aerodynamic center (a.c.)
Moment () = constant
Located  25% mac1                                  = center of
gravity

c 2006 LM Corporation                 Aerodynamics                                        16-6b
Design of UA Systems                                     Trim vs.
Neutral static stability

c.g. @ a.c.
     V

horizon

Trim = 0      T = Thrust
W = weight

Mean aerodynamic chord (mac)

Aerodynamic center (a.c.)
Moment () = constant
Located  25% mac1                                  = center of
gravity

c 2006 LM Corporation                 Aerodynamics                                        16-6c
Design of UA Systems                                               Geometry notation
Swet = Total wetted area
Side view                                          excluding inlet
L = lift                             and nozzle area
Ai = Inlet area
Swet-x = Wetted area of x
D = Drag           Svt = Exposed VT area
     V

horizon

 = Flight path angle
W = weight
Trim      T = Thrust

Sref = Wing reference area
cg = center of
(both sides to CL)                                             Anoz = Nozzle
gravity                      area
Cr = Root chord                       Ct
Swexp = Exposed wing area                           Ymac
(both sides)
Xmac
Sht = Exposed HT area
mac = Mean aerodynamic chord
c 2006 LM Corporation                  Aerodynamics                                                 16-6d
Cr                  Cr
Design of UA Systems                               Airfoils

Fundamental aero and notation
2-D aerodynamics (airfoils)
3-D wings (lift)
Lift curve slope
Cruise and loiter lift
Takeoff and landing lift
Maximum lift (stall)
Drag
Zero lift
Reynolds number effects
Mach number effects
Induced drag
Trim
Lift-to-drag ratio
Stability and control
Example problem

c 2006 LM Corporation      Aerodynamics                            16-6e
Design of UA Systems                                                                     2D airfoils

Wing incidence (i ): measured relative to air vehicle
Zero lift line (ZLL)    thickness (t)    datum, typically a fuselage “waterline” (WL)

Mean thickness (camber) line
Flap deflection angle ()

Velocity (V)
Wing chord  (c)
 = angle of attack                                      Lift characteristics
q = dynamic pressure (½ V2 )                                                                          airfoil
Zero lift angle = 0                                                                                   Clmax
Section lift curve slope (Cl)
Cl                   Slope =   Cl 
Symmetrical airfoils: Cl = 0 at  = 0
Cl
Cambered airfoils Cl = Cl 0 at  = 0                     Cl 0
Section lift coefficient (Cl) = Cl 0+ Cl 
Airfoils with flaps Cl = Cl + Cl                                0                       
Section lift = l = Clqc
Section profile drag = d0 = Cd0qc                               Reynolds number (Rn) = Vc/
Cd0= f(c, t/c,Rn)
c 2006 LM Corporation                      Aerodynamics                                                          16-7
Design of UA Systems                                    Plain
Flapped airfoil

c
Plain flap
LE flap

c’
Slotted Fowler

Type           Clmax
Cl l
C

Plain TE         0.9
Fowler TE        1.3c’/c
2 TE slots       1.6c’/c
3 TE slots       1.9c’/c
Rotating LE      0.3

During wing = f (sweep, t/c, camber); typical range  0.9 – 1.4
Clean early design phases, we ignore “clean” airfoil moments
-Nominal maximum value trimmed
-e.g. assume they can be= 1.5
+ Trailing edge flap = f are LE area increase, number of slots)
Our only real concerns (angle, and TE flap generated moments
- They edge device = f (type)
+ Leading can be very large and hard to trim

c 2006 LM Corporation        Aerodynamics                                        16-8
Design of UA Systems                      Airfoil design and/or selection

Primary design considerations
- Design lift coefficient (Cld)
- Defined by mission objectives
- Cruise vs. loiter vs. dash speeds
- Pressure distribution and transonic drag onset
- Stall characteristics
- Thickness ratio and camber

c 2006 LM Corporation           Aerodynamics                                 16-9
Design of UA Systems                                               Camber schemes

Camber schemes - historical
Drag polar from www.dreesecode.com.other.aflprimer.pdf

CL (L/D)max 0.5

CD (L/D)max 0.0078

CD (L/D)max 0.0054
CL (L/D)max 0.43

The benefit – Higher (L/D)max
NACA 0012  64
NACA 64-215  80
_Technology.airfoils.jpe
gov.essay.Evolution_of
www.centennialofflight.

