NASA/TM-97-206276

Analysis of Wind Tunnel Longitudinal

Static and Oscillatory Data of the F-16XL

Aircraft

Vladislav Klein, Patrick C. Murphy, Timothy ]. Curry, and Jay M. Brandon

December 1997

https://ntrs.nasa.gov/search.jsp?R=19980007406 2018-05-11T16:38:18+00:00Z
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NASA/TM-97-206276

Analysis of Wind Tunnel Longitudinal

Static and Oscillatory Data of the F-16XL

Aircraft

Vladislav Klein

George Washington University, Hampton, Virginia

Patrick C. Murphy

NASA Langley Research Center, Hampton, Virginia

Timothy Y. Curry

George Washington University, Hampton, Virginia

and

Jay M. Brandon

NASA Langley Research Center, Hampton, Virginia

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-2199

December 1997
Available from the following:

NASA Center for AeroSpace Information (CASI)

800 Elkridge Landing Road

Linthicum Heights, MD 21090-2934

(301) 621-0390

National Technical Information Service (NTIS)

5285 Port Royal Road

Springfield, VA 22161-2171

(703) 487-4650
SUMMARY

A wind tunnel experiment on the 10-percent-scale model of the F-16XL aircraft included

longitudinal static tests, and oscillatory and ramp tests in pitch. Static tests investigated the effect

of angle of attack, slideslip angle and control surface deflection on aerodynamic coefficients. For

dynamic testing and analysis, the report presents data from small-amplitude oscillatory tests at

nominal values of angle of attack between 20 ° and 60 °, five frequencies from 0.6 to 2.9 Hz and

one amplitude of 5 °. A simple harmonic analysis provided Fourier coefficients associated with the

in-phase and out-of-phase components of the aerodynamic coefficients. A strong dependence of

wind tunnel oscillatory data on frequency led to the development of models with unsteady

aerodynamic terms in the form of indicial functions. Two models expressing the variation of the

in-phase and out-of-phase components with angle of attack and frequency were proposed and their

parameters estimated from measured data. Both models with the estimated parameters were in

good agreement and represented unsteady effects observed in the aerodynamic forces quite well.

The estimated parameters were close to the results from the static test and both models

demonstrated good prediction capability.
A

a,bi ,c

a,b

b

CL ,CN ,Cm

CL_ (t),CLq (t)

f

J

k

g

m

n

q

S

S

T

rl

t

u

SYMBOLS

amplitude ratio

parameters in indicial function

Fourier coefficients (Appendix A)

wing span, m

lift, normal force, pitching-moment coefficients

indicial functions

wing mean aerodynamic chord, m

frequency, Hz

cost function

reduced frequency, k = tog / V

characteristic length, g = _ / 2

number of frequencies

number of angles of attack

number of cycles

pitching velocity, rad/sec

standard error

wing area, m 2

period, sec

time constant, T1 = Xlg/V, sec

time, sec

input (Appendix A)

aerodynamic derivatives in model for in-phase and out-of-phase

component of oscillatory data, respectively
U,V

V

Y

Zu ,Zv

IX

A

r_e

0

T,

'_1

CO

Superscript:

^

in-phase and out-of-phase components of oscillatory data,

respectively

airspeed, m/sec

output (Appendix A)

terms in model equation (10) and (11), respectively

angle of attack, rad or deg

sideslip angle, tad or deg

increment

elevon/flaperon deflection, rad or deg

parameter in Model 11

time delay, sec

nondimensional time constant, x 1 = V/_b 1

phase angle, rad or deg

angular frequency, rad/sec

estimated value

Superscript over aerodynamic derivative:

Subscript:

A

0

oscillatory data

amplitude

nominal value

Aerodynamic derivatives:

O3CA %(oo)=% for A= L,N, orm

a_._

q? tlC"2 t_

2V '4V 2 ,0_,'_--_,or t5e
INTRODUCTION

For better understanding of aircraft aerodynamics in large amplitude maneuvers, NASA

Langley Research Center conducted a series of wind tunnel tests on a model of the F-16XL

aircraft. These tests included measurement of aerodynamic forces and moments under static

conditions followed by oscillatory and ramp tests in pitch. Static measurements allowed

investigation of changes in aerodynamic coefficients due to angle of attack, sideslip and control

surface deflection. Dynamic testing quantified changes in aerodynamic coefficients with frequency

and amplitude.

The purpose of this report is to

(a) document static and small-amplitude oscillatory data for qualitative assessment;

Co) determine a mathematical model with unsteady aerodynamic terms for oscillatory data at

different angles of attack and frequencies.

The parameters in a model for small-amplitude oscillatory data were estimated by a nonlinear

estimation technique of reference 1. Then, a new procedure using splines for model formulation

and linear regression was applied.

The report begins with a description of the experiment. The results from static and oscillatory

test are then described followed by model structure determination and parameter estimation from

oscillatory data at various angles of attack and frequencies. The report is completed by concluding

remarks.

MODEL AND TESTS

A three-view sketch of the 0.10-scale F-16X'L model is shown in figure 1 together with some

basic model dimensions. Static and dynamic tests were conducted in the NASA Langley

12-Foot Low-Speed Wind Tunnel. For both tests, the model was mounted on a dynamic test rig

through a six-component strain-gauge balance. The dynamic test rig is a computer controlled,

4
hydraulically-actuatedsystemwhich was sting-mounted on a C-strut support system. The

mounting arrangement rotated the model about the reference center of gravity location of 0.558 E,

over an angle of attack range of -5 ° to 80 °. The maximum capability of the dynamic test rig was

260 deg/sec pitch rate and 2290 deg/sec 2 pitch acceleration. Further description of the dynamic test

rig may be found in reference 2. The tests were conducted at a dynamic pressure of 192 Pa (4 psf)

resulting in a Reynolds number of 106 based on the mean aerodynamic chord.

All data were obtained with the leading-edge flaps at 0 ° deflection. Static data were obtained

for angles of attack from -5 ° to 80 ° at zero sideslip and zero deflection of trailing-edges surfaces

(flaperons and elevons). Additional data were obtained for four values of sideslip, (13 = -5 °,

-10 °, -20% and -30°), and for two values of symmetric trailing-edge control surface deflections

(_5e =-20 ° and 20°). Oscillatory data were obtained at initial angles of attack (t_0) between 20 °

and 60 ° at five frequencies (0.6, 1.0, 1.41, 1.75, and 2.94 Hz) and an amplitude of +5 °. The

effects of sideslip and control surface deflections were measured only at an initial angle of attack of

35 ° and two frequencies (0.6 and 1.41 Hz) at the same sideslip values and control deflections as in

the static test.

Data recorded during the test runs included a linear variable differential transformer reading

from the dynamic test rig to determine the pitch angle, six-component force and moment data from

a strain-gauge balance, and wind tunnel dynamic pressure. Data were sampled at 100 Hz with an

in-line 100 Hz low pass filter.

filter.

All data channels were subsequently filtered using a 6 Hz low pass

STATIC DATA

Among the measured and computed data only three aerodynamic coefficients, CL,C N, and

Cm, are included. These coefficients are plotted against the angle of attack in figure 2. The

variation of C L with t_ is almost linear for tx < 25 °, the maximum lift occurs at o_ = 34 °. The

normal force is also changing linearly with 0_ fill t_ = 25 °, and reaches maximum value at

5
tx = 38 °. The model exhibits static instability for ct < 30 °. This pitch-up tendency is inherent to

highly swept wings at low speeds as documented in many publications, e.g., reference 3.

Figure 3 shows the effect of sideslip on longitudinal characteristics. For _ < 5 ° there are

almost no changes in these characteristics. Larger sideslips, however, cause a decrease in values

of all coefficients, mostly in the region of 0_ between 20 ° to 40 °. Pitching moment decreases due

to sideslip at all angles of attack > 20 °. Large sideslip angles eliminate the pitch-up tendency in

small segments of the angle of attack in the pre-stall region. The effect of symmetric elevon and

flaperon deflection is presented in figure 4. In the post-stall region the control effectiveness is

larger for negative (trailing edge up) deflection than for positive. The stability and conlrol

derivatives evaluated from the data in figure 2 and 4 with zero sideslip angle are plotted in figure 5

and 6. The control derivatives were computed for both positive and negative control deflections.

From these plots a rapid decrease in control effectiveness with increased tx in the post-stall region

is apparent. All the measured and computed data in figures 2 to 6 are summarized in tables I to IV.

