Unsteady Aerodynamic Effects on the Flight Characteristics of an F-16XL Configuration

15 Pages·2000·0.64 MB·English

by  Wang, Zhongjun

AIAA-2000-3910
UNSTEADY AERODYNAMIC EFFECTS ON THE FLIGHT CHARACTERISTICS OF
AN F-16XL CONFIGURATION
Zhongjun Wang" and C. Edward Lan _
Department of Aerospace Engineering
University of Kansas
Lawrence, KS 66045
and
Jay M. Brandon _
Vehicle Dynamics Branch
NASA Langley Research Center
Hampton, VA
Abstract I_, I_,, Ix product of inertia
F,.... F.... F..... T,.Tm,T.
Unsteady aerodynamic models based on windtunnel aerodynamic and thrust moments about
forced oscillation test data and analyzed with a fuzzy logic the x-, y- and z-axes, respectively
algorithm are incorporated into an F-16XL flight simulation W aircraft weight
code. The reduced frequency needed in the unsteady models p, q, r body-axis roll rate, pitch rate and yaw
isnumerically calculated byusing a limited prior time history rate, respectively
of state variables in a least-square sense. Numerical examples u, v, w aircraft velocity components along the x-,
are presented to show the accuracy of the calculated reduced y-, and z-axes, respectively
frequency. Oscillatory control inputs are employed to V total velocity
demonstrate the differences in the flight characteristics based
on unsteady and quasi-steady aerodynamic models. aerodynamic forces and thrust along the
Application of the unsteady aerodynamic models is also x-, y- and z-axes, respectively
presented and the results are compared with one set of F- ct angle of attack
16XL longitudinal maneuver flight data. It is shown that the angle of sideslip
main differences in dynamic response are in the lateral- control deflections in pitch, roll and yaw,
directional characteristics, with the quasi-steady model being respectively
more stable than the flight vehicle, while the unsteady model throttle position
being more unstable. Similar conclusions can also be made in Euler angles in roll, pitch, and yaw,
a simulated rapid sideslipping roll. To improve unsteady respectively
aerodynamic modeling, it isrecommended toacquire test data k reduced frequency
with coupled motions in pitch, roll and yaw. b span length
mean aerodynamic chord
Nomenclature
Ci) directional cosines
g gravitational acceleration
H altitude Introduction
Ix,ly,lz _moments of inertia about the x-, y- and z-axes,
respectively Aircraft dynamic characteristics have mostly been
"Graduate Research Assistant
' J. L. Constant Distinguished Professor. Associate Fclloxv AIAA
"Acrospacc Enginccr. Senior Mcmbcr AIAA
Copyright _320()0 by thc American Institute of Acronautics 1
and Astronautics. Inc. All rights reserved
American InslilulC of Aeroni|ulics and Astronautic,,
studied with a quasi-steady aerodynamic model in the past.
f_: rv- q_,+a,_,b
In a quasi-stead)' model, the dynamic effects on
aerodynamic coefficients are assumed to be linearly O=pw- ru +ay,b
proportional to the angular rates and time rates of change _,=qu-try +az,b
of variables with the coefficients being typically measured I_--_A, ,,÷_,_,2÷a,A,, (1)
at a fixed frequency. That is, the lag effect exhibited by the
varying reduced frequency along a maneuvering flight path,
_:fl, A_÷_ An+fl,A_
and the corresponding dynamic stall effect are not properly
accounted for. The present investigation on the unsteady
aerodynamic effect is underlaken in view of the fact that the
lag and dynamic stall effects may play an important role in where
aircraft stability characteristics and performancE. 2in some
flight conditions. ax.b=g(a x+ C13 )
%.s=g(%+cu)
To determine the unsteady aerodynamic effects, a.._: gf-a,,+C3s)
harmonic forced oscillation tests were conducted, s,' These a,=(T:F_,,,D/rV
test data were then analyzed to establish the aerodynamic a,={r,F+,,_o)/rv
models for use in the flight simulation. In the process of a,,=- (T +F.,,,,,)/Z:
application, the most uncertain quantity to be determined is
the reduced frequency. It is straightforward to calculate the
reduced frequency of harmonic oscillation motion used in
the test. However, the actual aircraft motion cannot be
described by one single harmonic oscillation, and the
reduced frequency of the actual motion will not be constant.
