1、NASA TECHNICAL NOTECO/V“73 -NASA TN D-7137MODELING OF AIRPLANE PERFORMANCEFROM FLIGHT-TEST RESULTS ANDVALIDATION WITH AN F-104G AIRPLANEby Robert T. Marshall and William G. Schweikhard Flight Research CenterEdwards, Calif. 93523NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. FEBRUARY
2、 1973Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1. Report No.NASA TN D-71372. Government Accession No. 3. Recipients Catalog No.4. Title and SubtitleMODELING OF AIRPLANE PERFORMANCE FROM FLIGHT-TESTRESULTS AND VALIDATION WITH AN F-104G AIRPLANE5
3、. Report DateFebruary 19736. Performing Organization Code7. Author(s)Robert T. Marshall and William G. Schweikhard8. Performing Organization Report No.H-7239. Performing Organization Name and AddressNASA Flight Research CenterP. O. Box 273Edwards, California 9352310. Work Unit No.136-13-08-00-2411.
4、Contract or Grant No.12. Sponsoring Agency Name and AddressNational Aeronautics and Space AdministrationWashington, D. C. 2054613. Type of Report and Period CoveredTechnical Note14. Sponsoring Agency Code15. Supplementary Notes16. AbstractA technique of defining an accurate performance model of anai
5、rplane from limited flight-test data and predicted aerodynamicand propulsion system characteristics is developed. With themodeling technique, flight-test data from level accelerations areused to define a Ig performance model for the entire flight envelopeof an F-104G airplane. The performance model
6、is defined in termsof the thrust and drag of the airplane and can be varied with changesin ambient temperature or airplane weight. The model predicts theperformance of the airplane within 5 percent of the measured flight-test data. The modeling technique could substantially reduce thetime required f
7、or performance flight testing and produce a cleardefinition of the thrust and drag characteristics of an airplane.17. Key Words (Suggested by Author(s)Aircraft performance testing techniquesPerformance modelingThrust-drag evaluation18. Distribution StatementUnclassified19. Security Classif. (of this
8、 report)Unclassified20. Security Classif. (of this page)Unclassified21. No. of Pages2822. Price*,$3.00 For sale by the National Technical Information Service, Springfield, Virginia 22151Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-MODELING OF AIRP
9、LANE PERFORMANCE FROM FLIGHT-TESTRESULTS AND VALIDATION WITH AN F-104G AIRPLANERobert T. Marshall and William G. SchweikhardFlight Research CenterINTRODUCTIONThe number of flight tests required to define the performance of“modern aircraftand the associated costs of the tests are increasing at an ala
10、rming rate. Larger flight .envelopes, the multitude of geometric variables (for example, wing sweep or inletgeometry, or both), and the variability of external store configurations of modern highperformance aircraft create a matrix of conditions that is nearly impossible to encom-pass with conventio
11、nal testing techniques. For this reason, studies are being conductedby NASA to develop a mathematical performance model from flight-test data so thatthe performance for the entire flight envelope of ah aircraft can be determined from alimited number of flight tests.An aircraft performance model dete
12、rmined from flight-test data can be defined interms of either excess thrust (thrust minus drag) or the specific values of thrust anddrag over the Mach number-altitude operating region. The use of excess thrust data todefine an accurate model is limited in that the individual values of thrust and dra
13、g arenot independently known; therefore, excess thrust must be determined for each geometricconfiguration and power setting under consideration. Thus many flight tests are neces-sary to obtain data over the operating envelope of an aircraft. Furthermore, once amodel is defined in terms of excess thr
14、ust, it is difficult to adjust it to variations fromstandard-day atmospheric conditions, again because the thrust and drag are combinedin one term, making it difficult to separate individual variations of the two parameters.This problem could be eliminated if a performance model were defined in term
15、s ofabsolute values of thrust and drag. The determination of thrust and drag in flight is acomplex, difficult, and tedious process, however, that requires considerably moreflight-test time and instrumentation than the definition of excess thrust.One way to solve this problem would be to develop a te
16、chnique of defining a perform-ance model for the flight envelope of a particular aircraft configuration from limitedflight-test data and the aerodynamic and propulsion system characteristics of the air-craft. Once defined, such a model could be used to predict the flight performance of theaircraft a