OSCILLATORY DATA

As indicated earlier, the basic set of oscillatory data was obtained at five frequencies, nine mean

values of the angle of attack, tx0, and one amplitude, txA = 5% The following table show the

values of frequencies and the corresponding reduced frequencies selected for the test.

e

co, f' k=--to

rad/sec Hz V

3.77 .60 .081

6.28 1.00 .134

8.86 1.41 .190

11.00 1.75 .237

18.47 2.94 .397
Themeanvaluesof a were 20.8, 25.9, 30.8, 35.8, 40.8, 45.8, 50.8 55.9 and 61.1 with the

maximum deviation from these values during the repeated settings less than 0.1 o.

The examples of the oscillatory data at one frequency and two mean angles of attack are given

in figure 7 and 8. For a 0 = 30.8 ° , the plot of CL(t) indicates a small change from a sine wave,

whereas the plot of Cm(t) shows the existence of at least one additional harmonic. For ot0 = 50.8 °

the departure of CL(t) from a sine wave is more pronounced and Cm(t) does not resemble a

simple harmonic motion at all. Further examination of the remaining time histories revealed severe

distortion of measured pitching-moment coefficient at a > 40 ° at all frequencies, and the response

can be characterized as a chaotic. The reason for this behavior has not been found yet.

For the following analysis of the oscillatory data it is assumed that the aerodynamic coefficients

are linear functions of the angle of attack, pitching velocity and their rates. Then, for example, the

increment in the lift coefficient with respect to its mean value can be formulated as

)2

AC L = CLa AO_ + -_ CL6 L_ +

(

VC'Lqq+tv )- CLeti1 (I)

where for the harmonic motion

AtX = _A sintot

tk = q = to(x A cosot

i2 = tl = -tO2a A sintot

Substitution of (2) into (1) yields

=Oa(C,o k2C,0)si. ,+Oak(C, +CLq)cos ,

= si. ,+ cos /)

(2)

(3)

7
where

_AC---La=O_A(CLa-k2CLi/ )

(4)

O_AkfLq =O_Ak(CLa +CLq ) (5)

represent the Fourier coefficients. The in-phase and out-of-phase components of CL(CLa and

CLq ) can be obtained by integrating the time histories of AC L over n c cycles as

2 ncT

= _ AC L (t) sin cot dt

CLa °_AncT o

2 ncT (6)

CLq - _ aknc T _ACL (t)coscot dt

o

where T = 2_/co. In the present analysis the integrals in equation (6) were obtained by a

numerical technique of reference 4 applied to the last three cycles of the steady harmonic outputs.

The in-phase and out-of-phase components of all three coefficients are presented in tables V to

VII and plotted against the angle of attack in figure 9. The figure shows the effect of frequency

which is especially strong on the out-of-phase components. The variation of these components

with the reduced frequency for two values of cto can be seen in figure 10. The plot of Crnq for

a 0 = 50.8 ° may indicate the problem with measured Cm(t ) mentioned earlier.

Figure 11 and 12 compare the measured coefficients C L and C m at one frequency and two

values of a 0 with those computed from eq. (3) and (4). These coefficients are plotted against the

angle of attack with time as a parameter. As shown in Appendix A, these plots should be ellipses

if the formulated model given by eq. (1) is correct. Any deviation of measured CL(a,t ) and

Cm(OL,t ) from this shape might be caused by aerodynamic nonlinearities and/or flow separation.

Substantial differences between measured and computed pitching-moment coefficient exist as

indicated by results in figure 11 and 12. When a and C L are considered as the input and output

variables of a dynamical system then their relationship is steady harmonic motion can be defined by

the amplitude ratio and phase angle, see Appendix A. The frequency response of these quantities
for two valuesof et0 is presentedin figure 13. Fromtheseplotsastrongeffectof frequenyon the

amplitudeandphasewithintherangeof k from 0 to 0.2 is apparent.

A comparison of steady and oscillatory data for all three coefficients is given in figure 14. The

oscillatory data presented are for one frequency and five values of ¢t0 from 20 to 60 °. For

a 0 = 20 ° the reduction of ellipses CL(_ ) and CN(O 0 to almost a line is caused by small values of

CLq and CNq. Possible reasons for distorted ellipses has already been discussed. The effect of

sideslip, elevon/flaperon deflection and tail-off configuration on the components of all three

coefficients are summarized in figure 15 and 16.

PARAMETERS ESTIMATED FROM OSCILLATORY DATA

A strong dependence of wind tunnel oscillatory data on frequency lead to the development of

models with unsteady aerodynamic terms, see e.g. reference 5 and 6. As an example, the model

for the lift increment was formulated in reference 4 as

AC L = _CLa (t-'c)_tld'c g t o +-V! CLa('-z)-_q('c)d'c (7)

where CL_ (t) and CLq (t) are the indicial functions.

For obtaining the model with limited number of parameters, it was assumed that the effect of

q(t) on the lift could be neglected and the indicial function CLa (t) can be expressed as

CLa (t)= a(1-e-blt)+c

Considering the above mentioned assumptions, equation (7) is simplified as

ACL =CL_ (oo)O_(t)-aSe -bl(t-'Q do@r)dx + -_CLq g (e_)q(t)

0

(8)

(9)

where CLa (_) and CLq (_) are the rates of change of C L with tx and q in steady flow. The

steady form of equation (9) for harmonic changes in tx is identical to that of equation (3), that is

9
ACL (t) = t_ A C"-L_sin tOt + O_AkCLq cos cot (3)

w

However, with the indicial function of equation (8), the expressions for CL_ and CLq

form

_ x2k 2

CL a =CL_(_)-al+_2k2

-- "[1

CLq = CLq (oo)- a 1 + "c"l_k2

have the

(10)

(11)

where x] = V/bl_ is the nondimensional time constant.

From the experiment, the in-phase and out-of-phase components are usually obtained for

different values of the angle of attack and reduced frequency while keeping the amplitude of the

oscillations constant. Then the equations (10) and (11) can be generalized as

Uji = U i -- aiZuj

vii = v i - aiZvj

These equations def'me Model I where for the lift coefficient

ui = CL a ({_i) vi = CZq (O_i)

X2 k2 '_l

- q -1+ q

(12)

(13)

for

i = 1,2 ..... n

j = 1,2,...,m

In equations (12) and (13) there are, in general, 3n + 1 unknown parameters: u i ,vi,a i and x I.

They can be estimated from experimental data u_i and v-_i by minimizing the cost function

Jl = _, uji - ui - aiZuj + vji - vi - aiZvj )1 (14)

j=l

10
More about the estimation procedure can be found in reference 1.

In formulating airplane equations of motion it might be more convenient to obtain expressions

for u, v, and a as a function of the angle of attack rather than their discrete values. For that reason

the previous model was reformulated as Model II defined by the following equations:

u-ji = u(txi ) - a(txi )Zuj

v-ji = v(t_i ) - a(t_i )Zvj

(15)

(16)

The form of expressions for u(ai), v(_i)and a(t_i) can be either specified from the variation of

estimated parameters in Model I or the form can be postulated in terms of polynomials and/or

polynomial splines. In the second case adequate models for u(tx),v(tx)anda(tx) can be

determined from measured data by a stepwise regression. The previously estimated value of

parameter x 1 can be used as an a priori value thus simplifying the parameter estimation procedure

using Model II and the cost function

JH = _ i_=l{[Uji-(u(_i)-a(_i)Zuj)] 2

j=l (17)

+[vji -(v(t_i)-a(_i)Zvi)l 2 }

Both estimation procedures were applied to oscillatory data at four frequencies and nine value

of the angle of attack. The measured data for frequency k = .190 were not included in the

estimation. This set of data was used to demonstrate the model prediction capabilities. The

estimated parameters u i,v i, and a i in Model I are plotted in figures 17 to 19. In these figures, the

2s confidence intervals for parameter estimates are also included. The minimum and maximum

values of standard errors are summarized in Table VIII. The parameters CLc t (oo) and CNa (_) are

in good agreement with those from static data displayed in figure 5. There is, however, large

discrepancy between Cma (oo) from oscillatory and static data caused by problems in measured

11
time histories Cm(t ), as discussed earlier. No values, theoretical or experimental, were available

for derivatives CLq ,CNq and Cmq for comparison with results from oscillatory tests. The

parameter values a i indicate smooth variation of unsteady terms with oc and the largest effect of

unsteady terms on the coefficients at ct around 40 °. The estimated values of x 1 , and computed

values of parameter b 1 and T1 are presented in Table IX together with their standard errors. These

results indicate that the time constant associated with the unsteady effects is about 0.4 sec. for the

lift and normal force, and about 0.6 sec for the pitching moment.

A comparison of measured in-phase and out-of-phase components of all three coefficients with

those estimated is given in figures 20 to 22. The predicted components computed from model

equations (10) and (l l) for k = .190 are presented in figure 23 to 25 together with the

corresponding measured values. These figures demonstrate that Model I for C L and C N is a good

predictor. No conclusion about predicted values of Cm_ and Cmq can be made because of chaotic

behavior of measured values C m (t) at et > 40 °.

