1、AERODYNAMIC PARAMETERS OF THE NAVION AIRPLANE EXTRACTED FROM FLIGHT DATA by WilliQm T. Sgit Langley Research Center Hampton, Va 23365 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION . WASHINGTON, D. c. .; MARCH 1972 2 11 , F? 1 -I ; 2 -_ I 2 I Provided by IHSNot for ResaleNo reproduction or networking
2、 permitted without license from IHS-,-,-TECH LIBRARY KAFB. NM EXTRACTED FROM FLIGHT DATA 6. Performing Organization Code i 17. KetWords (Suggested by Author(s) Parameter extraction Aerodynamic parameters Maximum likelihood 9. Performing Organization Name and Address , NASA Langley Research Center Ha
3、mpton, Va. 23365 12. Sponsoring Agency Name and Address National Aeronautics and Space Administration Washington, D.C. 20546 I 18. Distribution Statement Unclassified - Unlimited 10. Work Unit No. 136-62-02-02 11. Contract or Grant No. 13. Type of Report and Period Covered Technical Note 14. Sponsor
4、ing Agency Code 19. Security Clanif. (of this report) Unclassified -. 20. Security Classif. (of this page) 21. NO. of Pages 22. Price Unclassified 60 $3.00 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I AERODYNAMIC PARAMETERS OF THE NAVION AIRPLAN
5、E EXTRACTED FROM FLIGHT DATA By William T. Suit Langley Research Center SUMMARY An iterative method, which is characterized as a maximum-likelihood minimum- variance technique, was used to extract the aerodynamic parameters of a Navion airplane from flight data. The purposes were to compare the resu
6、lts with parameters obtained from wind-tunnel tests and with results obtained by analog matching of the same data, and to develop techniques for application of the parameter -extraction program. Results from the study showed that the parameter-extraction program can produce aerodynamic parameters wh
7、ich will permit close estimation of the aircraft time histories used in the extraction process. The program determined an estimate of the standard deviations of the states and parameters. These estimates were used to indicate how well the calculated states fit the flight data and the confidence in t
8、he values of the estimated parameters. The study also showed that the values of the parameters were affected by the data and mathematical model used during the extraction process. Because of the lack of confidence in the parameters extracted by using some of the sets of data, several parameters were
9、 estimated by other methods. By using a combination of methods, a set of parameters which gave a fit to the data was obtained. The extracted parameters agreed reasonably well with the values obtained by analog matching the same data, with the exception of the change in normal-force coefficient with
10、angle of attack (Cza). The agreement with wind-tunnel parameters was not as good for the variations of pitching-moment coefficient with angle of attack (Cma), side-force coef - ficient with sideslip angle Cyp), rolling-moment coefficient with sideslip angle (Clp, and yawing-moment coefficient with s
11、ideslip angle Cnp . However, of the parameters deter- mined by the program, only one had a standard deviation greater than 15 percent of the value of the parameter and the parameters determined gave a reasonable fit to the flight data. 0 ( INTRODUCTION Mathematical analyses of flight dynamics and ha
12、ndling qualities of an aircraft are required for determining the suitability of the aircraft for its mission. In order to make such analyses, it is necessary to have available the aerodynamic parameters. of the air- craft. There are several methods of obtaining the parameters. These methods include
13、Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-those presented in various books, wind-tunnel tests, and extraction of derivatives from flight-test data. Of these methods, derivatives from flight tests should be the most accu- rate since such results
14、 are obtained with the actual aircraft in its proper environment. There is, therefore, a continuing interest in developing and evaluating improved methods of extracting derivatives from flight data. In a recent study (ref. l), a comparison was made between various analytical meth- ods, wind-tunnel m
15、easurements with a full-scale airplane, and results obtained from flight-test data for a Navion airplane. In that study, an analog-matching technique (ref. 2) was used in extracting parameters from the flight data. Some rather large differences were found between the various methods. In particular,
16、some large differences were obtained between the wind-tunnel and the flight-test results. Analog matching requires a highly experienced operator to match flight data properly. It appeared desirable to use an alternate method of extracting the derivatives from the flight data. The method used in this
