Prediction of fighter aircraft dynamic derivatives using Digital

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Prediction of fighter aircraft dynamic derivatives using Digital Powered By Docstoc
					AI AA-85-4070
Prediction of Fighter Aircraft Dynamic
Derivatives Using Digital Datcom
W.,B. Blake, US. Air Force Wright
Aer'onaut ical Labs.,
Wright-Patterson AFB, OH

                    AlAA 3rd Applied
                Aerodynamics Conference
                          October 14-16, 1985
                       Colorado Springs, Colorado
 For permission to copy or republish. contact the American Instituteof Aeronautics and h t m u t i c s
                                1633Broadway, NewVwk, NV 10019
                                                          William B Blake
                                           U.S. Air Force Wright Aeronautical Laboratories
                                                  Wright-Patterson AFB, Dayton.Ohio

                                    Abstract                                              Introduccion
            Digital Datcom is evaluated a s a design tool                    Modern fighter aircraft designs are evolving
       for predicting the dynamic derivatives of fighter               away from naturally stable airframes towards
       aircraft. Comparisons are made with wind tunnel                 sophisticated flight control systems a s a means
       data, flight test results. and strip theory                     of achieving satisfactory flying qualities. This
       predictions for four modern fighter config-                     now results in tradeoffs between aircraft perfor-
       urations. Accuracy criteria taken fro= prior                    mance and flight-control-system complexity; in the
       studies are used to judge the Digital Datcom                    past tradeoffs were between performance and bare
       predictions. All comparisons except yaw damping                 airframe stability. This trend generally results
       are found to be within the accuracy criteria.                   in increased cmtrol-power requirements, and a
                                                                       need for more precise knowledge of the control
                                 Nomenclature                          derivatives in preliminary design. The advent of
                                                                       highly-augmented flight control systems has
       A        Aspect ratio, b Z / S                                  decreased the accuracy with which the dynamic
       b        Span, ft                                               derivatives must be known in preliminary design,
       c        Mean aerodynamic chord, ft                             but knowledge of these parameters remnins an
       CL       Rotary derivative, a C L / e , Ilrad                   integra! and important part of the flipht-control-
            q                                                          system design. Significant errors in the estima-
       CL6      Acceleration derivative,       acLla-6c
                                                     2v    llrad       tion of the dynamic derivatives can result in
                                                                       performance degradations, due to flight-control-
       Cm Rotary derivative, a C m / e , llrad                         system limitations, or require costly redesign of
          q                                                            the flight control system.
       .C   Acceleration derivative, aCm/+,    ]/rad
            a                                                               Currently available design tools for predict-
                Rotary derivative.     aca./a@,
                                                   llrad               ing the dynamic derivatives include handbook
       cQP                                                             methods, such as the USAF Datcom (Reference I ) ,
                Rotary derivative, a,%             llrad               and methods based on strip theory. Panel methods
                                                                       can predict dynamic derivatives, but the cost and
       cQr Acceleration derivative, ac la--,i b l/rad
       CE.                               a 2v                          time required by these methods makes them mare
         6                            b                                applicable co advanced design. A design tool
       cnP Rotary derivative, acP / a2v, llrad
                                      E                                which is currently in widespread use throughout
                                                                       industry is Digital Datcom (Reference 7 ) . It is a