Expressions for terms u(t_),v(_)and a(o 0 in Model II for the lift coefficient were selected

from results in figure 26 as

CL_ t (0_) -- u(0t) = 00 + 011_ + 020_ 2 +03(t_-0.803) 2

Ctq (0_) _ V(O 0 ---- 04 + 05iX + 06t_2 (18)

a(a) = 07 + 08ct + 09ct2 + 010 (a - 0.803) 2

where

(a - 0.803)2 = 0 for a < 0.803

= (a- 0.803) 2 for o_> 0.803

An identical model was postulated for the normal-force coefficient. There was no attempt to

estimate parameters in the pitching-moment equations.

The parameters in equations (18) were obtained by a linear regression for given values of

parameter x 1 . The mean values and standard errors of the estimates are summarized in table X.

12
Theresultsindicateparameteruncertainty in expressions for CLq (o0 and CNq ((x). Low accuracy

of these parameters could result from small number of data points and their small sensitivity due to

small magnitudes of CLq and CNq. The estimated terms of the in-phase and out-of-phase

components are plotted in figures 26 and 27, and compare with estimated parameters in Model I.

The agreement between both sets of results is very good. The measured and estimated

components of C L and C N are presented in figure 28 and 29. With the exception of CL_ and

CNa for k =0.397 and 0.081, the estimated components are close to the measured values.

Finally, figure 30 and 31 demonstrate prediction capabilities of Model II which are as good as

those of Model I.

CONCLUDING REMARKS

A wind tunnel experiment on a 10-percent-scale model of the F-16XL aircraft was conducted at

NASA Langley Research Center. This experiment concluded longitudinal static and oscillatory

tests. Static tests investigated the effect of the angle of attack, sideslip angle and control surface

deflection on aerodynamic coefficients from which only the lift, normal-force and pitching moment

are presented in this report. The variation of lift with angle of attack was found to be almost linear

for angles of attack less than 25°; the maximum lift occurred at an angle of attack of about 34 ° .

Similar results were obtained for the normal force. The model exhibited static instability for angles

of attack less than 30 ° . For small sideslip angles, less than 5 ° , there were almost no changes in the

longitudinal characteristics. Large sideslips, however, caused a decrease in values of all

coefficients. Changes in symmetric elevon and flaperon deflections indicated that in the post-stall

region the control effectiveness was larger for negative (trailing-edge-up) deflections than for the

opposite defections.

For dynamic testing and analysis, the report presents only data from small-amplitude

oscillatory tests at nominal values of angle of attack between 20 ° and 60 ° , five frequencies from

0.6 to 20.9 Hz and one amplitude of 5 °. A limited amount of data exhibiting the effect of sideslip

angle, control surface defection and tail-off configuration is also included without any discussion.

13
Time histories of the lift and normal force coefficients for angle of attack greater than 30 ° indicated

relatively large changes from a sine wave, probably caused by aerodynamic nonlinearities. The

time histories of the pitching moment, however, did not resemble a simple haromonic response at

all. With increasing angles of attack these time histories were getting closer to chaotic motion.

Regardless of these irregularities in time histories, it was assumed that for data analysis the

aerodynamic coefficients were linear functions of the angle of attack, pitching velocity and their

rates. Then, a simple harmonic analysis over three cycles of oscillation provided the Fourier

coefficients associated with the in-phase and out-of-phase components of the coefficients. These

components were plotted against the angle of attack for a given value of reduced frequency.

A strong dependence of wind tunnel oscillatory data on frequency led to the development of

models with unsteady aerodynamic terms in the form of indicial functions. These functions were

postulated as simple exponentials where the unknown parameters included aerodynamic

derivatives, the exponents and multiplication terms. Two models expressing the variation of the

in-phase and out-of-phase components with the angle of attack and frequency were proposed. In

the fast model, the unknown parameters, including the exponent, were estimated from measured

data by a nonlinear least squares technique at nominal values of angle of attack. In the second

model, polynomial splines expressing the variation of unknown parameters with the angle of attack

were formulated and their parameters estimated by linear least squares technique for a known value

of the exponent. Both models with the estimated parameters were in good agreement and

represented unsteady effects observed in the lift and normal force quite well. In addition, some of

the estimated parameters were close to the results from the static test and both models demonstrated

good prediction capabilities.

14
REFERENCES

° Klein, Vladislav and Noderer, Keith D.:

Characteristics. Part H--Parameters

TM 110161, 1995.

Modeling of Aircraft Unsteady Aerodynamic

Estimated From Wind Tunnel Data, NASA

2. Brandon, J. M.: Dynamic Stall Effects and Application to High Performance Aircraft.

Special Course on Aircraft Dynamics at High Angles of Attack: Experiment and Modeling.

AGARD Report No. 776, April 1991, pp. 2-1 to 2-15.

3. Wedekind, G.: Influence of Configuration Components of Statically Unstable Combat

Aircraft on the Aerodynamic Design for High Angles-of-Attack. AGARD-LS-121, 1982,

pp. 11-1 to 11-33.

4. Morelli, Eugene A.: High Accuracy Evaluation of the Finite Fourier Transform using

Sampled Data. NASA TM 110340, 1997.

5. Klein, Vladislav and Noderer, Keith D.: Modeling of Aircraft Unsteady Aerodynamic

Characteristics. Part I--Postulated Models, NASA TM 109120, 1994.

6. Goman, M. and Khrabrov, A.: State-Space Representation of Aerodynamic Characteristics

of an Aircraft at High Angles of Attack. Journal of Aircraft, Vol. 31, No. 5, 1994,

pp. 1109-1115.

15
APPENDIX A

HARMONIC MOTION

Let the input to a linear, time-invariant, dynamical system be

U = OtA sin tot

Then the steady state output of the system has the form

y = a sin tot + b cos tot

= Asin(tot- d_)

where

and

a=Acos_

b = -Asin_

A 2 = a 2 + b 2

b

tan_ = --

a

Replacing y by AC L and u by _ it follows from equations (A3), (A4) and (3) that

a = OrACLe t

b = O_Ak-CLq

and the expression for amplitude ratio and phase angle takes the form

A: aJCZo

= tan- 1 k_Lq_

CL a

(A1)

(A2)

(A3)

(A4)

(A_5)

(A6)

(A7)

16
Returningto equations(A1) and(A2), andconsideringunitamplitudeof theinputvariable

y = a sin tot + b cos tot

= a sin tot + b_/1 - sin 2 tot

= au + b_- u 2

Taking square of both sides of (A8) yields

y2 _2auy+(a 2 +b2)u 2 =b 2

Replacing again y by AC L and u by _ in equation (A9), and using, equation (A5) gives

AC2 - 2CLaACL t_ + (C___

The discriminant of eq. (A10) is

1

+ k2C-2Lq )_2 = k2C-2Lq

(A8)

(A9)

(A10)

which means that eq. (A10) represents an ellipse. For kC2q = 0 the ellipse is reduced to a line as

follows from (A8).

17
p= o- p = -5. p = -10- p -- -20. p = -30- p = o. p = o.

o_,dog

8e = O" 8e = O" 8e = O" 8e = O" 8e = O" 8a = 20" 8t = -20"

-4,0000

0.0000

5.0000

10.0000

15.0000

20.0000

22.0000

24.0000

26.0000

28.0000

30.0000

32.0000

34.0000

36.0000

38.0000

40.0000

45.0000

50.0000

60.0000

70.0000

80.0000

-0.1000

0.0535

0.2590

0.4977

0.7470

0.9774

1.0543

1.1468

1.2070

1.2529

1.2726

1.2780

1.2650

1.2388

1.2143

1.1347

0.9255

0.8377

0.7202

0.5403

0.2950

-0.1052

0.0500

0.2546

0.4959

0.7447

0.9831

1.0919

1.1593

1.2258

1.2716

1.2718

1.2696

1.2613

1.2233

1.1374

1.0445

0.8813

0.8235

0.7046

0.5240

0.2894

-0.1041

0.0478

0.2484

0.4781

0.7181

0.9672

1.0545

1.1202

1.1604

1.1700

1.1916

1.1907

1.1988

1.1806

1,1376

1.0513

0.8833

0.8153

0.6852

0.5O48

0.2850

-0.1102

0.038O

0.2337

0.4425

0.6625

0.8482

0.8800

0.9199

0.9724

1.0138

1.0029

0.9668

0.9926

1.0152

1.0244

1.0237

0.8518

0.7826

0.6658

0.4967

0.2742

-0.0877

0.0427

0.2249

0.4202

0.6119

0.8041

0.8358

0.8523

0.8629

0.8374

0.8447

0.8594

0.8588

0.8556

0.8682

0.8860

0.8402

0.7547

0.6289

0.4616

0.2567

0.2025

0.3555

0.5981

0.8221

1.0309

1.2382

1.3285

1.3994

1.4422

1.4577

1.4314

1.3981

1.3553

1.3389

1.2628

1.1145

0.9767

0.8798

0.7027

0.50O4

0.2331

=

-0.4338

-0.2586

-0.0692

0.1357

0.3637

0.6066

0.6879

0.7718

0.8462

0.9033

0.9484

0.9811

1.0126

1.0192

1.0033

0.9366

0.7748

0.7037

0.5963

0.4553

0.2629

Table I. Effect of angle of attack, sideslip, and elevons and flaperons on lift coefficient.

