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-,-,-