       cn Rotary derivative, ar. la-rb Ilrad
                                     2V'  "          .                 computer program based on the handbook methods
                                                                       contained in the USAF Datcom.
       c    '   Acceleration derivative, a c n / g , llrad
           %                                                                Digital Patcom has been under continuous
       Cy       Rotary derivative, acyl$$          llrad               development for ten years, and there is an ongoing
            P                                                          effort to upgrade and improve the program where
       EI       Mach number                                            possible. AS a part of this effort, a eomprehen-
       p        Angular velocity in roll, radlsec                      sive investigation of Digital Dateom dynamic
       q        Angular velocitv i~ pitch, radlsec                     derivative methodology was recently conducted; the
       I        Angular velocity in yaw, radlsec                       results of this study are presented in this paper.
       S        Area, ft2
       V        Freestream velocity, ftlsec                                 Accuracy criteria for predicting aircraft
       X        Reference axis longitudinal coordinate                 dynamic derivatives, for aircraft with both
       2        Reference axis vertical coordinate                     highly-augmented and unaugmented flight control
                                                                       Systems, were taken from three prior studies.
       a        Angle of attack, deg                                   These criteria were used to judge Digital Datcom
       6        Rate of change of angle of attack, radlsec             FrEdictions for four fighter configurations, the
       B        Sideslip angle, deg                                    F-15, the F-Ill, a three-surface P-15, and the
       B        Mach number parameter,-                                AEDC standard dynamics model (P-16 type planform).
                                                                       With one exception, Digital Datcom predictions
       i(       Rate of change of sideslip angle, radlsec              were shown to be within these accuracy criteria.
       A        Taper ratio, tip ehordtroot chord                      This exception, subsonic yaw damping, is discussed
       A        Leading edge sweep angle, deg                          below. In addition, geometric restrictions on
                                                                       Digital Datcom modeling of fighter aircraft and
       Subscripts                                                      techniques f o r overcoming them are discussed in
       ac       Aerodynamic center
       le       Leading edge

       *    Stability and Control Engineer, Member AIAA
               This paper is declamd a work of the U.S.

                   Digital Datcom                             dynamic derivative predictions for the P-16 by
                                                              Vwttasits in Reference 3. Further detnils on the
     Digital Datcom is a computerized version of              program capabilities may he found i n Reference 2.
the USAF Stability and Control Datcom. The Datcom
is a compendium of methods for predicting static                   Datcorn methods for dynamic derivatives,
stability, high-lift and control, and dynamic                 taken primarily from References 4 and 5, assume
derivative characteristics of flight vehicles.                attached flow and hence are restri.cted to the low
For those speed regimes and configurations where              ang1.e of attack regime. Mach number corrections                  w
Datcom methods are available, Digital Datcom                  at subsonic speeds are taken from Reference 6.
output provides the longitudinal and lateral-                 In goneral, 1,ongitudinaldynamic derivative
directional force and moment coefficients, as well            methods are available for all speed regimes,
as axial force and normal force. Output for                   while the lateral-directional dynamic derivative
configurations with a wing and horizontal tail                methodology is restricted to the subsonic speed
also includes downwash and the dynamic pressure               regime. In the Mach range 0 6 c M c 1.4, Digital
ratio in the region of the tail. The pitch rate,              Datcom uses ( a s a default) the Datcom transonic
acceleration, roll rate, and yaw rate derivatives             methods. The user may change these limits,
are also available.                                           however, and use the subsonic methods up to Mach
                                                              0.99, and the supersonic methods down to Mach
     Derivatives are output in stability axes, and            1.01. A detailed summary of available output a s
are available in degree or radian measure, at the             a function of configuration and speed regime is
option of the user. Component aerodynamic contri-             presented in Table 1.
butions and configuration buildup data are avail-
able through the use of a “BUILD“ option. With                              Configuration Modeling
this option the user can isalate component aero-
dynamic contributions in a similar fashion to                      Digital Datcom input data are divided into
break-down data from a wind tunnel. Digital                   sets of related data, each being input via the
Datcom also contains an experimental data option              namelist iaput technique. Data sets contain such
whereby the user may substitute experimental or               parameters a s flight conditions, body geometry,
refined analytical data for the Datcom computed               wing and tail planform and section
values. This option w a s not exercised in this               characteristics. Wing geometries (Figure 1) may
study, but was shown to improve both static and               be either conventional or non-straight-tapered.

