1、IoIfNATIONALADVISORYCOMMITTEEFORAERONAUTICSTECHNICALNOTE2555OFASPECTRATIO2.61JackD. BrewerandLewisR. FisherLangleyAeronauticalIaborat!oryLangleyField,Va.WashingtonNovember1951III- - . . . . _.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH41BRAR
2、yFBsNMlmillmlllllllw00L5Lb7.NATIONALADVISORYCOMMITTEEFORAERONAUTICS!IWHNICALNOTE2555EFFECTOFTAPERRATIOONTHELOW-SPEEDROLLINGSTABILITY133RlXATIVESOFSWEFTANDUNSWEPTWINGSOFASPECTRATIO2.611ByJackD.BrewerandLewisR.FisherAninvestigationhasbeenconductedona seriesoftaperedsweptwingsinthe6-foot-diameterrollhg
3、-flowtestsectionoftheLangleystabilitytunnelunderconditionssimulatin.grollingflight.Theresultsofthetestsshowedthata decreaseintaperratio(ratiooftipchordtorootchord)ofa sweptwingcaweda smalldecreaseindampinginrollatlowandmoderateliftcoefficients;athighliftcoefficients,decreasingthetaperratiocauseda la
4、rgereductioninthedampinginrollandgreatlyreducedtheincreaseobtainedfortheuntaperedwingpriortomaximumlift.Foranunsweptwing,a decreaseintaperratiocauseda smalldecreaseinthedampinginrollthroughoutthelift- coefficientrange.Therateofchangewithliftcoefficientoftheyawingmomentduetorollandofthelateralforcedu
5、etorollwereslightlydecreasedatlowliftcoefficientsbya decreaseintaperratio.Availabletheorygenerallypredictstheeffectofchangeintaperratioontherateofchangeoftheyawingmomentduetorollwithliftcoefficientandonthedampinginrollatzeroliftmoreaccuratelythanitdoestheeffectofsweep.Tip-suctioneffects,notaccounted
6、forbythetheory,maycauselargeerrorsinthetheoreticalvaluesoftheyawingmomentduetorollandthelateralforceduetoroll.Fora sweptwingtheyawingmomsntduetorollcanbeest-ted byapplyinga cor-rectiontotheavailabletheorybyutilizingtheexperimentalvalueofthelateralforceforanunsweptwingofthesameaspectratioandtaperrati
7、o(thetip-suctionforce)andthegeometriccharacteristicsofthewing.INTRODUCTIONAnextensiveinvestigationisbeingcarriedoutattheLangleystabilitytunneltodeterminetheeffectofvariousgeometricvariablesonrotaryandstaticstabilitycharacteristics.ThevaluesofthelSupersedestherecentlydeclassifiedNACARML8H18,“Effectof
8、TaperRatioontheIow-SpeedRollingStabilityIkrivativesofSweptandUnsweptWingsofAspectRatio2.61”byJackD.BrewerandLewisR.Fisher,1948.-. .- - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2stabilityderivativesarerequiredforflightcharacteristicsofanairplan
9、e.arereadilydeterminedbyconventionalNACATN2555thedeterminationofthedynamicThestaticstabilityderivativewind-tunneltests,andtherotarystabilityderivatives,heretoforegenerallyestimatedfromtheory,cannowalsobequicklydeterminedbytheutilizationofthestability-wind-tunnelcurved-androlling-flowtestequipment(re
10、ferences1 and2). thispaperresultsareyresentedoftestsnadeinstraightandrolltigflowtodeterminetheeffectoftqerratioontherollingchamc-teristicsofa 450sweptbackwingandanunsweptwing(bothhavinganaspecttio of2.61). Theeffectsofchangestntiperratioontheyaw-ingcharacteristicsoftheswept- arepresentedinreference3
11、.SYMBOISThedataarepresmted in the formofstandardNACAcoefficientsofforcesandmomentswhicharereferred.inallcases.tothestabilityaxes.withtheoriginatthequarter-chordfiointofthe “ .ofthemodelstested.Thepositiveradiansrollingangularvelocity,radianspersecond. . . .- . .- . Provided by IHSNot for ResaleNo re
12、production or networking permitted without license from IHS-,-,-4 NACATN2555acypCy =Pm acLKPPARATUSANDTESTSThetestsofthepresentinvestigationwere.conductedinthe6-foot-diameterrolling-flowtestsectionoftheLangleystabilitytunnel.Inthistestsection,itispossibletorotatetheairstreamaboutarigidlymountedmodel
13、insuchawayastosimulaterollingflight.(Seereference2.)ThemodelstestedconsistedoffivemahoganywingshavingtheNACA0012contourinsectionsnormaltothequarter-chordline.Theaspectratioofeachnmdelwas2.61. Threewingshavingtaperratiosof1.00,0.50,and0.25weresweptback45atthequarter-chordline;twowingshavingtaperratio
14、sof1.00and0.50hadzerosweepatthequarter-chordline.Planformsofthefivemodel-sareshowninfigure2.Themodelswererigidlymountedatthequarter-chordpointofthemeanaerodynamicchordona six-componentstrain-gage-balancestrut(reference4). Et, longitudinalforce,andpitchingmomentweremeas-uredinstraightflowthroughanang
15、le-of-attackrangefromabout-4toananglebeyondthestall;lateralforce,rollingmoment,andyawingmomentweremeasuredthroughthesameangle-of-attackrangeinrollingflowforwing-tiphelixanglespb/2VoftO.021radianandto.062radian.Allthetestsweremadeata dynamicpressureof39.7poundspersquarefootwhichcorrespondstoaMachnuni