18
p = o. I_= -5. p = -_ p = -20. p = -30. p = o. p = o.

o_,deg

8e = O" Be--O" 8e = O" 8e = O" 8e = O" 8e = 20" 8e = -20"

-4.0000

0.0000

5.0000

10.0000

15.0000

20.0000

22.0000

24.0000

26.0000

28.0000

30.0000

32.0000

34.0000

36.0000

38.0000

40.0000

45.00O0

50.0000

60.0000

70.0000

80.0000

-0.1022

0.0535

0.2612

0.5058

0.7714

1.0335

1.1269

1.2416

1.3256

1.3993

1.4480

1.4839

1.5012

1.5046

1.5115

1.4546

1.2840

1.2674

1.3642

1.4411

1.4643

-0.1075

0.0500

0.2568

0.5040

0.7690

1.0400

1.1689

1.2575

1.3495

1.4245

1.4526

1.4809

1.5044

1.4968

1.4311

1.3533

1.2354

1.2604

1.3566

1.4347

1.5223

-0.1064

0.0478

0.2505

0.4858

0.7414

i.0232

1.1291

1.2155

1.2794

1.3135

1.3638

1.3915

1,4320

1.4447

1.4298

1.3597

1.2374

1.2460

1.3196

1.3916

1.4958

-0.1123

0.0380

0.2358

0.4499

0.6847

0.8991

0.9456

1.0035

1.0775

1.1430

1.1467

1.1362

1.1921

1.2478

1.2908

1.3254

1.1949

1.2033

1.2935

1.3736

1.4383

-0.0899

0.0427

0.2274

0.4283

0.6346

0.8545

0.9008

0.9333

0.9608

0.9508

0.9779

1.0147

1.0360

1.0557

1.0972

1.1484

1.1730

1.1561

1.2230

1.2955

1.3444

0.1980

0.3555

0.6055

0.8426

1.0769

1.3297

1.4459

1.5457

1.6195

1.6677

1.6715

1.6692

1.6567

1.6773

1.6268

1.4834

1.4104

1.3962

1.4325

1,5044

1.5504

-0.4403

-0.2586

-0.0639

0.1469

0.3875

0.6553

0.7512

0.8534

0.9491

1.0306

1.1021

1.1637

1.2267

1.2634

1.2749

1.2268

1.1051

1.0979

1.1702

1.2660

1.3743

Table 1/. Effect of angle of attack, sideslip, and elevons and flaperons on normal-force

coefficient.

19
p=0. p=-5. p= -10- p = -20- p = -30. p = o. p = 0.

a, deg

8e = 0" 8e = O" 8e = 0" 8e = 0" 8e = 0" 8e = 20" 8e = -20"

-4.0000

0.0000

5.0000

10.0000

15.0000

20.00O0

22.0000

24.0000

26.0000

28.0000

30.0000

32.0000

i 34.0000

36.0000

38.0000

40.0000

45.0O00

50.0000

60.0000

70.0000

80.0000

0.0201

0.0242

0.0441

0.0733

0.1107

0.1530

0.1685

0.1858

0.2009

0.2161

0.2244

0.2256

0.2214

0.2183

0.2186

0.1995

0.1867

0.1793

0.1578

0.1208

0.0594

0.0156

0.0270

0.0458

0.0744

0.1107

0.1531

0.1734

0.1880

0.2059

0.2214

0.2243

0.2238

0.2222

0.2164

0.2020

0.1890

0.1728

0.1634

0.1493

0.1181

0.0466

0.0265

0.0318

0.0476

0.0755

0.1110

0.1515

0.1679

0.1841

0.1970

0.1995

0.2094

0.2168

0.2196

0.2162

0.2068

0.1943

0.1750

0.1596

0.1386

0.1065

0.0428

0.0163

0.0261

0.0428

0.0702

0.1040

0.1458

0.1605

0.1574

0.1726

0.1938

0.1985

0.1771

0.1738

0.1822

0.1863

0.1926

0.1701

0.1462

0.1371

0.1074

0.0560

0.0237

0.0329

0.0515

0.0764

0.1035

0.1051

0.1248

0.1470

0.1627

0.1577

0.1476

0.1377

0.1357

0.1407

0.1460

0.1479

0.1664

0.1386

0.1144

0.0794

0.0479

-0.0627

-0.0558

-0,0479

-0.0095

0.0385

0.0855

0.1047

0.1246

0.1437

0.1603

0.1680

0.1700

0.1708

0.1773

0.1698

0.1478

0.1594

0.1596

0.1374

0.1093

0.0458

0.0937

0.0998

0.1204

0.1525

0.1940

0.2359

0.2521

0.2694

0.2834

0.2931

0.2977

0.2966

0.2987

0.2955

0.2891

0.2631

0.2431

0.2386

0.2114

0.1706

0.0963

Table ITI. Effect of angle of attack, sideslip, and elevons and flaperons on

pitching-moment coefficient.

2O
_deg

-4.000

0.000

5.000

10.000

15.000

20.000

22.000

24.000

26.000

28.O00

30.000

32.000

34.000

36.000

38.000

40.00O

45.000

50.000

60.000

70.000

80.000

CLa

2.200

2.230

2.520

2.780

2.770

2.390

2.234

1.947

1.436

1.021

0.479

-0.064

-0.479

-0.989

-1.500

-2.010

-1.590

C N2.250

2.290

2.590

2.880

3.030

2.850

2.808

2.622

2.175

1.803

1.280

0.761

0.314

-0.207

-0.766

-1.400

-0.952

Cm=

-0.040

0.131

0.280

0.376

0.451

0.466

0.459

0.429

0.369

0.295

0.168

0.019

-O.070

-0.100

-0.212

-0.264

-0.100

CLse

0.911

0.882

0.957

0.986

0.957

0.905

0.917

0.900

0.854

0.796

0.693

0.596

0.493

0.458

0.372

0.292

0.287

CNse

0.917

0.882

0.957

0.997

0.986

0.968

0.997

0.991

0.963

0.911

0.814

0.722

0.619

0.590

0.504

0,367

0.435

-0.830

-0.830

-1.240

-1.560

0.165

0.537

0.277

-0.021

-0.100

-0.160

-0.286

-0.435

0.252

0,183

0.143

0.103

0.430

0.378

0.344

0.252

Cmse

-0.223

-0.223

-0.241

-0.235

-0.223

-0.218

-0.212

-0.206

-0.201

-0.189

-0.183

-0.183

-0.183

-0.172

-0.172

-0,166

-0.120

-0.115

-0.109

-0.086

-0.074

Table IV. Effect of angle of attack on stability and control parameters.

21
Component

D

aLex

CLq

, a, deg

20.8

25.9

30.8

35.8

40.8

45.9

50.8

55.9

61.1

20.8

25.9

30.8

35.8

40.8

45.9

50.8

55.9

61.1

k = .081

2,7173

2.0605

1.0483

0,4157

0.3572

-0.1074

-0.2827

-0.5163

-0.7259

0.6274

6.8878

13.4790

17.0380

18.0300

10.8080

7.3799

4.0848

3.5036

k = .135

2.7262

2.3022

1.5909

1.0925

0.7653

0.3471

0.0172

-0.3175

-0.6200

-0.6749

2.8420

6.8415

7.8742

7.8265

5.3759

3.6589

2.6166

1.7856

k = .190

2.7169

2.4510

1.8777

1.2745

0.9657

0.4584

0.2680

-0.1771

-0,4795

-0.4411

1.3282

3.5802

4.5156

4.2304

3.5004

2.0937

1.5641

1.3260

k = .237

2.6812

2.4699

1.9985

1.4028

1.0359

0.6013

0.2907

-0.0864

-0.4348

-0.4391

0.5986

2.3319

3.2101

2.9332

2.2017

1.2329

1.0655

1.0968

k = .397

2.7182

2.6217

2.1274

1.6543

1.2423

0.9278

0.4220

0.0863

-0.2624

0.1617

0.4959

1.0400

1.4278

1.4082

1.2853

0.6319

0.2893

0.2086

Table V. In-phase and out-of-phase components of lift coefficient.