The penalty
- Lower L/D outside the “bucket”
- Stall characteristics

c 2006 LM Corporation          Air vehicle geometry                                                         16-9a
Design of UA Systems                               Next

Notation
2-D wings (airfoils)
3-D wings (finite span)
Lift curve slope
Cruise and loiter lift
Takeoff and landing lift
Maximum lift (stall)
Drag
Zero lift
Reynolds number effects
Mach number effects
Induced
Trim
Lift-to-drag ratio
Stability and control
Example problem

c 2006 LM Corporation      Aerodynamics                        16-10
Design of UA Systems                                                        3D wings

le
x%                           i

Cr
Sref/2

Aspect ratio = AR = b2/Sref
Ct            Taper ratio =  = Ct/Cr
b/2                                      Thickness ratio = t/c

Incidence angle = i                                          • For pre-concept and early
Wing lift curve slope = CL                                     conceptual design we can
Wing zero lift coefficient (CL0) = CL at  = 0                 assume a symmetrical wing
Wing lift coefficient (CL) = CL0 + CL                       • Later when we better
Wing lift = L = CLqSref                                         understand aerodynamic
Wing profile drag = D0 = CD0qSref                               requirements we can
optimize using camber
Wing induced drag coefficient = CDi = CL2/Ae                 • In the interim, we use a
Wing induced drag = Di = CDiqSref                               nominal design lift
coefficient (CLd) as an
Incidence angle : required to meet lift
independent variable for
requirements with minimum overall drag penalty
calculating  required
and/or to stay within “deck” angle requirements

c 2006 LM Corporation               Aerodynamics                                                16-10a
Design of UA Systems                           3D Wing lift curve slope

CL = 2A(Swexp/Sref)(F)/{2+sqrt[4+(A/)2(1+tan2(max)/2)]
where
 = theoretical vs. actual airfoil Cl (M)          Example
• d/b = 0.1
 = sqrt(1-M 2)                                      • Sexp/Sref = 0.9
• 0.2 < M < 0.6
F = 1.07(1+Df/b)2                                    •  = 0.95

Df = fuselage diam
max = max thickness
sweep
CL = CL 
Significance
• Low AR = high 
required to generate lift
Relatively
• High sweep = ditto
Relatively

c 2006 LM Corporation            Aerodynamics                                      16-11
Design of UA Systems                          Mach number effects

CL = 2A(Swexp/Sref)(F)/{2+sqrt[4+(A/)2(1+tan2(max)/2)]
where
 = theoretical vs. actual airfoil Cl (M)
 = sqrt(1-M2)                                         Example
• d/b = 0.1
F = 1.07(1+Df/b)2                                       • Sexp/Sref = 0.9
•  = 0.95

Df = fuselage diam
max = max thickness
sweep
Significance
• CL improves with Mach
Although equation appears
to overstate Mach effect
Wind tunnel data is better
source

c 2006 LM Corporation         Aerodynamics                                      16-11a
Design of UA Systems                                Lift coefficient

For flight segments where angles are small (<  15), lift
(L)  weight (W) so that
- CL  CL = L/qSref = W/qSref
where
- q = V2/2 or in more common engineering terms
= 1481.35M2 (see see chapter 17-7)
-  (density) is a function of altitude (defined by the mission)
- V = true air speed (either defined or calculated)
- Cruise, ingress, combat and egress speeds are defined
- Climb and loiter are assumed to be at speeds for
(L/D)max (see 16-13a)
- Weight W is known or estimated based on fuel consumption
Note : speed (V) typically is in ft/sec. Other notation (KTAS) is
used when true air speed is given in knots (see chapter 17)

c 2006 LM Corporation        Aerodynamics                            16-11b

- Typically referenced to maximum gross takeoff weight (GTOW or W0)
Varies by vehicle
type
See Chapter 15-9
through 15-10
- W0/Sref  maximum in
flight value
- EW/Sref  minimum in
flight value
- Values in between are
determined by in-flight
weight
- Based on speed
and altitude effects
on fuel flow and

c 2006 LM Corporation          Aerodynamics                            16-12
Design of UA Systems              Typical cruise CL

c 2006 LM Corporation   Aerodynamics                       16-13
Design of UA Systems                              Stall lift coefficients (no flap)

Driven by airfoil section and wing planform characteristics
- Raymer recommends initial wing estimate at 90% of
maximum section lift with adjustments for sweep
- CLmax = 0.9ClmaxCos(0.25)(Swexp/Sref)
where
- First order section lift drivers are thickness and camber

Airfoil data from Roskam Part VI, Table 8.1

c 2006 LM Corporation    Aerodynamics                                                16-14
Design of UA Systems                                          CL for (L/D)max

