4 

. 

NASA Technical Memorandum 101631 

AERODYNAMIC PARAMETERS OF AN ADVANCED 

FIGHTER AIRCRAFT ESTIMATED FROM FLIGHT 

DATA, PRELIMINARY RESULTS 

VLADISLAV KLEIN 

KEVIN P, BRENEMAN 

THOMAS P, RATVASKY 

(IlaSA-TE-101631) ABRODY&iAlIC PARAllBTBES OF 1989 -268 6 1 

AH ADVAIICED PIGHTER AIRCRAPP ESTIMATED PROH 

langley Research Center) 59 p CSCL OlC Unclas 

PLIGHT DATio ,PBBLIMIIABJ RESULTS (MASAo i 

G3/08 0 2247 38 

JULY 1989 

National Aeronautics and 

Space Administration 

Lawley Resesrch Center 

Hampton, Virginia 23665 
SUMMARY 

Preliminary estimates of aerodynamic parameters of an advanced fighter 

aircraft were obtained from flight data of different values of the angle of 

attack from 8' to 54". The data were analyzed by a stepwise regression with 

the ordinary least squares technique. The estimated parameters, in the form 

of stability and control derivatives, are plotted against the angle of attack 

and compared with wind tunnel measurement and previous flight results. 

resulting parameters exhibit, in general, large scatter caused mainly by 

insufficient excitation of aircraft responses. The report also includes the 

data compatibility check of measured data. The effect of various input forms 

is demonstrated in two examples using simulated data. 

obtained, proposals are made for the future experiment for obtaining accurate 

parameter estimates. 

The 

Based on the experience 

i 
SYMBOLS AND ABBREVIATIONS 

Ixz 

m 

N 

n 

R 

R2 

S 

s(* 1 

2 S 

t 

V 

X 

X 

longitudinal, lateral, and vertical acceleration, g units 

wing span, m 

constant bias error in variable z 

general aerodynamic force and moment coefficient 

rolling-, pitching-, and yawing-moment coefficient 

lateral- and vertical-force coefficient 

wing mean aerodynamic chord, m 

acceleration due to gravity, m/sec 2 

vertical body axes, kg-m 2 

product of inertia, kg-m 2 

moments of inertia about longitudinal, lateral, and 

mass, kg 

number of data points 

me asureme nt-noise vector 

roll rate, pitch rate, and yaw rate, radlsec or deg/sec 

dynamic pressure, pV2/2, Pa 

measurement-noise covariance matrix 

squared multiple correlation coefficient 

wing area, m 

standard error 

va r iance e s t ima t e 

time, sec 

2 

longitudinal, lateral, and vertical airspeed component, 

mlsec 

airspeed, 

matrix of 

vector of 

m/sec 

r egr es so rs 

state variables or regressors 

ii 
Y 

Y 

Z 

a 

B 

6A 

6a*6r 

dh ” df ” dll f 

&H 

6h’6 f ’6Rf 

rl 

oa,nh,nr 

0 

oo,oj 

0 ,+ ,J, 

A 

z 

V 

P 

Abbreviations: 

c.g. 

m.a.c. 

vector of dependent variables 

dependent variable 

vector of output variables 

angle of attack, rad or deg 

sideslip angle, rad or deg 

input variable expressing combined effect of aileron and 

differential tail and trailing edge flaps, rad or deg 

aileron and rudder deflection, rad or deg 

differential tail and trailing and leading edge flap 

deflection, rad or deg 

input variable expressing combined effect of horizontal 

tail, leading and trailing edge flap deflection, rad or deg 

horizontal tail and trailing and leading edge flap 

deflection, rad or deg 

vector of input variables 

stick deflection in roll and pitch, and rudder pedal 

deflect ion, in 

vector of unknown parameters 

unknown parameters 

pitch, roll, and yaw angle, rad or deg 

scale factor error of 

vector of residuals 

air density, kg/m 3 

center of gravity 

mean aerodynamic chord 

variable z 

iii 
Subscript: 

E 

Superscript : 

,% 

measured value 

estimated value 

Matrix exponent: 

T transpose matrix 

-1 inverse matrix 

Derivatives of aerodynamic coefficients Ca(a = Y,Z$ ,m,n) referenced to a 

system of body axes with the origin at the airplane center of gravity: 

‘ a ‘a =- 

aP 3% 

aca =- ‘a aa 

a 

a ‘a 

ca - 

q a% 

3- 

a ‘a =- ‘a a6 B 

a ca = - rb 

, j = A,a,df,dh,daf,f,H,h,Lf,r a ‘a 

ca =as ti j 

iv 
INTRODUCTION 

In 1988, NASA initiated the High-Alpha Technology Program in order to 

accelerate the development of technologies which would expand high angle-of - 

attack capabilities of future fighter aircraft. The flight research portion 

oE the program has been using the F-18A High Angle-of-Attack Research Vehicle 

(HARV) as a flight research testbed. 

program is to obtain the high-alpha database for validation of wind tunnel and 

theoretical predictions and for postulating a mathematical model of the 

aircraft. 

longitudinal and lateral transient maneuvers intended for estimation of 

aircraft aerodynamic parameters using system identification methodology. 

