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Projectile on Inclined Planes

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									                                   U.S. DEPARTMENT OF COMMERCE
                                   National Technical Information Service


                                   AD-A024 073




AN IMPROVED PROJECTILE BOATTAIL
PART II




BALLISTIC RESEARCH LABORATORIES




PREPARED FOR
ARMY MATERIEL DEVELOPMENT AND READINESS COMMAND



MARCH   1976




        tV
132163




                  pA




         REPORT NO. 1866

 Cfl     AN IMPROVED PROJECTILE BOATTAIL.                             PART 11.


         Anders S. Piatou
       C~George 1. T. Nielsen


       SMarch 1976                                                      MA




         Approved f~or public release, distribution ui1imited.




         USA BALLISTIC RESEARCH LABORATORIES
         ABERDEEN PROVING GROUND# MARYLAND

                                      REPRODUCED BY
                                      NATIONAL TECHNICAL
                                     INFORMATION SERVICE
                                       U.S. DEPARTMENT OF COMMNER.E
                                            SPRINGFIELD, VA. 22161
                                          UNCLASSIFIED
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                                                         REPOR DOCINTAION
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                                       REPORT DOUMENTATION PAGE                                                  BEFORE COMPLETING FORM
                 1. REPORT NUMBER                                            . GOVT ACCESSION NO.       3.    FECIPIFNT'S CATALOG NUMBER

                       BRL Report No.            1866
                4.     TITLE (and Sublil#1)                                                             5     TYPE OF-REPORT       PERIOD COVERED

                                                                                                              Final
                       AN IMPROVED PROJECTILE BOATTAIL.                    PART I1.                     6.    PERFORMINGORG. REPORT NUMBEq


                7.     AUTHOR()                                                                         9     CONTRACT OR GRANT NUMBER(a)

                       Anders S. Platou
                       George     I.    T. Nielsen                                                       __
                 Sl
                ". PERFORMING ORGANIZATION NAME AND ADDRESS                                             1O. PROGRAM ELEMENT. PROJECT, TASK

                       USA Ballistic Research Laboratories
                       Aberdeen Proving Ground, Maryland 21005                                                RDT&E 1T161102A33D
        SU.S.   II.    CONTROLLING OFFICE NAME AND ADDRESS
                               Army Materiel Developmert & Readiness Command                            12.    REPORT DA"E
                                                                                                              MARCHl 1976
                       5001 Eisenhower Avenue                                                           13. NUMBEROF PAGES

                 14.
                       Alexandria. Virginia 22333
                        MONITORING AGENCY NAME & ADDRESSQI dilferent from Controlling Office)           15.
                                                                                                                144          ._         _
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                16.    DISI RIBSITION STATEMENT (of thle Report)                                                                                            .



                Approved for public release; distribution unlimited.



                17. DISTRIBUI ON STATEMENT (of the abstract entered In Block 20, 1idlfferent from Report)




                III. SUPPLEMENTARY N4OTES




                IS.    KEY WORDS (Continue on reverse aide it necessary and Identify by block number)

                 Projectiles
.....            Aerobal listics
                 Magnus
                 Bodies of Revolution
                 Gyroscopic Stability                                                                          .c.a
                20.    ABSTRACT (Continue en reverse sid              (Ica)
                                                               necoemy and Idenlv    by block numbe)
                 A series of projectile boattails have shown improved aerodynamic performance
                 over the standard conical boattail. These boattails have equal or lower drag
                 and an improved gyroscopic stability. Their Magnus and damping characteristics
                 appear to be satisfactory so that the projectile should be dyn:rmi½ally stable.
                 Also, these boattails increase the projectile wheel base considerably, thereby
                 decreasing the balloting in the gun tube. The improved aerodynamic performance
                 could lead to longer ranges, larger payloads, or lower spin rates for future
        •       •~1roi ectie.¢....
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                                                                                         SIECU~tlTy CLI.;FfUCATION OF THIS PACE (D -        Date Kntored)
                         iI


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                                          Do not return it to the originator.



                                          Secondary distribution of this report by originating
                                          or sponsoring activity is prohibited.

                                           Additional copies of this report may be obtained
                                           from the National Technical Information Service,
                                           U.S. Department of Conierce, Springfield, Virginia
                                           221SI.




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      DIMIAICA/TW'AYAIUITY COCO




                         IS
                                             The findings in this "port av not to be construed as
                                             an official Departmnt of the AzW position, unless
                                             so designated by thoe sIthorioed documents.
I!                                                   TABLE JF CONTENTS
                                                                                                                                                     P.Me
                  LIST OF ILLUSTRATIONS ............................                                                                                   S
            I.    INTROPUCTION   ........................                                                                                              7


           II.    TEST FACILITIES        .       .       .       . .      .   .        .     . .      .     .   .      . .8

          III.    WIND TUNNEL MODELS             .       . .          .   .   .        .     . .      .

           IV.    RANGE MODELS                           .   . . . . . . . . .                                          .          ..........          9
                                                                                                                                                       9.