One way to determine the reduced frequency of aircraft . ---p:_,.qr-%,
motion is an analytical method which assumes the mean n,---pz..-qz,,+,.z,
angle of attack and the amplitude being the same as those
I:l,,=rHy-qH+Ft_+ Tt
used in the harmonic oscillation tests.I If the forced
T_,=pn,,-n:_..,,. +r.
oscillation tests were performed at a constant mean angle of
attack and amplitude, the analytical method should produce I:I=,I--IqH .F,_,+T.
reasonable values of the "equivalent" reduced frequency.
On the other hand, when the wind tunnel data are obtained
at different mean angles of attack and amplitudes, this
----tan-1 (C23 / C33)
analytical method would not be applicable. One way to
0= - sin-_(Q3)
determine the equivalent reduced frequency is a numerical
one. = tan-l(G2/ell )
In the present paper, we will demonstrate one A n =(Iyl-12)/D
numerical method to determine the reduced frequency for A,_--A_=,(s,j=+U.p/D
use in flight simulation. The method is then employed,
A22 =(IF -P =)ID
together with the fuzzy-logic aerodynamic models
An =.432:(1j,_+IJ.)/D
established previously 3:, in an F-16XL simulation code to
investigate the unsteady aerodynamic effects on flight A33 =(IJy-12_ID
dynamics. A13=A31=(Zj_+IJ,,)/D
o:U/z-U _.-U _=-:/%-zrjj,_
Aircraft Dynamic Model
The flight simulation is implemented by the
The flight slate variables (u,v,w, p,q,r) are
following 6--degree--of-freedom model:
calculated by integrating these dynamic equations. The
following auxiliary equations arc then used to obtain the
American Inslitulc of Acronaulics and Aslronautics
angle
of attack and sideslip angle and their time rates : ct(t) and q(t), representing the longitudinal unsteady
motion characteristics. On the other hand, the reduced
frequency k2is calculated from the lateral-directional
tz=tan-l(w/u)
unsteady motion, mainly from the rolling motion if it is
¢t=(us.- _¢_)/(u 2+w2)
present. Note that there are no unsteady aerodynamic data
f_=sin l(v/_ (2) available with the lateral-directional control surfaces
f_:(V_-vC3/(v2cosf_)
deflected. Only the elevator effect is included in the
V= Cu 2+v2+w2 longitudinal model.
In flight simulation, the motion variables ct, _b,¢r
Aerodynamic Models and their time rates are calculated at every time instant.
The calculation of reduced frequency kt is discussed in the
Quasi-steady model next section. For the lateral-directional case, two reduced
frequencies can be obtained separately from _, _, and
For quasi-steady aerodynamics, the terms Fx._o,
_. In most cases, k2will be calculated from _band
Fy.... Fz,_o, Ft._o, F,_,_o, F,,,,o in the aircraft dynamic
model are functions of flight state variables and control unless there is no aileron input. In this latter case, _and
surface deflection angles, i.e., will be used to obtain k2. This approach is based on the
fact that the lateral-directional motion variables tend to
F_,y.,.t.,_,_,o_,o=h (tz, _, P, q, r, V, H, 5) (3)
have similar time histories.
In addition to the aforementioned unsteady
where 8 stands for the control deflection angle. When the aerodynamic models, the existing static aerodynamic model
flight state is known, it is straightforward to obtain the in the simulation code is used to provide the basic
corresponding aerodynamic forces and moments through aerodynamic properties. The unsteady aerodynamic effects
interpolation. The aerodynamic effects caused by the time are added to the basic static aerodynamics according to the
rate of angle of attack are not included in the present quasi- following expressions:
steady aerodynamic model for the F-16XL.
