1、CODVeNFmElwFbw=2 -wM *5$;:-i- .RESEARCH.- .-MEMORANDEXPERIMENTALmDAMPING PITCHUAArOF 45 TRIANGULAR WINGSMurray Tobak, David E. Reese, h.,and Benjamin H. Beam - -Ames Aeronautical LaboratoryMoffett Field, Calif.C.”IW,;fiO(01chanot0.,G4ELQL NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS -r-a71-,I+WASHINGT
2、ON -,-,.+Decemkr 1, 1950 _- 4+9hH4BEhLTAL./.- ,f,”.- . fd “2- rProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1 . NACA RM A54)J26TECHLIBRARYKAFB,NM+-lllmlfllilllllllllllllllllll: “-. .:”:oL4294i - -NATIONAL ADKLSCRY COMMITTEE F AERONAUTICS.RESEARCH
3、W-EXPERIMENTAL IMMPING IN PITC!HOF 45 TR12UWUURThe resultsdamping in pitchBy Murray Tobak, Wtid E. Reese, Jr.,WINGSemd Ben;.5(equivalentto tri-r wing S,XISat 0.35 F)Range ofwuil-onfrequency(Cps)10-1311-136-1o11-14lriction-Q3 forces, and the third due *O IU9ChSZliCdforces. and aerodynamic restoringPl
4、The total damping Pa ,is written as Pz =whereaerodynamic dampingtare damping due to thethe aercdyaamic dampinginternal friction of the supporting springswhich whsn reduced tomoment is (P,)he wing+cdy ccmbinatim pivotedat 45 percent M.A.C. (fig. 9) at 35 percent M.A.C. (fig. 10) showedthat, as predic
5、tedby the theory, results obbined at 45 percent M.A.C.,gave both higher damping at a given Mach number and a smaller range ofMach nimrs over which negativel.ydemped oscillationswere encountered. .-Wing with cut-off tips at supersonicspeeds.- Theoretical calcula-tions based on the results of referenc
6、e 9 ve indicated that significantimprovement of the dampinin-pitch characteristicsof a triangularwingmay be realized by emplog swepWback trailing edges. Since thisimprovement is accomplishedby reducing the area of the triangularwingaft of the center of gravity, the possibilitywas suggestedtt thedamp
7、ing-in-pitchcharacteristicsof the wings of this report could like-wise be im$movedby removing ths tips of the wings. The results of cal-culations for such plan forms (see section an theory) also tended tosupport this suggestion.nProvided by IHSNot for ResaleNo reproduction or networking permitted wi
8、thout license from IHS-,-,-,NACA RM A50J26 17In order to investigate this possibility, the wings of this report. were modified.as shown in figure 3, removal of the wing tips reducingthe aspect ratio of the wings from 4.o to 2.67. For this investigation,the mcdel was pivoted.at 47.5 percent M.A.C., w
9、hich is the same roo-chord position as that for the trianar ting pivoted at 35 percentM.A.C.Results of the tests made with the mdified wings (shown in fig. 11)can thus be c-red tith those of the triangularwings pivoted at35 percent M.A.C. (shown in fig. 10). This compmison, which is usefulprimarily
10、for the purpose of verifying the theory, shows that, as pre-dicted, a significant reduction of the region of Mach numbers over whichnetively dsmped oscillationswere encounteredwas realized as theresult of removing the wing tips. It is recognized that a more idealcom$!arisonof the damping-in-pitch ck
11、racteristics of the two wingswould be one in which the axes of the wings were located so as to giveequivalent static margins. Structural limitations of the model pre-vented such an experimental comrison from being made; however, a the-oreticalcomparism on this basis indicated that the wing with cut-
12、offtips possesses superior damping-bitch characteristicsfor all values. of static margin, although the improvement is small for static marginsless - 0.03. Triamgular wing at subsonic speeds. W order to obtain a morecomplete picture of the variation of the damping coefficientswith Wchnumber, the roun
13、d leading-edge sectim” (EACA 06-J53) triangular wingwith body attached was investited In the Ames 12-foot pressure windtunnel.In figure U?, the experimental variation of C + C% with stib-%sonic Mach nunibersis presented for a pitching axis located at 37 percent M.A.C., for Reynolds nunibersof 1.25 m
14、illionamd 0.55 million.Examination of fligure12 shows that for both Reynolds ntiers the damp-ing coefficientsbe more negative as the Mach numiberwas increaseduntil a limitingMach number was reached at which they abruptly becamepositive. The sudden appearance of this condition of instability isbeliev
15、ed to be associated with the establishment of local regims ofsupersonic flow over the surface of the airfoil.Also shuwn in figure E are theoretical values of q + C%through the subsonic ch nuniberrange calculatedby two differentmethods. The values calculated using low-aspect-ratiotheory (refer-ence 1
16、1) indicate no change with Mch nmiber and are numerically muchlarger than the experimental values. In reference 11, it is pointedout that assmrptions made in the derivation limit application of the a Mach nuniberof 1.4, where the dynamic pressureand thus any aeroelastic effects are.greatest, shuws g
17、od agreementbetween the results of the two experiments. It was therefore concludedthat, in the present investigation,aeroelastic effects on the staticparameter c% a also the dynamic remeters c% and werenegligible.It is interesting to note that the results of the present investi-gation shown in figur