F
:'   -'     V.    RESULTS AND ANALYSIS                       ....................                                                                      0
                                                                                                                                                       0

           "VI.   CONCLUSIONS                                                                                                                         i15

                  RE.FERENCES                                                     ..         .......................                                  16

                  APPENDIX       .           .       .       .    .       .   .        . . . . . . . . . ........                                     35
                  LIST OF SYMBOLS ........                                                 ..............                                       ..   159

                  DISTRIBUTION LIST ...........                                                                     ............                     163




                                                                                                                    3I

                                                                                           3                    Preceding               Page blank
                             LIST OF ILLUSTRATIONS

gyur                                                                                                                      Page

 1.    The Cylindrical and Conical Boattail, Dimensions in
         Calibers.                                                                                                         17

 2.    The Square and Triangular Boattail,                  Dimensions ia
         Calibers         .........................                                                                       18

 3.    The Added Lifting Surfaces, Dimensions in Calibers                                        .              ..         19

 4.    A Canted Boattail                                                                                                   2..................20

 5.    The Wind Tunnel Model of the Cruciform 'Wedge Boattail,
         Dimensions in Calibers, k = ', 6, or 7 Calibers .     .                                                  .        21

 6. Cross Sectional Areas of 70 Boattails                           . .   .    .     .      .        .     .         ..    22

 7.    The Zero Yaw Drag of the Improved Boattails.                                .....                                   23

 8.    The Drag Polars for Various Boattails at M = .5                               .               ...                   24
 9.    The Drag Variation Due to Spin on the Straight Square
         Boattail at M = .9. .        .   .   .   .   . .   .....         ...............                                  25
10.    The Normal Force on the Improved Boattail Configurations.                                                           26

11.    The Pitching Moment on the Improved Boattails                                     .....                             27

12.    The Normal Force Cciter of Pressure on the Improved
         Boattails                 ................                                                        ....            28

13.    The Magnus Moment on the Improved Boattails at Low
         Angles of Attack.               ................                                                                  29

14.    The Side and Magnus Forces on the Straight and Twisted
         Boattail          .........     .    .....      .....                                                             30

15.    The Magnus Characteristics of the Triangular Boattail at
         M = 2.5, pd/V = .27,       Rdia          .94 x 106 .........                                      ..              31

16.    The Magnus Offsets and Slopes on the Triangular Boattail
         at M = 2.5, Rdia = 950,000.        .............                                                                  32

17.    The Magnus Characteristics of the Triangular Boattail
         With a 1/20 Twist at a Spin Rate (pd/V = .412),
         M = 2.5, Rdi a  950,600.   ...........                                                            .               33




                                                                    PcPmeding pap blank

                                                                                                                                                   J
                     LIST OF ILILUSTRATICNS (Continued)

F:igure                                                   Page

  18.     The Damping in Pitch of Variius Boattails.       34..........




                                      6
                               1.   INTRODUCTIGN

     The main purpose of a projectile boattaall is to reduce drag, over
that of a cylindrical boattailed projectilc* (Figure I), thereby
increasing the range of the projectile.   In past years various geometric
shapes (a conical boattail has been the most popular) have been used to
form the boattail and have depended on the reduced base area to reduce
the drag.  These boattails have worked well in reducing the drag; how-
ever, all of them develop a negative lift  on the boattail which
increases thk wustable pitching moment and reduces the gyroscopic
stability.  These boattails (especially the conical boattail) also
generate large Magnus forces and moments at transonic velocities which
can adversely affect the dynamic stability cf the projectile.    Satis-
factory gyroscopic and dynamic stability must be maintained so that the
average angle of attack remains within low limits as the projectile
moves along its trajectory.   This permits accurate prediction of the
projectile range.

     Recently, the BRL has experimentcd with a series of boattail
shapes, which do not have axial symmetry and which have a niunber of
advantages over the axisymmetric boattails.   These boattails are formed
by cutting the main projectile cylinder with planes, inclined at a
small angle to the main projectile axis, such that flat surfaces are
created on the boattail.  The flat surfaces increase the boattail lift
so that the unstable pitching moment is decreased and the drag is
reduced by the smaller base area.  Also, these boattails have elements
of the main cylinder extending to the base which increases the wheel
base over that of the axisymmetric boattails.   The increased wheel base
will reduce gun tube balloting and possibly reduce muzzle jump and gun
tube wear.  Possible versions of these boattails are:

     (1)  A boattail formed using four cutting planes so that the base
becomes an inscribed square (Figure 2).**

     (2)  A boattail formed using three cutting planes so that the base
becomes an inscribed triangle (Figure 2).**

     (3)  Boattai]s formed similar to (1) or (2) but with the cutting
plane widths limited so that added lifting surfaces are formed at the
base corners (Figure 3).**

      (4) Boattails formed similar to (1), (2), and (3) but with cutting
planes canted so as te reduce the roll dampiiig during flight (Figure
4) .**

* Previously known as a square base configuration, but changed here to
avoid confusion with the new version (1) boattail.

**   Patent No.   3,873,048.
                                       ~7
      (5) A boattail hormed by eliminating all of the main body cylinder
volume not included inside the volume of two orthogonal wedges (Figure
S).* This version can he extended to zero base area or can be cut off
at any station to form a crucifoxm base.

       Characteristics ef these new boattails which may be important are:

     (1) The flat surfaces generated on the boattails may act as llf'-
ing surfaces, thereby increasing the lift on the aft portion of the
                                                                             I
projectile and decreasing the unstable pitching moment.

      (2) All of these boattails have a more gradual reduction in cross
sectional area than the conical boattails (Figure 6).  This reduces the
rapidity of flow expansion over the boattail and may be the reason for
the reduction in Magn1s forces observed at transonic speeds.

      (3) The cylinder elements which extend to the base will form crude
rotating fins which should have Magnus forces acting opposite to those
on the body 1 . The opposing forces should minimize the resultant Magnus
force and moment about the projectile center of gravity.

     Aerodynamic tests on these boattail configurations have been made
to verý fy these characteristics and also to find the configuration
having the best overall aerodynamic performance.   These tests have been
run in U.S. Government wind tunnels and ranges which were available to
us for these purposes.


                            II, TEST FACILITIES

       The wind tunnel facilities used for the tests si far are:

      (1) The NASA Ame> Research Centei 12 ft. subsonic wind tunnel,
M   .5, .7, and .9, 44" model, Re/ft = 1.35 to 2.8 x 106 (Re/m = 4.23
to 9.2 x 106).