CL for maximum lift-to-drag or (L/D)max is an
important parameter for calculating performance
- Loiter is typically at or near CL (and V1) for (L/D)max
- Climb performance can be approximated at this speed
- Ditto for power off descents
By definition (L/D)max occurs when minimum drag
(Dmin) equals induced drag (Di) or:
CDmin = CDi = CL2/ (Are)
therefore
CL(L/Dmax) = sqrt(CDminARe)
Although calculating CL (L/Dmax) requires knowledge of
CDmin, simple approximations provide first order
estimates. See see 16-30/36 for additional details
1   q(L/D)max = (W/Sref)/CL(L/Dmax) , V(L/Dmax) is calculated from q(L/Dmax)
c 2006 LM Corporation               Aerodynamics                                     16-14a
Design of UA Systems                    In flight constraints

Aircraft typically fly at speeds that provide stall margins
- Except in training (practice stall recovery)
- Or combat (minimum turn radius, force overshoot)
Stall margins vary by flight segment (and risk)
- Takeoff (10% stall speed margin = 21% CL margin)
- Climbs/descent (30% stall speed margin = 69% CL
margin)
Loiter stall margins are often intentionally small ( 10%)
- To fly at or near CL(L/Dmax)
- Example
- W0/Sref = 40
- CDmin = .025
- A = 25
- e = 0.85
- CL(L/Dmax) = 1.29 vs. CLmax = 1.2?
c 2006 LM Corporation   Aerodynamics                            16-14b
Design of UA Systems                               Next subject

Fundamental aero and notation
2-D aerodynamics (airfoils)
3-D wings (lift)
Lift curve slope
Cruise and loiter lift
Takeoff and landing lift
Maximum lift (stall)
Drag
Zero lift
Reynolds number effects
Mach number effects
Induced drag
Trim
Lift-to-drag ratio
Stability and control
Example problem

c 2006 LM Corporation       Aerodynamics                               16-14c
Design of UA Systems                            Flap effects – wing CL

Driven by airfoil and wing planform characteristics
- Raymer (Eq 12.21-12.22) recommends initial estimate be
based on 90% of the section lift increment with adjustments
for sweep and area
- CLmax = 0.9Clmax[Sflapped/Sref]Cos(HL)
where                                                   c
- HL = flap hinge line sweep          Plain
c’
Type                    Clmax                   le
Plain TE                0.9       Cr
HL
Fowler TE type                                                 Sref/2
Single slot            1.3c’/c
Double slot            1.6c’/c
Triple slot            1.9c’/c                                         Ct
Rotating LE             0.3                      b/2

c 2006 LM Corporation               Aerodynamics                               16-15
Design of UA Systems           Planform effects on stall (no flaps)

Low AR and/or high sweep () wings can have benign
stall characteristics….
- High drag condition but no dramatic loss of lift
Swept wing tip stall, however, can cause abrupt pitch up
c 2006 LM Corporation        Aerodynamics                             16-16
Design of UA Systems                    Typical takeoff lift coefficients

Typically driven by W0/Sref and takeoff requirements
- For low values of W0/Sref – no flaps required
- For moderate W0/Sref – minimum flap deflection
- For higher W0/Sref – moderate flap deflection
c 2006 LM Corporation         Aerodynamics                                       16-17
Design of UA Systems        Typical maximum lift coefficients

c 2006 LM Corporation   Aerodynamics                                 16-18
Design of UA Systems                            Takeoff and landing constraints

Conventional tail                      CLt/o constrained by geometry and ability of tail
and canard                            to trim out powerful high lift system moments
Wing flap deflected         Tail req’d to trim
for additional lift         TE flap and rotate

    V

Ground effects increase CL compared to free air
max determined by landing
gear length and location        Tail scrape defines max

No horizontal
tail                CLt/o constrained by geometry and absence of high lift system

Trailing edge deflected up
for rotation , lose wing lift
    V

Ground effects increase CL compared to free air

c 2006 LM Corporation                 Aerodynamics                                                         16-19
Design of UA Systems                                                          Other constraints

Pusher prop – aft                                   Works fine for low W0/Sref concepts
fuselage location                                       with high CLd- e.g. Predator
Tail generates moment
for trim and rotation

      V

Takeoff flap (if any)
Ouch
Ground effects increase CL compared to free air                    !

c 2006 LM Corporation                     Aerodynamics                                                16-20
Design of UA Systems                               Next subject