17、t every point in the flight envelope without additional flight testing. If thiscould be done, it would reduce the time required for performance flight testing and pro-duce a clear definition of the thrust and drag characteristics of an aircraft. This reportpresents the results of a study made at the
18、 NASA Flight Research Center to developsuch a technique. The technique is applied to an F-104G airplane. The measured per-formance of the airplane is compared with the computed performance of the model.SYMBOLSPhysical quantities in this report are given in the International System of Units (SI)Provi
19、ded by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-and parenthetically in U. S. Customary Units. Measurements were taken in CustomaryUnits. Factors relating the two systems are presented in reference 1.Cn drag coefficient, D/qSCT lift coefficient, L/qS_LjD t
20、otal airplane drag, N (Ib)-F net thrust, N (Ib)FU fuel used, kg (Ib)2 2g acceleration due to gravity, 9. 8 m/sec (32. 2 ft/sec )g mass-to-force conversion factor, 9. 8 N/kg (1 Ibf/lbm)Oh pressure altitude, m (ft)V2he specific energy, h + , m (ft)95- rate of change of altitude, m/sec (ft/sec)dtp rate
21、 of change of specific energy, m/sec (ft/sec)Kj-v model coefficient for drag, D/DpK-p model coefficient for thrust and fuel flow, F/Fp andL airplane lift, N (Ib)M Mach numberN normal load factor, L/g Wt/p compressor inlet total pressure, N/m2 (lb/in2)*2q dynamic pressure, N/m2 (lb/ft2)f oS wing refe
22、rence area, m (ft )SFC specific fuel consumption, ks/ec (T total temperature, K (R)Ta ambient temperature at altitude, K (R)2Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-tVdVdtWWfayelapsed time, secvelocity along flight path, m/sec (ft/sec)rate of
23、 change of velocity, m/sec2 (ft/sec2)airplane gross weight, kg (Ib)total fuel flow, kg/sec (Ib/sec)angle of attack, degflight path angle, degchange in specific parametertocompressor inlet total pressure ratio, “ x 3 ,thrust deflection angle, degpredictedstandard daytest dayPRINCIPLES OF PERFORMANCE
24、MODELING TECHNIQUESThe term “performance model“ is used inits simplest form in this report to refer to amathematical description of the motion of anaircraft in the vertical plane as given byequations (1) and (2). For this discussion theforces were resolved parallel and perpendic-ular to the flight p
25、ath, as indicated in theadjacent sketch, and the angle of attack wasassumed to be small.g WdVF - D - g W sin? = c gdtL - g W cos 7 = g W (N - cos 7)C CPtcSubscripts:Pst(1)(2)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-In the development of the pe
26、rformance model, only nonmaneuvering flight (that is,a normal load factor of 1, constant direction of flight, and constant power setting) wasconsidered. For a normal load factor near 1, equation (2) becomes a secondary correc-tion to the model. As shown in references 2 to 4, equation (1) can be rewr
27、itten in termsof the rate of climb, acceleration, and velocity of the airplane as follows:(VDt)vt /dh ydvgcWt Vdt+ gdty/t (3)The right side of this equation can be determined easily by measuring the velocity andthe rates of change of altitude and velocity of an airplane. On the left side of this“equ
28、ation, the weight can also be obtained easily; however, thrust and drag cannot beexplicitly defined in flight and are unknowns in the equation. Therefore, a secondequation must be developed which allows either the simultaneous solution of the twoequations or the determination of an explicit value of
29、 thrust or drag.Experience with in-flight thrust measurements on the XB-70 airplane showed thateven though the measured thrust did not usually agree with the predicted thrust, thepredicted specific fuel consumption, SFCD, which is the ratio of fuel flow to thrust, wasgenerally accurate. The ratio of
30、 the measured to the predicted specific fuel consump-tion is presented in figure 1 for the XB-70 airplane at maximum power. As indicatedby the dispersion in the data at any given Mach number, the predicted specific fuel con-sumption is generally within 5 percent of the measured value. On the basis o
31、f thisobservation, it was assumed that the ratio of the in-flight measured fuel flow to thrustshould be approximately equal to the ratio of the predicted fuel flow to thrust correctedfor the test-day temperature as shown by equations (4) and (5):I D fi t * whereWf = Wf + AWf(5)The values of AWf and
32、AF are obtained from equations (A5) and (A 6) of appendix A. ,Furthermore, reference 5 indicates that the climb and acceleration performance of anaircraft Is fairly insensitive to nominal errors in specific fuel consumption. In refer-ence 5 a 10 percent deviation in specific fuel consumption resulte
33、d in a -0. 4 to 0. 7 per-cent change in the climb and acceleration performance of an F-111B airplane at maxi-mum power.A second assumption that must be made for equation (4) to be valid is that the pre-dicted propulsion system characteristics available for the airplane are consistent withinthemselve