     (2)  The Naval Ship Research and Development Center (NSRDC) 7 ft.
x 10 ft. transonic wind tunnel, M = .5, .7, .9, .94 ard .98, All model,
Re/ft = 2.65 to 4.0 x 106 (Re/m = 8.69 to 13.1 x 106).

     (3)  The Ballistic Research Laboratories (BRL) 1 ft. supersonic
wind tunnel, M = 1.75 to 4.0, 2¼" model, Re/ft = 3.6 ta 7.0 x 106
(Re/m = 11.8 to 23.0 x 106).

*    Patent disclosure has been submitted.

1.    Anders S. Platou, "Magni.v Character-'Xstics of Finned and Ncnfinned
      Projectiles," AIAA Journal Vol. 3, No. 1, January 1965, pp. 83-90.

                                      8
          The range facility used for the tt ts is-

           (1) The Ballistic Research Laboratories (BRLI aerodynamic range,
    M    .5 to 4.0, 20m models, atmospheric free flight Reynolds numbers.


                             III.     WIND TUNNEL MODELS

         These boattails are being tested using the ArT'-Navy Spinner
    Rocket nose and body with the complete configurations being 5, 6, or 7
    calibers long.

         Two sizes of models, 2¼" (5.71S cm) ano 44" (10,7.95 cm) diameters,
    are required for the wind tunnel tests because of the variation of the
    tunnel sizes available for the different speed ranges.    The models are
    designed according to the specifications described in reference 2.    They
    consist of a central body mounted on ball bearings and a strain gage
    balance with various tails and noses attached to the central body.
    Variations in the lengths of the noses and tails maltc it possible to
    test body lengths of 5, 6, or 7 calibers.   Tails for cvich boattail
    version, listed previously, are made using a 70 cutting plane angle for
    both the 2V" and 4¼" diameter models.   Also, a straight cylindrical
    tail and a 1 caliber long 70 conical boattail are .aialable for compar-
F   ison (Figure 1).   Each boattail version can be teste-1 on the 204"
    diameter body with configuration lengths of 5, 6, or 7 calibers; however,
    the 5 caliber, 4¼•" model is limited to the straight cyIlnder, the
    conical boattail, and the square boattail.   Six and seven caliber, 41-"1
    diameter models of all of the boattail versions can be tested.


                                IV.     RANGE MODELS

         Five caliber long, 20mm diameter, models of these configurations
    have been fired in the BRL Aerodynamic Range at transonic and supersonic
    velocities.   These models are solid aluminum and have their centers of
    gravity approximately 60% of the length from the nose.   All of the
    pitching and Magnus moment data have been transferred to the 60%
    location.   The models were launched from two rifled barrels having
    twists of one revolution in 15.2 calibers and 1 revolation in 19
    calibers.




    2.   Andcre S. PZatou, Raymond Colburn, and John S. Pedgooy, "The
         Design and Dy,xonic Balancing of Spinning Models an, a , tn
         Technique for Obtaining Magnus Data in Wind TunnelL.," B.,.mo
         randun, Report No. 2019., U.S. Azwi Ball1istic Research Laloratories,
         Aberdeen Proving Ground, Maryl•atd, October 1969.   AD 69L)B03.


                                            91
                         rlow-
                         V. RESULTS AND ANALYSIS
       The results presented in this paper compliment,    add to, and modify
the results presented in reference 3 and prenent the main aerodynamic
rcsults presently available on the new boattails.     The results are
I.kased on tl,e experimental free flight range and wind tuiriel data
tobtained on the S caliber long models.    Some data have heun obtained on
the 6 and 7 caliber wind tunnel models, but these data are not suffi-
cient to give a complete picture.     The range flights yield the free
flight drag, pitch data, Magnus, roll damping, and pitch damping
moments at low angles of attack.     The wind tunnel tests yield angle of
attack drag*, detailed pitch data, Magnus force and moment over a range
uf spin and range of angle of attack (-10* to +150).     The data in the
main report are presented mainly as faired curves for clarity; however,
the detailed data are presented in the appendix of this report for the
interested reader.

       All of t 1
                he supersonic wind tunnel data have been obtained using a
boundary laye. :ansition strip 1 caliber aft of the nose tip. The
transonic test,- lid not use a trip, but depended on tuvnei turbulence
or high Reynolds number to trip the boundary layer.      Shadowgraphs taken
during all of the wind tunnel tests show the boundary layer to be
turbulent at Ieast from the base of the nose.     Thie 20mm range models
depended on firing conditions to trip the boundary layer so that all of
the data presented here are for a turbulent boundary layer over the
configuration.     Previous tests on smooth wind tunnel bodies without a
transition strip have shown that the boundary layer transition can move
with spin.    This, in some cases, results in nonlinear variations in the
,'1agnus characteristics with spin.

        The zero angle of attack drag coefficient,   CD
                                                    , for the variouE
                                                  0
beattails are compared in Figure 7.  The triangular boattail has the
lowest drag while the square boattail has a drag neai the conical boat-
tail.  The cruciform boattail has the highest drag of all the configura-
tions at supersonic speeds which is apparently due to low base pressures.
The high drag rules out the use of che cruciform tail for long range
projectiles; however, its low drag at high subsonic speeds and its
relatively high stability, as explained later, at all Miach numbtrs may
make it useful for other purposes.
3.    Anders S. Platou, "Ay? Imptroved Projectzl.e Boattail," BRL Memorvidum
      Report No. 2395, U.S. Axrwn Baclistic Research Laboratol-ics, Aberdeen
      Proving Ground, Nanjland, JuZy 19;4. AD 78d20O.     Also, AIAA Farcr
      No. 74-779, AIAA Mechanics and Control of Flight Co•,ference, Anaheim,
      CaZifornia, 5-9 August 1974.
*    Some wind tunnel drag data are available, but breakage of drag
     br.lances due to model spin resonance with the drag link has caused
     Fivere problems in obtaining drag data with the model spinning.