One of the objectives of the flight 

For that reason the first set of flights included several 

The purpose of this report is to summarize the preliminary results from 

the analysis, assess the accuracy of the instrumentation system and parameter 

estimates, and consider possible changes in the design of future experiments. 

The report starts with the description of the aircraft and flight and wind 

tunnel data available. Then, procedures for data analysis are briefly 

outlined. The results presented include checks on compatibility of measured 

responses, variation of estimated aerodynamic parameters with the angle of 

attack, and the comparison of these estimates with wind tunnel measurements 

and a limited number of previous flight results. Finally, a possible 

selection of different input forms and their effect on parameter accuracy is 

discussed. 

1 
AIRCRAFT 

The test vehicle is a twin engine, single seat fighter aircraft. It has 

a moderately swept wing with highly swept leading-edge extension (LEX). 

all-moving horizontal tail surfaces are mounted behind and below the wing, 

twin vertical tails are canted and toed out. The aircraft is controlled by 

four digital computers working in parallel. The computers are used in conjunction with redundant electrohydraulic servoactuators and analog sensors to 

provide two fail operate primary control capabilities. There is also a backup 

mechanical control of the stabilator surfaces and open-loop analog control of 

the aileron and rudder. Longitudinal control uses symmetric deflections of 

the stabilator, leading and trailing edge flaps. Lateral control is provided 

by the ailerons, differential deflections of the stabilator, leading and 

trailing edge flaps, and synchronous rudder deflection. A drawing of the 

aircraft is presented in figure 1. The basic geometric, mass, and inertia 

characteristics are summarized in table I. A more detailed description of the 

aircraft and its control system is contained in references 1 and 2. 

The 

The tested aircraft was modified by adding a nose boom and right- and 

left-wing-tip booms with Pitot-static heads and a- and $-vanes (not shown in 

fig. 1). The aircraft has a pulse-code modulation instrumentation system with 

telemetry as the only source of data. The measured data are recorded at the 

telemetry ground station. The instrumentation system includes transducers for 

the measurement of closed- and open-loop input variables, response variables, 

pressures on the prebody and quantities defining aircraft configuration, 

control system and engine operation, and instantaneous mass and inertia 

characteristics. 

FLIGHT AND WIND TUNNEL DATA 

The flight data of the tested aircraft were obtained from NASA Dryden 

Flight Research Facility in the form of time histories sampled at 50 samples/ 

sec. The measured data were corrected for the c.g. offset of the linear 

accelerometers, and a- and 6-vanes. In addition, the a-vane readings were 

corrected for the upwash effect. The air data for the analysis were taken 

from the nose-boom sensors. 

lateral maneuvers were analyzed. These maneuvers were initiated from mostly 

steady flights at altitudes between 5,000 and 9,500 m (17,000 and 31,000 ft) 

and an angle of attack between 8' and 54O. The pilot input for the longitudinal maneuvers was a pitch command in the form of a simple doublet. 

lateral responses, separate roll and yaw commands in the form of doublets were 

applied. 

are presented in figures 2 to 5. 

From the data obtained, 33 longitudinal and 41 

For the 

Time histories of input and response variables from four maneuvers 

In figure 2 the longitudinal response of the aircraft at a = 8" is 

shown. 

leading and trailing edge flaps. In this case, the short period motion of the 

aircraft seems to be well excited. Figure 3 shows an example of the longitudinal maneuver initiated at a - 44'. Problems of insufficient excitation and 

maintaining uncoupled response are visible from the time histories of both the 

input and output variables. 

The open-loop inputs included deflections of the horizontal tail, 

An example of lateral response of low angle of 

2 
attack is given in figure 4. The wide time separation of roll and yaw 

commands, and the short duration of the rudder doublet resulted in low 

information content of the measured data. Finally, the lateral maneuver 

initiated at a = 54" is presented in figure 5. The resulting responses 

exhibit strong coupling between the lateral and longitudinal motion and 

insufficient excitation of the lateral acceleration. 

The estimated parameters from flight data were compared with the 

aerodynamic functions and parameters in the NASA LaRC flight simulator. These 

aerodynamic data are based on wind tunnel measurements with some adjustments 

for a previous flight test basis. The data are summarized in reference 1. 

The stability and control derivatives presented in this report were computed 

from aerodynamic functions for scheduled flap positions and horizontal tail 

deflections required to turn the aircraft at given flight conditions. 

computed parameter Cm is referenced to the c.g. positions at 25 percent of 

the m.a.c. U 

The 

FLIGHT DATA ANALYSIS 

The first step in data analysis included a check on measured data 

compatibility and estimation of unknown bias errors in the measurement. 

the unknown parameters, in the form of stability and control derivatives, were 

estimated from postulated expressions for the aerodynamic coefficients. 

the compatibility check the maximum likelihood method of reference 3 was 

applied. 

Then 

For 

The state equations were represented by kinematic equations 

m 

and 0 is a vector of unknown bias errors in measured input and response 

variables. The vector of response variables was formulated as 

T 

z = [V,B,a,tJ,WI 

Each measured response variable was expressed as 

z = (1+Az) z E 

+ bZ+ nZ 

where X 

nz is tge measurement noise. 

scale factor errors and the measurement noise are equal to zero. 

is the unknown scale factor error, b, is the constant bias error and 

For the measured inputs it was assumed that the 

The unknown parameters and their Cramer-Rao bounds were obtained by 

minimizing the cost function 

3 
where 

* 

u(i) = z,(i) - z(i,O) 

R is the covariance matrix of measurement noise and N is the number of data 

points. 