Longitudinal unsteady aerodynamic increments:
Unsteady aerodynamic model ACunsteadyi : ACL,D ..... t,y = f (ct,&,_, kt,/3, 6e)
(6)
- f(ct, a = 0,_ = O,k_ = O,fl,6,)
The longitudinal and lateral-directional unsteady
aerodynamic models were established based on the results Lateral-directional unsteady aerodynamic
increments:
of large-amplitude pitch, roll and yaw forced oscillation
tests, and a limited amount of rotary balance data. 3,4The ACur_teady2 = ACL, D,_ n,t,y = g(a,_,_,k2, Ig,_t)
(7)
tests were conducted in separate pitch, roll and yaw -g(a,_,_ : 0,k 2= 0,W,W =0)
motions. These models were set up to have the following
functional forms: Generally, _and _/,are replaced by pand r, respectively.
Therefore, the total aerodynamic coefficients at every time
Longitudinal unsteady aerodynamics model: instant are expressed by:
CL.D..... t.y= f(a,6,_t,kl,fl,,_e) (4) CL,D ..... t,y : Cstat,c + ACumtea@l + ACumteady2 (8)
Lateral-directional unsteady aerodynamics model: For the purpose of stability analysis, the
derivatives of aerodynamic coefficients with respect to the
(5) angle of attack etc. can also be derived from the above
equations. In addition to the numcrical central difference
method and spline interpolation to obtain these derivatives,
where the subscripts L, D, m, n. /..v stand for lift, drag,
pitching, yawing and rolling moments, and side force, the small-amplitude harmonic oscillatory method _will be
rcspcctivcly. The reduced frcqucnc 3' k_is computed from used and comparcd
American lnsliltllc of Acron;.itfllcs :rod Aslron:lutics
Equivalent Reduced Frequency Assume the number of points in the motion histor).,
preceding the current instant is n. If n > 20, it is set to 20.
In tile present unsteady aerodynamic models, However, if n < 20, then only those available points are
different types of forced oscillation test results (different used to determine the unknowns. As is well known, the
mean angles of attack and different amplitudes) are used as initial values assumed will significantly affect the
source data to train the fuzzy logic models. This was done convergence of numerical optimization. Therefore, the
in the testing to accommodate a wider range of reduced initial values of the unknowns for the current time segnmnt
frequency without exceeding the loading capability of the are always taken to be the results from the previous
measuring balance. As stated previously, the angle of attack segment. At the beginning, the initial values of mean ¢x
(_- ) and amplitude (a) are assumed to be 35.0 deg. (the
¢x,and the time rate of angle of attack a are part of the
value used in the windtunnel testing), and the difference
input parameters to calculate the unsteady aerodynamic between the actual _xand the assumed mean cx,
coefficients in the longitudinal fuzzy logic model. The time respectively. The initial values of angular frequency and
history of these variables is fitted with one of a harmonic phase angle are 1.0 and 71:,respectively.
motion at that instant, i.e.,
Figure 1presents the comparison between the
aft) = ff +acos(rat +7) assumed harmonic motion with to = x/2 and the predicted
(9) results. Except a small deviation when n < 20, the present
d(t) = -aco sin(r_at + 7)
method is shown to predict accurate results. The method
has also been tested for various other assumed harmonic
where those terms on the left hand side are given and the
motions with similar good results (not shown).
unknowns are _ ,the local mean angle of attack, "a", the
The convergence of the present algorithm is fast.
local amplitude of the harmonic motion, _, the phase lag, For an ¢x(t) response with 150 points, it took only one
and 60, the angular frequency. The reduced frequency k_ second of the CPU time to calculate the reduced frequency
and k2are defined as at all 150 points on an Alpha VAX machine.
kI = o_ / V,k 2= _ /2V (10)
The frequency to and other parameters are calculated The variation of longitudinal dynamic derivatives
through an optimization method by minimizing the with the angle of attack based on the concept of small
following cost function (least squares) amplitude harmonic oscillation is presented in Figure 2.