                                     10
F
pr




          The lower drag of the triangular boattail at supersonic speeds is
     probably due mainly to the smaller base area.   lowever, recent super-
     sonic wind tunnel tests have shown that the triangular boattai I has a
     higher base pressure than the conical boattail, thereby indicating
     lower viscous losses in the boattail flow.

          The geometric asymmetry of the triangular hoattail may also
     decrease the drag at low angles of attack.   At zero spin the asynumetry
     produces an asymmetric drag polar (Figure 8), so that drag values at
     constant angle of attack with spin will be the average drag betwect,
     plus and minus angles of attack.   It appears that this will decreane
     CDL) at least at low angles of attack; however, this thought has vat

     been thoroughly investigated due to strain gage balance difficulties.

          "The first transonic wind tunnel tests at Ames and NSPI)C and a few
     free flight tests at transonic velocities showed that the drag of the
     added lifting surface version QFigure 3) is considerably higher than
     that of versions 1 or 2 (Figure 2).   This plus the minimal increase ;n
     stability have curtailed further testing of version 3 to a later date.

          The wind tunnel tests have shown some variation of drag ,ith spin
     on the new boattails (Figure 9).  The straight boattails have minimum
     drag at zero spin while the twisted boattails have minimum drag at the
     twist rate. Again, the available data to confirm these results are
     limited due to mechanical failure of the drag oalance.

          The gyroscopic stability of a projectile is directly proportional
     to the spin squared and inversely proportional to the aerodynamic
     pitching moment.*   Since stable flight of a projectile requires that
     the gyroscopic stability remain above 1, it behooves the designer to
     select a projectile shape having the best pitching moment.   Conical
     boattails reduce the normal force (Figure 10) and increase the unstable
     pitching moment, especially at transonic velocities (Figure 11).    Hlow-
     ever, as seen in Figures 10, 11, and 12, the new boattails not only
     reduce the unstable pitching moments at all Mach numbers below that of
     the conical boattail, but at all supersonic Mach numbers of interest
     reduce the pitching moment over that of the cylindrical tail.    For the
     first time in artillery projectile design we can employ a boattail
     which not only decreases drag, but also increases the stability if the
     projectile.   This could aid projectile design, for, in most instaiioes,
     the projectile design is governed by the maximum unstable pitching
     moment attained at any Mach number within the projectile flight
     envelope.



     *   All presented pitching moments are about a C.6.   locatcd   W0% of the
         body length aft of the nose.

                                          11
     Some interest has been shown in comparing these boattails to a
conical boattail with fins or strakes.   However, a direct comparison
is impossible with r .evious data since the finned boattails have been
tried on other projectile shapes. To obtain a direct ýimparison a I
caliber long, 70 conical boattail with 4 in-caliber fins was tested on
the 2¼" wind tunnel model at supersonic speeds.   The results (Figures
10 and 11) show that the finned conical boattail has about the same
normal force and pitching moment as the square boattails. The finned
boattail drag will be greater than the bare conical boattail due to the
additional fin drag.

     One of the aerodynamic problems of the new boattails is the high
roll damping inherent in the straight configurations.  Roll damping
moment coefficients up to -. were measured during the range flights
                            1
and this is sufficient to despin a typical projectile to instability
during flight. To circanvent this, it is necessary to twist or cant
the boattails so that spin will be maintained during the flight.
Range firings of these boattails with 0 and 1/15 (rev/cal) twists
yield the following rolling moments.


                                                C_        C


         Square Boattail                      -. 055     +.037
         Triangular Boattail                   -. 098    +.084
         Cruciform Boattail                   -.073      +.063
         Conical or Cylindrical Boattail       -. 015      0


     Even though it is not possible to theoretically predict the Magnus
force on a projectile, it is possible by studying shadowgraphs and
analyzing the force and moment test results to visualize the mechanisms
producing the Magnus force. The picture which is visualized is that of
an aerodynamic body composeC of the actual projectile body surrounded
by a warpable, viscous, aerodynamic body made up of the boundaxy layer.

      At all Mach numbers the Magnus force is generated to a large extent
by the shape of the boundary layer, and the shape in turn is influenced
greatly by the viscous twist or warpage due to the projectile spin
 (reference 4).  At zero angle of attack the warpage of the boundary
layer due to ".in is axisymmetric about the main centerline, so that
the resultin aerodynamic forces and moments are zero except for drag
and rolling moment.   At small angles of attack, the boundary layer
thickens on the lee side of the body, but at zero spin the boundary
layer maintains mirror symme ' y. A normal force and pitching moment
are generated, but the side forces and moments remain zero.   With spin


                                    12
the thickened portion of the boundary layer twists in the direction of
spin, all symmetry is destroyed, and a side force and moment are
generated.

      If a conical boattail is used in place of the cylindrical tail, at
subsonic or transonic velocities, the boundary layer thickens due to
the flow expansion over the boattail. The thicker boundary layer is
distorted more by spin and a larger Magnus force is created (Figure 13
and reference 5).   At supersonic speeds the Prandtl-Meyer expansion
over the conical boattail holds the boundary layer to thinner values
so that large increases in Magnus force do not occur, The large
increase in Magnus force and moment caused by the conical boattail at
transonic velocities may be sufficient to destabilize an alreedy
marginally (gyroscopic) stable projectile (reference () by causing
 large changes in dynamic stability.