Table 1     Dynamic Stability Characteristic Output a$ a Function of Vehicle Configuration and                 Speed   Regime
Configuration           Speed Regime
                                         cL     ‘rn           ‘L~    ‘.
                                                                      m     c,       ‘n               ‘n
                                           9          9                          P        P       P
Body                   Subsonic          0      0             0      0
                       Transonic         0      0             0      0
                       Supersonic         0      0            0      0

wing                   Subsonic           0      0            0      0       0       0        0       0           0             b.
                       Transonic          J      J            J       J
                       Smersonic         0       J            0      0       0       0        0

Horizontal Tail        Subsonic
                                                              4      7       0

                       Supersonic        0       J            0      0       0

Vertical Tail-         Subsonic                                              0       0        0       0          0
Ventral Fin            Transonic
                              ~                           ~

Wing-Body              Subsonic          0                    0      0       0       0        0       0           0
                       Transonic          J      7            J      J
                       Supersonic        0       f            0      0      0        0        0

Wing-Body-             Subsonic           J      J            J      J      0        0        0       0          0
Horizontal Tail        Transonic          J      J            J      J
                       Supersonic         J      J            J      f      0        0        0

Wing-Body-             Subsonic          0                    0      0       0       0        0       0          0
Vertical Tail-         Transonic          J      7            J      J
Ventral-Pin            Supersonic        0       J            0      0

Wing-Body-             Subsonic           J      J            J      J      0        0        0       0          0
Aorizontal Tail-       Transonic          J      J            J      f
Vertical Tail-         Supersonic         J      J            J      f
Ventral Fin

o   output available
J   output only for configurations with straight-tapered wings

       Both aft and forward swept wings m y be input.           The equation governing this displacement are:
       Wing planforms may have incidence, dihedral, and
       a linear twist distribution. Both conventional           xlle=xle-(~7-1) ( 1 + 2 k ) tanAle / [ 6 ( lrh) ] + c / 4 !
       (wing-body-tail) and canard (canard-body-wing)
       configuratiovs may be evaluated using Digital            and
       Datcom. For canard configurations, the canard
       should be input as the "wing" and the wing a s the                             i-l)
                                                                ~ ' ~ ~ = z ~ ~ - ( f[b(l+ZA)/6(I+A)l
       "tail". There are three body methods available,
       each allowing an arbitrary longitudinal                  Three-Surface Configurations
       cross-sectional area distribution. Body
       cross-sections may be axisymetric or ellipticsl;               A   third limitation is that Digital Datcom
       bodies input a s elliptical will have a constant         can handle only two horizontal lifting surfaces
       ellipticity (height to width ratio) from nose to         simultaneously. Three-surface configurations
       tail. Cambered bodies may be evaluated by                (canard, wine, horizontal tail) cannot be
       specifying the upper and lower body heights at           evaluated in a single run. The Datcom methods
       each longitudinal body station. Inlets, extern81         for the rate (p,q,r) derivatives ignore
       stores, and other protuberances cannct be                interference between lifting surfaces, so a
       modeled.                                                 superposition of solutions is possible.
                                                                Three-surface configurations should be run by
                 Overcoming Datcom Limitations                  adding the canard increment to the wing-body-tail
                                                                increment, i.e. (Wing-Body-HorizontaI-vertic31-
       Cranked Wings                                            Canard) = (wing-Body-Horizonta1-vereical)   +
                                                                (Canard-Body) - (Body).  Tnere is no simple
            Uhen modeling fighter type configurations,          technique for obtaining the h derivatives for
       there m e several limitations in Digital Datcom          three-surface configurations.
       which must be addressed. As is evident from
       Table I , the Datcom methods are very limited in              Care should be exercised in running
       their application to configurations vith                 wing-body-canard configurations. Digital Datcom
       non-straight-tapered (cranked) wings. P!odern            ignores the horizontal tail contribution to the
       fighter configurations, however, are moving away
       from simple wing planforms rewards wing planforms
                                                                derivatives C , Cnp, Cer, and Cn             .
                                                                                                       Thus, the
                                                                               P                   r
       with large leading edge strakes (e.g. F-18) and          wing contribution would be ignored if the wing is
       blended wing-body configurations (e.%. F-16).. It        input as a "tail" (as in a canard configuration).
       is possible to obtain approximate results for            In order to get the effect of the wing included
       configurations having cranked wings, however, by         in these derivatives, an addition of solutions is
       using the experimental data option. An initial           required: (CTing-Bady-Canard-Vertical)  =
       run of the wing or wing-body combination using a         (1Jing-Body-Vertical) + (Canard-Body) - (Body).
       cranked wing should be made. A second run should
       then be made of the entire configuration,                Future Improvements
       approximating the wing a s straight-tapered. The
       output from the initial run should be input a s               Digital Datcom has been under continuous
.asi   experimental data in the second run, thus                development for ten years, and there is an
       simulating the effects of a cranked wing on the          ongoing effort to upgrade and improve the program
       configuration. The straight-tapered                      where possible. Planned improvements to the
       approximation will only he used to calculate the         program include:
       downwash at the horizontel tail. However, the
       effect of a srrake vortex on the horizontal tail              a ) Incorporation of methods for fuselage
       will not be accounted for.                               mounted twin vertical tails. These methods ace
                                                                currently under development, and should be ineor-
       Twin Vertical Tails                                      porated in 19R6.
            A second limitation in Digital Datmm is                  b) Addition of a downwash method for
       that there are no methods for twin vertical tails        cranked wings. This i s planned as an in-house
       mounted on the fuselage. There is a method for           effort, commencing in 1986.
       "H" tails, but it does not include the dynamic
       derivatives, and experience has shown that it                 c) Improved body methods, perhaps with the
       provides poor Static derivative predictions for          capability for handling inlets. These methods
       fuselage mounted tails. At the current time, the         may be taken from the Vissile Datcom computer
       recommended procedure for fuselage mounted tails         program.
       is to use an "equivalent" single vertical tail
       mounted on the body centerline. The total tail                                 Accuracy Criteria
       area, aspect ratio, taper ratio, and sweep should
       he held constant. For tails which are canted,                 Three studies (References 7-9) developed
       the projected side area should be used in lieu of        accuracy criteria requirements for predicting
       the total area (Datcom methods assume that the           aircraft dynamic derivatives. Thomas (Reference
       vertical tail area includes the portion covered          7) investigated the closed-loop responses of an
       by the body).  In addition, both the longitudinal        F-15 and a three-surface F-15 including the
       and vertical location of the quarter-chord of the        effects of systematic variations of the stability
       total mean aerodynamic chord should be held in           derivatives. Each aircraft was investigated at
       the same position. This requires a shift i n the         various levels of static instability. For small-
       position of the leading edge vertex ( s e e Figure       amplitude maneuvers, three-degree-of-freedom
       2).                                                      analyses were used to assess the impact of

