NASA NACA-TR-1031-1951 A study of the use of experimental stability derivatives in the calculation of the lateral disturbed motions of a swept-wing airplane and comparison with fli.pdf

1、, . , .:. . . . . .REPORT 1031 A STUDY OF THE USE OF EXPERIMENTAL STABILITY DERIVATIVES IN THE CALCULATION OF THE LATERAL DISTURBED MOTIONS OF A SWEPT-WING AIRPLANE AND COMPARISON WITH FLIGHT RESULTS b By JOHN D. BIRD and BYRON M. JAQUET 1951 ” Provided by IHSNot for ResaleNo reproduction or network

2、ing permitted without license from IHS-,-,- I I REPORT 1031 A STUDY OF THE USE OF EXPERIMENTAL STABILITY DERIVATIVES IN THE CALCULATION OF THE LATERAL DISTURBED MOTIONS OF A SWEPT-WING AIRPLANE 4 AND COMPARISON WITH FLIGHT .RESULTS By JOHN D. BIRD and BYRON M. JAQUET Langley Aeronautical Laboratory

3、Langley Field, Va. I Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-National Advisory Committee for Aeronautics Headquarters, 1724 F Street NIV., Washington 25, D. C. Created by act of Congress approved March 3, 1915, for the supervision and directi

4、on of the scientific study of the problems of flight (U. S. Code, title 50, sec. 151). Its membership was increased from 12 to 15 by act approved March 2,1929, and to 17 by act approved May 25,1948. The members are appointed by the President, and serve as such without compensation. JEROME C. HUNSAKE

5、R, SC. D., Massachusetts Institute of Technology, Chairman ALEXANDER WETIORE, SC. D., Secretary, Smithsonian Institution, Vice Chairman DETLEV W. BRONK, PH. D., President, Johns Hopkins Univer- sity. JOHN H. CASSADY, Vice Admiral, United States Navy, Deputy Chief of Naval Operations. EDWARD U. CONDO

6、N, PH. D., Director, National Bureau of Standards. HON. THOMAS W. S. DAVIS, Assistant Secretary of Commerce. JAMES H. DOOLITTLE, SC. D., Vice President, Shell Oil co. R. M. HAZEN, B. S., Director of Engineering, Allison Division, General Motors Corp. WILLIAM LITTLEWOOD, M. E., Vice President, Engine

7、ering, American Airlines, Inc. THEODORE C. LONNQUIST, Rear Admiral, United States Navy, Deputy and Assistant Chief of the Bureau of Aeronautics. HON. DONALD W. NYROP, Chairman, Civil Aeronautics Board DONALD L. PUTT, Major General, United States Air Force, Acting Deputy Chief of Staff (Development).

8、 ARTHUR E. RAYMOND, SC. D., Vice President, Engineering, Douglas Aircraft Co., Inc. FRANCIS W. REICHELDERFER, SC. D., Chief, United States Weather Bureau. GORDON P. SAVILLE, Major General, United States Air Force, Deputy Chief of Staff-Development. Hos. WALTER G. WHITMAN, Chairman, Researh and Devel

9、op- ment Board, Department of Defense. THEODORE P. WRIGHT, SC. D., Vice President for Research, Cornell University. HUGH L. DRYDEN, PH. D., Director JOHN F. VICTORY, LL. D., Executive Secretary JOHN W. CROWLEY, JR., B. S., Associate Director for Research E. g. CHAMBERLIN, Executive Ofleer HENRY J. E

10、. REID, D. Eng., Director, Langley Aeronautical Laboratory, Langley Field, Va. SMITH J. DEFRANCE, B. S., Director, Ames Aeronautical Laboratory, Moffett Field, Calif. EDWARD R. SHARP, SC. D., Director, Lewis Flight Propulsion Laboratory, Cleveland Airport, Cleveland, Ohio TECHNICAL COMMITTEES AEROPY