Fundamental aero and notation
2-D aerodynamics (airfoils)
3-D wings (lift)
Lift curve slope
Cruise and loiter lift
Takeoff and landing lift
Maximum lift (stall)
Drag
Zero lift
Reynolds number effects
Mach number effects
Induced drag
Trim
Lift-to-drag ratio
Stability and control
Example problem

c 2006 LM Corporation       Aerodynamics                           16-21
Design of UA Systems                      Overall drag (subsonic only)

Many different approaches (differences mostly notational)1
• We use Raymer Chapter 12 methodology and focus on 3 components:
 Minimum drag (Dmin) =  of individual drag components that vary
primarily with speed (dynamic pressure)
 Induced drag (Di) = Drag-due-to-lift relative to CL at min. drag (CLmin)
 Trim drag (Dtrim) = Control surface drag due to trim (primarily pitch)
Minimum drag has multiple contributors, primarily
 Skin friction  CfeqSwet total = ( CfiSweti)q
 Pressure - represented by individual geometry form factors (FFi)
 Interference - represented by individual interference factors (Qi)
where          CDmin = Dmin/qSref =  (CfiSweti/Sref)FFiQi
 Other shapes such as stores and struts (RayAD Table 12.5)
Induced drag is estimated using the classic parabolic approximation
 Di/qSref = (CL-CLmin)2/Ae’
where e’  Oswald efficiency (applicable only for symmetrical sections)
Trim drag initially is estimated as a percentage of wing Di (10%)
1   Propulsion related drag is accounted for as an engine performance knockdown
c 2006 LM Corporation             Aerodynamics                                       16-22
Design of UA Systems                            Skin friction drag

First order estimates are based on wetted area (Swet) only using
 CDmin = CfKd(Swet/Sref) = Cfe(Swet/Sref)
where
Cf = flat plate skin friction coefficient (See RayAD Fig 12.21)
Kd = Non-friction drag factor (for pressure and interference)
Cfe = Equivalent skin friction coefficient (RayAD Table 12.3)
Next Reynolds number (Rn) effects are included using calculated
speeds, characteristic lengths (l) and boundary layer assumptions
• For laminar boundary layer assumption (RayAD Eq 12.25)
Cf = 1.328/sqrt(Rn)
• For turbulent boundary layer assumption (RayAD 12.27) use either
Cf = 0.455/[(Log(Rn))2.58(1+ 0.144M2)0.65] or a “cutoff” value
Cf = 38.21(l/k)1.053 (whichever is lower)
where k is given by RayAD Table 12.4
Boundary layer assumptions reflect design objectives, e.g. 30%
laminar for a wing, 10% for a fuselage, etc.

c 2006 LM Corporation       Aerodynamics                                  16-23
Design of UA Systems                   Form factors and interference

Form factors (FF) account for fineness (L/De) and thickness ratio
effects by component (See RayAD section 12.5)
 Wings and tails : FF = [1+1.2(t/c)+100(t/c)4][1.34M0.18Cos(m)0.28]
 Fuselage: FF = 1+1.3(L/De)-1.5 + 44(L/De)-3
 Pods and nacelles: FF = 1+0.35/(L/De)
where m = sweep at max thickness
L/De = fineness ratio, De = sqrt(4Axc/)
Axc = max cross section area
Interference drag factors account for flow interactions between
components such as wing-body, tail-body, tail-tail, etc.
 A well designed tail or wing-mid fuselage intersection will
experience little interference drag (Qi = 1.01 and 1.0, respectively)
 An intersection with an acute angle and no fillets on the other hand
can have Qi values from 1.1-1.5
discussion of interference drags associated with different tail types

c 2006 LM Corporation        Aerodynamics                                   16-24
Design of UA Systems                                   Wind tunnel model example

Fuselage: L = 20”, De = 3.44” ,Swet = 1.19sqft
Wing: b = 30”, Sref = 1.04 sqft, AR = 6
 = 1.0, t/c = 0.12
Test: Rn/l = 3.1 106 ft (V  487 fps),  = 0
Fuselage Only
Rn = 5.17 106, FF = 1.32
Laminar Cf = 0.0006,Turbulent Cf = 0.0033,
Laminar CD0 = .0009, Turbulent CD0 = .0049
Test CD0 = .0042  % Laminar  21%
Wing Only
Rn = 1.29 106, FF = 1.41
Laminar Cf = 0.0012,Turbulent Cf = 0.0042,
Laminar CD0 = .0033, Turbulent CD0 = .0119
Test CD0 = .0099  % Laminar  42%
Wing + Fuselage (predicted @ 21-42% laminar)
Wing CD0 = .0071(exposed portion only)
Fuselage CDO = .0041
Wing-Body CD0 = .0112
Wing + Fuselage (Test Data)
No fillet - CD0 = .0115  Qi = 1.03
From NACA Report 540, March 1935                Fillet - CD0 = .0112  Qi = 1.00
Variable Density Wind Tunnel at Rn = 3.1 106

c 2006 LM Corporation                       Aerodynamics                                           16-24a
Design of UA Systems                                                                                    Fuselage Lf/De