17、 study is a mathematical formulation of the logic required to select derivatives to best match a set of flight data. The method selected is an iterative procedure which selects the aerodynamic parameters to maximize a conditional maximum likelihood func- tion and is equivalent to determining the set
18、 of aerodynamic parameters which will maxi- mize the probability that the calculated state of an airplane will match the measured state for the same control inputs (ref. 3). The maximization process used minimizes the mea- surement error covariance matrix. The resulting parameter adjustment equation
19、s are of the same form as those obtained by use of a modified Newton-Raphson or weighted least- squares technique (ref. 4). The main difference is that with the maximum likelihood for- mulation, the weights are updated at each iteration. The program will speed up derivative determination, give a fit
20、 to the flight data based on mathematically minimizing a cost cri- terion, and determine a matrix which indicates the variances of dependency between the estimated derivatives. The primary purpose of the present paper is to use the flight data employed in the analysis reported in reference 1 and ext
21、ract the aerodynamic parameters for comparison with the results presented in reference 1. A second purpose of this paper is to indicate the procedure used in applying the parameter estimation program to the data herein. A third purpose is to relate the experience gained from this investigation and t
22、o point out the advantages of the program used. A fourth purpose is to indicate the confidence in the parameters obtained. SYMBOLS Values are given in both SI and U.S. Customary Units. The measurements and cal- culations were made in U.S. Customary Units. The aerodynamic parameters are refer- enced
23、to a system of body axes with the origin at the aircraft center of gravity, and with body axes orientation as shown in figure 1. 2 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a b - C F g I i it K L It M m N AP P q 6 R acceleration, m/sec2 /sed) w
24、ing span, m (ft) wing mean geometric chord, m (ft) force, N (lb) acceleration due to gravity, m/sec2 (ft/sec2) moment of inertia, kg-ma (slug-ft2) index tail incidence angle, radians or degrees weighting factor likelihood function distance from aircraft center of gravity to center of pressure of hor
25、izontal tail, m (ft) moment, N-m (ft-lb) mass, kg (slugs) number of data points change in parameter from iteration to iteration rate of roll, radians/sec rate of pitch, radians/sec dynamic pressure, ipV2, N/m2 (lb/ft2) estimate of error covariance matrix 3 . Provided by IHSNot for ResaleNo reproduct
26、ion or networking permitted without license from IHS-,-,-r S U V V W CY P Y 6 e rate of yaw, radians/sec wing area, m2 (ft2) nondimensional Thrust (Dynamic pressure) (Wing area) velocity along X body axis, m/sec (ft/sec) aircraft total velocity, m/sec (ft/sec) velocity along Y body axis, m/sec (ft/s
27、ec) velocity along 2 body axis, m/sec (ft/sec) angle of attack, radians sideslip angle, radians flight-path angle, radians control deflection, radians or degrees pitch angle, radians air density, kg/m3 (slugs/ft3) roll angle, radians r ol ling - mom en t c oeff ic ien t , M E , a aileron I Czq =- aC
28、Z a- 2v b body C computed 5 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-e elevator f flap m measured 0 r rudder t indicates coefficient at trim conditions indicates state at trim conditions X x-axis Y Y-axis Z Z-axis Superscript : T transpose A d
29、ot over a symbol signifies a derivative with respect to time. DESCRIPTION OF AIRPLANE AND FLIGHT TESTS Instrumentation The flight data used for extracting derivatives was obtained from flight tests of the Princeton University variable-stability Navion airplane, N91566. The physical character- istics
30、 of the Navion are presented in figure 2 and table I. included: I I Accuracy Normal acceleration . Roll rate . Pitch rate Yaw rate . Angle of attack Altitude Indicated airspeed Control surface position . 6 *0.01 g i0.044 radians/sec i0.024 radians/sec iO.010 radians/sec k0.8 i30.48 m (il00 ft) 1.03
31、m/sec (i2.3 mph) i1 percent The data recorded for this study Response frequency Hz 2 4 2 2 2 CPS 2 4 2 2 2 .-.-.-. . I I I I, , + I, I I Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-The data were sequenced by a commutator at a rate of 10 points pe
32、r second and telemetered to a ground station as a frequency-modulated signal where it was recorded on magnetic tape. The angle of attack was corrected for upwash effects but required no correction for angular rates. The accelerations and angular rates needed no correction. Flight Data The flight-tes
33、t data used in the present study were obtained from tests made by pa- sonnel of the Princeton University Aeronautical Laboratory. The data were recorded on magnetic tape and were processed at the Langley Research Center for parameter extrac- tion. The calibrations used during processing were furnish