11、NAMICS OPERATING PROBLEMS POWER PLANTS FOR AIRCRAFT INDUSTRY CONSULTING AIRCRAFT CONSTRUCTION Coordination of Research Needs of Military and Civil Aviation Preparation of Research Programs Allocation of Problems Prevention of Duplication Consideration of Inventions LANGLEY AERONAUTICAL LABORATORY, A

12、MES AERONAUTICAL LABORATORY, LEWIS FLIGHT PROPULSION LABORATORY, Langley Field, Va. Moffett Field, Calif. Cleveland Airport, Cleveland, Ohio Conduct, under unified control, for all agencies, of scientijic research on the fundamental problems oj p= -# in wind-tunnel tests (tan- 9) angle of attack of

13、wing root chord line 6 A P s b A i7 T, I 1 Subscripts: a 1 .f V to thrust line, positive when trailing edge is down control-surface deflection, measured in a plane perpendicular to hinge axis angle of sweepback, degrees free-stream dynamic pressure ( i p V2 wing area wing span aspect ratio (b2/S) ma

14、ss density of air time time to damp to half amplitude period tail length aileron rudder flap vertical tail WIND-TUNNEL TESTS APPARATUS AND MODEL The experimental static-lateral-stability derivatives, rolling-stability derivatives, and yawing-stability derivatives were determined from tests c.onducte

15、d in the Langley stability tunnel in which rolling or curved flight. is simulated by rolling or curving the air st,ream a.bout a rigidly mounted model. The tests were made on a conventional six-component. balance system wit#h the model mounted at the flight center of gravity which is at 2 I .8 perce

16、nt of the mean aerodynamic chord of the wing. The full-scale airplane (a swept-wing version of a conven- tional fighter) had the quarter-chord line of the wing, just. outboard of the intake ducts, swept back 35. Some of the pertinent airplane characteristics are given in t,able I. More details of l,

17、he airplane may he obt,ained from refer- ences 5 and 0. The $scale model shown in figure 2 and in the photo- graphs of figures 3 to 6 was constructed of laminated mahog- an-y, finished in clear lacquer, and all surfaces were highly polished. The model propeller had t.hree meta! blades set at an angl

18、e of 28” at the 0.75 radius. All propeller-on tests were made with windmilling propeller. The model wing had a removable leading edge so that slats of 0 percent, 40 per- cent, and 80 percent of the swept span could be used inter- changeably to simulate those of the full-scale airplane. The top surfa

19、ces of the slats were cast to the contour of the air- foil and the slats were extended by means of metal brackets which also act as fences to reduce spanwise flow along the slot. A cross section through the slot and slat is shown in reference 5. Provided by IHSNot for ResaleNo reproduction or networ

20、king permitted without license from IHS-,-,-A STUDY OF THE USE OF EXPERIMENTAL STABILITY Fo,D hinge line on 0.849 chord he Removable LE.- -* men f- do fs -44.82 FlcunE Z.-Ucometric clrorncteristics of 6.scale model of test airplane. All dimensions are in inches. Fmun 3.-Side view of $kz.ale model mo

21、unted in B-foot-dinmeter rolling-flow test section of Langley stability tunnel. DERIVATIVES IN LATERAL-MOTION CALCULATIONS 3 FIGURE 4.-Rear viow of %scnle model mounted in G-foot-diameter rolling-flow test section of Langley stability tunnel. FIGURE 5.-Close-up of 40-percent leading-edge slots on $

22、whereas the nose wheel and nose-wheel doors were removed for all flaps-up tests. Shown in figure 2 are the two ventral fins tested on the model. The large ventral fin was used for all tests except a few with the 80-percent-span slot configuration for which the small ventral fin was used. TEST AND TE

23、ST CONDITIONS Trim tests.-Model trim lift coefficients of 0.33, 0.55, 0.76, and 0.95 were selected as representative of those obtained in flight tests. The angle of incidence of the horizontal t.ail was measured with respect to the thrust line. In order to determine the trim angles of the horizont,a