Estimates of aerodynamic parameters were obtained by using a stepwise 

regression method presented in reference 4. Because all the maneuvers 

exhibited small perturbations around initial conditions, the aerodynamic model 

equations were postulated with linear terms only. For the longitudinal 

maneuvers the regression model was formed as 

- 

+‘a &h 

=Ca +Caa +Ca 2~ qc 

‘a 0 a q 6H 

where a = Z and m, and for lateral maneuvers as 

6 rb 

ca= ca + ca 6 + ca 2” +ca +‘a 6a+ ‘a r OB P r 6A 6r 

(4) 

(5) 

where a = Y, R and n. 

In these equations the control effectiveness Ca includes the effect of the 

6H 

horizontal tail, as well as leading and trailing edge flaps deflection 

&f &Qf 

62 f ‘a =C +- c +- ‘a 6H a6h 6h a6f &h 

and the control effectiveness C includes the effect of aileron, differentia1 tail, and differential leading and trailing edge flaps deflection 

6A a 

&dQ f +- 

a 

6 6L f ‘a 

df +- 

6df ‘a 

- &dh 

6 ca - ca +-g6dh a a 6A 6a a 

(7) 

The regressors in (4) and (5) are represented by the increments of output and 

input variables from initial conditions. The unknown parameters are the 

stability and control derivatives and bias term Ca . The dependent variables 

were computed from the following expressions: 0 
cy= - mg ay 

is 

In these equations, the angular accelerations were obtained by fitting cubic 

splines to measured angular velocities and then by differentiating the 

analytical expressions obtained. 

The unknown parameters were obtained by minimizing the cost function 

where y is the dependent variable, xj are the regressors, and II is the number 

of statistically significant terms in (4) and (5). 

the parameters was estimated as 

The covariance matrix of 

2T 

cov (6) = s (x XI-l 

where X is the matrix of regressors and ones, and s2 is the variance of the 

measurement noise. 

RESULTS AND DISCUSSIONS 

The results of flight data analysis are summarized in the following four 

The 

sections. The first one contains a check on the compatibility between 

measured and predicted responses with the emphasis on air data accuracy. 

second and third sections include estimates of longitudinal and lateral 

parameters and their comparison with wind tunnel measurement and flight 

results of reference 5. These results were obtained from several maneuvers 

using data partitioning and stepwise regression (see refs. 5 and 6). In the 

last section the effect of different input form on the accuracy of estimated 

parameters is addressed. 
Data Connpatibility Check: 

Two large amplitude maneuvers were used in the data compatibility 

check. 

longitudinal transients. In the second maneuver, slaw deceleration was 

combined with the lateral responses initiated by aileron and rudder 

deflections. 

maneuver are shown in figure 6. Bias errors, their standard errors, and 

resulting fit errors estimated from the data of the first maneuver are 

presented in table 11. The data were analyzed first by dividing the maneuver 

into three overlapping segmnts. Then, the data from the whole maneuver were 

used. The inconsistency among the four sets of estimates is probably caused 

by low excitation of transient motion and various amounts of information 

contained in each segment of the data. Small excitation of transient motion 

also resulted in strong pairwise correlations between parameters. These 

correlations degraded the accuracy of the estimates specified in table 11. 

The first maneuver consisted of slow deceleration with superimposed 

The time histories of the output and input variables in this 

Table 111 contains the results of estimation based on the data from the 

second maneuver. 

previously. This time, however, the postulated unknowns included constant 

8' biases in longitudinal and lateral variables, and scale factors X and X 

The accuracy of the estimated scale factor Xa was again degraded by strong 

correlation between b and X . For that reason, it was not possible to verify 

the accuracy of upwash corrections applied to nose boom a-vane readings. 

estimated values of X 

angle of attack. 

The approach to the analysis was similar to that used 

a 

a a 

8 

The 

indicate a possible change in the sidewash with the 

For better evaluation of assumptions concerning the air data measurement, 

the time histories of residuals in the air speed, angle of attack, and 

sideslip angle were plotted in figure 7. These plots show a presence of 

uncorrected systematic errors which means that measurement equation (2) could 

not explain variations in measured air data. The same residuals are also 

plotted against the angle of attack in figure 8. From these plots a 

pronounced disagreement between measured and predicted angle of attack 

for a > 30" is seen. For further verification of air data accuracy the air 

speed and angle of attack are plotted in figure 9 against the corresponding 

variables VL and a 

figure the nose-boom sideslip angle was compared with the average value B' 

obtained from both left- and right-wing-boom vanes. 

sidewash corrections were applied. 

V > VL in the whole range of a and there is a substantial discrepancy 

between a and a for a > 30". 

right-wing boom exhibited the same pattern. 

correction used in computing a is not correct for a > 30" and also that it 

needs some improvement for a from 10" to 18'. Finally, there are differences 

between B and s' which increase with increased sideslip angle. 

obtained from the left-wing-boom sensors. In the same L 

When calculating s', no 

From the plots in figure 9 it follows that 

The similar plot of a against aR from the L 

This means that the upwash 

Assuming that 

6 
the sidewash corrections for the nose-boom 8-vane-are small (see results in 

table 111) it can be concluded that the computed 8 is in error. 

