NASA NACA-TN-2146-1950 On the effect of subsonic trailing edges on damping in roll and pitch of thin sweptback wings in a supersonic stream《关于亚音速机翼后缘对在超音速流下薄后掠翼滚动和倾斜阻尼的影响》.pdf

1、NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSTECHNICAL NOTE 2146ON THE EFFECT OF SUBSONICROLL AND PITCH OFTRAILING EDGES ON DAMPINGTHIN SWEPTBACK WINGSINA SUPERSONIC STREAMBy HerbertS.RibnerLewis FlightPropulsionLaboratoryCleveland,Ohio. ,WashingtonIN.-,1$-3-JProvided by IHSNot for ResaleNo reproducti

2、on or networking permitted without license from IHS-,-,-1,I1.,.)*_. - _. - _-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECHLIBRARYKAFP,NMHATIONALAmIsoRY COMMITTEETECHNICALI?OrEIlll!llnllulllllll!lllullOClbSi174FORAERONAUTICS2146ON TEEEFI!ZCTOF

3、SCBSO191CTMIIJXG MX2ES019DAMPINGIN. ROLLAND PITCHOF TEIXSW3PJ!MCKWINGSR?ASUPKRSONIC4By HerbertS.RlbnerSUMMARYTheprincipaleffectof subsonictmaildngedgeson thedampinginrollandpitchof thinsweptbackwingsina supersonicstreamisevaluatedwititheaid of someconicalandquasi-conicalflowspre-viouslyderived.Thise

4、ffectis expressedin theformofapproximatecorrecticmtermstobe addedto thecorrespondingexpressionsthatareobtainedwhenthetrailing-edgedisturbanceis ignored.Theresultsarelimitedto thoseplanformsandMachmmibersforwhichthe_itsgnitude is chosento equalthevalueof thebasicdelta- owingflowat themldepan. The out

5、erportion8constitutethe sought-foressure disturbanceon thewingin thetrailing-edgeregion.SixWar conceptscanbe employed”to evaluatein simplefashiontheprincipalportionof thesubsonic-trolling-edgepressuredis-turbancein thecaseofrollhg orpitching.ForrollingmotionthekaslcMft tobe canceledisantisymmetiic.T

6、he appropriatepartialcancellationisforded by a certainflowlXIin themnner showninfigure2(b). Forpitchbg motionthebasicliftto be canoelediI1.0?3S?S- downstream.Theappropriatepartialcancellationis affordedby superpositionofa cone-t negativeJdft (flbwI)andanotherlift (flowIV)thatincreasesin oportlon to

7、thedis-tancedownstreamof theapexof theil.ing edge(fig.2(c).Thedeiailedderivationof theseseveralcancellationflowsor“wakecorrections”and othersis carriedthroughinreference4. Thepresentreportis cca withtheapplicationof someof theseresultsto thedeterminationof dampinginrollandpitchforthine“. - -. . - .-

8、 -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I!?ACATN 2146 3sweptwingswithsubsonicianai13ngedges. !5eseapplicationstaketheformof correctiontermsto be addedto thecorrespondingees-sionsthatare obkined whentheirailing-edgedisturbanceis ignored.l!he

9、effectof subsonictrailingedgeson thedampinginrollofsweptbackwings,whichispartof thepesent subJect,hasalsobeentreatedrecentlyinreference2. The treatmentthereinachievesnearlyexactcancellationof theliftbehtndthetraildngedgeby thesuperpositionof infinitelymanyinfhitesiml flows. Theprocedureisa developme

10、ntof theapproachusedinreference1. Thepresenttieat cliffersin employingapprote cancellaticmby super-positionofa singleflow. Thissimpldficatimpermitsgivingtheova -aJ1resultcompactlyin closedform.The resultspresentedhereinareapplicableforthosesuper-sonicspeedsforwhichthetrailJng-edgedistmbancedoesnot e

11、xtendbeyondtheleadingedge. At thelowerMwh numbersfa whichtheleadingedgeis envelopedfurthercorrectionisrequired.ThislowMachnumberproblemis studiedfor thecaseofangleofattickinreference5. .ccmEcTIoxvFORRAMPINGm ROLLFora sweptbackwingwithsubsonicleadingedgesrollingwithangdar velocity 3, thebasicdelta-wi

12、ngliftdistributiontobe amceled behindtietz%ilingedgeis (2)themutualinteractionbetweenthetipsandtheimiling edge(blaokregionsof fig.1) isneglected.h moreebborate treatments(referenoe1 fa angleofattack,reference2 forrollingmotion)thellftin thewakeis canceledahmst completely,andthemutualintemction-betwe

13、enthetipand the * isalsotakenintoacoount. lh reference1 twoexamplessrepresentedfromwhichthe seperatecontributionsd the severaldegreesofapproxlm%tionmaybe assessed. (Similar examples In refer-ence2 arenot sowellsuitedto suohan assessment,becataseofanrfect oorrespondmoe.Oneof theseexamplesis,however,h

14、ere-inafterconsidered.) The examplesreferto an untap=edwingof . _. -. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.,NACATN 2146aspectratio1.72ratio0.179,bothchanda taperedwingofwith63leadQg-edge13aspectratio3985and tapersweephck. TheMachnumberis