22
Component

CN a

CNq

a, deg

20.8

25.9

30.8

35.8

40.8

45.9

50.8

55.9

61.1

20.8

25.9

30.8

35.8

40.8

45.9

50.8

55.9

61.1

k = .081

3.2712

2.8836

2.0690

1.5553

1.5905

1.0970

1.0552

0.9679

0.9027

0.6466

7.4524

15.0792

20.4228

23.1772

15.4526

11.8092

7.4302

8.0909

k = .135

3.2778

3.1394

2.6814

2.3672

2.1257

1.7409

1.5107

1.3127

1.1141

-0.8186

2.9259

7.4842

9.2855

9.9533

7.5281

5.7557

5.2961

4.2358

= .190

3.2707

3.3009

3.0051

2.5946

2.388O

1.9091

1.9158

1.5457

1.4076

-0.5106

1.3458

3.9208

5.3797

5.4853

4.9940

3.3916

2.7569

2.3987

k = .237

3.2352

3.3276

3.1475

2.7657

2.5087

2.1241

1.9464

1.7166

1.5303

-0.4904

0.5894

2.5651

3.8608

3.8410

3.2200

2.1095

1.8374

2.0903

k = .397

3.2971

3.5424

3.3558

3.1757

2.8960

2.7033

2.3034

2.1429

2.0425

0.1744

0.5346

1.1490

1.7763

1.9113

1.8646

1.2027

0.6297

0.3287

Table VI. In-phase and out-of-phase components of normal-force coefficient.

23
,Component

Cm(x

Cmq

a, deg

20.8

25.9

30.8

35.8

40.8

45.9

50.8

55.9

61.1

20.8

25.9

30.8

35.8

40.8

45.9

50.8

55.9

61.1

k = ,081

0.5183

0.4529

0.1901

0.1090

0.1509

0.0323

-0.0921

-0.1755

-0.2081

-0.8553

-0.1240

1.7197

2.3630

1.3537

-0.1715

0.3532

0.0235

-0.0310

k = .135

0.5096

0.4775

0.2764

0.2378

0.1682

0.0706

-0.0733

-0.1386

-0.1714

-1.1161

-0.7076

0.4942

0.5519

-0.3968

-0.5400

-0.0418

0.1021

0.0538

k = .190

0.5076

0.4937

0.3429

0.2325

0.1318

0.0253

0.0041

-0.1546

-0.1520

-1.0749

-0.8825

-0.1789

-0.3245

-0.7955

-0.4869

0.0527

0.1407

0.0567

k = .237

0.5013

0.4941

0.3668

0.2419

0.1336

0.0458

0.0489

-0.0612

-0.1195

-1.0589

-0.9682

-0.2611

-0.4752

-0.7878

-0.6901

-0.1078

0.1023

0.2266

k = .397

0.4656

0.5023

0.3865

0.2278

0.0124

-0.0816

0.0633

0.1958

0.1636

-1.0527

-1.0761

-0.7195

-0.7640

-0.6640

-0.6076

-0.4099

-0.2927

0.0463

Table VII. In-phase and out-of-phase components of pitching-moment

coefficient.

24
Standard Error

Measured s(,_) s(ca(oo))*

Data min max min max

,T

0.13 0.15 i

CL a

CLq

m

CN a

CNq

Cm_

Cmq

0.056

0.091

0.034

0.074

0.12

0.14

0.19

0.21

0.30

0.069

0.090

0.21

0.25

0.34

0.17

0.11

* for index A a = La,L q ,Na,N q ,ma,or m q

Table VIII. Minimum and maximum values of standard errors of estimated parameters.

Measured

Data

EL a , CLq

CN a , CNq

Cm a , Cmq

17.2 + 1.0"

17.1 + 1.3

25.1 + 8.7

Parameter

b I ,sec -1

2.71 + 0.16

2.73 + 0.21

1.86 + 0.64

* the second value indlchtes the stanclard error

T! ,sec

0.368 + 0.023

0.365 + 0.028

0.540 + 0.190

Table IX. Estimated and computed parameters.

25
Parameter CL CN

o

O0

01

02

03

04

05

06

07

08

09

010

1.4

4.8

33.6

-50.9

-2.0

5.7

-3.4

12.1

-46.2

35.7

-57.8

3.8 32.4

11.3 -44.6

1.7 -2.6

3.9 7.2

2.7 -4.1

0.51 13.8

1.7 -51.8

1.3 38.9

3.4 -59.5

2.1

7.1

5.7

16.9

2.5

5.8

4.0

0.75

2.5

1.9

5.0

Table X. Estimated parmeters and their standard errors in Model II for measured lift and

normal-force coefficients.

26
II

\

\

j

i

LO

I

Cd

EEE

II II II

{/) ._ I0

08E

_JX

CO

14. 0

..C:

.¢=.. 0

co

,>0

elIJ_

27
CL

C

.4 "mr- I r

1.2

1

0.8

0.6

0.4

0.2

0

-0.2

2

1

N

0.5

1.5

................... ._..................... , ..................... _...................... .:'..................... ._....................

0

-0.5 ,, i I L,, I I = , , , I , , , T I ,

0.25 --_ ..... , ..... z ......

0.15

0.1

0.05 ................... i.................... _..................... :................ -:..................... _.............

0 , , , I , , , , , , , , , ......

-20 0 20 40 60 80 1O0

a, deg

Figure 2. Variation of longitudinal coefficients with angle of attack. 13--0°, 8_--0°.

28
CL

1.4

1.2

1

0.8

0.6

0.4

0.2

0

-0.2

2

1.5

1

C]v

0.5

0

0.2

0.15

0.1

0.05

i I t I I I I t I I I I I I I I I I

............................................... i ............................................ i ....................

.................... i..................... ' .................. i ..........................................

...._.................. --_- _=-2o_ .................. _....................

L-- ----_-- _ = -30 deg

I I I I I I I , , , i _ , , , I I l I I l I

f I I I I I t I I I I I t I I I I I I t

................. !.................. ' ...... i.................... !...................... i................... -1

: ?

__II_.L.__L._ _._:=L± I I I, _ I I I I L

0

-20

I I I I I I I , i i i i i I I I I i I I

, , _ I, _ , I , __, I,,, I , , ,

0 20 40 60 80

a,deg

100

Figure 3. Effect of sideslip on longitudinal coefficients. 6e--0°.

29
.5 -i 6 i

CL 0.5

0

-0.5

2

1.5

1

c_

0.5

0

-0.5

0.3

0.25

0.2

0.15

Cm

0.1

0.05

0

-0.05

-0.1

-20

A.. . ..................

t I

..... -- = eg ..........i....................

---+--- 6e= -20 deg

_J[,J_l i;illll

!!!! i!!!!!!!

iiTiii:

i!iii!!!!!

r f , _ , , _ / f , _ / = , , I , , I I , , ,

0 20 40 60 80 1O0

tx,deg

Figure 4. Effect of elevon and flaperon deflection on longitudinal coefficients. IB=O°.

30
3

2

1

-1

-2

4 ' ' ' I ' ' ' ! ........... F--

E

3

2

1

0

-1

-2 .................................................................. '..................................................................

-3 _ I i I I I L I J _ I 1 _ L I I I I I I i i l

0.6

q _ i j i i i ! i i i i i i J _ I b I J

0.4

0.2

0

-0.2

-0.4

-0.6 ....................................................................................................................................

-0.8 ,,, _,,, i,., i,,, i,,, I , , ,

-20 0 20 40 60 80 1O0

ot,deg

Figure 5. Variation of stability parameters with angle of attack.

31
0.8

0.2

0

1

0.9

0.8

0.7

CNs_ 0.6

, , , I I I , I l , t I , I-1 I , I I i I K A

0.3

0.2

-0.05

-0.1

-0.15

_- F_ ] TT_ _" I ! I I I t I I I I '

0.5 ....................................................................................................................................

0.4 ......................................................................... _-" '........................................... """"i

I I I I L _ , I , _ , l_l r I , I I t,t I I

-0.2

I I I I I I I I I [ | l I I I f I i i

1 I J I _ 1 I I | 1 I _. I I I | l I I [ I

0 20 40 60 80 1O0

a,deg

Figure 6. Variation of control effectiveness with angle of attack.