Because of low accuracy of estimated bias errors and the preliminary 

nature of the following results, no additional corrections to measured data 

were applied. For better assessment of the accuracy of measured responses 

more data from carefully designed experiments would have to be analyzed. In 

addition, the computing procedure for obtaining corrected values of V, 8, 

and a should be revised and complemented by results from wind tunnel 

measurement of upwash and sidewash corrections. 

Longitudinal Parameters: 

The vertical-force and pitching-moment parameters are presented in 

figures 10 and 11. In these figures the variation of parameter estimates with 

the angle of attack, their consistency, and degree of agreement with wind 

tunnel measurement can be seen. The scatter in the most important parameters 

Cz , Cm , and Cm is, in general, large and unacceptable for results of this 

research program. The consistency of the remaining parameters was expected to 

be low because of the low sensitivity and identifiability of these parameters. 

An improvement in parameter accuracy can be achieved by improving the accuracy 

of air data measurement and by selecting inputs which could improve the shortperiod excitation, especially at high angle-of -attack flight regimes. 

a a 6H 

The parameter estimates are in variable degrees of agreement with wind 

tunnel measurement. 

22" and Cm 

effectiveness, 6" is about 10 percent smaller than that from wind tunnel 

The main discrepancies are in Cz for a between 13" and 

a 

for a between 10" and 20". The estimated horizontal tail 

a 

data. The wind tunnel values of Cz are also substantially lower than the 

q 

estimated values. 

Lateral Parameters : 

The same applied for Cm for a between 20" to 40". 

4 

The estimates of lateral parameters are presented in figures 12 to 16. 

The parameters expressing the sideslip effect are shown in figure 12. All 

three sets of these parameters exhibit large scatter, thus indicating poor 

accuracy of the estimates. 

lateral modes and uncorrected bias errors in measured sideslip angles. In 

addition, the values of Cn 

lity of this parameter. 

is difficult to assess their agreement with wind tunnel measurement or 

previous flight results. The exception is the parameter C , whose values 

for a between 8" and 30" are closer to the estimates from reference 5 than to 

wind tunnel data. 

The reason for this is insufficient excitation of 

are low which further decreases the identifiabiBecause of large scatter in all three parameters it 

8 

y13 

7 
The roll-rate and yaw-rate parameters are shown in figures 13 and 14. 

for a < 23" and 

P 

Good identifiability can be observed only in parameter C R 

Cy for a < 30". The values of these parameters at higher angles of attack 

r 

and the estimates of the remaining dynamic parameters were found either 

inconsistent, statistically insignificant, or having nonphysical values. As 

in the previous case, the main reason for that is the small excitation of 

lateral modes. 

The control parameters expressing the combined effect of the aileron, 

differential tail, and trailing edge flaps are plotted in figure 15. Large 

scatter and high values of C for a > 23" are caused by a near linear 

relationship between aileron and rudder deflections which can be seen in 

figures 4 and 5. As discussed in reference 7, near linear dependence among 

regressors, called data collinearity, results in inaccurate parameter 

estimates. The trend in the estimates in figure 15 indicates, however, that a 

new experiment which will decrease data collinearity and/or the use of biased 

estimation techniques introduced in reference 7 might result in estimates 

close to wind tunnel data. Similar conclusions can be made about the second 

set of control parameters expressing the effect of rudder deflection. These 

parameters are plotted in figure 16. Only the parameter 

with acceptable accuracy and good agreement with wind tunnel prediction. 

%A 

was obtained 

''6 r 

Effect of Input Form on Parameter Estimates: 

As indicated in the preceding sections, one way to improve the accuracy 

of estimated parameters is to select inputs which would sufficiently excite 

all modes included in the postulated model for the longitudinal and lateral 

motion of the aircraft. In order to demonstrate the effect of various input 

forms, the data from the flight simulator were recorded for two sets of 

inputs. The first set included repeats of pilot commands used in flight test. 

The second set contained the proposed inputs formed by a simple combination of 

doublets. Both sets of inputs and the pertinent response variables are shown 

in figures 17 to 20. The resulting parameters from the longitudinal data are 

given in table IV. This table includes estimated mean values, their standard 

errors, and increments of the multiple squared correlation coefficient. The 

last quantity mentioned indicates the amount of information in measured data 

explained by including individual terms into the regression equation 

representing the postulated aerodynamic model (see equations (4) and (5)). 

The selected input in figure 18, which combines three doublets in control 

stick deflection, substantially improves the accuracy of the estimates when 

compared with results where the input in the form of a single doublet was 

used. Also improved was the significance of the term C in the model as 

indicated by the corresponding values of AR . m 

a 2 The difference in the estimated 

values of 

different amount of excitation in a. In both cases with different inputs the 

Cm is caused by the nonlinear form of the Cm(a) curve and by 

a 

8 
parameter Cz 

of Cm remains small. 

was not identifiable, and the possibility of accurate estimation 

q 

q 

The selected input in figure 20 for the excitation of the lateral motion 

combines rudder doublet immediately followed by the aileron doublet and then 

by a repeat of both doublets. This form of input excited the transient motion 

better than the input used in the flight test. The improvement in the 

information content of the data again reflected in improved accuracy of the 

parameters, especially of those expressing the sideslip effect, as shown in 

table V. In this table, only parameters of greater importance are included. 

