NASA NACA-TN-4390-1958 Effects of frequency and amplitude on the yawing derivatives of triangular swept and unswept wings and of a triangular-wing-fuselage combination with and wityawi.pdf

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1、t,generally,atthehighanglesofattacktheoscillatoryvalueswerecon-siderablylargerthanthesteady-statevalues,especiallyforlowampli-tudesandlowfrequenciesofoscillation.Fortheunsweptwingtherewasgenerallylittledifferencebetweenthesteady-statevaluesandtheoscillatoryvaluesofthedamping-in-yawderivativeandthede

2、rivativeofrollingmomentduetoyam inthelowangle-of-attackrange;athigheranglesofattack,thesteady-statevaluesusuallyweregreaterthantheoscillatoryvalues.Althoughforthecompletewing-fuselage-tailmodelthevsriationoftheoscillatorydamping-in-yawderivativeswithangleofattackwassimilargenerallytothesteady-statev

3、ariation,someoscillatoryvalueswereobtainedwhichwerefourtofivetimesgreaterthanthesteady-statevaluesthroughouttheangle-of-attackrange.Theeffectsofamplitudeontheyawingderivatives:,althoughsmellatlowanglesofattack,becamegreateratthehighersinglesofattack;andthegreatesteffectsoccurredatlowvaluesofamplitud

4、eandfrequency.Thealgebraicsummationofthecomponentderivativesgaveresultswhichwere,ingeneral,infairagreementwiththederivativesobtainedinthecom-binedform.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACATN4390INTRODUCTIONCurrentairplanesofrelativel

5、yhighdensityhavebroughtintoconsiderationtheimportanceofsomefactorsassociatedwiththedynmnicstabilityofaircraftwhichheretoforewereconsiderednegligible.Amongthe,factorssretheeffectsoffrequencyandsmplitudeonstabilityderivativesandthepossibilitythataccelerationderivativesmaybeofsuchmagnitudeastobeimporta

6、ntforcertainairplaneconfigurations.Somedatatohelpassesstheimportanceofthesefactorshavealreadybeenobtainedexperimentallybyuseofoscillationtechniquesfromwhichcm.ibinationderivativeswereobtainedandarepresented,forexsmple,inreferences1to3. Someinvestigationsusinga somewhatmorecomplicatedtechniquehaveres

7、ultedindirectmeasurementofthesideslip-accelerationderivatives(ref.4)andhavealsoresultedintheevaluationofthederiv-ativesassociatedwithsideslipvelocityduringa sinusoidalsidesl.iposcillation. Theinvestigationyresentedinreference5wasmaiietodeterminethestabilityderivativesassociatedwithyawingvelocityanda

8、ccelera-tionforonefrequencyandamplitudeofoscillation.Thepresentinves-tigationwasundertakentoextendtheresultsofreference5tootherfrequenciesandamplitudesofoscillation.Oscillatoryderivativeswereobtainedinthepresentinvestigationfortriangular,swept,andunsweptwings.Inaddition,somedatawereobtainedfora tria

9、ngular-wing-fuselageconibinationwithandwithoutatriangulartail.Theoscillationdataarecomparedwithdataobtainedfromsteady-stateyawingtestsmadeinthe6-by6-footcurved-flowtestsectionoftheLangleystabilitytunnel.Inaddition,theresultsofthepresentinvestigationandofadditionaltestssimilartothosepresentedinrefere

10、nce4 srecomparedbothindividuallyandasanalgebraicsumwiththecombinationderivativesdeterminedinreference6.SYMBOLSThedatapresentedarereferredtothestabilitysystemofaxeswiththeoriginlocatedatthequarter-chordofthewingmeanaerody-namicchord.Thepositivedirectionsofforces,moments,andangulardisplacementsareshow

11、ninfigure1. Thecoefficientsandsymbolssredefinedasfollows:Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN4390 3JiLftliftcoefficient,Icos$+Rcos27cft. ForsmalJangulardisplacementsofthemodel,y= + R cos2xft;hence,thevelocityofthemodeltowardthedrive