These dynamic derivatives are calculated by integrating the
out-of-phase aerodynamic coefficients obtained from the
j = _ [% _ (-_ + acos(tot i + _))]2 +
fuzzy logic model. The amplitude is assumed to be 5
t-t (11) degrees and two different reduced frequencies are presented
[_t_ - (-a_osin(_t t + _))]2 in the calculation. The pitching moment is referenced to a
i-I
pitch center at 0.558 ?. The results show that predicted
pitch damping derivatives are mostly positive because of
the aft pitch center location. Their sign agrees with the
where n is the number of dam points used, and is assumed hysteresis direction in that a clockwise loop produces a
to be 20 (equivalent to 0.7 sec) in the present application. positive value for the damping derivatives. Their
Those twenty points preceding the current time are magnitude is decreased with increasing reduced frequenc3',
employed in the above equation. The least-square method is having the same trend of variation with that calculated _,
found to converge well and gives reasonably accurate the indicial integration method) This exercise
results. The lateral-directional equivalent reduced demonstrates the generality and usefulness of fuzzy logic
frequency, is computed in the same manner. models as steady and unstead3' aerodynamic data base.
Numerical Results and Di_ussion I_'namic Response to Oscillator), Input
Equivalcnt Rcduccd Frcqucnc'_ and Pitch Damping Thc acrod_namic momcnl reference point of the
Amcric:m ]nslilule of Acrotl:tulics and Aslronaullc_,
F-16XL simulation code is at x_2 =0.45 ?, being different in addition to _ and k. One important difference between
from the ones used in the longitudinal and lateral- the unsteady model and the quasi-steady model is that the
directional wind tunnel tests. Therefore, the pitching latter features less pitch damping at low _ and higher
moment and yawing moment coefficients obtained from the damping (i.e., values being more negative) at high co,being
fuzzy logic models must first be transferred before being opposite to what the unsteady model indicates. The lift due
incorporated into the simulation code by using the to pitching is in general much smaller with the quasi-steady
following expressions: model. Note that during the simulation, the existing control
system is still operational. The resulting angle of attack
time history is seen to be the same for both the quasi-steady
c.-- C..o,.,. c,(x_2-
(12) and unsteady models. This is achieved by the control
C.: C..,oa,z+ Cr(x,,._- xh_) system with different final elevator deflection angles to
compensate for the differences in dynamic characteristics.
Later, a test case will be shown that this is not the case in
Note that xt,,_ = 0.558 _and xiat= 0.46 _. other unsteady flight conditions where the control system
designed with the quasi-steady data becomes inadequate. In
To see the differences in the dynamic response the following, all stability derivatives will be calculated
with unsteady and quasi-steady aerodynamic models, the with the central difference method.
following oscillatory elevator input by the pilot is assumed:
Comparison with Hight Test Data
8e_ot = 15.0+25.0 sin(2_/8 t), in deg.
The longitudinal dynamic response is first
The resulting dynamic response is presented in Figure 3. calculated with the quasi-steady aerodynamic model, the
The lateral-directional state variables, such as the sideslip pilot longitudinal control (8_ot) being the only input, in
angle, roll rate and yaw rate etc., are zero. Two methods in addition to the contributions from flight control systems.