CONCLUDING REMARKS 

Aerodynamic parameters of an advanced fighter aircraft were estimated 

from transient maneuvers at different angles of attack varying from 8 to 54 

deg. 

technique was applied. The resulting estimates were obtained in the form of 

aircraft stability and control derivatives. 

variations with the angle of attack and compared with wind tunnel measurement 

and a limited number of previous flight results. In addition to the analysis 

mentioned, the compatibility of measured data was checked and uncorrected bias 

errors in measured data estimated. The possible effect of various input forms 

on the accuracy of parameter estimates was demonstrated in two examples using 

simulated data. From all the results obtained the following conclusions can 

be drawn: 

For data analysis a stepwise regression with the ordinary least squares 

They were then presented as 

1. The existing maneuvers of data compatibility did not have enough 

information for accurate estimation of bias errors, especially for 

scale factor error in the a-vane readings. For that reason, no final 

statement about the accuracy of the measured data could be made. 

2. Response variables in the longitudinal and lateral maneuvers for 

parameter estimation were, in general, not sufficiently excited. 

This was apparent mainly in low amplitudes of vertical acceleration, 

sideslip angle and yawing velocity, and also in some segments of 

lateral data where almost no transient motion occurred. Low 

excitation of response variables was caused by the selection of input 

forms and, in some cases, by difficulties in maneuvering the aircraft 

in the requested way. 

3. Insufficient excitation of transient maneuvers resulted in large 

scatter in the estimated parameters and therefore in their low 

accuracy which is unacceptable for results of this research program. 

4. The accuracy of lateral parameters was further degraded by near 

linear dependency between the aileron and rudder deflections. 

9 
5. Because of low accuracy of the parameter estimates it was not 

possible in many cases to comment on their agreement with wind tunnel 

measurement and previous flight data. 

6. Simulated study showed that more careful selection of input forms can 

significantly improve the identifiability of the main parameters in 

the model. 

The future experiment of obtaining accurate parameter estimates should 

include the following: 

1. Special maneuver designed for the assessment of data compatibility. 

2. Selection of input forms for an adequate excitation of transient 

maneuvers for parameter estimation. 

to the pilot and verified in the simulator. 

These inputs must be acceptable 

3. Excitation of longitudinal and lateral maneuvers at different values 

of the angle of attack covering the range from approximately 8" to 

50". 

4. Repeat of maneuvers at two or three selected values of the angle of 

attack for better assessment of parameter accuracy. 

10 
REFERENCES 

1. Anon: "F/A-18 Stability and Control Data Report," Vol. 1 and 11, 

MDC A7247, McDonnell Aircraft Company, 1982. 

2. Anon: "F/A-18 Flight Control System Design Report," Vol. I and 11, 

MDC A7813, McDonnell Aircraft Company, 1982. 

3. Klein, Vladislav; and Morgan, Dan R.: "Estimation of Bias Errors in 

Measured Airplane Responses Using Maximum Likelihood Methods," NASA 

TM-89059, 1987. 

4. Klein, Vladislav; Batterson, James G. ; and Murphy, Patrick C.: 

"Determination of Airplane Model Structure From Flight Data by Using 

Modified Stepwise Regression," NASA TP-1916, 1981. 

5. Hess, Robert A.: "Subsonic F/A-18A and F/A-lSB (TF-18A) Aerodynamic 

Identified From Flight Test Data," System Control Technology (Patuxent 

River Office), Report No. 4522-220-1, 1987. 

6. Batterson, James G. ; and Klein, Vladislav: "Partitioning of Flight Data 

For Aerodynamic Modeling of Aircraft at High Angles of Attack," Journal 

of Aircraft, Vol. 26, No. 3, April 1989, pp. 

7. Klein, Vladislav: "Two Biased Estimation Techniques in Linear 

Regression. Application to Aircraft," NASA TM-100649, 1988. 

11 
Table I. Geometric, Mass and Inertia Characteristics 

of Aircraft. 

Total length, m 

Wing : 3 Area, m' 

Span, m 

Mean geonetric chord, m 

Aspect ratio 

Quarter-chord sweep angle, deg 

Horizontal tail: 

Area (wetted), m 

Span, m 

Mean geometric chord, m 

Aspect ratio 

Quarter-chord sweep angle, deg 

Moment arm (c.g. at 0.25 m.a.c.1, m 

2 

Vertical tai 1: 

2 Area (wetted), m 

Mean geonetric chord, m 

Aspect ratio 

Quarter-chord sweep angle, deg 

Cant, deg 

Moment arm (c.g. at 0.25 m.a.c.1, m 

Mass, kg 

17.07 

37.16 

11.41 

3.51 

3.5 

20.0 

16.35 

6.58 

1.91 

2.4 

5.12 

42 .a 

9.66 

2.13 

1.2 

35.0 

20.0 

3.10 

14,400 

28,880 

165,930 

185,030 

- 2,630 

12 
Table 11. Estimates of Bias and Fit Errors From 

Longitudinal Maneuver. 