Low Lf/De                                  Acceptable values of Lf/De vary
with speed range and application
- For low subsonic speeds, fuselage L/De
 5, nacelles and pods Lth/Deq  4
- For higher speeds, higher values are
required
www.grumman.net/gallery/N15LM.jpg              - Fore and aft body shapes are critical

High Lf/De

www.nasa.dfrc.gov.Altair .jpg

Fuselage unit weight (psf) is minimized when Lf/De is minimized,
overall weight (and drag) is minimized when Lf/De is optimized

c 2006 LM Corporation                                 Air vehicle geometry                                               16-25
Design of UA Systems                        Mach number effects

For local Mach numbers < 1.0, drag is approximately
constant across the subsonic speed range
- Thick section, unswept wings can start having local sonic
flows starting at M0 > 0.6 (i.e. 345 KTAS @ 36 Kft)
- Therefore, MDD (drag divergence Mach)  0.6
- Low fineness ratio bodies have similar problems
- Thinner and/or swept sections can delay drag rise, e.g.
for typical transports 0.85 < Mdd < 0.9
Above Mach 0.9, transonic effects must be included
- Raymer and other texts provide methodologies to
estimate transonic lift and drag but most aerodynamicists
are uncomfortable with these estimates
- They stay uncomfortable until they get into the tunnel and
start getting configuration specific data
c 2006 LM Corporation     Air vehicle geometry                   16-26
Design of UA Systems                                                          Fore and aft body shape

Drag is minimized when
bodies are shaped to

Nominal Drag Rise Characteristics

MDD

c 2006 LM Corporation                                       Air vehicle geometry                                                             16-27
Design of UA Systems                                         Other drag

All aircraft have shapes and components that do not lend
themselves to detailed aero-analysis
 Landing gear                External stores
 Struts                      Antenna
 Pylons                      Instrumentation
 Sensors                     Etc.
Drag for these items can be estimated using simple D/q
“drag areas” or “drag factors”
 Examples from RayAD Table 12.5
 Wheel and tire = 0.25 sqft
 2000 lb bomb on wing = 0.2 sqft
300 gallon tank on wing = 0.5 sqft
 To turn these factors into drag coefficients divide by Sref
These methods are often used in pilot’s handbooks for
estimating effects of various external store configurations on
performance

c 2006 LM Corporation           Aerodynamics                                     16-28
Design of UA Systems                               Next subject

Fundamental aero and notation
2-D aerodynamics (airfoils)
3-D wings (lift)
Lift curve slope
Cruise and loiter lift
Takeoff and landing lift
Maximum lift (stall)
Drag
Zero lift
Reynolds number effects
Mach number effects
Induced drag
Trim
Lift-to-drag ratio
Stability and control
Example problem

c 2006 LM Corporation       Aerodynamics                           16-29
Design of UA Systems                             Drag due to lift

Induced drag [(CL-CLmin)2/Ae’] driven by three (3) fundamental factors
 Camber
 Aspect ratio
 Oswold efficiency
Camber determines magnitude of CDi for given value of CL
 But also increases CDmin (and Cmac)

CDi
CDi

CDmin

c 2006 LM Corporation             Aerodynamics                           16-30
Design of UA Systems                        Oswald efficiency

drag-due-to-lift (Di) for planform effects, where
CDi = Di/qSref = CL2/Ae
and            e = 1 for an elliptical planform
In its original form, e was applied only to symmetrical
(uncambered) airfoils
- Values were based on experience and test data
- Primary drivers are taper ratio () and sweep (25 c)
Application of e to cambered airfoils is not straight forward
since          Di/qSref = (CL-CLmin)2/Ae’
and            e’ ≠ e except when CLmin = 0
Nonetheless, both e and e’ are called Oswald efficiencies
- Sometimes the terms are kept straight and other times not
The differences can be significant

c 2006 LM Corporation     Air vehicle geometry                  16-30a
Design of UA Systems                                                Oswald efficiency drivers