      Wind tunnel and range tests on the new boattzi is indicate that nj
large Magnus forces and moments are generated at any of the tested Mach
numbers (Figure 13).   The wind tunnel tests at M > I show the Magnus
forces and moments to be linear over the spin range tested (Figure 14)
and approximately linear over an angle of attack rang.e of at least ± 3O
 (Figure 15)*.  When nonlinearities do occur they appear to be in the
direction of decreasing Magnus force and moment.




4.    J. C. Martin, "On Magnus     Effects Caused by Boundary Layer Displace-
      ment Thickness on Bodies     of Revolution at Small An,!<`es of Attack,"
      BRL Repor-' ,1*. 870, U.S.   Army Ballistic Research Laboratories,
      Aberdeen Proving Ground,     Maryland, June 1955. AL' 72055.

5.    George I. T. Nielsen and Anders S. Platou, t:"ffect 2 Boattail
      Configuration on the Magnus Characteristicsof a Pat ,.ectile Shane
      at Subsonic and Transonic Mach Numbers," BEL Report,o. 2720, U.S.
      Army Ballistic Research Laboratories, Aberdeen Proving Ground,
      Maryland, June 1974. AD 921823L.
6.     C. H. Murphy, "Free Flight Motion of Synmetric Mlissi ess,     4
                                                                    B" L
                                                                     1

       Report No. 1216, U.S. Army Ballistic Research Labort,:;ortes,
       Aberdeen Prov,,ng Ground, Maryland, July 1963. AD ;2?57.
*    Additional subsonic and transonic wind tunnel tests must be run to
     verify this at the lower speed ranges. The subsonic and transonic
     wind tunnel tests run to date have given sketchy Magnus results due
     to the high sensitivity of Magnus characteristics to tunnel
     turbulence and flow inclination.


                                         13
     The side force generated on the twisted boattails modifies the
above boundary layer picture appreciably and results in smaller Magnus
forces.* At small angles of attack and zero spin the boundary layer
is distorted by the twist in the opposite direction from the intended
spin. For a right hand twist the thick or lee side of the boundary
layer twists to the left and creates a side iorce to the right. When
the body spins in the direction intended or caused by the twist a
Mtagnus force is          generated to the left (Figure 14).        This was also
noticed by M. Sylvester in reference 7.  As the spin increases, the
combined side force changes sign so that at typical projectile spin
rates the side force is less than on a straight boattail configuration.
From Figure 14 it can be seen that foi a given a the side force and
moment for a twisted boattail can be expressed as:




                                    C    C   +C           pd
                                     n    no   N          V
                                    Cn    Cn     + CM     pd
                                                          V
                                               0    p


where C           and C     are the zero spin offsets at each angle of attack and
             o        n

CN       and Cm
             are the Magnus slopes at each angle of attack.  These have
     p
           p
been determined from wind tunnel tests (Figure 16) at supersonic
speeds.   It c-n also be seen that CN   and Cm   are spin dependent
                                                     PQ        pa
(Figure 17) for the twisted configurations and must be evaluated for




7.       Maurice A. Sylvester, "Wind Tunnel Magnus Tests of Cylindrical and
         Boattail Arry-Navy Spinner Projectiles with Smooth Surface c•' 20m
         Equivalent Engraving (Rifling Grooves)," BRL Report No. 1758, U.S.
         Army Ballistic Research Laboratories, Aberdeen Proving Ground,
         Marylane, February 1975. AD B002628L.

*    Figure 16 of reference 3 is         in    error.     At the time these data were
     taken, the offsets, a and b, mentioned in this paragraph were not
     measured.


                                                14
all spin rates (pd/V) encountered during flight. References 8 and 9
present Magnus data on finned boattail configurations. Even though
these data show fins reduce the Magnus properties, they do not indicate
the zero spin offset shown by the BRL datd.

     Aerodynamic pitch damping measurements have been limited to range
data and indicate that the aerodynamic damping is independent of the
configuration (Figure 18). This is surprising for the lifting surfaces
on the new boattails should increase the pitch damping. No pitch
damping data are available on a corresponding finned boattail configura-
tinn; however, unpublished data on the Navy 5 inch/54 projectile with
and without boattail fins show the same degree of damping.    Possibly
the longer 6 or 7 caliber configu'eations will show a difference in the
damping coefficient when they are tested.


                            Vl.   CONCLUSTONS

     The aerodynamic data obtained show that all of the new boattails
change the aerodynamic characteristics of a projectile considerably.

     (1) The new boattails improve the pitching moment of projectiles
over that of the conical boattail.

     (2) The square boattail has about the. same drag reduction as the
conical boattail.

     (3) The cruciform boattail drag is too high and eliminates it as
a viable configuration.

     (4) The twisted triangular boattail has the best aerodynamic
properties for projectiles.  It has the lowest drag, good pitching
moments, and low Magnus moments for good stability.




8.   Leroy M. Jenke, "Experimental Magnus Chcrracteristicsof Ballistic
     Projectiles With and Without Anti-Magnus Vanes at Mach Numbers 1.5
     Through 2.5," AEDC-TR-73-162; AFATL-TR-73-188; von Karman Gas
     Dynamics Facility, Arnold Engineering Development Center, Air Force
     Systems Command, Arnold Air Force Station, Tennessee, December 1973.

9.   Leroy M. Jenke and Jack B. Carman, "Experimental Magnus Character-
     istics of Ballistic Projectiles With Anti-Magnus Vanes at Mach
      Numbers 0.7 Through 2.5," AEDC-TR-73-126; AFATL-TR-73-150;
     Propulsion Wind Tunnel Facility, Arnold Engineering Development
     Center, Air Force Systems Convand, Arnold Air Force Station,
     Tenneasee, December 1973.

                                    15
                               REFERENCES
1.   Anders S. Platou, "Magnus Characteristics of Finned and Nonfinned
     Proje,ýtiles," AXAA Jouznai, Vol. 3, No. 1, January 1965, pp. 83-90.