34、ed by Princeton University. The data processing included digitizing the data, converting the recorded signal to engi- neering units, and interpolating to give all the data at the same times on the tape. The interpolation was required because the commutated data gave each state at a different time. F
35、light-test conditions are listed in table II. The applied control disturbances included an elevator doublet, an aileron doublet, and a rudder pulse. PARAMETER-ESTIMATION PROCEDURE The parameter-estimation procedure used in this study is an iterative procedure which maximizes the conditional likeliho
36、od function L(aerodynamic parameters, weights, initial conditions): where R is the estimate of the error covariance matrix and X is the vector describing the state of the aircraft. Maximizing the likelihood function minimizes the difference between the measured and calculated aircraft motions. The w
37、eighting matrix R-l can be the complete error covariance matrix, the diag- onal terms of the error covariance matrix, or a diagonal matrix with fixed weights on the diagonal, at the discretion of the investigator. If the diagonal form of the weighting matrix is used, the weights represent the estima
38、ted lower bound of the noise on the measured states. The use of the likelihood function in parameter identification is discussed in ref- erence 3. Maximizing the likelihood function results in a parameter updated equation which is given by 7 Provided by IHSNot for ResaleNo reproduction or networking
39、 permitted without license from IHS-,-,-where M is the matrix of sensitivities of the calculated states with respect to the unknown parameters (ref. 5). The matrix will be called in this paper the estimated parameter covariance matrix. The updated equation is determined by forming a set of different
40、ial equations with the changes in the unknown parameters as the variables. This set of simultaneous equations is then solved by least squares to give the updated equation (see ref. 5.) The steps in the iteration procedure are outlined in figure 3. The procedure is to write a set of equations of moti
41、on for the aircraft under consideration. These equations will include a number of aerodynamic parameters. The parameters must be initially estimated so that the motions of the aircraft can be calculated. These calculated motions are then compared with the motions of the actual aircraft for identical
42、 control inputs. The parameter estimation program uses the differences between the measured and cal- culated data to calculate the updated values of the parameters. The parameters are then corrected and new aircraft motions are calculated. The process is repeated with updated parameters until the di
43、fference between calculated and measured motions are within some acceptable range. The complete details are given in reference 3. During this investigation the mean-squared error between the measured and calcu- lated states was displayed at each iteration. When the mean-squared error became con- sta
44、nt for several iterations, the problem was terminated. A printout of an estimate of the variance of the states, the changes in unknown parameters at each iteration, the estimated lower bound on the standard deviations of the unknown parameters, and the determinant of the R matrix were obtained. Data
45、 from the printout were examined to determine the fit to the flight data and the confidence in the extracted parameters. If all these criteria indicated a fit in the order of the instrument uncertainty and if the unknown parameters had changes less than 5 percent from iteration to iteration, the par
46、ameters obtained were considered to be as good as could be determined. The program is set up so that the fit to the flight data can be monitored on a cathode ray tube (CRT) as the parameters are updated. The mean-squared error was displayed on a digital voltmeter. The program can be stopped at any i
47、teration and the states used in the likelihood function changed or unknown parameters added to or taken from the mathematical model. Also, any of the parameters in the mathematical model can be con- sidered to be known and fixed at specified values. These characteristics of the program allow the ope
48、rator to have a close interaction with the program and give the operator a very flexible tool to use. Because the operator can see any large effect of changes in the parameters, there is a considerable saving in time over letting the computer run unob- served for a fixed number of iterations and the
49、n examining a printout of the results. Also, the turnaround between runs is seconds rather than hours if batch processing had been used. The operators console and cathode ray tube (CRT) are shown in figure 4. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-PRELIMINARY CONSIDE