Data: Courtesy of Greg Costa, Air Vehicle Directorate, Air Force Research Labs

c 2006 LM Corporation                        Aerodynamics                                            16-31
Design of UA Systems                                          Methodology differences

Contentious

Sweep measured
Sweep measured
at wing 25%
at 25% chord line
(quarter) chord line

Source - Lee Nicolai, Conceptual Design Process, LM Aero

c 2006 LM Corporation                               Aerodynamics                       16-32
Design of UA Systems                        CDi differences

AR        5            10    15     20      25

1/Ae        .0670 .0354 .0223 .0199 .0168
(Nicolai)

1/Ae        .0707 .0419 .0337 .0300 .0296
(Raymer)

c 2006 LM Corporation        Aerodynamics                     16-33
Design of UA Systems                                   Bottom line

Good wing designers can get good “design point”
aerodynamic efficiency for a range of wing geometries
Examples (from Roskam, Vol VI, Table 5.1)
Unswept wings                    All it takes is time (both in and
Beech 35: 0.82                 out of the tunnel)
Cessna 182: 0.84                - Performance doesn’t come
P-51B: 0.86                       cheap!
Downside: high performance
B-29: 0.94                     can be point in the sky (PITS)
Swept wings                      specific
B-52A: 0.924                    - Off PITS performance can
Gulfstream GII: 0.95              suffer
Boeing 707-320B: 0.983 For your projects assume e  0.8,
Lockheed C-141B: 1.067 if you need e  0.9, plan spending
bucks for CFD and/or tunnel time
Lockheed C-5A: 1.091
c 2006 LM Corporation        Aerodynamics                                  16-34
Design of UA Systems                                            Trim drag

Conventional aircraft pay a price for inherent pitch stability –
• Negative tail lift required for balance  drag due to lift
Canard configurations are balanced by positive tail lift

• Conceptual design trim forces are calculated as a function of c.g.

Customer requirement
and speed and added as appropriate (conventional and canard)
• During pre-concept design, a trim estimate will suffice
• e.g. CL is “trimmed” at a nominal trim drag penalty
- Assume 10% CDi for conventional tail, 0% for canard
• Cruise and loiter performance is adjusted accordingly
Neutral stability can eliminate the trim drag penalty
• Requires fly-by-wire (typically digital) flight control technology
• The technology is well developed but adds cost
c 2006 LM Corporation           Aerodynamics                                    16-35
Design of UA Systems                               Next subject

Notation
2-D wings (airfoils)
3-D wings (finite span)
Lift curve slope
Cruise and loiter lift
Takeoff and landing lift
Maximum lift (stall)
Drag
Zero lift
Reynolds number effects
Induced
Trim
Lift-to-drag ratio
Stability and control
Example problem

c 2006 LM Corporation      Aerodynamics                          16-35a
Design of UA Systems                            Lift-to-drag ratio (L/D)

L/Dmax represents the maximum slope of a line tangent
to CL vs. CD
- For symmetrical airfoil, CL = 0 at CD = CDmin
Camber increases maximum slope and L/Dmax
- CL > 0 at CD = CDmin

CDi
CDi

CDmin

c 2006 LM Corporation                 Aerodynamics                          16-35b
Design of UA Systems                                                       (L/D)max

Theoretical (L/D)max
• If CD = CD0 + KCL2 then D/L = CD0/CL + KCL) and
(L/D)max will occur when d(D/L)/dCL = 0
or….    - CD0/CL2 + K = 0 or CD0 = KCL2 = CDi
Nominal Drag Characteristics
(uncambered airfoil)
1.2
Max slope = L/Dmax                            (L/D)max @
1
Minimum drag
0.8
CDmin
0.6
CL@ L/Dmax
0.4

0.2
CDmin =
0
0           0.02        0.04          0.06
CDi
CD

At any given weight, flight at (L/D)max minimizes drag and fuel flow required
c 2006 LM Corporation                          Aerodynamics                            16-35c
Design of UA Systems                               (L/D)max cont’d

Since (L/D)max occurs when
CD  2CD0 ≈ 2Cfe(Swet/Sref)
then…..
CL  sqrt (AReCD0)
and….
(L/D)max = sqrt{[e/Cfe][b2/Swet]}/2 Compare this to
For typical aircraft
Cfe = .003 - .005 (Table 12.3), e ≈ 0.8, Kd = 1.2
(L/D)max ≈ 11.2-14.5sqrt (b2/Swet)
Airspeed at (L/D)max (aka LoDmax ) is estimated using
these equations
- At other conditions (where speed is given) q is
calculated from 1/2V2 and CL from W/qSref

c 2006 LM Corporation           Aerodynamics                              16-36
Design of UA Systems                                   L/D parametric

