The program objectives are fully defined in the original proposal entitled Program of Research in Flight Dynamics in GW at NASA Langley Research Center, which was originated March 20, 1975, and in the renewals of the research program from January 1, 2003 to September 30, 2005. The program in its present form includes three major topics: 1. the improvement of existing methods and development of new methods for wind tunnel and flight data analysis, 2. the application of these methods to wind tunnel and flight test data obtained from advanced airplanes, 3. the correlation of flight results with wind tunnel measurements, and theoretical predictions

Klein, Vladislav

Murphy, Patrick C.

NASA Technical Reports Server

Program of Research in Flight Dynamics 
The George Washington University 
at 
NASA Langley Research Center 
NASA Cooperative Agreement NCC1-03004 
FINAL REPORT 
For the Period 
January 1,2003 through September 30,2005 
NASA Tech Officer 
GW Principal Investigator 
Patrick C. Murphy 
Vladislav Klein 
School of Engineering and Applied Science 
The George Washington University 
Washington, DC 20052 
https://ntrs.nasa.gov/search.jsp?R=20050192561 2019-08-29T19:59:26+00:00Z
OVERVIEW 
The program objectives are fully defined in the original proposal entitled “Program of 
Research in Flight Dynamics in GW at NASA Langley Research Center,” which was originated 
March 20, 1975, and in the renewals of the research program from January 1,2003 to September 
30,2005. 
The program in its present form includes three major topics: 
1. the improvement of existing methods and development of new methods for wind 
tunnel and flight data analysis, 
2. the application of these methods to wind tunnel and flight test data obtained from 
advanced airplanes, 
3. the correlation of flight results with wind tunnel measurements, and theoretical 
predictions. 
The Principal Investigator of the program is Dr. Vladislav Klein. Two Graduate 
Research Scholar Assistants (M. M. Eissa and N. M. Szyba) also participated in the 
program. 
SPECIFIC DEVELOPMENTS 
Specific developments in Aerospace during the period January 1,2003 through 
September 30,2005: 
1. Data Analysis of highly swept delta wing, aircraft from wind and water tunnel data 
a) Wind tunnel experiments were performed on the 18% scale model of the 
F-16XL aircraft in the NASA Langley Research Center 14x22 Foot 
Subsonic Wind Tunnel in 1997 and 2004 and included static tests and 
dynamic forced oscillation tests in roll, pitch and yaw angles. Data were 
collected with varying mounting techniques for both static and dynamic 
tests. Data from static tests were used to compute non-dimensional 
aerodynamic derivatives with respect to angle of attack and sideslip angle. 
Results varied for different mounts and Reynolds numbers. 
The measured data from forced oscillation tests were obtained at different 
angles of attack, amplitudes, Reynolds numbers, and frequencies. Some 
of the tests were performed with initial offsets in either roll or yaw angle, 
for roll or yaw oscillations, respectively. Harmonic analysis was applied 
for obtaining the in-phase and out-of-phase components of aerodpamic 
coefficients. Responses varied with amplitude, Reynolds number, 
frequency, and mounting method. In general, decreased model accuracy 
was observed at angles of attack greater than 30". Increased higher 
harmonic in the math model improved accuracy for large amplitude and 
offset data. Harmonic analysis as well as power spectral analysis 
indicated an increased measurement noise at these low amplitude 
oscillations. 
Frequency dependence was observed mostly between 20" and 50" for all 
components in pitch, roll and yaw oscillations. For frequency dependent 
data a two-step linear regression algorithm was used to obtained 
parameters in an unsteady aerodynamic model. The static coefficients 
computed from forced oscillation tests were compared to static 
coefficients measured from static tests. Axial and normal force 
coefficients from pitch oscillations had high model accuracy. Rolling 
moments coeficient had the highest accuracy for roll oscillations when 
the linear model was used. There was some variation in results between 
small and large amplitudes. 30" amplitude oscillations at zero offset had 
high model accuracy, but the necessity for higher order terms in harmonic 
analysis brought into question the applicability of the relationships 
between the first order Fourier coefficients and the aerodynamic 
coefficients. The variation or the non-dimensional time constant showed 
an increased unsteady effect between 35" and 45" angle of attack. Very 
few yaw oscillations had acceptable unsteady model accuracy. 