12、flywheelis = +M?R sti% hence,theaerodynamicmomentsB, C, D,and Ecouldbeobtainedreadilyandthederivativescouldbedeterminedbyuseoftheequationspreviouslypresented._RESULTSANDDISCUSSIONInfigures6 and7 areshowntheliftdata.plottedagainstandeofattackforthethreewingssndwing-fuselage-tailco.uibination,respec-t

13、ively.Thesedatahavebeenpresentedanddiscussedinreferences4and7,respectively,andarenotdiscussedhereinbutareincludedyrimarilytorelatethelifttoangleofattack.Thedatameasuredduringoscillationtestsarepresentedinfig-ures8 to17. Infigures18to21thewing-aloneresultsofthepresentinvestigationarecomparedwithdatao

14、btainedfromsidesl-ippingtestssimilsxtothosepresentedinreference4.Inaddition,thederivatives Marecomps.redasanalgebraicsumwiththecombinationderivativesdeter-minedinreference6. wProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN4390 u.Dmng inYaw C?r

15、,awing s alone.-Thevariationofthedsxping-in-yawcharacteristicswithangleofattackforthewingsaloneisgiveninfigures8,9,and10fordifferentamplitudesanddifferentvaluesofreduced-frequencyparam-eter. Forthe60triangularwing(fig.8)andforthe45sweptwing(fig.9),thevaluesof C4,LD generallyaresmallinthelowangle-of-

16、attackrangebutincreaseastheangleofattackisincreased.T!hisisespeciallytrueforthedataobtainedat # =0.04.Atthelargeanglesofattacktheoscillatoryvaluesof C% alsoareconsider-ablylargerthanthesteady-statevaluesof C%? whichshowamuchsmallervariationwithsingleofattack.Thesteady-statevaluesofc% obtainedfromref

17、erence7 areshownbythedashed-linecurveineachfigure.Fortheunsweptwingatthelowvaluesofsmplitudeandreduced-frequencyparsmeter,thevsriationof C4,U withangleofb attackisgenerallyratherirregular(fig.10);whereasforthelsrgevaluesofamplitudeandreduced-frequencyparsmeterthevariationofC%,m withangleofattackissm

18、all. fact,thevariationof C. 4,Uw withangleofattackissmallerthanthevsriationofthesteady-statevalues,andatthehighanglesofattacktheoscillatoryvaluesarepositiveorlessnegativethanthesteady-statevalues.Figures11,12,and13arepresentedinordertoshowmoreclesrl.ythevariationwithamplitudeofthevaluesof C%,0 forth

19、ethreewings. Forallthreewingsthesefiguresshowthatatlowanglesofattackthereisonlya smalleffectofamplitudeon C%,0 forallvaluesofthereduced-frequencyparsmetershown.Atthe-higheranglesofattacktheeffectofamplitudeonthevaluesof C4,U islarger,thelargestchangesoccurringinthelow-fiplituderangeandatthelowvalues

20、ofthereduced-frequencyparsmeter.wing -fuselage confipTuL-ation.-ThevariationofthedsmpinginyawC%r,uwithsingleofattackforthetriangular-wing-fuselageconfigura-tionisshowninfigure14fordifferentamplitudesanddifferentvaluesofthereduced-frequencypsrameter.Ingeneral,thevaluesof C%,lm.becomemorenegative(incr

21、easeddamping)withincreaseofangleofattackProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 NACAm 4390forall testvaluesof ;however,theincreasewithangleofattack2Vismuchlessforthelargervaluesof . Thesteady-statevaluesofc+ donotvaryappreciablywithangleof

22、attackandsremuchlessnegatiVeatthehighanglesofattackthantheoscillatoryvaluestheclosestagreementoccurringatthehighervaluesof .Thevariationsofthe C4,U datawithamplitudeforthewing-fuselageconfigurationaresh infigure1.5fordifferentvaluesofmb. Becauseoflackofsufficientdata,thecurvesarefairedonlymthroughth