24、l t,ail for the previously mentioned lift coefficients, tests were made through the angle-of-attack range wi t.h the horizontal tail set at -5O, -3, and 1 incidence. From these test,s the trim angles of the horizontal tail were determined. (See table II.) Static tests:-111 order to determine the sta

25、tic-st,abilit#y derivatives C2$, C,+, and Cl;, t,he model was tested at #= f5 through an angle-of-attack range of cr=-2O to 01=23 for the flaps up (trim CL=0.33) and cu=-2 to a=18O for the flaps down (trim C=O.76) for each of the slot configurations. Tests were also made at all selected test trim li

26、ft coefficients through an angle-of-yaw range of $= therefore, the tares for the 4O-percent-span slot, configuration were applied to all con- figurations. The Jiach and Reynolds numbers for the tests PIP 0.17 and 1 .Ol X 1 06, resprctivrly. Rolling-flow tests.-Tests wcrc conducted in the O-foot- dia

27、meter rolling-flow kst spct,ion of the Langley stabi1it.y t,unnel, wherein rolling fligh 1. of the model was simulat.ccl by. rot,at.ing the air stream. Tbc model was mounted rigidly on a conventional support strut. Details of this test pro- cedure are given in reference 1. All slot configurations we

28、re tested through the angle-of- attack range with the flaps up (trim C,=O.33) and with the flaps down (trim C,=O.76) at helix angles pb/2V of 0, f0.0253, and 10.0757 radian. The slopes of CL, C, and C,- plotted against pb/2V n.rc the derivatives Clr, C,?,), and C,.p. The 40-percent-span slot configu

29、rat,ion (flaps up and down) was tcst.ed at, the selected trim lift, roefficirnts for the previously mentioned values of pb/2V from $=O” to +=20 t.o determine the variation of Cb, CnP, and Cyp with $. The Mach number and Reynolds number for the rolling-flow tests wcrc 0.17 and I .Ol X 106, respectivr

30、ly. Yawing-flow tests:-Yawing-flow t.ests were conducted in the 6- by 6-foot curved-flow test section of the Langley stability tunnel. In this section, curved flight is simulated approximately by directing the air in a curved path abotit a fixed model. All slot configurations were tested in curved f

31、low through the angle-of-attack range with the flaps up (trim C,=O.33) and with the flaps down (trim C,=O.76) at values at rb/2V of 0, -0.039, -0.082, and -0.108. The slopes of Cl, Cn, and Cy plotted against rbl2V are the derivatives C1, C, and C,. The 40-percent-span slot configuration (flaps up an

32、d down) was tested through an angle-of-yaw range of ti= 520” for values of rbf2V of 0, -0.039, -0.082, and -0.108 at the previously mentioned trim lift coefficients to determine the variation of Cc?, C,(, and C, with $. The values presented herein are the average of the results at corresponding posi

33、- tivr and ncgat,ive angles of yaw. The 40-percent-span slot, configuratibn (flaps up) was ksted at) a trim lift coefficient of 0.33 through the angle-of- yaw range with the propeller off. The yawing-flow tests were made at a Xlach number of 0.13 and a Reynolds number of 0.8 X 106. CORRECTIONS Appro

34、ximate j and, as a result, the deriva,tives Cb, Cnn, Py , CL?, P, , a.nd C,; are not corrected for the effects of t,he su;port stkt. The derivative C5 was correct,ed for the effective pikhing velocit,y, which exists when the model is tested at an angle of yaw, by the following equation: where Pld is

35、 measured about the wincl axis, and j(A, A, $), which is small as compared with Cl cos $, is a function determined by use of the methods Gf reference 4. Corre- sponding effective pitching corrections were not applied to the derivatives Cn and C, . A correction w”as also ippliecl to the derivative C,

36、-T to account for t.hc error caused by the cross-tunnel static- pressure gratlien t. which is associated with curved flow. EXPERIMENTAL RESULTS The experim.enta,l dat.a are discussed briefly witB reference to t,hr effects of the slots and angle of yaw on tbc aerody- na.m.ic characteristics of the m.

