NASA NACA-WR-L-444-1942 A flight investigation of short-period longitudinal oscillations of an airplane with free elevator《带有自由升降机的飞机短时纵向振荡飞行研究》.pdf

1、1,IiI.- . .NATIONAL AQWSORY COMMITTEE KM AERONAUTS., ORIGINALLY ISSUEDMay 1942 aEAdvance Restricted ReportA FIZGHT INVESTIGATI OF SHORT-EERIODImGmnmL oscms OF mKmPLAm WrI!HFREE ELEVATORBy William H. PhillipsLangley Memorial AeronauticalLaboratoryLangley Field, VQ.m%REFERENCE( - “-N”A(iiAi-: “-”NACA

2、WARTIME REPORTS arereprintsofpapersoriginallyissuedtoproviderapiddistributionofadvanceresearchresultstoanauthorkedgrouprequiringthemforthewareffort.Theywerepre-viouslyheldunderasecuritystatusbutarenowunclassified.Someofthesereportswerenottech-nicallyedited.AU havebeenreproducedwithoutchangeinorderto

3、expeditegeneraldistribution.L-kkkProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-3 1176013655270NATIONAL ADVISORY COMM$T!J!EE3OR AERONAUTICS. . .: -” ,“. ”.” .ADVANCE RESTRICTED RZPORT “ .-. , .A FLIGHT INVESTIGATION W SHORT-PERIODLONGITUDINAL OSCILL

4、ATIONS OF ANAIRPLANE WITH FREE ELEVATOR .By William . Phillips ,SUXMARY . “ :. .A flight investigation has been made to check theresults of a theoretical analysis of longitudinal stabilityof an airplane with free controls. Tests were made of aFairchild XR2K-Z airplane on which the weight.mornent and

5、the aerodynamic balance of the elevator were varied to bringit into a condition where unstable short-perfo.doscilltiionswere encountered. The amounts of aerodynamic balance andweight moment required for instability were found,to begreater than the amounts predicted by the theory. Timehistories of th

6、e oscillations are included to show thenature of the instability.INTRODUCTION . During tests made to determine .” . . ,. .:.H elevator hinge moment. .“6 elevator defection. . . . .Ch. hin”ge-mornqt coefficiez.it ( -.H : .- (-f.-a :,., . . . .- . .e2. o . Ce,-, .:. . .,-. s . .wing area . . . ,. . .:

7、. . ,.- .c- wing.chord . . .:. . . .“. ,se elevator area ., .:. . . . . -.Ce elevator chord . ., . . .- P,air density . . .:. -q dynamic pressure .- , .- . .:.” . . . .,:. . .,.”. . .,:,. . .,.”e,c)elevator density ratio3mass of elevatornormal acceleration (;J- VOQ)normal component of velocity id%,d

8、tdab6, , etc.=, R, etc.moment of inertiaaChaerodynamic hi”nge-moment parameter()xeCh .=z. -. .- . . . . -= - -.- - -; . - -:- -.-. -., .,. ,. . . . . . . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.-4.D operator indicating differentiation wit

9、h respect “()to distance dzs distance along flight pathA diagram showing the convention of axes used iSgiven in figure 1.THEORETICAL INVESTIGATION. .In the theoretical study of stability (reference 1)$the airplane and control-system characteristics are ex-pressed in terms of nondimensional ratios de

10、fined previouslyin the list of symbols. All distandes are expressed innondimensional form in terms of half-chord lengths of thewing. Quantities are differentiated with resyect to dis-tance rather than time. Stability derivatives dependingon the rate of change of a quantity must therefore beaomputed

11、with the aid of the formula for the differentialoperatorsFor example,chD=g= .da c/2The following parameters are found to be important indetermining the stabiity of the motion*eYe elevator mass-unbalance parameteraPeke elevator moment-of-fnertia parameter fThe solution of the equations of motion show