calculating the dynamic derivatives with the unsteady The net control deflections are plotted as 8_, 8,, and 8,. The
aerodynamic model are presented: one with the small initial flight state variables are found to be the same as the
amplitude oscillation method mentioned earlier and the initial flight data with acenter of gravity location at
other based on acentral difference method. For the latter, x_=0.45923 _. Figure 4 shows the simulation results in
the following equation is used: comparison with flight data. Although the longitudinal
responses (_, 0 and q) follow the trend of flight data well,
C_ = [f(a, A,E,k_,fl,&) - f(a,-A,&,k_,fl,&)l / (2A) (13) there are time periods in which the predicted 0_is much
lower than the data. These are also the time periods with
= ?A / (2V)
lower magnitude in pitch damping. The lateral-directional
where A= q + & ffthe sum is greater than 5 deg./sec.;
motions are not excited at all, although there are some
otherwise, A = 5 deg./sec. For the lateral-directional
initial inputs from the control system. The aforementioned
derivatives, the following expression is used:
longitudinal responses are repeated with the unsteady
aerodynamic models as shown in Figure 5. Assuming that
C_, =lg(a, _,p+Ap,k2,_',r) - g(a,¢, p- ZXpk,2,_,, r)]/ (2_) (14) the control system in the simulation code models accurately
the one in the flight vehicle, the discrepancy, in the
where Ap=3 deg./sec, and AP=bA1N(2V). The yaw responses must be caused by the static aerodynamic data
damping derivative is calculated in a similar manner. Note which are also used in the unsteady models. The biggest
that pitching derivatives are calculated differently to avoid differences between these two aerodynamic models occur in
the effect of static data when the dynamic data are not the lateral-directional responses. However, the excited
symmetrical about the static data. The calculated results lateral-directional motions with the unsteady models appear
indicate that the derivatives by the small amplitude method to be more unstable than what the flight data show. in
vary in a more orderly manner as compared with the particular in roll and sideslip.
central difference method: but the order of magnitude is
comparable. One reason for this is that in the small Sideslipping Roll
amplitude method, the results depend only on _ and k:
_ hilc the central difference method depends on &as well To help explain the aerodynamic causes of somc
American lnslitulc of Aeronautics and Aslronaulics
loss-of-contrfoliglhtconditionssu, chasthcUSAirFlight
aerodynamic model. The resulting code was employed to
427accidenint 1994
°,the initial flight scenarios with a investigate the differences in flight characteristics with
hard-over rudder malfunction will be postulated with the these two t)qges of aerodynamic models. For the unsteady
present F-16XL model. The present configuration is model, the reduced frequency needed in the model was
trimmed at M=0.1718 and 6000 ft. of altitude. With the calculated with a least-square method to fit a harmonic
longitudinal stick fixed at the trim position, the lateral- variation to prior time history of state variables over about
directional control systems are disconnected; but the 0.7 second. Methods to extract dynamic derivatives while
longitudinal system is left on. In the initial 1.5 seconds, a performing time integration of dynamic equations were
left bank is created by applying aileron and at the same developed based on the concept of central differences and
time the rudder is set at a nose-left 20 deg.. After 1.5 small-amplitude harmonic oscillation. These two methods
seconds, right aileron is applied to try to make the wing showed similar results which were significantly different
level. These are the scenarios indicated in Ref. 6. The from the original quasi-steady data. Hight data in a
results of simulation are presented in Figure 6. It is seen longitudinal maneuver were compared with the simulation
that with the quasi-steady aerodynamic model, apositive results. The main differences in dynamic response based on
sideslip up to 12 deg. can be quickly generated while the these two types of aerodynamic models were the lateral-
angle of attack is increased to 36 deg. by the control system directional responses induced by the longitudinal motion.
to counteract perhaps the increasing negative pitch attitude. For the quasi-steady model, the lateral-directional motion
Because of the positive sideslip, the resulting rolling was not excited, as compared with the flight data. On the
moment overpowers the right aileron and the configuration other hand, the unsteady model produced a more unstable
keeps rolling to the left. Therefore, rapid sideslipping roll motion than what the flight data indicated. In a simulated
may generate loss-of-control flight conditions. sideslipping roll, again the configuration was shown to be
more directionally unstable with an unsteady model. To
If the unsteady aerodynamic models are used in improve the unsteady aerodynamic modeling, test data with
the simulation, the situation gets worse, with the aircraft coupled motions in pitch, roll and yaw would be needed.
responses in t_and [3being divergent within five seconds.
Typically, unsteady aerodynamics will make an unstable or Acknowledgment
marginally stable configuration with quasi-steady
aerodynamic models more unstable. In the present case, the This research was supported by NASA Gram
main reasons for the divergence are Cm_being positive and NAG-l-1821 for the first two authors.