37、odel, because the effects of these variables on the rotary deriva,tives have not been investigated extensively to date. The figures which present the results obtained in the present investigation arc listed in table III. Provided by IHSNot for ResaleNo reproduction or networking permitted without li

38、cense from IHS-,-,-A STUDY OF THE USE OF EXPERIMENTAL STABILITY The basic lift and longitudinal-force data of figures 7 and 8 are generally in good agreement with larger scale tests of another model of the same airplane, as given in reference 7. The main effect of the slots is to extend the linear r

39、ange of those stability derivatives which are largely contributed by the wing to higher lift coefficients in a mamler similar to the ,%_ ., effect of slots on the liftcurveof a wing- .(See,figs. .7. to 10 and 12, 13, 15, and 16.) One significant effect of the slots is on the damping in yaw Cnr which

40、 increased as the slot span is increased. When the % $=O”; S/=0”; R=l.OlXlO. The relative constancy of CYp, C$, CnD, CYr, Cl, and Cfi, with angle of yaw as indicated by figures 14 and 17 and the linearity of the curves of C, CZ, and C;, plotted against $ for angles of yaw up to approximately loo (fi

41、g. 11) were factors which indicated that nonlinearities were not of first- order importance for this airplane in the calculation of motions involving reasonably small variations in #. Conse- quently, most of the motion calculations neglect the effect of $J on the stability derivatives. The results o

42、f unpublished tests of swept wings at Reynolds numbers to 8.0X lo6 in the Langley 19-foot pressure tunnel indicate that the linear part of the curve of CliG plotted against C, is increased by an increase in Reynolds number. The curves of CJ+ against CL given herein agree well with those obtained in

43、flight (references 5 and 6) and in test.s of a L-scale model (reference 7) except at lift coefficienk above 4.5 C= 1 or Act=1 at a time T=k,n, and 6,-, is the fraction of the unit disturbance applied by the rudder or aileron at a time T=k(m-n). The rudder and aileron effectiveness were Provided by I

44、HSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-A STUDY OF THE USE OF EXPERIMENTAL STABILITY DERIVATIVES IN LATERAL-MOTION CALCULATIONS 7 obtained from reference 7. In a few cases, unit solutions to the equations of motion This procedure is essentially an approxi

45、mate evaluation of Duhamels integral and was con- were obtained by a Laplaco transform procedure which has siclered sufhciently accurate for these calculations. been adapted for use with automatic digital computers. Refer- ence 8 gives a more exact graphical evaluation of this integral. The yawing m

46、oment caused by aileron deflection and the The results were, of course, identical with those presented rolling moment caused by rudder deflection were not con- sidered of enough significance to warrant their inclusion in these -calculations. In some cases, however, these factors in this report. may

47、be of greater significance. Calculations of the lateral motions for a few cases employ- ing a nonlinear variation of rolling-moment and yawing- The flight records corresponding to the motions calculated moment coefficients with angle of sideslip and a variation of C, with angle of sidoslip were carr

48、ied out by use of tho for this report showed that the motions resulting from right Kutta three-eighths rule for solving the lateral equations of motion. and left control movements were not exactly of opposite (See reference 9.) All lateral-motion calculations were made on an automatic digital comput

49、ing machine. magnitude. ._ This result indicates that there was some asym- CALCULATED LATERAL MOTIONS metry in the characteristics of the airplane, although the GENERAL .008 (b)b 1 1 1 1 1 1 ( I 1 1 1 1 f.2 :2 0 .2 .4 .6 .8 I.0 /.2 Lift coefficient, CL (n) Trim C=0.33; Q=O”. (b) Trim C=0.70; 6f=40. FIGURE %-Variation ollntcral static-stability dcriwtivcs with lift coelfcicnt for three slot configurati