32
36

34

32

a,deg

30

28

26

1.45

1.4

1.35

CL 1.3

1.25

1.2

1.15

1.1

1.05

1.8

1.7

1.6

CN

1.5

1.4

1.3

1.2

0.27

0.26

0.25

0.24

Cm 0.23

0.22

0.21

0.2

0.19

.... I .... I'' ''1'' '' I'_*'1'_'_ I''"_1 _f_

....... _............ _............ _............ _............ _...........

.......... _............ _............ _............ _........... _............ _.......... _...........

i LLI I

! i i i !

i : i

.......... _............ _.......... _............ _............ _............ _............ _...........

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

t,sec

Figure 7. Variation ofangle ofattack andlongitudin_ coefficien_ withtime, k=.190,

_o=30.8 °.

33
56

54

52

_,deg

50

48

46

0.9

0.88

0.86

0.84

0.82

0.8

0.78

1.5

1.45

1.4

CN 1.35

1.3

1.25

1.2

1.15

1.1

0.18

0.175

Cm

0.17

0.165

,,,|,ft ..... I .... I ............ t ....

! iiiiiiiii

.......... i........... i............ i............ i.......... !............ i.......... i...........

' ' '=_=1.... I ........ I .... t .... t .... I ....

rF'_rr_T_'''l'' '' t .... t ........ I .... 1

2-......... ,'............ _............ _........... ,'............ _............ _.......... ,:.......... ] 2

.... i .... i .... i ....... : a=t j..,_._

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

t,sec

Figure 8. Variation of angle of attack and longitudinal coefficients with time. k=.190,

_o=50.8 °.

34
3

2.5

2

__ 1.5

CL_ 1

0.5

0

-0.5

-1

20

15

10

%

5

I ' ' ' ' i i i i i J--i -i _ , • , "r_

..... i........................ !..............................|

: ----e_- k=.081 i

k=.134 II......

k=.190 |

k=.237 |

.... _ -- k=.397 _ ....

___ I I 1 ] ] 1 I I [ I I I ] I I i ] i I £ __JL---J,----

0

-5

20

i

, , , , I = _ , , J , , = = , , LJ._l_l , = =

30 40 50 60 70

a,deg

Figure 9. Variation of in-phase and out-of-phase components with angle of attack for

different values of reduced frequency.

35
a.s ...._i ...................................................... i---t----e- k=.081 I---

,_.--,_-_ ._.._ i I _ k=.134 |

_--_._ _ _ i I --_- k=.190 |

__. ....................... i----t - _ k=.237 |+--

CNot 2"5

2

1.5

1

o.5 .... i ....

i

25 _,,,_ .... _,,,,! .... p....

20

15

Gvlo

5

0

-5 , .... t .... I , , i , I , I I _ i , I , ,

20 30 40 50 60 70

a,deg

Figure 9. Continued.

36
0.6

0.4

0

-0.2

2

1.5

_ 1

Cmq 0.5

0

-0.5

-1

................................................... _........................... _........................

......................... ;........................... i-.................. ;,........................

- I ------E_ k-_134 _''_"-,,_-._;_

- I _ k=.397 i i i

-I ; i i

.... i,,, ,i .... i, ,, , i ,,,,

L.

1 I I I I I I I I I I f I I ] I I I I I I

30 40 50 60 70

t ,deg

Figure 9. Concluded.

37
14 , T_i_, _r_ .... i_,,_1,, ', .....

12

10

-- 8

CLq 6

4

2

, ---4--- !

i_lt .... t,ij,i,,,L i iiI 11 I, , I ....

• r T _ _ ] * i , i , o i _ i _ 1-_ I i i i i I i I , ,

- i i i i _ :

14

12

_ 10

CNq 8 ................. i................ _..................._..................."..................;...................!.................

6

4

2

o !,,

2 ,

1.5

1

Cmq 0.5

0

-0.5

-1 L

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

k

Figure 10. Variation of out-of-phase components with reduced frequency.

38
CL

C_

0.2

0.15

0.1

0.05

0

-0.05

-0.1

-0.15

-0.2

0.04

.....I -- ---Measured I: ........................ :_._

I -- -- -Computed l i____-_ /_

......., I-__---_ .......

.................... ;iiiiiiiiiiiii_iiiiiiiii__

0.03

0.02

0.01

0

-O.01

-0.02

-0.03

-0.04

........................... ___ iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii i- ̧

f

-5 0 5

a,deg

Figure l 1. Comparison of measured and predicted values of CL and Cm. k=. 190,

ao=30.8 °.

39
0.06

0.04 /j/ _ \

0.02 ___ _'_,_

o ................................................

/ -- /i -'111/

-0.02 1............................... _.._ ............... _ .....................

-0.04 _.._--_ _ ........... !......l--- Measured

\ ---1t/" I Computed

-0.06

c_

-0.005

0.01 _ •

// "_

) "\ ,-

0.005 .t:_ ........................... / ................................................... 1/ ...............

Ill_'\/'_ \.'_ "'1- - /_. _,/,/ /-S

ot-__ ....... :_ff "_:J__" .....

11 \\ _ / _ /

/

........................................ _----_ ............................................................................... I-

-0.01

-5 0 5

a,deg

Figure 12. Comparison of measured and predicted values of C L and Cm. k=.190,

0_0=50.8 °.

40
05 .... , ....

A

O_A

2

1.5

1

O_

-20

-40

¢,deg

-60

-80

-100

...................................................... :..:..e._.._..=_.L.z..z..7..5..ZZZS.ZZ2.

..o-"

,/ 1!

/

J

/

0. "

-1

\ i i i i

" _ i i i _L---_---¢

• _ i i _-o-!--- i ::

..... x.......i................i................ _-----7__'-}-'--.............i...............{................. _..............

" _ i i .i" ! ! ! i

• ', i -_, i i i

..............!-._............_-,,............_................_................!............ _................-.:.............

-120 .....................................

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

k

Figure 13. Amplitude and phase characteristics of CJo_ transfer function.

41
CL 0.5

lll---_|J Ill ill I'il III

0.25

0.2

Cm

0.15

0.1

0.05

0

-20

.......................................... i................. !.............................

.................... i.................... _H. ' ................i......................i....................

.................... _..................... i......................_............................................_....................

0 20 40 60 80 1O0

a,deg

Figure 14. Longitudinal coefficients obtained from static and oscillatory data for k=.190.

42
1.4

1.2

0.6

0.4

0.2

2O

15

cL, lo

5

0

k = .190 ....._.....................t .........................................

• k = .081 tail off :

• k= .190 tail off ; ;

............................................................. i ..............................................................

................... _................................... i...................... _.........................................

I I I I I , , , I ' ' ' ' , I I [ t I I I I I I I

I I I I i I I I _. I I i i i I I_._] l I I I ] I I I

0 -5 -10 -15 -20 -25 -30

13,deg

Figure 15. Variation of in-phase and out-of-phase components with sideslip angle.

43
2.6

2.4

2.2

CNa 2

1.8

......................................................................................................... i ................... !

i, i=i,,i ........... iiiiiiii 

1.6 _

20

15

10

5 _ ....................

0 _L_j, I l, i, I J _-LL_ , , , , I , , , i I ....

0 -5 - 10 - 15 -20 -25 -30

Figure 15. Continued.

44
0.3 , .... , .... . .... ! .... ,_p,, _..._q

_- / --_m.._....i ...................... i... _ k = .190 |-J

......... i _ _ • k=.o81tailoffII

0.25 i • k = .190 tail off I_

Cm !

£Z

O. 1 _ ..... i...................... i..................... i...................... ;.................

0.05

0

2.5

2

1.5

-Cmq 1

0.5

0

-0.5

0 -5 -10 -15 -20 -25 -30

I_,deg

Figure 15. Concluded.

45
1.5

1 ---r-, , , ....

m

CL,_ 0.5 .................... _...................... _..................._............................................. _' ....................

0 ....I _ k : .081 ................ i...................... i..................i....................

I

16

14

_ 12

CLq 10

, , , ,_[ , , , , I , , , ,

E

[ ] i i i i l J I

8

6

4

2

-30

.................... ! ............................................................................................................

-20 -10 0 10 20 30

8 e ,deg

Figure 16. Variation of in-phase and out-of-phase components with elevon/flaperon.

(Zo=35.8 ° .

46
2.5

2

%

1.5

0.5

25

i I I i I j R j i l J I [ t i i i I ]____.j___

2O

15

10

5

0

-30

I _ I I J _ I I I I t I _ I I I I I-T I-'-I -_ I I T_

I I | I I 1 I I I i I I ] _.,L _ _--,_ I I _ 1 I I I i ! I L

-20 -10 0 10 20 30

8 e,deg

Figure 16. Continued.