2.   Anders S. Platou, Raymond Colburn, and John S. Pedgonay, "The
     Design and Dynamic Balancing of Spinning Models and a Testing
     T echitique
                 for Obtaining Magnus Data in Wind Tunnels," BRL Memo-
     randum Report No. 2019, U.S. Army Ballistic Research Laboratories,
     Aberdeen Proving Ground, Maryland, October 1969. AD 699803.
3.   Anders S. Platou, "An Improved Projectile Boattail," BRL Memorandum
     Report No. 2395, U.S. Army Ballistic Research Laboratories,
     Aterdeen Proving Ground, Maryland, July 1974. AD 785520. Also,         A
     AIAA Paper No. 74-779, AIAA Mechanics and Control of Flight
     Conference, Anaheim, Califo..nia, S-9 August 1974.

4.   J. C. Martin, "On Magnus Effects Caused by Boundary Layer Displace-
     ment Thickness on Bodies of Revolution at Small Angles of Attack,"
     BRL Report No. 870, U.S. -'my Ballistic Research Laboratories,
     Aberdeen Proving Ground, ký:ryland, June 1955. AD 72055.

5.   George I. T. Nielsen and Anders S. Platou, "Effect of Boattail
     Configuration on the Magnus Characteristics of a Projectile Shape
     at Subsonic and Transonic Mach Numbers," BRL Report No. 1720, U.S.
     Army Ballistic Research Laboratories, Aberdeen Proving Ground,
     Maryland, June 1974. AD 921823L.

6.   C. H. Murphy, "Free Flight Motion of Symmetric Missiles," BRL
     Report No. 1216, U.S. Army Ballistic Research Laboratories,
     Aberdeen Proving Ground, Maryland, July 1963. AD 442757.

7.   Maurice A. Sylvester, "Wind Tunnel Magnus Tests of Cylindrical and
     Boattai1 Army-Navy Spinner Projectiles with Smooth Surface and 20mm
     Equivalent Engraving (Riflino Grooves)," BRL Report No. 1758, U.S.
     Army Ballistic Research Laboratories, Aberdeen Proving Ground,
     Maryland, February 1975. AD B002628L.

8.   Leroy M. Jenke, "Experimental Magnus Characteristics of Ballistic
     Projectiles With and Without Anti-Magnus Vanes at Mach Numbers 1.5
     Through 2.5," AEDC-TR-73-162; AFATL-TR-73-188; von Kalman Gas
     Dynamics Facility, Arnold Engineering Development Center, Air Force
     Systems Command, Arnold Air Force Station, Tennessee, December 1973.

9.   Leroy M. Jenke and Jack B. Caiman, "Experimental Magnus Character-
     istics of Ballistic Projectiles With Anti-Magnus Vanes at Mach
     Numbers 0.7 Through 2.5," AEDC-TR-73-126; AFATL-TR-73-lS0;
     Propulsion Wind Tunnel Facility, Arnold Engineering Development
     Center, Air Force Systems Command, Arnold Air Force Station,
     Tennessee, December 1973.
                                   16
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                                       APPENDIX A

          Aerodynamic Data on the Improved P'roJectile Boattails



Aero Range Data - 20mm Models ......                       ..................                        . 37-39

Wind Tunnel Data

   Zero Boattail ..............                .....................                                   40-48

   7* Conical Boattail ................                          ...................                   49-69

   70 Square Boattail Straight.            .   .    ..............                                     70-96
   70 Square Boattail Capted .......                          ..................               ... 97-113

   70 Square Boattail w/1-ins Straight . ..............                                     .....     114-121
   70   Square Boattail w/Fins Canted .....                              ................             i22-127

   70 Triangular Boattail Straight .....                             ...............                .. 128-133

   7* Triangu'ar Boattail Canted ......                              ................           .. 134-142
   70   Cruciform Boattail Straight ........................                                          143-148
   70 Cruciform Boattail Canted ......                               ................           .. 149-156




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                                                                S CAL.   A-N SPINNER ROCKET. WUURRE 1ORTTAIL CANTED
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                          5 CAL. A-N SPINNER ROCK~ET, $tQUAE 50TiTAi.. CANTED
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                                ZERO SPIN SIDE FORCE AND YAWINI                     MOMEWT NOT OBTAINED.



    ,5-: 5.30    RUN=           16,
                                                                         103
                                                     U,5,     14RMY BRLL13T|C RE'#L4R~rd LASORqTOR•EG                                                    .

                                                                   WIND TUNNEIS, BRANCHi. E5L                                                            I
                                                           NSRDC 7XIC FT. TRN5NIC WIND TUNNEL -
                                             5 C.RL.       A-N SPINNER ROCKET.    QUARRE 8ORTTAIL. CANtLD




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gCNFIG= 5.30       RUN=                15.                                             104
.i                                                   U.5. ARMY BAOLL                       TICTRtgtAnCO LIR•PATaRIC5
                                                                           WINO TUNNEI S BRANCH,                                     ESL

                                                         NSROC ?XlO cT, rRFRNaNI.                                               WIND TUJNNEL
                                       6 CAL. A-N
                                              A                    PINNER ROCKIET. 5QUARE BVATTAIL,                                                     CANTED
                                     MACH O9%'                          PD/V O.3E.          If.ORIAI                                                                X    10 $
                        0.15-0


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                                                                           AING' F Of A;TTACK. DEG.

                                     ZERO SWIN SIDE FORCE AN8YAW14 MOMENT NOT OBTAINED.


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                                    5.CAL.     A-N SPINNER ROCKET, SQURRE BOATTAIL.          CANTED
                                  MACH 2.,0                        PD/V 0.31         R(DIR3 0.94 X 105
                  0.15




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                           MACH 4.00                      R(OIR) 0.99 X 10.