C_ being negative as shown in Figure 7. Based on the
present simulation, even maintaining a small rudder References
deflection will make the model highly unstable (not
shown). Whether these highly unstable conditions with the JHu, C. C., Lan, C. E. and Brandon J.M. "Unsteady
unsteady aerodynamic models exist can only be verified Aerodynamic Models for Maneuvering Aircraft", AIAA
with more appropriate test data. These needed data should Paper 93-3626CP, August, 1993.
be those obtained with coupled motions in pitch, roll and 2Rotary-Balance Testing for Aircraft Dynamics, AGARD
yaw. From a theoretical point of view, this is because the Advisory Report, No. 265, 1991
lateral-directional aerodynamics, such as roll and yaw 3Wang, Z., Lan, C.E. and Brandon, J.M."Fuzzy Logic
damping, depend on wing boundary layer characteristics Modeling of Nonlinear Unsteady Aerodynamics", AIAA
and the associated wake, which in turn strongly depend on 98-4351, August, 1998.
the angle of attack and its time rate of change. Another 4Wang, Z., Lan, C.E and Brandon, J. M."Ftmzy Logic
implication is that these appropriate unsteady aerodynamic Modeling of Lateral-Directional Unsteady Aerodynamics".
data may be needed in control system design. AIAA 99-4012, August, 1999.
5Lin, G., Songster, T. and Lan C. E "Effect of High-alpha
Concluding Remarks Unsteady Aerodynamics on Longitudinal Dynamics of an
F-18 Configuration" AIAA 95-3488, August, 1995.
Longitudinal and lateral-directional unsteady 6Dornheim, M. A. "'737 Simulation Recreates Accident
aerodynamic models obtained in separate wind tunnel Sequence" Aviation l._'eek and Space Technology. March
testing were incorporated into an F-16XL simulation code 22, 1999, p 42.
which was based on a conventional quasi-steady
American Iilstilulc of Acronaulics and A.,_troJlaulics
6O 40
30
5O
20
._. 40
G" 10
13)
O)
-a 30 0
"O
20 ._ -10
-20
10
-30
0 -,,,,I .... t .... I_lkLllkll] -40 :.... I .... I .... I .... Illtll
0 1 2 3 4 5 0 1 2 3 4 5
time(sec) time(sec)
60 50
40
4O
"-- 20
"_ 30
C_ 0
I_ 20
:_ -20
-40 10
-60 .... t .... I,,lll_k,ll,1111 0
0 1 2 3 4 5 0 1 2 3 4 5
time(sec) time(sec)
5O 6
,• •assumed motion 4
40
prediction
2
30
(D
-o 0
20 "--i
-2
10
-4
0 -6
0 1 2 3 4 5 0 1 2 3 4 5
time(sec) time(sec)
4
Figure 1Comparison between
3 predicted results and assumed
motion:
2 a=35+20*cos(p/2*t)
v
1
,! .... ]
0 1 2 3 4 5
time(sec)
Amcrican Instilutc of Aeronautics and Astronautics
30 -
1.5 --
k=O 0535
25
20 0 0 0
0
._1 0 • • 0
o 15
o_J 05 + 0 0
k=0.0535 _" Jo'10 0 @ • 0
0 o • k=O 107 * o
5
0 _--@ •
-L"
0
-05 ,,,I .... I.... f.... I,,,,I .... I.... I -5 _,,,I .... I.... I.... I,,ltl,,,JlIJh,I
0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70
cz(deg) a(deg)
1,5 D _
k=0.0535
3 0 0
1 0
0 0
E 2 0 • @ • 0
0
(._ 0.5 + 0 •
k=0.107 o" • 0
E 1 0 •
o
0 o . k=0.107