The results from wind tunnel data are summarized in NASA TM and M.S. 
Thesis (see Publications 1 and 2). Some examples are included in Figures 
1 to4. 
b) The problems of general methodology for testing and data analysis were 
addressed using data from water tunnel tests. These tests were conducted 
with a 2.5% scale model of the F- 16xL at Rolling Hills Research 
Company to identify nonlinear and unsteady aerodynamic model 
parameters. Although forced oscillation tests were performed about all 
three-body axes, only roll axis oscillation data were analyzed. 
Harmonic analysis of the small-amplitude oscillatory data was performed 
on single oscillations formed by averaging 30 cycles of data. This 
analysis provided a basis for the nonlinear analysis. Harmonic analysis 
was also applied to the large amplitude data. 
A general formulation of the aerodynamic model for aircraft that includes 
nonlinear unsteady aerodynamics was attempted. The resulting model 
could predict a broad class of aerodynamic responses of a rigid-body 
aircraft. The structure allowed easy interpretation of the model parameters 
by retaining conventional stability and control derivations for static and 
dynamic terms. Unsteady terms in the form of indicia1 hnctions were 
added to allow frequency dependent phenomena to be included. 
Experimental data and resulting model for the rolling-moment coefficient 
are presented in the AIM Paper (see Publication 3). 
c) The oscillatory data obtained from the NASA LaRC 12-Foot Low Speed 
Tunnel for a 10% model of an F-16XL were used in previous years for 
mathematical modeling. 
A portion of the data; however, was analyzed for obtaining a measure of 
their accuracy. In this analysis the accuracy of the time stamp and the 
sample of time fidelity were first evaluated. Then, the effect of the timing 
signal was investigated. In the following step, the commanded and 
measured input signal was compared. The last part of the accuracy 
assessment was the evaluation of measured outputs. A measure of 
precision was obtained from repeated measurements under the same 
conditions. For the final statement in the accuracy, the outlier rejection 
rules were applied. The results of the data accuracy assessment are 
summarized in NASA TM Report (see Publication 4). 
2. Aerodynamic characteristics and instrumentation system calibration of Free 
Flying Aircraft Sub-scale Experimental Research Aircraft (FASER) 
The FASER program was established at the NASA LaRC to provide an 
affordable, easy-to-modify testbed to conduct research in the area of stability and 
control and system identification. Since the remote-control airplane will be used 
in high amplitude rapid maneuvers, it was desired to have a simulation program of 
FASER to allow the pilot to practice the maneuvers before the actual aircraft is 
flown. In addition, the simulation program can be used to design the experiment 
and to aid control law development. 
In this part of the research the existing aerodynamic model equations were 
updated using wind tunnel data. These data were obtained in the form of 
aerodynamic coefficients and their variation with the angle of attack, sideslip 
angle and control surface deflections. The analytical expressions for these 
dependencies were developed by applying the multivariate orthogonal modeling 
technique. An example of the resulting equations is given in Table 1. 
Wind tunnel data were also analyzed for obtaining calibrations of the alpha and 
beta-vanes. The analytical forms of these calibrations were developed by a 
stepwise regression. Examples of the calibration equations are given in Table 2. 
The complete results of the research conducted are in the NASA DSCB Internal 
Memo (see Publication 5 ) .  
3) System Identification Methodology 
The past, present and future of system identification applied to aircraft at NASA 
LaRC were discussed in the Journal ofAircraft (see Publication 5) .  
The purpose of this paper was to present a general approach to aircraft system 
identification, as formulated at NASA LaRC. The paper starts with a historical 
survey of flight testing and stability and control parameter estimation at NACA 
Langley Memorial Aeronautical Laboratory, and later at NASA LaRC, which lead 
to the present state of the art. The individual steps in the methodology are 
introduced and briefly explained. Four recent examples are mostly of the 
methodology application are given. These examples are mostly related to 
problems that go beyond traditional stability and control estimation from flight 
data. The paper is concluded by some thoughts about the future development of 
the methodology. 