parameter variation on the resultant flylng               derivatives consist of fairings between the
qualities. Six-degree-of-freedom analyses were            computed v a l u e s at Mach 0 . 6 sub?onirallv and Mach
performed on large-amplitude maneuvers, to                numbers 1.2 fq derivatives) and 1 4 ( (r.
investigate conditions where control surfaces             derivatives) supersonically. Comparisons with
were rate or position limited. It was found that          F-15 flight test data show very good correlation
with increasing control augmentation, the                             .
                                                          from Hach 0 6 to Vach 1 6   ..
importance of accurately predicting the dynamic
derivatives decreased, while the control
derivatives became more critical. The p
                                                          Longitudinal     -     Supersonic                          b w

derivatives, however, had an impact on the rudder              At Mach 1.3 (Figure 6 the transonic pre-
power available for coordinating roll maneuvers,          diction for the SDM is quire good, while t h e
so no specific criteria could be set for these            supersonic prediction is low. The Datcom methods
parameters.                                               for supersonic wing-body Cm is based on
     Runciman (Reference 8) and Stewart                   linearized potential flow theory, and consists of
(Referepce 9) investigated the open-loop response         a set of equations for wing with subsonic leading
of a transport (STOL) and fighter (F-18)                  edges, and a set of charts for w i n g s with
configuration respectively. They also found that          supersonic leading edges. The charts do not
the static and control derivatives were of                yield values if the parameter f A is less than 3,
primary importance. Due to the lack of control            so an extrapolation is required to obtain these
system augmentation, however, the criteria                values. Thus, at some Mach numbers, predictions
developed in these studies were more restrictive          for wings with supersonic leading edges may be
than those found in Reference 7 . The accuracy            poor. For Some configurations, a zone of
criteria determined from these studies are                inapplicability will exist between the Mach
summarized in Table 2.                                    number where the wing leading edge becomes sonic
                                                          and the Mach number where BA becomes 3. This
Table 2 Dynamic Derivative Accuracy Criteria              zone is given bv:

                   Predictive Accuracy Required                      sec   Ale      < M <      (1)
                                                                                              J3A'   + 1
Parameter          (open loop)    (closed loop)
                                                          Predictions should be obtained in this region by
                      25 %              50 %              making a smooth fairing between the transonic
                                                          prediction at Mach 1.4 and the supersonic pre-
                      25 %              50 %              diction at the Mach number where 6A becomes 3  .
                                                          Table 3 contajns the region where Datcom pre-
                      0 . llrad          -                dictions w j l l be questionable for several fighter
                      0.05lrad           -
     r                                                    Table 3 Range of Poor Supersonic Cm. Predictions
                      O.l/rad           0.2lrad
                      O.l/rad           0,2/rad                                                                      =w
  n r                                                     Aircraft         A,.          A            Mach Range

     Since these criteria were developed for
specific configurations, direct application to              F-18           26.7        3.13          1.12-1.39
other aircraft can be misleading. Configuration             F-104          27.3        2.07          1.13-1.76
geometry and mass properties will alter both the            P-16           40          2.59          1.31-1.53
numerical values of the derivatives and the                 F-15           45          2.44          1.41-1.58
resultant aircraft response to derivative                   F-105          45          2.89          1.41-1.44
changes. Nevertheless, in order to judge the                F-106          57          2.03            none
Datcom methods, the accuracy criteria were used
for all of the configurations in this study.                   The predictions become progressively worse
                                                          towards the lower end of the Mach range. As a
            Comparisons With Test Data                    result, any inaccuracies in the transonic pre-
                                                          diction should be minimized, since it is faired
Longitudinal   -   SubsoniclTransonic                                                        . . At this
                                                          into the supersonic value at Mach 1 4
                                                          Mach number, any extrapolation required from the
        Subsonic comparisons with the AEDC standard       Datcom charts is usuillly small.
dynamics model (SDM) are presented in Figure 3.
The Mach 0.6 prediction is very good; the                      Experience has shown that use of the
decrease in the predicted magnitude above 12              transonic methods is preferable to the supersonic
degrees alpha is due to a decrease in the                 methods in the Mach range 0.8 < M < 1.4.
predicted magnitude of the dovnwash gradient.
Figure 4 shows comparisons f o r the F-111 TACT           Lateral
(Transonic Aircraft Technology) configuration.
The data shown are for the wing in the 16 degree               Roll damping comparisons are shown in Figure
sweep position. Excellent agreement is obtained           7 and 8.  Digital Datcom does very well f o r the
throughout the angle of attack range. At Mach             F-15 configuration, and is slightly low for the
0 . 8 , both subsonic and transonic predictions for       F-111, but within the accuracy criterion at low
the SDM are s h o w in Figure 5, and both are very        angles of attack. These comparisons are taken
good. The Datcom methods for the transonic                from wind tunnel data which include the C .sinu
                                                                                                    '6               L~
      acceleration derivatiy. Digits1 Datcom 2 o e s not       2.   Longitudinal derivatives are predicted to
      currently predict the f derivatives, hut their           within the open loop (most restrictive) accuracy
      contributicns at low angles of attack are                criterla.
      negligible. For the basic F-15 and F-111,
      Digital Datcom C predictions are within the              3.   Subsonic yaw damping is predicted to within
                       P                                       the closed loop (least restrictive) accuracy
      accuracy criteria, as shown in figures 9 and 10.         criterion. The addition of the body-alone incre-
Ma'                                                            ment improves the predictions for the complete
      Directional                                              configuration, but a discrepancy is still
           As seen in Figures 11 and 12, Digital Datcom
      yaw damping predictions are consistently low by          4.   The roll rate derivatives and C,   are pre-
      about O.l/rad. This cannot be attributed to the                                               r