18、es 13 ana 14 indicate that the triangularwing-body combinationpivoted at 45 percent M.A.C., hid become staticallyunstable at a Mach nmiber of 1.55 for the round leading-edge sectimNACA 00C663 wing and 1.46 for the sharp leading-edge sectioriwing. .Provided by IHSNot for ResaleNo reproduction or netw
19、orking permitted without license from IHS-,-,-NACA RM AXXl!26 .- 19.The fact that this reversal in sign of the pitching+ment coefficientwas not observed in the results of the force tests of the wingody co-binathn may be attributed to the differences in airfoil-+ection thick-ness and baiy shape betwe
20、en the two models. Both of these differenceshave more pronounced effects on the lift and pitching moment as the Machnumber increases.Reynolds Number EffectsIn view of the relatively law Reynolds numbers at which the presenttests were conducted, it was deemed advisable to obtain some measure ofthe ef
21、fect of Reynolds nuuiberon the damphg-fnitch coefficients.Since the maximm Reolds number was limited to that used in the super-sonic investition (1.37million) by strength limitations of the model,the investigationof Reynolds nuribereffect could only be made by tesking at a lower Remolds nuniber.Acco
22、rdingly, subsmic tests of the damping in pitch of the roundleading+dge section NACA O-3 triangularwingmly model were madeat constantReynolds numbers of 1.25 mini cm and 0.55 million. Theresults (fig. 12) show a sigdficant reductfon in the damping coeffi-cients with reduction in Reynolds nuuiber,the
23、damping coefficientsatthe lower Reynolds nuniberbeing about half the values obtained at thehigher Remolds nuuiber. However, the results of a check run made atsupersonlc speeds at a Reynolds nuniberof about 0.8 million, shown bythe flagged sbols in figure 10(h), did not exhibit this reduction inthe m
24、agnitudes ofthe damping coefficients.The reason for there being a large effect of Remolds nuniberon thedamping coefficientsat subsonic speeds and little effect at supersonicspeeds is not yet understock. tither tests are needed at Reynolds num-bers more closely aroximating those of full-scale flight
25、in order toclarify thts point.Applicati(m of the Results to the Prediction of theDynamic Behavior of N14cale AircraftThe previous discussion has shown that for the singltiegreeaf-freedom oscollations studied in the present experiments there exists arange of Mach nunibersover which dynamic instabilit
26、y occurs. Theseresults are summarized in figure 15 for the triangular wing-bcdy combi-nation which was investi.tedat both mibsonic and supersonic speeds.For the NACA 000ti3 wing model pivoted at 35 percent M.A.C., it is seenthat, for Mach numbers n= 0.94 and 1.38, mdamped or netively dampedProvided
27、by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-20 - “ NACARM A50J26-.oscillations occur. Although the evidence is not conclusivedue to liitations of the research equipment, the presmqdz!.onis that negatively *damped oscillationswill occur over the entire ran
28、ge of Mach numbersbetween 0.94and 1.38.These results, however, are not directly applicable to the predic-tion of like phenomena for these wings in flight, since in flight amaircraft is free to respond to the impetus of the oscillatinglift fdrce.The motion of the airfoil in flight, therefore, consist
29、s of a coupledtwo-degref-freedom motion wherein the airfoil experiencesverticaltranslatiau as well as a pitching motion. In the present experiments,since the center of gravity of the model was fixed, only the pitchingmotion was experiencedby the model.Scam calculations (seeappendfx C) have been made
30、 for thecoupledtwo-degree.+f-freedommotion of a tailless aircraft with fixed controlshaving the same leading+dge sweep as the models of this investigationand with representativefull-scale dimensions. Results of these calcu-lations (figs.16 17) indicate that, as expected, the time to dsmpto one-halfa
31、mplitude is decreased and the range of Wch numbers in whichdynamic instability occurs is reduced, though not eliminated,by consid- *eration of the coupled motion. These calctions have also indicatedthat the terms contaimtng the stabilityderivatives c% amd Cm inequation (4) of appendix C are small an
32、d may be discarded. *This slmpli-ficatian permits the results of this investigation,combinedwith theresults of static wind-tunnel measurements of the lift-curve slope c the mgnitude of the reduction of the region of instabilityisdependent primarily cm the inertiss ratio of the aircraft and thelift+m
33、rve slope c%While discussing the range of Mch numbers in which unstable oscil-lations maybe expected, it should.alsobe pointed out that the theoryof reference 1 fndfcates that aspect ratio lays a significem.troll indetermining the dampl-in-pitch characteristicsof triangularwings atsupersonic speeds.