12、s theexistence of two modes of oscillation. One mode is well-damped and the other, which involves reinforcement of thepitching motion of the airplane by the flapping of theelevator, is likely to”be poorly damped or unstable if theelevator has a large weight unbalance, a high degree ofaerodynamic bal

13、ance, or a large moment of inertia. CurvesProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-5showing the limiting values of these quantities allowablefor stability are given in figure 2, which has been adaptedfrom reference 1. In this figure, any desig

14、n that fallsto the left of the boundary of stability defined by its3particular value of eke2, in the area labeled .Ilstableregionll will theoretically be stable, while a design thatA gives a point to the right of this boundary will experienceunstable oscillations .The llegion of divergencell on thel

15、eft side of figure 2 shows that designs on which tihe ele-vator center of gravity is ahead of the hinge line mayexperience instability in the form of a.rapid “divergence.Because this type of instability was not the subject of thepresent investigation, the reader is referred to reference1 for a more

16、complete explanation.Boundaries for stability were obtained in the investi-gation by assuming typical values of airplane density,moment of inertia, and aerodynamic derivatives. None ofthese characteristics were found to have any large effecton the stability of the oscillation when they were variedwi

17、thin the range customarily used in airplane design. Theonly factor, other than those mentioned, that is likely tohave an appreciable effect on the oscillation is the damp-ing of the elevator motion ch a71 This factor is difficultto evaluate, because it includes friction in the elevatorsystem. Its ef

18、fect will be discussed more fully later.EXPERIMENTAL INVESTIGATIONIn order to check the boundaries of stability computedfrom the theory by actual fllght tests, the elevator systemof the XE2K-1 airplane was linked to a pivoted rod to whichmovable lead weights were attached. This rod was placedwithin

19、reach of the pilot so that the moment of inertiaand the mass unbalance of the elevator system could bevaried during flight.A description of the XR2K-1 airplane is given in theappendix. A photograph of the airplane is shown in figure3. Figure 4 shows the linkage used to attach the leadweights to the

20、elevator-control system.The program offlight tests included measurements ofthe elevator force and position at various airspeeds-andwith three positions of the center of +zravity of the air-plane . From these measurements the elevator restoring-moment coefficient Cha could be computed. The elevatorPr

21、ovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6mass unbalance and the moment of inertia were then varied ;into the range shown by the theory-to ,cause instabilitywith the value of ch6 which was found to exist.When the flight tests were made, however,

22、 it wasfound that.no U.nsta%l e,oscillations were obtained at theboundaries indicated in figure 2. Vibrations in the ele-vator motion introduced by abruptly deflecting the controlstick and releasing it were damped out almost immediately.In an effort to reach an unstable condition, a balance tabwith

23、variable linkage was laced op the elevator. By theuse” of this tab to reduce th elevator restoring-momentcoefficient Chs to a very small “value, unstable o The location of the weights usedto unbalance the elevator near the cockpit instead of onthe elevator itself, “and the existence of a large amoun

24、t. .of friction in the elevator-control system. “. ,Further tsts were. made with the-weighted rod removed.from-the cockpit and with a lead weight attached to the/elevator behind the hinge line. Theoretical considerations .-indicated and the flight teSts verified th -, ;”,”,.-r /Provided by IHSNot fo

25、r ResaleNo reproduction or networking permitted without license from IHS-,-,-11teristics affect the stability of both types of oscillationsimilarly. If a conventional elevator is mass-balanced toprevent the occurrence of flutter, no trouble should beexperienced from control-free oscillations .3A CON

26、CLUSIONS. .1. Violent short-period longitudinal oscillationsmay occur in an airpla”ne- tiitlithe “elevator control re-leased If the elevator has a high degree of aerodynamicbalance and a large mass unbalance.2. The curves representing the boundaries of elevator-$ree stability can be used. to”determi

27、ne the limits beyondwhich the mass unbalance, the aerodynamic balance, and themoment of inertia- of the elevator control may ceuse insta-bility. The values determined from these curves are likelyto be very conservative for small, ow-speed airplanes whosecontrol systems have appreciable friction. The

28、 values willprobably not be .conservative for large or fast airplaneswith control systems having a small amount of friction.!Langley Memorial Aeronautfeal Laboratory,National Advisory Committee for 22ft ., .,Distance from wing aerodynamic center .“to elevator hinge line. . 15ftWihg area . 171 sqft .