Parameter 

O<t<40 sec 

O<a<32 deg 

- .84 

(.023) 

.02 * 

(.022) 

- .020 * 

( .0026) 

- .0159 * 

(.00013) 

- .127 * 

(.0030) 

.0046 

(.00017) 

.0069 * 

(.00027) 

.SO8 

.I39 

.069 

Segment of data analyzed 

20<t<60 sec 

18<a<37 deg 

- .32 

( .020) 

.61 * 

( .040) 

- .040 * 

(.0016) 

.0191 * 

(.0012) 

.098 * 

( .0027) 

,0036 

(.00010> 

.00718 

(.000088) 

.44a 

.I76 

.061 

39<t<79 sec 

23<a<46 deg 

.20 

( ,060) 

- 2.3 * 

(011) 

.os1 * 

(.0031) 

.0146 * 

(.00074) 

.38 * 

(.017) 

.0208 

(.00037) 

.004 1 

(. 00023) 

1.281 

.726 

.393 

10<t<70 sec 

12<a<46 deg 

.03 

( .047) 

.55 * 

(.095) 

- .034 * 

(.0053) 

- .0220 * 

(.00013) 

- .050 * 

(.0046) 

,0060 

(.00027) 

.0053 * 

( .00039) 

.874 

.634 

.089 

Numbers in the parenthesis are standard errors 

*) Parameter with strong correlation 

13 
Table 111. Estimates of Bias and Fit Errors From 

Lateral Maneuver. 

Parameter 

b,, m/sec 

ba, deg 

‘a 

bs, deg 

AB 

be, deg/sec 

bq, deg/sec 

br, deglsec 

b6 * deg 

be’ deg 

ba,, g units 

bay, g units 

ba,, g units 

Segment of data analyzed 

O<t<30 sec 

9<a<27 deg 

.13 

(.093) 

.2 * 

(. 16) 

- .02 * 

(.021) 

.29 

(.096) 

.04 

(010) 

.025 

(. 0039) 

.0127 * 

(.00078) 

.147 

( .0040) 

- .03 

(. 065) 

- .05 * 

(.013) 

,0112 

( .00090) 

,017 

(.O019) 

.009 * 

( .0023) 

15<t<45 sec 

14<a<41 deg 

.33 

(.033) 

.86 * 

(.036) 

- .056 * 

( .0025) 

- -104 

(-0083) 

- -008 

(.0035) 

.0051 * 

(. 00064) 

.0165 * 

( .00030) 

.1276 

( .00024) 

.01 

(.012) 

.040 * 

(.0051) 

.0189 

(.00027) 

- ,0069 * 

(. 00020) 

.0084 * 

( ,00038) 

29<t<59 sec 

24<a<47 deg 

~ ~ -~ 

1.52 

(.071) 

- 3.9 * 

(-14) 

.lo8 * 

( .0046) 

.23 

( .018) 

- .090 

(.0018> 

.007 * 

( .0011) 

.0482 * 

(. 00049) 

.lo5 * 

(.0010) 

- .44 

(.016) 

.lo9 * 

(.0082) 

.0388 

( .00037) 

- .0044 * 

( . OO040) 

.010 * 

(.O015) 

lO<t<47 sec 

ll<a<47 deg 

2.48 

( .070) 

.20 * 

(.053) 

- .138 * 

(.0031) 

.13 

(.015) 

- .091 

(.0036) 

.0083 * 

(.00056) 

.0083 * 

(.00031) 

.1218 

(. 00034) 

- .232 

(.017) 

.176 * 

(.0082) 

.0290 

(.00032) 

- .0041 * 

(.00024) 

.0126 

(.00027) 

Numbers in parenthesis are standard errors 

*) Parameters with strong correlation 

14 
Table 111. Concluded. 

Par a met e r 

s(V>, m/sec 

s(a>, deg 

~(31, deg 

s(6), deg 

s(8>, deg 

s(JI), deg 

Segment of data analyzed I 

O<t<30 sec 

9<a<27 deg 

,182 

,102 

.115 

.186 

.042 

.095 

15<t<45 sec 

14<a<41 deg 

.569 

.159 

.154 

.265 

.097 

.174 

29<t<59 sec 

24<a<47 deg 

1.442 

.873 

.339 

.461 

.158 

.340 

10<t<47 sec 

ll<a<47 deg 

1.293 

.665 

.236 

e367 

.140 

e336 

15 
Table IV. Estimates of Parameters From Two Longitudinal 

Maneuvers With Different Input Forms. 