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                                                   NCFRMPL FORCE COEV.

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                                       ANGLE OF ATTACK, DEG.
                                                      4




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                                             112
                                                 U.S.
                                                   RMY B5qLLISTIL R, ESEARCH LRAORRTOR!IES
                                                       WIND TUNNELS BRRNCH. EOL
                                        5 CRL'. A-N SPINNER.-RCIKET. 5oURRE    R'oTRIL. CRNTED
                                      MACH 4.00                     Po/V 0.26                RfD1R) 0.99 X 10o


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                                                     -6               -        3             9        12         le   .i


                                                                qNGLF OF ATTACK, DEG.
                                  THESE DATA MU.ST BE ;0MINED WITH ZERO SPIN SIDE FORCE AND



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                                     5 CRL.       R-N SPINNER ROCKET. 5JURRE BOATTRIL W/FINS,                           STRRIGHT
                                                 MACH 0.50             ROLL ZERO DEG.                 R(DIR)   1.00 X la



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                                                                                       -,NORMAL   FORCE COEF.

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                                               U.S. ARMY BALLIS1C RESEARCH LABORATORIEb.
                                                        WINO TUNNEL. BRANCH. EBL
                                                   AMES 12 FT. 5UB5ON]C WINO TUNNEL
                                5 CAL.       A-N SPINNER ROCKET,         SOUARE BOAT-TAIL-W-FINS-STRAIGHT
                                  MACH 0.50                                             RE PER FT.   ?,834 X 10
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                                                                         116
]INFJI'     5 40         RUN"     43.
                                                                          -         -,-~--I-*I.,                            •




                                                   U.S. ARMY BRLL15TIC RESEARCH LRAORRTORIEI
                                                            NiND TUNNELS BRRNCH, EBL
                                                                                                                            ]
                                                       RAES 1e FT. SUBSONIC WINO TUNNEL
                                    5 CAL.       A-N SPINNER ROCKET, SQUARE BORTTAIL W/FINS.                    5TRAIGHT
                                            MACH 0.50              ROLL 45 OEG.                RtGIR)   1.00 X 106
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         U.'     .




CONFIG= 5.40          RUN=            46,                                117
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                                                  5
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                                  1.2-
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                                                             0.70       ROLL         1RRO DEC.          RSDIAI
                                                                                                                          STRAIGHT
                                                                                                                 0.57 X 10•

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                                                                       RNLFFRTCO8
      CONFIG- 5.40                RUN=       42.                                 119       3
                                              U.S.     'RMY OALLIVTIC REULRCN LABORATORIES
                                                           WIND TUNNEL5 OSRNWN. E8L
                                                      RAES 12 FT. SUS5ONIC WIND TUNNEL
                                5 CAL.       R-N SPINNER ROCKET.            SOUARE SOATTAIL W/FINS. bTRRIGHT
                                        MAlCH 0.70               ROLL 45 DEC.             otOiR)   0.57 x 10

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                                                                            SMRMRL       FORCE COEF.
             -0.8




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                           -12          -9      .-6        -3       0         3                        12        is   )s15
                                                                ANGLE OF ATTACK.          DEC.




ONF[G= 5.40        RUN=           45.
                                          U.-5,       AR"V BLLISTIL RE5LRRCH LABORRTOR!UI
                                                         WINC TUNNLLS BRANCH. EDL
                                                  RAES 12 FT.       WUDSONIC WIND TUNNEL
                           5 CAL.       A-4 SPINNER ROCKET.             SQUARE SOATTAIL W/fINS,    STRAIGHT
                                    RACH 0.90             ROLL ZERO ODE.           RIOJA) O.U9 x    D0

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     5,40        RUN=        41.           S•CONF]G=
                                                                12..
                                            4.]




                                                  Ui. ARMY BRLLIOT|E RZýEARCH LRBO5RTORIL
                                                    WIND TUNNEL6 BRRNCH, EOL
                                               RMES 12 FT. SUBSONIC WiNn TUNNEL.
                                 5 CRL. R-N SPINNER ROCKET. 5UURRE BORCTRIL W/FINS. eTRRIGHT
                                       MACH 0.89      ROLL 45 DEG.    Rt0o1l 0.48 X 10 6




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                                                                        x     NORMRL FORCE COEF.
                   -0.8

                          14




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                               -12          -9      -6     -3       0          3     6          9   12   15   18

                                                                RNGLE OF RTTRCK.         DEG.




CONFIG:   6.40        RUN=            44.                               122
                            UJ.S3   R.RMY BlvlLlJICt.
                                         WIND 1JNNC..'
                                                         PE5rE';!Ci
                                                             B~RPNCI.
                               NSRDC 7X.10 FT.. TRPNSJNIC W4IND TUNNV
                                                                        tLDCR'O
                                                                         EBL                *
                                                                                            4!
                    5 CAL. P-N 3PJNNER ROCKET, `)UPRE BP'RTTRIL. W/FtN'4          CrnNTED
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                                       5 CRL A-N SPINNER ROCKET. W0URRE BORTTAIL. ;4/FINS. CRNTED
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                                                  ARMY BRLLISTIC RErLARCH LRBORRTORIES
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          •t--,             :                                                       ~       128                                                 :;
                                            U-15. ARMY O'LLISTIL RiEJLq~e            LASRAiTMZL.
                                                    WIND TUNNE!S OR
                                                               r-        E51.V
                                  5 CAL. R.N 5SPINNER. P.5.K  T RINrULAR SORTTAIL. S3TRA!GHT
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                                             WIND TUNNELS BRRNCH,   EBL
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                                             U.S   RRMY 8BLLISTIC RE5ERRCH LRBORATORIES
                                               WIND TUNNEL.$ BRANCH. FBL
                              5 CAL- A-N SPINNER ROCKET, TRIRNGO3LAR BOATTAIL. 5TRRIGHT
                               [MAC 2.50          P0/V 0.27           R(DIAI 0.94 X 106
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                                                          134
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V                                  ~~5 CIRL. A-N SPINNER ROCKET'.     ftIAN(AULAR OWMI. .A'4TLTJ