15、 1.5. Thebrealniownforliftii asfollows:source ofIift Un*pered(percent)(1)(2)(3)(4)(5)in thetipered-uingexample,T = 0.926.Now considervsxiationsofwing sweep,tayer,andMachnudmrthatleave T constxmt.It is expectedthatitem(4)willchangeapproximatelyin proportionto item(3)(exactly,if thetrail.ing-edge-swee

16、p-Machnumberparameter n is unchanged).On thisbasisitem (4)in theeles maybe adjustedto equal1 percentanditem(3)scaledupaccordingly.TheresultsareI Item 3)in1-+bk2r0.629 -14.7 -12.9.926 -4.6 -4.2Thesefourpointsare plottedin figure4. A stiaight-linevariationof T againstitem (3)isnot inconsistentwiththep

17、oints. Thelinedrawnin is consideredto representapproximatelytheconditionthatitem(4)equals1 percent. Accordingly,forvaluesof T belowthellnetheneglectof item(4)willeld an errorof lessthan1 per-cent(basedonbasicdelta-tig lcding = 100percent). Theper-ameter T maybe calculatedfromtheformula1J.f. m1-+ 4A

18、(26)m “AB(l+A).Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6NACATN 2146A correspondinginterferencebetween35criterionfortheneglectof item(5),themutualtipsand trailingedge,cannotbe formulatedwithmuchconfidence.Thentio of thearboththisand thearea-mo

19、mentlimitatiaact in thesamedirection.Of thetwo,thatonegovernsthatresultsin the smallerSxea-momentratio.Theseseveralcriterionsfor thesuitabilityof theapprotionsof thisreportwereinferredfromeqles workedoutfora wingat anangleofattack. The similarityof thefeaturesof theloadcancel-lk .E (n l-m2E ()l-n2in

20、completeellipticintegral.of firstkindtithamptude # andmodulus kfunctionof 0 definedin textl-m2(1-13n2)E1(m)+m2K(m)distanceof centerof gravitydownstreamofwingapexa71.I- _ . . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 2146 19I(m)K(k)K(m

21、)K(n)kLLIMmnPrBU,v,wvx)y,z2(1-m2)(2-m2)131(m)-m% (m)compleh ellipticintegraloffirstkindwith1.modulus k = F ,kK (j 2liftrolling moment (positivein senseofright-lymdscrewproceedingupstream)pitchingt (yositive in senseproceeding spahwise to right)B tfihly-axishorizontalandtowardtheright,lookingupstream

22、;z-axisverticallyupward,.,. . -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.20 NA!2ATN 2146 .a angleofattackA tayerratio(tipohd/rootchord)P deneityofairT= ()9E =b (Seefig.2 anddiscussionin text) amplitudeof eld.ipticintegral(”-G).Subscripts: -A b

23、aaicdelta-wingflowI flowIIv flm IV_.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 2146PoAPPENDIX B23.AIDSTO ImTlmRATIoNThe integrationsin this“paperthatinvolveellipticintegralsaremosteasilyevaluatedwiththeaid of thefollowtngelJ$pticfunotiaus

24、ubstitutions,togetherwiththetablesof integralsinreferences7 and 8J and integrationby parts:whereF(,k)= UJuE(,k)= d112U duor 1.2.ku(Y=p. 18. .Jahnke,Eugene,andlhmie,and Curves. Reprintofpp. 96-97.&Pitch and RollRep. 892,1948.andCo.,3d cd.,Fritz: TablesofFunctionswithFormulas1943Edition,DoverPub. (New

25、York),-.- .-.- .-. . . - _ . . . . . _ _ _ _ _Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1III ,1 /(a) Delta wing.Figure 1. - Related wings(b) Sweptback wing formedfrom delta wing./“ ein supersonicflow. Hatched(c) Sweptback wing formedfrom delta

26、wing at lowersupersonicMach number.,-gregions explained in text. 9INc00!2-CProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 2146 */ o 25i!1.0,-,k.T“D.I :“ AII CP1Basic delta-wing liftCancellationflow(1)Basic delta- “wing liftCancellationflOw (I

27、II)./ (b)Rolling motion.asic delta-wingllftancellationflows(c) Pitchingmotion vFigure 2. - Sweptbackwing showi basio delta-wingloaddistributionalong section A-A and approximatecancellationof this load behind wing by superpositionof special flows.Special flows are plotted with reversed sign. Cross-ha

28、tohed areas representinduced changes in loading aheadof trailingedge.- . . _ - .-. . .-. - -. . .- - -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-26 NACATN 2146 .u.FigureApex of trailing edge730-Mach lineTrailingedge1x- DisturbedrightC3=nportion

29、of trailing edgewing panels(,t)edgeofI!, Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NAcAm 2146 271.0.40 cmA CL Curvefor item-0 10 20Trailing-edgecorrection,item3, percentFigure4. - Esttited variationof % withtrailing-edgecorrectioncomputedby pre

30、sentmethodunderconditionthaterrorin correc-tion,exclusiveof tip interaction,equals1 percentof contribu-tionof basicdelta+tng loading.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- . - -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-