47
.3 _7"-- i

0.25

0.2

0.15

0.1

2.5

2

1.5

0.5

0

, i

----e--- k = .081 I

k = .190

.... I , , _ I .... I .... l , , , , ,,, ,

-20 -10 0 10 20 30

t_e ,deg

Figure 16. Concluded.

48
3

2

-2

-3

0.6

0.4

a

-0.2

-0.4

0

-0.5

-1

-1.5

-2

-2.5

-3

-3.5

' .... &' 'o"_ .... ! .... I .... i .... i .... i .... _

l__LS,a,icOata I

.............. i........... !--..%........ i..... I ' Oscillatory Data

.i.....__.__oi I } 2s c°nfldence interval!! .............. i................i................. L................ i................ _................ J............

: i

_= _=1 JJ J I I I I .... I .... I .... I ....

..............i,I,,,I,,_I_I _'''-

....................................iii . ii!iiiiiiiiiiii

,I

/

:1

/

, , , , I , , ,, , , I , , , , IZ, , , , I .... I .... I , , , r

I I t I I I I I I I I I I I I I

,,,,I,,,,l,,,,I,,,,i,,,,I .... t,,,,1,,,,

0 10 20 30 40 50 60 70 80

a,deg

Figure 17. Estimated parameters of lift components. Model I.

49
4

3

2

0

-1

-2

1

0.5

-0.5

0

-0.5

-1

-1.5

a -2

-2.5

-3

-3.5

-4

_t_ r,_ --_,'l .... ! .... ! .... I .... I''

I i I o Static Data

.............=--.---o......._,.-...........i .......i _ Oscillatory Data

o _ _,_ i I } 2sconfidence interval /

Q

i i :o i i i !

i ! i i _ 6 i

............. ................ .............. ............ ...........

7, _ TP_-_-I V ............... ! ........

............. $ ................ i .............. i ................ ,,'-................ " ............... _................ ::..............

.............. _................................. i........ _\iJi........ !................ _.............................

0 10 20 30 40 50 60 70 80

ct,deg

Figure 18. Estimated parameters of normal-force components. Model I.

50
........ ooo.... _o, 2s°'C'"at° 

n--,li

cm (oo)0 ......................................, , i

o i i ' i

0 :

i o! i

-0.5 ,,,, I ...... L_ ...... :,__

0.2 r , , , , , _ , , _ i , _ _ , i i i i i _ _

0 .............. i................ i................ i................ T................ i......................... _..............

-0.2

Cmq (oo)_0.4.0.8_0.6

.,._il. ......

0

-0.2

a

-0.4

-0.6 .............. ._.............. _............. _......................._................ _............. _...........

-0.6 _-_ _,, I ....

0 10 20 30 40 50 60 70 80

a,deg

Figure 19. Estimated parameters of pitching-moment components. Model I.

51
3

2.5

2

1.5

1

0.5

0

-0.5

-1

! __ _ :i ....................... o Measu k=.081 o: =_] I_

._-_,___.......................... [] k=.l_ =t

- _[]_,,, i o k= 237 |:

- ..........."_ ._ ....................... :.......................... t_ k=:397 __

- \ \_" i Estimated: I--

- r "" A :

:_ \i_.\ ............. __+- k=.osl I:

............. X_-._--tC_-i............. __. - k=._34 I:

::'e \ -_J, .. -- _.- - k=.237 I1:

15 .......................

-- 10 ......._........................... :........................

Cz.,,,

5

-5 L..,__,__--,_- i i

20 30 400_,deg 50 60 70

Figure 20. Measured and estimated in-phase and out-of-phase components of lift

coefficient. Model I.

52
4

3.5

3

CN_, 2.5

2

1.5

1

0.5

25

' ' ' ' ! .... ! ' ' ' ' I ' ' ' ' ' ' ' , -1-

i Measured: E o k=.081

............ zx.........- ..........................i...........................i .... [] k=.134

• . =. _ i_ i o k=.,'Z37

" _ <,,_ i i A k=.397

_ _,,__,._-_._ A I " Es._ted:

::D _ _\ A i -- _ - k=.237 \ _ _ : i - - .*. - - k=.397

io'X ,, i

....... + .................... i......................,_-!.................. :z_

................................................... :..........................!.o...........o .........";.........................

! ! i

__ 15 ........................ + ......... _.......................... _....................

CNq 10

5 ........... _.......................... i........................... i_..o ......... i......................

o _<t-....--..._ ....................... '........ ................... '....... :_.-....-..,_ .....................

-5 , f _ t_i ........ , , , , I , •.._t.._.t_

20 30 40 50 60 70

a,deg

Figure 2 l. Measured and estimated in-phase and out-of-phase components of

normal-force coefficient. Model I.

53
0.6

0.4

0.2

Cmo

0

-0.2

-0.4

2.5

2

1.5

1

Cmq 0.5

0

-0.5

-1

-1.5

_ I I + I I I I I t t t I I [ t I I !

i -. _ ! i

............. :.......... i0-..-,-..--..

.....--------___ +:_i.......................... i -_ i; ...............

Measured_-._::.: .................... i ........................

o k=.081 i _ i -

o k=.237 i i i _ ,

k=.397 i i [] iZ

Estimated" i i o i u --If

• " " +" .......................... _........................... ' "0" ...................

- -e - k=.081 _ i /

-+ _. - K=.I_ ! i 1

-- _ - k=,237 ! i J

k=.397 t

_ _ • - _ J

,_L , , _ , I , + , , , , , ,/

iiiiiiiiiii +++ ..........

.......,):5._._.-::.-:_ .......... :.+.;_.._!.+. ....................... ?........................ ......... .......................... +........................... +.........................

+...........

2:0 30 40 50 60 70

_x,deg

Figure 22. Measured and estimated in-phase and out-of-phase components of

pitching-moment coefficient. Model I.

54
3

2.5

2

CLa 1.5

1

0.5

0

-0.5

I I I I J I I I I I I I 1 I I I I T- T_

-_-i I o Measured l t

...................ii......... .................. i[.................. I .- Predicted. d Ill

4 ....................... i....... ................... _........................... i....................... -:

] o i i

3

CLq 2

o io

1

0

-1 , I I I

2O 3O 40 50 60 7O

o_,deg

Figure 23. Measured and predicted in-phase and out-of-phase components of lift

coefficient. Model I, k=.190.

55
3.5 "--_--r _ _ ,-r_--_ , , , I ....

3

CN,_ 2-5

2

1.5

- _ i

_.., i o ,,,,ea_,.,re_, I

........................ _ ....................... _................. ---+I- Predicted Ii i I

0

, ,o , 'iiiiiiiiiiiiii

" i ::o

.._[ i I _ 1 I I I __.l l [ _L i l i I I I [

5 2-....................... :.............. e......... _...................... .,........................

4

CNq 3 _ i

2

1

0

-1

20 30 40 50 60 70

a,deg

Figure 24. Measured and predicted in-phase and out-of-phase components of

normal-force coefficient. Model I, k=.190.

56
o._.................. i......................

i o .o_,0_o0 i---_ 0.4 -_ ........................... _............... I ' Predicted I-_

_ 0.3........................ !........................ i............... ;.......... _......................_................ ".__..j

Cm_ 0.2

o,

0

-0.1 ...............:....................................................

0 0

-0.2 , , , , r .... _ , , , , i , , , , I , , , ,

0.2 I o _ -

i i i i i i i i i i i i i I i i i 1

0 !o io

-0.2

Cmq " o i i -

lore 4

_o,o -0.8 ...................... _........................... io........................ i.......................... _.........................

-1

-1.2 ,_=_L____.___.

20 30 40 50 60 70

a,deg

Figure 25. Measured and predicted in-phase and out-of-phase components of

pitching-moment coefficient. Model I, k=.190.

57
3

2

-1

-2

-3

0.6

0.4

(_)0.2

0

a

-0.2

-0.4

0.5

0

-0.5

-1

-1.5

-2

-2,5

-3

-3.5

.... (_ i ;01 i 1_11 ........... i tlIi[-T .... i i i i

0 ) _\\\ I ' ' I

i •_ | Osc'llatory Data:

.............._................. i_r_ .............................. | ..... Model I

::_ i :: | ..... Model I

............................................................... i................ i................ i.........

.............. i.............. i__---:--o ............ i............. _................ "."............... !..............

.............. _................. _.__o-----i ........ __ ............... i..............

0 ., o

.... I .... i .... I;,,,I;i,AI,,,,I,,,,I,,,,

--Fi I I I I I L * i I J i I _ t_r j i t I J i t i i t I * , _

,i a' i i

) ;l i )

; I $ i

.......................................................... T....T.....7..._.T.. i ................)...............................