0
-0 •
,,,I .... I.... I.... IILJlllrll[Jlt_l ,',,t .... I.... t.... I.... I,jt,I,Ls,I
-0.5 -1
0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70
a (deg) (z(deg)
0.25 -
Figure 2 Static aerodynamics
0.2
and calculated dynamic derivatives
o
0.15 based on samll amplitude harmonic
oscillation(amplitude: a=5 deg)
E 0.1
0
0.05
0 ,,,I .... I.... I.... thl_,l,,,,12,111
0 10 20 30 40 50 60 70
(deg)
025 -
(3
_o 0.15
E 0.1 l/ k=O 107
0
0.05 _"
0 ,_t i ..... I.... [ _i.... i_l
0 10 20 30 40 50 60 70
0c(deg)
American Institute of Aeronautics and Astronaulics
4O 0.2
• .. quasi-steady
30
unsteady 0.15
20
03 0.1
10
005
0
-10 ,,,,I .... ),,,,I,_,l,_,l,,,,I .... I.... I.... I.... I,,,,1111)1
0 5 10 15 20 25 30 5 10 15 20 25 30
time(sec) time(sec)
25 0.5
20 central-difference central-difference
0
•_ 15
,._1 E
0 0
+ 10 + -0.5
_r cr"
,_l E
o 5 0
-1
.... quasi-steady • -. quasi-steady
-5 -,,,,I,,,,I,,,,t .... I.... I.... ] -1.5 .... I.... I,,,_lt_,,t_,,I,,,tl
0 5 10 15 20 25 30 0 5 10 15 20 25 30
time(sec) time(sec)
25 D 0.5
small-amplitude
20
0
•_ 15
...J E
(..) 0
+ 10 + -0.5
ID" O"
J E
0 5 0
-1
0
-5 -1.5 .... I,,i,1,,,,I,,,,I .... I.... I
0 5 10 15 20 25 30 5 10 15 20 25 30
time(sec) time(sec)
50 20 m
40 • • •quasi-steady
unsteady
30
_. 10
-o 20 (3')
v
=o 10
0,.
0
0
-10
L_
-20 -10 .... I.... ].... i.... !.... [.... I
0 5 10 15 20 25 30 5 10 15 20 25 30
time(sec) time(sec)
Figure 3 Simulation results with unsteady aerodynamic model and quasi-steady
aerodynamic model(pilot elevator input only), xcg=0.45923 _'
9
Amcrican IJlSlilulc of Acronautics and Aslrol)aulics
40 5
• .- simulation data
--flight test data
30 3
"_ 20
41,
_+,,°"............................................................
10
0 -3
',%..:* ''
-,,,,I .... I,+,_I.... l,,j,l,,,,l,,,,l I.... I
-10 .... -5
0 5 10 15 20 25 30 35 40 45 5 10 15 20 25 30 35 40 45
time(sec) time(sec)
20 E 3O
15 20 i A .
10
..-.. 10
G"
"- 5
0
0 __" .:'.,: --'.ii i_ !_"'-.
0.. o- -10
-5
-10 -20
-15 .... I.... I.... I.... l.... l,,,+ltll,lll,r],+,+l -30 _,,,I .... I,,,,I,,,,I .... I,,,,I,,,,I,,,,I .... I
0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45
time(sec) time(sec)
4 60
50
2 40
30
G"
o_ 20
0
vlO
,¢D
0
-- ... -
-2 -10 _--:_
-20
-4 ,,,I .... 1.... t.... I,,,,I .... 1.... I.... IAIIII -30 _,,,I,,,,I .... I,,,,I .... I.... I.... I.... I.... I
0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45
time(sec) time(sec)
10 240
220
200
+6180
0
160
140
-5
120
-10 _,_1.... t.... ].... I.... /.... ],,,_t,,i,!,,h,I 100 -,,,,I .... I.... t.... l, ,_l.... I.... 1,7t-,4....I
0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45
time(sec) time(sec)
Figure 4 Comparison between flight test data and simulation data with
quasi-steady aerodynamics at M=0.4243, H=14931.03ft and xcg=O 45923_
It)
Amcrican Institute of Acronautics and Aslronautics