34、s. It is also assumed that the relationship of the thrust and fuel flow is accu-rately described and that the temperature corrections for these quantities are accurate.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-If these assumptions are valid, th
35、e in-flight thrust can be calculated with equation (4)by measuring the fuel flow and making use of the predicted propulsion system charac-teristics of the airplane as follows:Ft=(Wf./Wf_ |FDx (6)The drag can then be determined from equation (3). With this technique the thrust anddrag of the airplane
36、 can be determined for each test point for use in the performancemodel.Rather than calculate the thrust and drag for each test point, it was easier to use amodel which incorporated the predicted drag, thrust, and fuel flow and then to refinethese values by determining a set of coefficients, Kp and K
37、, so that the performanceof the model matched the test-day performance of the airplane. This was done by firstcomputing the coefficient Kp as defined by equation (6) as follows:KF = Wf /Wf = Ft/Fn (7)*t *Pt *PtThe coefficient KD was then determined (for test conditions) from the following versionof
38、equation (3):V, +W) model x airplane(KFFpt -KDDP“ (dtwhereKD = Dt/Dp (9)Values of Kp and KQ were determined in this manner for each point in a test trajec-tory, and since values of predicted thrust and drag were available in the model, thetrue thrust and drag of the airplane were readily calculated.
39、The data analysis procedures used in this investigation are discussed in detail inthe appendix.VALIDATION OF THE PERFORMANCE MODELING TECHNIQUEThe performance modeling technique was validated on the basis of the followingcriterion: That having determined a set of coefficients (Kp and KQ) from a seri
40、es oflevel accelerations performed at different altitudes, weights, and temperatures over theflight envelope of an airplane, it should be possible to calculate the performance of theairplane for any arbitrary flight trajectory encompassing climbs, dives, and accelera-tions as long as the maneuvering
41、 load factor increments are low (0. 2g). For theProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-validation, the modeling technique was applied to level acceleration flight-test dataobtained on an instrumented F-104G prototype airplane (fig. 2) and re
42、ported in refer-ence 6.The F-104G is a fixed-wing, fixed-inlet-geometry airplane powered by a J79-GE-11A,high-pressure-ratio, afterburning turbojet engine. The airplane is 16.7 meters(54. 8 feet) in length and 4. 1 meters (13. 5 feet) in height, with a wingspan of 6.7 meters(21. 9 feet) and a sea-le
43、vel ratio of maximum power thrust to weight of 0. 78. The testinstrumentation, the airplane, and the engine are described in detail in references 6,7, and 8, respectively.Model Coefficients Computed From Level Acceleration ManeuversThe model coefficients KF and KD were determined from the level acce
44、lerationflight-test data using a computer program. (See appendix.) The coefficients computedfor two level acceleration maneuvers at an altitude of 9144 meters (30,000 feet) arepresented in figure 3 together with curves faired through each set of coefficients. Theanalysis procedure was then repeated
45、for level accelerations made at 3048 meters(10,000 feet), 6096 meters (20,000 feet), 9144 meters (30,000 feet), 12,192 meters(40,000 feet), and 15,240 meters (50,000 feet) to define the model coefficients for eachof these test altitudes. The fairings of the coefficients K-p and Kp obtained fromthis
46、analysis are presented in figures 4 and 5, respectively.A complete performance model of the F-104G test airplane was then obtained bycombining the set of model coefficients presented in figures 4 and 5 with the predictedaerodynamic and propulsion system characteristics of the airplane (tables 1 to 4
47、, adaptedfrom refs. 7 and 8) in a digital trajectory analysis computer program. To validate thecoefficients, the trajectory program, which constitutes the performance model of thetest airplane, was used to compute the model test-day performance for each of the levelaccelerations, with the test-day M
48、ach number-altitude profile and the test-day tempera-tures at altitude used as inputs to the program. Computed and measured test-day per-formance of the airplane for the level accelerations made at 9144 meters (30, 000 feet)is compared in figures 6(a) and 6(b). As shown, an excellent match was obtai
49、ned, thusvalidating the coefficients for this altitude. The coefficients for the other altitudes werevalidated in the same manner. The performance model for the test airplane wasobtained from approximately 31 minutes of flight-test data.The computer model could also have been obtained by adjusting the predicted dragpolars and the thrust and fuel flow curve