/ _ ' i i ,,, )

, . i, i ,

..............:............... _.............•................. !................-................,............... _..............

i t

I

' i

'' _' i_ _ I_T' I' '-_--' I........

i ! i !

.............. ;................ i............... i................. i................ i................ i................. .............

i i, i ) i ) i

i i, i i i i i

.............. _................ i.............. _................. ._................ ,_.............. -_................ _..............

) ) "',! ) ,'i ) )

.............. _.............. i............ i............... )....' ......i............... l............. !...........

!

................................................ _ _.......... _-,............................ i..............................

................................................ i........... ?.-_-i, ................................ i..............................

J__.L_I , _ ; , I , , ,_ I _ _ , , I _ , __ I , , , , I , , L_

0 10 20 30 40 50 60 70

_,deg

80

Figure 26. Estimated parameters of lift components.

58
4

3

2

cNo( )1

0

-1

-2

1

0.8

0.6

0.4

CNq (°°)

0.2

0

-0.2

-0.4

-0.6

1

i\ ! I Osci,ato_Data:lt-'

.............6......o.......i.',_............i.................I ..... Model I I_ : .o_,_ i i l -- ModelII I_

o i i_', i ::1 o Static Data |7

.............. i................ i' oi ................ i................. ................ .................. "

i _,,,,61 i i i

............._................ _............. __iiii_ .................L...............- ................................ i...........

i i i,o i ! i

i i .x i cb

i i i ,o i L _ o

\'4---'4" i i

.............. _-................ _................ _................. ,k,.....D ...... _................ i................ _......... :....

.... I .... I .... t , i_, , J , ,, j I .... J .... ! ....

I I i I I I l I l I I I I,,, I ' i I l I I J I I I I I I I I I

................................................................. _........ !_ ......................................................

i t 'l

............................... _................ _................ ._.......L....._.:....J..._.3.._._................ <..............

i i !, i

___ i .... '. __,'j ___ i _ i i

i i / !, _ .......................]..............

i i ,i i i _ !

i i , i i == i i

, , , , ] .... I , J i i I i i I_d_ , I , . , , I ,._ _ I . . ,

I I I I I I I I I I I I I I I I I I • ] i I [ Tq I'--F

a

o

-1

-2

-3

-4

.............................. ° .............. ° ..............

i i_ i i i i i

i

..............,';................ i....._........i................_..............."................................ i...........

..............i .............................__................ .."................•............._................_.............

i i :_ i , i i i

.... -_.......... i ........... i ,, _ i i i

]......:,-.......V;';.......... i.............................. i..............

i ,,i, i i

i 'i,

.... _..... ,,,,,,,,,' .............. ] i ,,

0 10 20 30 40 50 60 70

_,deg

8O

Figure 27. Estimated parameters of normal-force components.

59
3

2.5

2

1.5

1

0.5

0

-0.5

-1

20

"'-7 I l I I I I I I [ • • I J I I I | i I l

_'- z_ Measured:

- .-_. _ .........,..-.................................................... o k=.081

-- \"'_ -. i [] k=.134

- \i_. ::A o k=.237

__ _ ..................... i........................... _ k=.397

- \ _ _.. i Estimated:

: _ il_ _: J_,,, i ----e- k=.081

........."_T......"__Z:-.] ......................... i----m -k=.134

- _ "/, _ J -- .- -k=.237

........................ .!o..___ ___,_(_.;_.... _i__.__k:.397

- i i imp\ A _ -

I- .... i, ,,, I,,, ,--L,,,, I I,, ,-1

!o

15

eL ' 10 .....---:---

5

0

-5

20

I I I t t I I I I

: !......................... i........................i...................

i i o i i

o ilw-_ _iiiiii

30 40 50 60 70

a,deg

Figure 28. Measured and estimated in-phase and out-of-phase components of lift

coefficient. Model II.

60
4

i _a..,_-I:

A _ o k=.081 II- 3.5 ....................._.......................... :........................... _ [] k=.134 IL- _ _ i A _ i o k=.237 I:

3_,,,.----._:,...-._ A i i ,,, k=.397 I:

3 \ ii _ i ! Estimated: t

....... \o_i ......._:'_ ........r_ ......................._.... + k=.081 I-

"_ "116 $_..". i -_m - k=.134 I:

-- _ iO .. _il _ i -- i- - k=.237 t

CN_ ' 2.5 ................-_i .........:::_-_-_-_ ..............i.... - - • -- _.3_;' I:

_,. o _\:..,. i,. _ ,-

2 ........................ ?_:_ ............. _._: ................... i_....................

:0

0.5 , , , , I , , , , I , , , , I , , , , i , , , ,

25 ...... T-, i , , , , l_ _ r T _, r,--

_0

E

:iiiiiiiiiiiiiiiiill iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiill

5 /,_ _._ ,,..__:_....................

0

//.//_r- '-.-J---_----: ......_.......................... ':.......................... _...........................-I--__i-_....................

-5 , , _ , I , , , , I .... I .... J__L__,_

20 30 40 50 60 70

a,deg

Figure 29. Measured and estimated in-phase and out-of-phase components of normal-force

coefficient. Model II.

61
2.5 .........._.........-.." ........................ _.....................: ........

i ! I o Measuredl _

2 __iii ii ,--Predicted, __

e,.o_.s °\i

........................ i.......................... i....................... r.......................... E.........................

0.5 ........................ (.......................... i.............. o ........ }........................ !.........................

O ........................ i ...................................................

"O, 5 i I I L 1 I I I I L i I I I I I ,, I i I

i o t i

3

0 i0 -

1

0

-1

20 30 40 50 60 70

_x,deg

Figure 30. Measured and predicted in-phase and out-of-phase components of lift

coefficient. Model II, k=.190.

62
3.5

3

CNa 2"5

2

1.5

_,,, , ! ..... -_ , ! , , , , ! , , , _-

o i i i

I o Measured I

' ......................"_-"' ................I _ Predicted I .............

i o i i i

i io i i

.........................i..........................._......................... ';.........................._.........................

_0

I I I I I I I ] l I I J I ] I I , 1_ L__

_llll llll tll_ lI]iIT_ _

: i i

5

I .......... " ....................

CNq 3

2 ....................... _.......................... [........................... _.......................... _.........................

o i i ! i :

1 ...................... _........................... i........................... _.......................... _.........................

o /

......................+......................... i..........................._.........................._.........................

-1

20 30 40 50 60 70

a,deg

Figure 31. Measured and predicted in-phase and out-of-phase components of normal-force

coefficient. Model II, k=.190.

63
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1. AGENCY USE ONLY (Leave blank) | 2. REPORT DATE 3. REPORT TYPE AND BATES COVERED

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December 1997 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Analysis of Wind Tunnel Longitudinal Static and Oscillatory Data of the

F- 16XL Aircraft 522-33-11-05

6.AUTHOR(S)

Vladislav Klein, Patrick C. Murphy, Timothy J. Curry, and

Jay M. Brandon

ill E

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

REPORT NUMBER

NASA Langley Research Center

Hampton, VA 2368 I-2199 L- 17682

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) ' 10. _PONSORING/MONITORING

AGENCY REPORT NUMBER

National Aeronautics and Space Administration NASA/TM-97-206276

Washington, DC 20546-0001

II

11. SUPPLEMENTARY NOTES

Klein and Curry: George Washington University, Hampton, Virginia

Murphy and Brandon: NASA Langley Research Center, Hampton, Virginia

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE "

Unclassified-Unlimited

Subject Category 08 Distribution: Standard

Availability: NASA CASI (301) 621-0390

I

13. ABSTRACT (Maximum 200 words)

Static and oscillatory wind tunnel data are presented for a 10-percent-scale model of an F-16XL aircraft. Static

data include the effect of angle of attack, sideslip angle, and control surface deflections on aerodynamic

coefficients. Dynamic data from small-amplitude oscillatory tests are presented at nominal values of angle of

attack between 20 and 60 degrees. Model oscillations were performed at five frequencies from 0.6 to 2.9 Hz and

one amplitude of 5 degrees. A simple harmonic analysis of the oscillatory data provided Fourier coefficients

associated with the in-phase and out-of-phase components of the aerodynamic coefficients. A strong dependence

of the oscillatory data on frequency led to the development of models with unsteady terms in the form of indicia]

functions. Two models expressing the variation of the in-phase and out-of-phase components with angle of

attack and frequency were proposed and their parameters estimated from measured data.

14. SUBJECT TERMS

Wind Tunnel Testing, Static and Oscillatory data, Unsteady Aerodynamics,

and Indicial Functions

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OF REPORT OF THIS PAGE OF ABSTRACT

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68

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A04

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Standard Form 298 (Rev. 2-89)

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