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                           YAWING METONXTPAGE TO OBTAN 'Ct AND 1*M


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                                                           136
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                                                    WIND TUNNEL.5 BRANCH, E9L
                                    5 CRL. q-N 3PINNER ROCKET. TR!RNSULRI BORTTRIL. CRNTED
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                           :.-0.8
                                -3138
                                           U4.S. ARMY BALLI15T1I. RESERRCH LR5RERRTOi•.F
                                                     WIND TUNNEL.S BRANCH. ESL
                                    5 CAL- R-N SPINNER ROCKET. TRIANGULAR BOATTAIL. CNtVED
                                    MRCH 2.50           PD/V 0.28            R(DIR) 0.9f X 10




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                                                                  ANGLE LF FiTTACK,             DE.G.

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                                     YAWING MOMENT Oi NEXT PAGE TO OBTAIN CN AND Cm


tONFIG= 5.70           RUN=          2.

                                                                                 139
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rLINFI(z 5.70    RUN=         3.'

                                                                  141
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                                    MACH #.D00         PD/V 0.18           RlDIA) 1.00 X 10t




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                                                                    142



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                         143
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                                                                       144~;
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                                         5 CARL. R-N SPINNER ROCKET, CRUCIFORM BORTTRIL, STRAIGHT
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    to                                                             144
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                                                                  U.5, qRRv BRLL15TIC RESERRCH LASORART•!RLZ
                                                                           WIND TUNNELS BRANCH, EBL
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                tLINFIG"         5.90           RUN=      14.                             147




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                                                            153
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                                                     U.S. RRMY BRLLISTTC RESLRRCH LRI30RRTORIES
                                                              NINO TUNNELS BRFINCH. EBL
                                            5 CAL. A-N SPINNER ROCKET. CRUCIFORM BOATTRILo CANTE:D
                                           MACH 2.50          P0/V0O,•.          POIA) 0.94J X la
                        0.15                                             1


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     tONFIGz 5.,J0             RUN=        5.
                                                                         154




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                                  6 CARL,         -N SPINNER ROCKET,          CRUCIFORM BOATTAIL.            CRNTED
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                   -0.05 -
                    0

                  0--

                   S-0°10-
          co




                                            •                       x    CNP
                   -0.20


                           6           -'
                                                                        -do
          7                                                     I




                                                  -       3 -12 6
                                                            0 3                                U9   2 !
                                                                                                    II   I      I   I




                                                            ANGLE O•F ATTACK.       DEG.

                                 ZERO SPIN SIDE FORCE AND YAWING MOMENT NOT OBTAINED.



"tONFIG: 5,90             RUN=    6.

                                                                    S,7
                                                                     LIST OF SYMBOLS


     CDD       CD                        i
                                                  DragA
                                                    a2
                                                 p V2 S     positive direction is aft


     C                                   zero angle of attack drag coefficient

              D~t
     C 2drag 00                                      coefficient slope due to angle of attack
                a                            (from C         CD       + CD   a2



     C£                                  roll damping.moment coefficient--negative moment tends to
           p                             decrease :;pin

     C                                   roll moment coefficient due to fin cant--positive moment
V.                                       tends to increase spin
               CmPitchingl                                Moment
                                         Pc     M                       moment center is    .6 k calibers from nose.
      m                                   1   2
                                          -FpV Sd
                                         Positive moment is due to positive normal force ahead of the
                                         moment center.
                                         SdC
      m                                      dj      at a = 0O per radian


                                         Magnus Moment moment center is .6 Z calibers from nose.
         m                                   1       2       p
                    p-pV
                                             Positive moment is due to positive Magnus force ahead of
                                             moment center.

                                             d C
     CmdP                                       m        at a =0° per radian
           Pa


     Cq         +    C                       Damping Moment
           q          m                      1       2           t
                                             2                   V

               CNNormal                                  Force
         N                                       1
                                                 1       2           positive direction is up

      CN                                     d CN                0
           N                                 da      at a =00 per radian
                                                                   159


                                                                                           Preceding page blank


                .         ............
                                           LIST OF SYMBOLS (Continued)
i~i   C~p               Mag[nus Force
      CN                     VF            positive direction is to right looking upstream
           p            1        2s~
                            PV
                  CNN   d CN
           pC N-                  at a     O* per radian
                                            PI

      C                 Magnus or side moment at zero spin
       no
      Cyo               Magnus or side force at zero spin
              0

      d                 body diameter and reference length

      I                 axial moment of inertia

      I                 transverse moment of inertia
          y
      k           ~     axial radius of gyration

      ky                transverse radius of gyration

      Mcp               Magnus force center of pressure

      N                 normal force center of pressure
          CP
      p                 body axial spin rate. rad/sec (positive is clockwise looking
                          upstream)

      q•                complex transverse angular velocity

      Rd                Reynolds number based on 4
                                      d2
      S                 body area      -

                                                       2 (CL   + kx -2 Cm)
                                                                         MPQ
      S                 dynamic stability = C.                      (m       .
                                                   L    16
                                                       -D      ky

                                                        160
                           LIST OF SYMBOLS (Continued)   I
S        gyroscopic stability        (   d3              '


V        freO   stream velocity


         angle of attack

6        cant angle of fin or twisted surface

p        free stream air density

 r• z     V•    k    " 1   V2
                            Moment                       A
SIRoll
          V•P    p    -    V.p d
                             S




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