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
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
RREDICTION OF FIGHTFF PIRCFSTT PYb!PJIC WRIVATIVES USING DIGITAL DATCOM
William B Blake
U.S. Air Force Wright Aeronautical Laboratories
Wright-Patterson AFB, Dayton.Ohio
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
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 .
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
r Table 3 Range of Poor Supersonic Cm. Predictions
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
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
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,
(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,
QI) EOUNALENT SINGLE TAIL
NGURE 2. TWIN VERTICAL TAIL MODELING
Figure 5 D i g i t a l Datcam vs S'
D! IJind Tunnel Data,
8 0 0_------- c
4- -so -
-8 I -.15 I I I I
d -2- -c-
1 - f
+ Cnp ONLY
b 0 "
-3 I I I
DlwTAL OATCOM (Cnr ONLn
-1 - -_--OIGIIAL DATCOM +BODY Cnr
: -2 -
-s- 2 - z ONLY 5
0 Cfp 13
,L -.4<1 0
4 - u 0
0 0 -5 -
I I I I 1 1 I I I
0 4 8
DIGITAL OATCOM (Cn, ONLY)
OlGllRL OATCOM+BOOY Cnr
12 16 20
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
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,
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