      limitation on twin vertical tails, since the             dicted to within the open loop (most restrictive)
      F-111, which has a single vertical tail, is also         accuracy criteria.
      underpredicted. F-111 configuration buildup data
      from Reference 1 show a significant wine-body            5.   Care must be exercised in modeling the
      contribution to yaw damping. Digital Datcom has          configuration, and in obtainins results at low
      no method for body-alone yaw damping (see Table          supersonic Mach numbers.
      l , so its contribution is set to zero. This,
      however, may be a poor assumption for
      fighter-type configurations. For axisymetric                                  References
      bodies at zero alpha, Cn is by definition equal
                                  r                            1.    Finck, R.D., "USAF Stability and Control
      to (c/b)zCm    .
                     For non-axisymmetric bodies, P is
                                                               Datcom," AFWAL-TR-83-3048, October 1960, Revised
                 9                                             1978.
      equivalent to (c/b)2Cm of the body rotated 90
                              9                                2.   Vukelich, S.R., and Williams, J.E., "The
      degrees about its longitudinal axis. This                USAF Stability and Control Digital Datcom,"
      technique (90 degree body rotation) was used to          AFFDL-TR-79-3032, April 1979.
      estimate the body C contribution for the F-15 and
                           r                                   3.   Mattasits, G.R., "An update of the Digital
      F-111; the results are included in Figures 11 and        Datcom Computer Code for Estimating Dynamic
      1 2 . These increments do not eliminate the              Stability Derivatives," AEDC-TR-81-30, August
      discrepancy, but they are in the right direction,        1982.
      and move the F-111 predictions closer to the open
      loop accuracy criterion boundary. C predictions,         4. Toll, T.A., and Queijo, M.J., "Approximate
                                                               Relations and Charts for Low Speed Stability
      shown in Figure 13, are low at higher angles of          Derivatives of Swept Wings," NACA TN 1581, May
      attack, but within the accuracy criteria.                1948.
4                   Comparisons with Strip Theory              5.   Campbell, J.P., and McKinney, M.O., "Summary
                                                               of Methods for Calculating Dynamic Lateral
           Reference 7 contains a dynamic derivative           Stability and Response and for Estimating Lateral
      prediction program, Dynamic, which is based on a         Stability Derivatives," NACA Report 1098, 1952.
      modified strip theory. Roll damping estimates
      made for a three-surface F-15 in Reference 7 are         6.   Fisher, L.R., "Approximate Corrections far
      compared to Digital Datcom predictions in Figure         the Effects of CompressibiIity on the Subsonic
      14. The Digital Datcom prediction is slightly            Stability Derivatives of Swept Wings," NACA TN
      low at moderate angles of attack, but within the         1854. 1949.
      accuracy criterion of O.l/rad.  The non-linearity
      in the Dynamic prediction is caused by interfer-         7.   Thomas, R.W., "Analysis of Aircraft
      ence between the wing and canard. Datcom methods         Stability and Control Design Methods," AFWAL-TR-
      ignore~liftingsurface interference for the               84-3038, May 1984.
      rotary derivatives, so this trend I s not
      predicted by Digital Datcom. Yaw damping                 8. Runciman, W.J., et al, "STOL Tactical Air-
      comparisons are shown in Figure 15. Dynamic              craft Investigation," AFFDL-TR-73-19, May 1973.
      predicts a small positive increment due to the
      canard (destabilizing), while Digital Datcom             9. Stewart, V.R., "STOL Vehicle Stability and
      predicts a small stabilizing increment. Due to           Control Methods - Interim Report," North American
      the lack of a Datcom body increment, however, the        Aircraft Operations Report NA-84-0017, September
      predictions disagree by about 0.7Jrad.                   1984.
                            Conclusions                        10. Hellmann, G . K . , "A Comparison of Estimated
                                                               and Wind Tunnel Measured Stability and Control
           The following conclusions are drawn:                Data," Symposium on Transonic Aircraft Technology
                                                               (TACT), AFFDL-TR-78-100, August 1978.
      1.   Digital Dateom is a useful and reliable tool
      for predicting fighter aircraft dynamic deriva-          11. Grafton, S.B., Croom, M.A., and Nguyen,
      tives.                                                   L.T., "High-Angle-of-Attack Stability
                                                               Characteristics of a Three-Surface Fighter
                                                               Configuration, NASA TM 84584, March 1983.