Simple AR correlation to
include sailplanes
- See AirVehicleData.xls

- See AirVehicleData.xls
Parametrics by definition include all lift and drag effects, e.g. Rn and trim
c 2006 LM Corporation          Aerodynamics                                       16-37
Design of UA Systems                               Next subject

Fundamental aero and notation
2-D aerodynamics (airfoils)
3-D wings (lift)
Lift curve slope
Cruise and loiter lift
Takeoff and landing lift
Maximum lift (stall)
Drag
Zero lift
Reynolds number effects
Mach number effects
Induced drag
Trim
Lift-to-drag ratio
Stability and control
Example problem

c 2006 LM Corporation       Aerodynamics                           16-38
Design of UA Systems                   Static stability and tail sizing

Pre-concept and early conceptual design stability
and control (S&C) focus is static stability
• Aerodynamic center (a.c.) location This chapter
• Center of gravity (c.g.) location        Chapter 19 - Weight
• Overall horizontal and vertical tail sizes
- Initial estimates are based on historical
ratios vs. wing area (Sht/Sref and Svt/Sref         Chapter 20
- Geometry
- Later estimates are based on historical tail
“volume” coefficients (Cvt and Cht )
Later conceptual design S&C focus is dynamic
stability and control
• Cm : pitch moment coefficient            • Control
• Cℓ : roll stability coefficient           surface sizing
• Cn : yaw stability coefficient           • Flap sizing
• Propulsion induced forces and moments • Etc.
c 2006 LM Corporation        Aerodynamics                                 16-39
Design of UA Systems                                    Static stability

Static Stability - determined by the relative locations of the
air vehicle aerodynamic center (a.c.), center of gravity (c.g.)
and control surface for a given stability axis
- Initial focus is on pitch stability
Three (3) basic static stability concepts
(1) Statically stable: disturbed air vehicle returns to trim
condition from disturbed state
(2) Statically unstable: disturbed air vehicle departs from
disturbed state
(3) Neutral stability: air vehicle maintains disturbed state
Dynamic Stability - manner in which a disturbed air vehicle
returns to a trim condition
- Highly damped: dynamically stable, no over shoot
- Lightly damped: dynamically stable, monotonically
decreasing overshoot
- Dynamically unstable: increasing overshoot or divergence
c 2006 LM Corporation             Aerodynamics                                  16-40
Design of UA Systems                                                        Static stability

c.g.  0.15 - 0.2 mac
Lw                                             (15% stable)
     V      

Statically stable                  a.c.
“Static margin”  15%                       Lht  0.1 Lw

Subsonic a.c.
Neutral stability               and     aligned, Lht = 0                         0.25 mac1

c.g.  0.25 - 0.35 mac
Lw                                           (10% unstable)
Lht  0.1 Lw
     V      

Statically unstable               a.c.
1Aircraft a.c. depends on configuration but typically ranges from
“Static margin”  -10%              20% to 40% mac with unswept, high AR a.c.  25% mac

c 2006 LM Corporation                Aerodynamics                                                              16-41
Design of UA Systems                                          Control

Multiple design and analysis objectives
- Control surface size: to ensure adequate control at critical
flight conditions
- Control surface rates: to achieve dynamic stability objectives
- Control forces : to size actuators and structure
Involves multi degree of freedom (DOF) modeling
1 DOF: Pitch, yaw and roll assumed to be uncoupled
3 DOF: Velocity vector limited to plane of symmetry,
control coupling limited to single plane
6 DOF: Control interactions full coupled

• Pre-concept and conceptual design analyses typically
limited to 1 DOF or simple 3 DOF assessments

c 2006 LM Corporation               Aerodynamics                             16-42
Design of UA Systems

Fundamental aero and notation
2-D aerodynamics (airfoils)
3-D wings (lift)
Lift curve slope
Cruise and loiter lift
Takeoff and landing lift
Maximum lift (stall)
Drag
Zero lift
Reynolds number effects
Mach number effects
Induced drag
Trim
Lift-to-drag ratio
Stability and control
Example problem

c 2006 LM Corporation       Aerodynamics                16-43
Design of UA Systems                  Notional example