23、etestpointsfor =0.08.Theeffectofsmplitudeisgenerallysmallinthelowangle-of-attackrangebutismuchgreateratthehighanglesofattackwherethedampingincreaseswithamplitude.Itshouldbepointedout,however,thattheeffectsofamplitudeonCnr,umaybedifferentforotherfrequenciesofoscillation.wing-fuselage-tailcotiiguratio

24、n.-Forthecompletewing-fuselage-tailconfiguration,thevariationofc%,0 withangleofattackis.showninfigure16fordifferentfrequenciesandamplitudesofoscilla-tion.Alsoincludedinthisfigureisthevariationwithangleofattackofthesteady-statevaluesof wc%?“ Ingeneral,theoscillatoryvaluesf cnr,areconsiderablymorenega

25、tivethanthesteady-statevalues.Withfewexceptionsthevaluesoftheoscillatoryderivativesareatleasttwicethesteady-statevaluesand,insomecases,theoscillatoryvaluessreasmuchasfourandfivetimesaslargeasthesteady-statevalues.Thelargestdifferencesoccurusuallyforlowvaluesofsmi-tudeandfrequency.Aswasthecaseforthew

26、ing-fuselageconfiguration,insufficientdatawereobtainedtoshowthevariationof C% withaaitudeforYtherangeoffrequenciesintheinvestigation.erefore,infigure17a curvewasfairedonlythroughthedataobtainedat =0.08.Thefaireddatagenerallyshowedthat C% becomeslessnegative(reduced.dsmping)withanincreaseinsmplituhow

27、ever,thedifferencebetweenthesteady-statevaluesandtheoscillatoryvaluesof CZr ismuchlessatthehighervaluesofamplitudeandfrequency.Fortheunsweptwingatthehigheranglesofattack,hbwever,thesteady-statevaluesaregreaterthantheoscillatoryvaluesof %r forthehighervaluesofamplitudeand .mbor10wtiesf m athighangles

28、ofattack,valuesof Cz aref)ulobtainedwhich,dependingontheamplitudeofoscillation,aresomettiesa71 greaterandsometimeslessthanthesteady-statevalues.Thevariationwithamplitudeoftherollingmomentduetoyawingofthethreewingsisshowninfies 11,12,and13. Generally,thereisonlya comparativelysmalleffectofsmplitudeon

29、 cl atlowrjaaaglesofattack.Theeffectsofsmplitudesregreateratthehigheranglesofattack,andgenerallygreaterchangesin cr,u takeplacein thelowerrangeofamplitudes.wing-fuselageandwing-fuselage-tailconfigurations.-ThevariationofthederivativeCZ withangleofattackforthetriangularwimgr,ufuselageconfiguration-wi

30、thandwithouta tail(figs.14and16,respec-tively)isverysimilartothatobtainedwiththetriangularwingalone(fig.8)sinceCZ ismainlyduetothewing.Therelationbetweenr,uthesteady-statevaluesandtheoscillatoryvaluesforthecompletewing-fuselage-tailconfigurationandthewing-fuselageconfigurationisalsosimilartothatobta

31、inedforthewingalone. Forboththewing-fuselageandwing-fuselage-tailconfigurationsthereappearstobea decreasein c% withanincreaseinamplitude* ra)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 NACATN4390 v(figs.15and17),andthegreatestchangesappesmtota

32、keplaceatthelowervaluesofamplitude;asbeforeitshouldbepointedoutthatinsuf- -ficientdatahavebeenobtainedtomakea generalstatementforallvaluesoffrequency.AccelerationDerivativesC%,U and Cz.rju.)Wingsalone.-TheaccelerationderivativesC%,U and cl.rjmplottedagainstsugleofattackforthethreewingstestedareprese

33、ntedinfigures8,9,and10fordifferentfrequenciesandamplitudesofoscillation.Ingeneral,thederivatives=e significantonlyatthelowerfrequenciesandamplitudesofoscillqion.wing-fuselageandwirig-fuselage-tailconfigyrations.-Thevariationwithangleofattackoftheaccelerationderivativesforthewing-fuselageandwing-fuse