29、,.Gross weight ;.a71 fa71 a71 *:.* . 1750 Ill” Wing loading a71 *.0a71 a71 . , lo.2.lb/sq :ft. . .Stabilizer span a71 ?. a71 -a71 .-a71 a71 *a71 9 ft L in;., . .Stabilizer area 22.0 Sq ftElevator area .10.4 Sq.ftThe tail surfaces used in the tests described werenot those originally provided with the

30、 airplane,REFERENCES1. Jones., Robert T., and Cohen, Doris: An Analysis ofthe Stability of an Airplane with Free Controls.Rep. No. 709, NACA, 1941,2. Theodorsen, Theodore: General Theory of AerodynamicInstability and the Mechanism of Flutter.Rep. No. 496, NfiCA, 1935. .Provided by IHSNot for ResaleN

31、o reproduction or networking permitted without license from IHS-,-,-.1I:.4.,1,i,.,“lL-, .i, .:., “!,./,.1,“:/. .:1“:,.,.,$1“j f, ,F/guri k Notazio#for,a71/(7Ag/Yud/hdCON T/-?o.LSTICK(I%24R COCKPIT)cPUSH ROD TO .Jt?LEVA TOR,sfublwq. /0 POUND LEAD WEIGhTS,.Provided by IHSNot for ResaleNo reproduction

32、or networking permitted without license from IHS-,-,-IT W, ; y, 1.79*(Adaptationof fig. 3 ofrefarence l.)n,/.,1 iProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,. .“.1L,., ,., , ,. . . . -“:-”- . ,. . . . ,/Figure 3. Fairohild X.R2K-1 airplane-#-:-2

33、./-”-.:1,. .,- ,4,Pma71CaProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-3.AINACA., .Fig. 5.-. Flw 5.- VulatonOrnm-mhl aao.eleration, olevabr OIWle, elevatm enUwlar .006kA10=v-“r-.- .+!4-120 -tJ-. /“; _ -i3 El/,10 -y- 4 ,1 A* Lh .g Static w3i#st “.,

34、:=. “,0-10 I-.5 0 .5Trl”rrrrrrr- . - .- .-t/ L. 1f - / .-/ +.-kkt-t-I-P-1.0 1.5Timo,ocoudsFiO 6c- Variation of inertia mommt about lovctorbingo caued byin control-freelonitudinal oscillation.Fairchild XR2K-1Ii.2.0 2.5 3.0unbalnce m&Ze (&+26) with tigairplane with weighted elevator, 1.lJ1/,mProvided

35、by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. . .100-lo/0-L. l-5-.Variation of totaloscillation.Totaluith weight.od ,/,/+.- - - . )/1.L_ /I I Ioxtornal1.0 1.5 2.0 2.5 3.0Time, secondsbingo momont on olov:torwith tirno.incontrol-freo longitudinalhinge momo

36、nt,- I(+e) + mo(ti-,e+%) . Fairchild XR2X-1 airplanoProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NM4. l?ig.8A.n_ar velocity, cieg/secFigure 8.- Variation of dampiug of olovatormotion withangular velocity of olwaior during control-froo longitudinal

37、 oscillation.I?airohildXFLZ-3 airplanewit-nweighted elcwator.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.1iI-+- -+_I- +- ._&_p I /t I #o Jl _+_vIIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,:(I.,-“1“i,/,:1(.!II:, ,.,.,+_-+4_J-. -. -.,. .1,-.I I0 -+-A-J5J+-704-lP-+- +u- +J-1 , ,0. +-. Io &J& (1I I0 , I ,0 +-+-.-+-+- -&-L-I+r. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-