Table1 . Aerodynamic model equations for two different subspaces 
c, (a, p7 4 7 6f 1 
I - 7.5" I: a! I 10" and - 10 5 /3 I 10 
.0405 + 1 . 6 3 6 5 ~ ~ ~  + .212df  + .263ldc - .0476,'6, + 
.062a + .0136, + -108 16,' + .04265/ 
c, (a, p7 4,6f 1 
c, (aP7 6, 7 s, 1 
4 .2977~~ + .62756, + .29158, + .046 - .608&; - 2 . 8 7 1 4 ~ ~ ~ 6 ~  
-.7241JC - .4917~r-.0335/?+.06466, -.8846a2 
Cy(K!,,J,,J,) 
c, (a,/% 8, 1 
c, (a7 p, 6, 7 6, 1 
- .346%&8 + .O 126f 
-.35p+.O8936, -.0256, +.02965~~-.1662pS,~ -.04462dr + . l l@ 
-.1986, -.041 lp-.227~~/?+.245726; +.0272~6, 
-.043S, +.058~-.118loG~+.0764~6, +.0235Wr -.135P26, 
C,  (%!%6, Jf 1 -.257+1.99a+.404dc +.5586: +.1186,' -.736: -.185de6, 
c,(a,P,&Jf) 1 -.003+1.366, -.654a6, -.71~6; +.1426,Sf +.513S, + 6 . 8 9 5 ~ ~  - 11.892d 
-.01366,6r2 +.0136, 1 
C, (a, p9 6, 9 s, 1 
Cy (a,P,6,,6,) 
.348-.8249d, -3.12a+ 2.183aP2 +1.32a2&, +1.776a2 +.89486: 
+ .722ade3 
-.31p+.096796, +.81a6, -.417a26, +3.376a+.381@ -.2025@ + 
.396p26, -.08982PS,' -.00616,' +15.41a3 -.2764-.262p2 -.11276, 
-1 .643~~6 ,  -1 2 . 7 ~ ~ '  -.0696,' 
C, <CZ,P,J,,S,) 
c, (a, p9 9 6, 1 
-.1316, -9.1a2P-.368da -.037 -.7591ap2 -.00S96Sr2 +1.731a26, 
- .661P + 4.24ap t 3.59p3 + .127/?6: - Ma2&, - .0456,6r2 - .O054Sa2 
- .0O4/3Sa6, -1 .3773a3 + .306a 
- .0896, + 2.59p3 - .328a26, + .196a -. 1 138P2 + . 1 5 8 2 ~ ~ ~ 6 ,  
- 7.23a2P - .O13a8: - .OOO78,8, - .888a3 - .02836 - -0838; 
+ 3.622oCp - .4578 + .056p6,' + .2837~~6, + .04636,' - .09p26, 
Table 2. Calibration equations for alpha and beta vanes 
Region 
-7.5" I a 210" 
10" < a: < 40" 
Relative Voltage 
Limits 
a,,,, 2.43681 
-29692 < a,,, e .43681 
40" 5 a 5 80" 
10" 5 p I 3 0 "  
- 10" < p < 10" 
a,,,, S.29692 
pa,, 2.51086 
.42711< p,,,, < -51086 
Equation l 
- 30" 5 p 2-10" 
a" = 99.539 - 201.8 la,,, - 4.2825pn, 
pm I .42711 
a" = 106.98 - 2 2 9 . 7 1 ~ ~ ~  + 45.279pnt - 68.554p,', 
a" = 98.419 - 180.03am + 4O.879pn,, - 164.08~~~~p,,,,  
p" = -229.29 + 64O.23Pnv - 35 1.8SP,2, + 3 9 . 0 7 5 ~ ~  
- 62.O5anvP, 
p" =-11741.1+7222.2pm -15273p,', +11031p; 
+ 60.448am - 170.78a:,, + 176.99aiv 
p" = -148.06 + 456.25& - 326.72p:, + 8.4967aw 
0.1 
0.05 
0 
-0.05 
-0.05' 
40 -20 0 20 40 
4,  deg 
40 -20 0 20 40 
$ 1  deg 
-0.1 
-40 -20 0 20 40 
40 -20 0 20 40 
4 1  deg 
Figure1 . Effect of angle of attack and amplitude on lateral coefficient, C, , for rolling 
oscillations with k = 0.171. 
Figure 2. Variation of in-phase and out-of-phase components of rolling moment 
Coefficient with angle of attack. Rolling oscillations. 
a 
T-- 15 ............. 
I 
10 I.... ..... ...... 
5 ................. i 
....... ., ........... 
I 1 I 
i .............. 
I 
I ...... .........._ 
................ i 
Figure 3. Estimated time delay and gain parameter with their 2-sigma intervals. 
Rolling-moment coefficient. Rolling oscillations. 
0.1 
f l  -0 1 
c, (4 
--- k=a'91 ............ 
I 
0 : ~ ~ ~  ............. 
\ 
'\ 
'\ 
- ....... ! .-.... ---:---~ .............. i...~. 
~ \, 
; \  
....... .... ............. i ........................ - . , .-.; 
I \. 
............ ......... ......... 
................ ... ........... ............. .................. ................. ................. L J. .L , I  -4.. ; .+'. I .J 
~ *> ' ,  
-. ..,;_ /.@---- ; 
.............. .... ............. .................. .... ~ 
I I I 
I 
0 10 
_. 
-3 ' I I I I I 
20 30 40 50 60 
a, deg 
Figure 4. Estimated rolling moment parameters fiom static and oscillatory tests. 
PUBLICATIONS 
1. Klein, Vladislav; Murphy, Patrick C. and Szyba, Nathan M.: “Analysis of Wind Tunnel 
Lateral Oscillatory Data of the F- 16XL Aircraft.” NASA TM-2004-2 13246. 
2. Szyba, Nathan M.: “Unsteady Aerodynamic Modeling of Dynamic Oscillatory Wind 
Tunnel Data of the 18% Scale F=16XL Aircraft.” M.S. Thesis, The George Washington 
University, 2004. 
3. Murphy, Patick C.; Klein, Vladislav and Szyba, Nathan M.: “Progressive Aerodynamic 
Model Identification From Water Tunnel Test of the F- 16XL Aircraft.” AIAA Paper 
2004-5277. 
4. Kim, Sungwan; Murphy, Patrick C. and Klein, Vladislav: “Evaluation and analysis of F- 
16XL Wind Tunnel Data from Dynamic Tests.” NASA TM-2004-213234, April 2004. 
5. Eissa, Mohamed M.: “Model Structure Definition and Analysis For the Wind Tunnel 
Force and Moment Coefficients For a Sub-Scale Research Airplane.” NASA DSCB 
Internal Memo, August 2004. 
6. Morelli, Eugene A. and Klein, Vladislav: “Application of System Identification of 
Aircraft at NASA Langley Research Center.” Journd ofAircraft, Vol. 41, No. 2, 
January-February, 2005, pp. 12-25. 


Program of Research in Flight Dynamics, The George Washington University at NASA Langley Research Center

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