34、lage-tailconfigurationsareshowninfQures14and16respectively.Ingeneral,thepositiveorlessnegative,andpositiveormorenegativewithangleofattackofabout16.appearstodependonsmplitude-uesf C%,(Dtendtobecomemorethevaluesof Cl. tendtobecomelessr)uanincreaseinangleofattackuptoanAthigheranesofattackthevariation a

35、ndisratherirregular.Atlowangles wofattackandlowvaluesof theeffectofamplitudeon C2V %,0 smuchgreaterforthecompleteconfigurationthanitisforthewing-fuselageconfiguration. .Inordertoillustratethevariationoftheaccelerationderivativeswithamplitudeatseveralanglesofattack,figures15and17werepre-paredwhichsho

36、wmoreclesr?l.ytheeffectoflitude ntionedThereissomescatterofthedatapointsfortheVariOUSfrequenciesfromthe _ ._curvefairedfor mb_0.08;however,therewerenotenoughdatapointsm toestablishobtainedatothervaluesof 2Vattheatherfrequencies.ComparisonofYawingandAccelerationdefiniteamplitudeeffectsDerivativesWith

37、CombinedDerivativesforWingsAloneForpurposesofCOmPWiSwiththemeasedc*tion derivat.,a)theaccelerationtermscontributeasmuchormoretother,umeasuredcotiinationderivativesasthe C% and Clr,uportionsforallthreewingsthroughouttheaugle-of-a.ttabrange.BecauseofthefactthattheaccelerationtermsC!n+,U d %,0 aremulti

38、pliedbygenerally,atthehighanglesofatacktheoscillatoryvalueswereconsiderablyl=gerthanthesteady-statevalues.Fortheunswept.wingtherewasgenerallylittledifferencebetweenthesteady-statevaluesandtheoscillatoryvaluesofthedsmping-in-yawderivativeand%Provided by IHSNot for ResaleNo reproduction or networking

39、permitted without license from IHS-,-,-16 NACATN4390.thederivativeofrollingmomentduetoyawinginthelowangle-of-attackrange;athigheranglesofattack,thesteady-statevaluesusua14were .-greaterthantheoscillatoryvalues.2. Althoughthevariationofthedsmping-in-yawderivativewithangleofattackwassimilsrgenerallyto

40、thesteady-statevariation,forthetriangulw-whg-fuselagecombination-withverticaltail,someoscil-latoryvalueswereobtainedwhichwerefourtofivetimesgreatertthesteady-statevaluesthroughouttheangle-of-attackrange. 3.Theeffectsofs.mplitudeontheyawingderivativesweresmallatlowanglesofattackforthewingsalone.Theef

41、fectsofsmplitudeandfrequencyweregreateratthehigheranglesofattack,andthel2.316002.1842.5652 ( , 4Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.I t(b) Drive flywlmeland lirisageB.Figure 3.- Concluded.L-94582.1Provided by IHSNot for ResaleNo reproduc

42、tion or networking permitted without license from IHS-,-,-24 NACATN4390+.TL$60/5.59 Affowttng pointCvcubr km! edge3L/8 A1; ,= Yfivekdporiron;1 4.28L ,LA /8+-f36TriangularwingAS?Ctmt10. . . . . . . . . . . . . . . 2.3fLeiwkqedgesweepongId-. . . . . . . WDfW%fongie,c 6076 07640481P 16202426.&# Oftimdq

43、(a) =o.04.16 O.?.ao+6K.?24/sEJ o*./6-4048” i?162Z -24A#c/mak,c”(b) = 0.08.Figure8.- Stability derivativesfor the 60 triangularting meaauredmduring oscillation.n)mProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-, r16 16-/6 -16/6 16J-O $ 0-16 -16(c) *. O.12. (d) =o.16.igure 8.- conthmed.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-