Parameter 

Flight input 

- 5.3 .22 64.9 

- .97 .097 5.4 

- .20 .075 .3 

- 9. 2.3 .9 

- 1.42 .034 81.5 

Selected input 

- 5.52 .062 93.0 

- .88 .063 1.6 

- .43 .022 3.3 

- 4.1 .98 1.1 

- 1.35 .022 87.3 

16 
Table V. Estimates of Parameters From Two Lateral 

Maneuvers With Different Input Forms 

~~ 

Pa rarne t e r 

cyB 

c2* 

CQ6A 

6r 

P 

B ‘n 

cnr 

‘n fir 

Flight input 

- 1.11 .041 14.2 

,209 .0047 69.2 

- .124 .004 1 5 .O 

- .411 -0085 5.5 

- .121 .0010 87.8 

.13 .027 1.7 

- .2 .24 .1 

- ,081 .0031 51.3 

Selected input 

- 1.11 .007 6 70.5 

.245 .0024 27.6 

- .123 .00076 14.3 

- .418 ,0042 6.8 

- .113 .00059 74.6 

.131 .0049 15.8 

- .14 .069 .1 

- .081 .0015 70.1 

17 
7 n4.66 m 

ft.) 

t-” (37.5 it.) -i 

Figure 1. Three-view drawing of test aircraft. 

18 
*; 

-2 

9 

1 

0 2 4 6 8 

t, sec 

-7 

Figure 2. Time histories of measured input and response 

variables in longitudinal maneuver (a % 8'). 0 

19 
g; 5 

3 

-5 

t, sec 

Figure 2. Concluded 

20 

. 
0 

0 2 4 6 8 U 

t, sec 

Figure 3. Time histories of measured input and response 

variables in longitudinal maneuver (a % 44'). 0 

21 
.. 

-3 \ 

-1 9 

-4 

0 

4 

20 h 

t, sec 

Figure 3. Continued 

22 
48 

$g 44 

40 

5 

1 

-3 

t, sec 

Figure 3. Continued 

23 
a 

-2 

degfsec 

-1 2 

0 r, 

degtsec 

0 2 4 6 a -4 

t, sec 

Figure 3. Concluded 

24 
2 

2r 

-2 

0 4 a 12 16 

t, sec 

Figure 4. Time histories of measured input and response 

variables in lateral maneuver (a0% 11'). 

25 
-9 t 

* 

11 

19 F 

11 

3 

-5 

‘c 

* 

-2 0 * 4 8 12 16 

t, sec 

Figured 4. Continued 

26 
8eg 

-1 

P, 

degkec 

4 8 12 16 

t, sec 

Figure 4. Concluded 

27 
4€ 

t, sec 

Figure 5. Time histories of measured input and reaponse 

variables in lateral maneuver (a 0 % 54'). 

28 
-- 0 8 16 24 

t, sec 

Figure 5. Continued 

29 
' 71 dsec 

67 

lo h 

t, sec 

Figure 5. Continued 

30 
q, 2 deglsec 

-2 

8 Pt 

deglsec 

-1 2 

lo 6 

deglsec r, 2 

-6 

. 

ar 0 

g units 

0 8 16 24 

t, sec 

-.l J 

Figure 5. Concluded 

31 
150 

130 

110 Wsec 

90 

I I I I,!! I [I I I It, II I I I II I lllIII,,IIIIll,I IOIII IIII[IIII 

19 

h 

dzg 

49 

39 

29 

19 

9 - 

0 10 20 30 40 50 60 

t, sec 

Figure 6. Time histories of measured response variables 

in large amplitude longitudinal maneuver. 

32 
17 

7 

-3 

-1 3 

18 

8 

68 

t 

58 

48 

38 

0 10 20 30 40 50 60 

t, sec 

Figure 6. Continued 

33 
a 

X.' 

g units 

a Y .' 

g units 

.6 

.4 

.2 

0 

.2 

.1 

0 

-. 1 

-.2 

-.4 

-.8 

-1.6 

-2.0 

€- 

EFigure 6. Continued 

34 

? 
t 

-I4 E 

** 

:+ 

** 

4 

c -4 p 

t 

€ 

ti 

f 

0 10 20 30 40 50 60 

t, sec 

Figure 6. Concluded 

35 
r 

.5 

0 

-.5 

Figure 7. Time histories of residuals. 

36 
l*O EFigure 8. Variation of residuals with angle-of-attack. 

37 
29 - E ? 

c 

t - 

€ 130 

t 

AO- 0 

/' 

Figure 9. Relationship between air data from nose boom 

and left wing boom. 

38 
C 

z a 

-100 0 

-120t ' ' . ' * ' ' ' ' ' ' ' 

-0.5 r 

C 

ZSH -1.0 

0 

0 10 20 30 40 50 60 -1.5' - I " ' I ' I a ' * ' 

a, deg 

Figure 10. Comparison of vertical-force parameters 

obtained from flight and wind tunnel 

measurement. 

39 
- Wind tunnel 

0 Flight 

20 

10 

0- 

m -10- C 

q 

-20 

-30 

0.0 

-0.5 

-1 .o 

C 

ma 

0 

- 

B 

0 

0 

0 0 

- 

0 ; 

I 0 

-0.4 E 

t 

0 10 20 30 40 50 60 -1.4' ' I * I * I ' I a ' 

Figure 11. Comparison of pitching-moment parameters 

obtained from flight and wind tunnel 

measurement. 

40 
- Wind tunnel 

-0.0 c 

-0.2 - 

-0.4 - 

-0.6 

P 

-0.8 

-1.0 - 

Flight 

----- Ref 5 

0.2 

Oa3 F 0 

Figure 12. Comparison of parameters expressing sideslip 

effect estimated from flight and wind tunnel 

measurement. 