                                                                 -10   c            I
CONVENTIONAL                     CRANKED                         -12
(STRAIGHT-TAPERED)               (NON-STRAIGHT-TAPEREO)                -5           0         5             10         15          20
                                                                                                  a , deg
            FIGURE 1. WING PLANFORMS                          Figure 3      D i g i t a l Datcon vs SDN Iiind Tunnel Data,
                                                                            ?l=O. 5

                     Xie   x.c

    (a) TWIN VERTICAL TAIL (LEFT PANEL ONLY)                     40
                                                                       0            4         8             12          16         20
                                                              Figure 4       D i g i t a l i)atcon vs F-111 IJind Tunnel Data,
                                                                             ?*a.   h

                                                                                                                 SUBSONIC METHOD
                                                                                                                 TRANSONIC M€MO

               X'ie        Xac


                                                               Figure 5      D i g i t a l Datcam vs S'
                                                                                                      D!    IJind Tunnel Data,
                                                                             x=o. 2

                                                SOPERSONIC MmlOO

                                                TMNSDNIC MmOD

            -2    -
d <
       '5                                                                       M

       , 4-
                              8   0    0_-------                            c

            4-                                                                            -so      -

            -8                                                      I                     -.15             I                   I           I          I

              0                                                                             .
                                                                                            1      -

             -1                                                                             0



   0   -
       d     -2-                                                                    -c-
                                                                                           1       -                                   f
       +                                                                            0
                                                                                    +                                         Cnp ONLY

                                                                                    z?                                                                0
                    b                                               0           "
                                                                                           -2      -

             -4                                                     1
                                                                                           -3                                   I          I          I

                                                                                                                           DlwTAL OATCOM (Cnr ONLn
                                                                                            -1       -                 -_--OIGIIAL DATCOM +BODY Cnr

                  0 .
                                                                                    : -2             -

       -s- 2 -                                          z ONLY                       5
                                                                                    .= -9-

                                                                                                                           I o
       0                                                      Cfp                   13

                                                                                     ,L -.4<1                      0
              4       -                                                             u                                                                 0

                              0   0                                                         -5         -
                                      I     I            I              I                                      1       1           I           I          I
              -6                                                                            -6

                                                                                             I                                -
                                                                                                                                          OlGlTAL OATCOM

                                                                                                                                          STRIP THEORY

                                  !-            0

       0            4             8
                                               DIGITAL OATCOM (Cn, ONLY)

                                               OlGllRL OATCOM+BOOY Cnr

                                                12             16          20
                                                                                             0          4
                                                                                                         I            ,

                                       0.e                                                                                 a , der
 F i g u r e 12    D i g i t a l Datcom vs F-111 Wind T u n n e l Data,              F i g u r e 15   D i g i t a l Datcom vs S t i i p Theory P r e d i c t i o n s
                   FW.6                                                                               f o r a Tnree-Surface F-15, X=3.2

                     I             I              I             1           I
       0             4            8             12             16          20
                                         a.   e
F i g u r e 13    D i g i t a l Datcom vs F-15 Wind T u n n e l Data,
                  E!=O. 1

       I                                  -           OlGlTAL OATCOM

   "   0            4             8            12             16           20
 Fieure 1 4        D i g i t a l Datcoi. vs S t r i p Zieoly P r e d i c t i o n s
                   f a r a Three-Surface F-15, ?l=O.2