34、 According to the theory, the regton of supersmicMach numbers in which negatf.velydaqped oscilhiticmsrmybe expected dis-appears entirely for all center-ofatity positicms when the asct ratiois reduced to about 2.5 or less, even for the singleegree+f-freedomcase. This, incidentally,may account for the
35、 fact that no dyoamicpitching instabilitywas experiencedwith the tailless free-flighttissile employing a triangularwing swept back 600, reported in reference 13.4Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACARM A50J26 21CONCLUSIONS.Results of a
36、n experimental investigation of the single degree+f-freedom damping in yitch of two triangularwings hating leading edgesswept back h”,with and withoti a Ixxly,made at subsmic seeds in theAmes 12-foot pressure wind tunnel and at supersonic speeds in the Ames6- by 6-foot supersonicwind tunnel lead to
37、the fol.lowlngconclusicmsz1. Theoretical and experimental values of theparameter c% +C. were in qualitative aeementsupersmic speeds, except for subsonic Mach numbersdynamic instability,which was observedat mibsonic0.94, was not predicted by the subscmic theory.2. The prediction by the supersonic tha
38、xcy ofdcunping-in-pitchat tithsubsonic amda%ove 0.94. TheMach nunhers abovethe existence ofregions of Mach number sad center+f-gravity positiaas in which nega-tively dampd oscillations my be cted was confirmed by the resultsof eeriments for two axis-of-rotatian positions located at 35 percentand 45
39、percent of the wing m= aeralynemd.cchord. .3. Considerable improvement in the damping-in-itch characteristics. of a triangularwing can be realized by reducing the s- of the wing.Removal of the tips of the wings, which reduced the aspect ratio from4.0 to 2.67, resulted in a significant reduction in t
40、he r-e of Machnumbers over which negatively damped oscollationswere encountered4. Calculatims made for the twMegree+f-freedom motion whichccmibinesthe pitching motion stbiiiedin the present investigationwitha vertical tramslatory motion shows that, while the additiol dampingof the oscillation result
41、ing frcm the translatcry notion reduced therange of kch nuuibersover which dynand.cinstability is experienced, theunstable range was not eMminated.Ames Aeronautical Iabozator,National Advisory CA%ee for Aeronautics,Moffett IMeld.,Calif.Provided by IHSNot for ResaleNo reproduction or networking permi
42、tted without license from IHS-,-,-22EVAZUATION OFAPPENDIX ATHE STABILITYDERIVATIVESNACA RM A50J26c%Am-c FCREVALUATIONIn the followingderivation forSumsomc SmImOF C%the parametir Cm, the momentsabout the pitching axis of a thin flat wing in steady itching flightare assumed to be the same as the momen
43、ts about an equivalent thin wingin straight flight which has been camberedand twisted.to the curvatureof the pitching path. The charts and _bles in references 6 and 7 canthen be used to determine all the necessary characteristicsof such awing except the pitching moment at zero lift due to pitching c
44、aused bythe effective camber of the wing. lhislast moment cambe approximatelyevaluatedby twmensi.aal theory.The stability derivative C% for a pitching axis at a distanceAxcg. ahead of the aerodynamic center is (reference14).(Al)where M* is t tcMng+om,nt oefficlentdue to “pitchingwhen thelift due t:
45、pitching is zero, and c%a.c._ is the rate of change of liftcoefficientwith the pitching paramster gc/2V for pitching about theaeraiynamic center.Yor a wing in pitching flight, the th of the wing has a radius of .curvature of T/q. The curved flight introducesanangle-of-attack vari-atfon along the cho
46、rd. The resulting moments have been approximatelyevaluated by assuming a wing in straight flight with a csmiberand twistsuch that the angle-of-attackdistributionalong the chord is the same asthat existing on the fist wing in curved flight.Consider first the pitching moment due to the equivalent camb
47、er ofthe wing when the lift due to pitching is zero. Ths pitching+mment coef-fioient at zero lift for a two-dimensionalwing section is (reference15) . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACARMA50J26 23where is defined.geometricallyalso
48、 in reference 15. In terms of the. triangular wing under considerationP = 1 qcz2 2V (JL3)where cl is the localcember at zero lift forintegrating the sectionchord. The pitchingaoment coefficientdue tothe entire wing canbe approximately-obtainedbypitching+oment coefficient. methe.(A4)(A5)contrilnrtionto caused by the effective caer becomes, fortriangular wing, =(%lJcThis result should indicatethan actually exist becauseac% = a(2V) = 32 (A6)slightly more negjativevalues of ()end effects have not been considered,btthere should be considerably less error in (C%)c t