41 
0 

0 

- Wind tunnel 

0 Flight --e-- Ref 5 

C 

'P 

-4 0 0 0 

-0.2 

-0.4 

-0.8 

-OX i 0 

0 

0 

0.4 Oa6 F 0 

0 

U 

0 

C "p 0.0 o*21 

-0.2 1 

-0.4 1 0 

0 

0 

-0.6 

0 

0 

10 20 30 40 50 60 

a, deg 

Figure 13. Comparison of oscillatory roll-rate parameters estimated from flight and wind tunnel 

measurement. 

42 
*Oi 10 

- Wind tunnel 

0 Flight 

0 

-lo. -20 

2c 0 0 

-l t 0 

0 

1 

o 

a 

::I . I . , . , . I , , 

-3 

0 10 20 30 40 50 60 

a, deg 

Figure 14. Comparison of oscillatory yaw-rate parameters 

from flight and wind tunnel measurement. 

43 
2 

1 

C 

A 

0 

-1 

-0.0 

-0.1 

'16A 

-0.2 

-0.3 

0.1 I 

C 

"A 0.0 

-0.1 

- Wind tunnel 

0 Flight 

0 

0 

. 

D 

a 

0 

0 10 20 30 40 50 60 

-0.2 

a, deg 

Figure 15. Comparison of aileron-effectiveness 

parameters estimated from flight and 

wind tunnel measurement. 

44 
Oa4 0.3 E 

0.00 

-0.02 

c -0.04 

-0.06 

“66r 

-0.08 

-0.1 0 

- Wind tunnel 

0 Flight 

----- Ref 5 

0 

- 

- 

- 

- 

- 

0 

1.1.1.1.~.J 

0.06 0 

0.04 1 

-O.O2 -0.04 F 

Figure 16. Comparison of rudder-effectiveness parameters estimated from flight and wind tunnel 

measurement. 

45 
2 

0 

-2 

10 

0 

-1 0 

t 

0 2 4 6 a 

t, sec 

Figure 17. Time histories of flight inputs and simulated 

longitudinal response variables. 

46 
l6 k 

c 

2

-1 5 

0 

a z; -1 

g units 

72 

F . 

0 2 4 6 a 

t, sec 

Figure 17. Concluded 

47 
in 

-2 

0 2 4 6 a -10 

t, sec 

Figure 18. Time histories of selected inputs and simulated 

longitudinal response variables. 

48 
3 

-1 5 

-2 o' 2 4 6 a 

t, sec 

Figure 18. Concluded 

49 
'a, 

in 

-2 

ia 

0 

-1 8 

30 

0 

,..,, 1 ,,..,, ,...,,..,. 

4 8 

t, sec 

12 16 

Figure 19. Time histories of flight inputs and simulated 

lateral response variables. 

50 
PI 

deg/sec 0 

-50 

r, deglsec 

-1 0 

$0 -.5 

0 

-11.1.: 

4 a 12 'I." - 16 

t, sec 

Figure 19. Concluded 

51 
-2 1 

-2 

-1 8 

0 

: 

'111 

-30 o' 4 8 12 16 

t, sec 

Figure 20. Time histories of selected inputs and simulated 

lateral response variables. 

52 
10 c 

k 

. 

-1 0 

50 

deg/sec pt 0 

-50 

10 

r, deglsec 0 

-1 0 

.5 

aY: 0 

g untts 

-.5 

I 

€ 

3 4 a 12 16 

t, sec 

Figure 20. Concluded 

53 
Report Documentation Page 

1. Report No. 

NASA TM-101631 

2. Government Accession No. 

4. Title and Subtitle 

Aerodynamic Parameters of an Advanced Fighter 

Aircraft Estimated from Flight Data. Preliminary 

Results 

17. Key Words (Suggested by Author(s)) 

7. Authork) 

Vladislav Klein, Keven P. Breneman, and 

Thomas P. Ratvasky 

18. Distribution Statement 

9. Performing Organization Name and Address 

NASA Langley Research Center 

Hampton, VA 23665-5225 

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages 

UNCLASSIFIED UNCLASSIFIED 58 

12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

22. Price 

A04 

3. Recipient's Catalog No. 

5. Report Date 

July 1989 

6. Performing Organization Code 

8. Performing Organization Report No. 

10. Work Unit No. 

505-66-01-02 

11. Contract or Grant No. 

13. Type of Report and Period Covered 

TECHNICAL MEMORANDUM 

14 Sponsoring Agency Code 

15. Supplementary Notes 

Vladislav Klein, Keven P. Breneman, and Thomas P. Ratvasky: The George 

Washington University, Joint Institute for Advancement of Flight Sciences, 

Langley Research Center, Hampton, Virginia. 

16. Abstract 

Preliminary estimates of aerodynamic parameters of an advanced fighter 

aircraft were obtained from flight data of different values of the angle of 

attack from 8" to 54". 

the ordinary least squares technique. The estimated stability and control 

derivatives are plotted against the angle of attack and compared with wind 

tunnel measurement and previous flight results. The report also includes 

the data compatibility check of measured data. The effect of various input 

forms on the estimates is demonstrated in two examples using simulated 

data. 

The data were analyzed by a stepwise regression with 

parameter estimation 

linear regression 

data compability 

input forms 

UNCLASSIFIED - UNLIMITED 

Subject Category 08