A subsonic UA has the following characteristics
W0/Sref = 40 psf
AR = 20
LE = 0 deg
Swet/Sref = 5 or b2/Swet = 20/5 = 4
Cfe = .0035
From chart 16.6 at AR = 20 and  = 0 deg, e ≈ 0.8 and
CD @ (L/D)max ≈ 2Cfe(Swet/Sref) = .035
 CDmin = .0175
CL @ (L/D)max = sqrt (AReCDmin) = 0.938
LoDmax = sqrt{[e/Cfe][AR/(Swet/Sref)]}/2 = 26.8
q @ (L/D)max = (W0/Sref)/CL = 42.6 psf
EAS @ (L/D)max = 112 KEAS

c 2006 LM Corporation   Aerodynamics                          16-44
Design of UA Systems                      Example problem

In Chapter 15 we assumed a nominal starting value of
(L/D)cr = (L/D)lo = 23 for our example TBProp
- Assuming nominal values of Cfe = 0.0035 and e = 0.8,
from Chart 16-9:                         Form factor
2/S
(L/D)max = sqrt{[e/Cfe][b wet]}/2
or…..                                       and Rn effects
b2/Swet = AR/[Swet/Sref] = 2.95       not included
- For a typical wing-body-tail configuration where
Swet/Sref = 5 (RayAD Fig 3.5), AR = 14.75
- This value would be at the upper range of AR for
typical commercial regional TBProps
The corresponding aerodynamic coefficients would be
CD0 = Cfe(Swet/Sref) = 0.0175 (175 “counts”)
CL @ (L/D)max = sqrt (AReCDo) = 0.805
This estimate would be the starting point for a more
refined estimate using the component buildup method
c 2006 LM Corporation     Aerodynamics                          16-45
Design of UA Systems               Example problem – cont’d

Without configuration information, however, we have
no basis for applying the component buildup drag
methodology
- We need to know, for example, wing and tail mac,
fuselage and nacelle length to make the next level of
detail drag estimate
- Therefore, we will make a first cut drag estimate based
only on gross configuration features
- We will apply drag methodology refinements when we
have actual configuration data
- This will not occur until, at a minimum, we work our
way through Chapter 20
Welcome to the iterative world of aircraft design where
we start off with first order estimates and continuously
refine them as we get more knowledge and information
c 2006 LM Corporation    Aerodynamics                         16-46
Design of UA Systems                                                    Correction factors

For pre-concept studies, (L/D)max = sqrt{[e/Cfe][b2/Swet]}/2
will yield reasonable estimates of lift and drag
• Nonetheless it is good practice to always compare
estimates to data from similar aircraft and to apply
appropriate correction factors
• Our previous calculation
LoDmax comparisons
of (L/D)max = 26.8 for AR =
35
20, Swet/Sref = 5, for
example, when compared 30
25

(L/D)max
to parametric data from
20
other aircraft shows that                Chart 16-10
15
our estimate is consistent               estimate
10
with the parametric data
5
• If not we could correct the                      Manned aircraft
Global Hawk (est)
0
estimate by putting a                             0             2            4
Wetted AR = b^2/Swet
6   8

multiplier on CDmin                      Manned aircraft data
: LM Aero data handbook

c 2006 LM Corporation          Aerodynamics                                                                16-47
Design of UA Systems                                      Expectations

You understand basic subsonic aerodynamics
 Initial estimates (parametric)
 Lift coefficients (how to calculate)
-At takeoff to meet BFL requirements
-At specified speeds and altitudes
-At (L/D)max
- All consistent with specified stall margins
 Drag coefficients (how to calculate)
- Minimum drag
- Corrected for Rn
- Based on % laminar flow objectives
- Corrected for Form Factor
- Corrected for interference
- Induced drag
- Trim drag (at specified static stability levels)
 Horizontal and vertical tail size required
 Mach number and methodology limitations
 Parametric comparisons

c 2006 LM Corporation            Aerodynamics                            16-48
Design of UA Systems               Recommended reading

Raymer - Aircraft Design - A Conceptual Approach
• Chapter 4 : Airfoil and Geometry Selection
4.3 – Wing Geometry
4.5 – Tail geometry
• Chapter 12 : Aerodynamics
12.1 – Introduction
12.3 – Aerodynamic Coefficients (subsonic only)
12.4 – Lift (subsonic only)
12.5 – Parasite (Zero-Lift) Drag (subsonic only)
12.6 – Drag Due to Lift (subsonic only)

c 2006 LM Corporation    Aerodynamics                       16-49
Design of UA Systems              Intermission

c 2006 LM Corporation   Aerodynamics             16-50

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