16、berof0.17.ThecorrespondingReynoldsnumber,basedontheman aerodynamicchord,wasl.b x 106for_ - . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN2555 5.theuntaperedwings,1.45X 106forthewingswithtaperratiosof0.50,and1.56 x 106forthewingwithataperra
17、tioof0.25.A photogaphofoneofthemodelsmountedinthetunnelispresentedasfigure3.CORRECTIONSCorrectionsfortheeffectsofjetboundaries,basedonunswept-wingtheory,havebeenapplie,dtotheangleofattack,thelongitudinal-forcecoefficient,andtherolling-montcoefficient.Nocorrectionsfortheeffectsofblocking,turbulence,o
18、rfortheeffectsofstatic-pressuregradientontheboundary-layerflowhavebeenapplied.RXSU13SANDDISCUSSIONThelift,longitudinal-force,and pitching-momentcharacteristicsforthethreesweptwingstestedarepresentedinfigure4 (fora dynamicpressureof39.7lb/sqft).Theseresultsa$yeewellwiththeresultspreviouslyobtainedfor
19、thesamewingsandpresentedinfigure4ofreference3 (foradynamicpressureof24.9lb/sqft). Therearwardmove-mentoftheaerodynamiccenterwithadecreaseintaperratioisapparentfromthepitching-mentresults;theeffectoftaperratioontheliftandlongitudinal-forcecharacteristicsissmallatlowandmoderateliftcoefficients.Athighl
20、iftcoefficients,largerlongitudinal-forcecoefficientswereobtainedwiththenmrehighlytaperedwings.Ataliftcoefficientofabout0.6,anincreaseoccurredinthelift-curveslope;thisincreasebecamesmallerasthetaperratiodecreased.Reducingthetaperratiooftheunsweptwingfrom1.00to0.50(seefig.5)causeda smallincreaseinthel
21、ift-curveslope.Aswastrueinthecaseofthesweptwing,taperratiohadanegligibleeffectonthemaximumvalueofliftcoefficient.Theangleofattackatwhichthemaximumvalueoccurreddecreasedwitha decreaseintaperratio,aresultoppositetothatobtainedforthesweptwings.Thepitching-monentresultsfortheunsweptwingsindicatealmostno
22、shiftoftheaerodynamiccenterwitha changeintaperratio.Changingthetaperratiohadanegligibleeffectonthelongitudinal-forceresultsfortheunsweptwings.Theeffectofsweepontheliftcharacteristicsofataperedwingcanbedeterminedfromthedatapresentedinfigure5. Sweepcausedadecreaseinthelift-curveslope,anincreaseinthema
23、xhmmvalueofliftcoefficient,andanincreaseintheangleofattackatwhichit_ ._ -. -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. .6 NACATN2555occurred.Theshiftrearwardoftheaerodynamiccenterwithsweepisapparentfromthepitching-nmmentresults;thereislittlech
24、angeinthevalueofthelongitudinal-forcecoefficientuptotheliftcoefficientatwhichthewingstalls.Inreferenoe3,itwasshownthat,forthesweptwings,therewasalargechangeh theslopesofthelateti-stability-derivativecurvesandoftheyawing-derivativecurvesata t coefficientofabout0.6,tieCL2liftcoefficientatwhichtheq,umt
25、i - benti increaserapidly. Forthesamewin therollingparametersCzp,Cnp,andcyPplottia atit liftcoefficientinfigure6 ofthepresentpaperdsoshowlargechangestnslopeata liftcoefficientofabout0.6.figure 6 it oanbeseentiata decreasetitaperratiocausedasmalldecreaseindamp3nginroU.atlowand.moderateliftcoefficient
26、s;athighliftcoefficients,decreasingthetaperratiocauseda largereductioninthedampinginrollandatly reducedtheincreaseobtainedfortheuntapered priortomaximumlift.Therateofchangeof CyP .withliftcoefficientwasslightlydecreasedwitha decreaseintaperratioatlowliftcoefficients;athighliftcoefficientstherewasnoc
27、onsistentvariationwithtaperratioforeither% or c%”Fortheunsweptw3ngs(fig.7) a decreaseintaperratiocausedaa decreaseinthedampingtirollthroughoutthelift-coefficient-e” Therateofchangeof C-%p withliftcoefficientwasslightlydecreasedbya decreaseintaperratio.Thevariationwithtaperlift-coefficientrangeandof(
28、CZP)CL=O)arepresentedinratioof C% and Cyp forthelowCL CLdampinginrollatzeroliftcoefficientfigure8. Experimentalvaluesof CZPatzeroliftarecomparedwithvaluesindicatedbythetheoriesofrefer-ences5 and6. Theoreticalvaluesof cnpCLand Cy wereobtainedpCLbythemethodofreference5 whichisbasedonalifting-line-theo
29、ryconceptandwhichdoesnotconsiderthe-effectofunbalancedtipsuctionunderasymmetricconditions.Theexperimentalvaluesof CyP(and CypcL)forthewingswithzerosweepshowthatsuchunbalancedsuctiondoesexist. “Ifthesuctionforcesaremsed tobetidependentof-ep a correction-.Provided by IHSNot for ResaleNo reproduction o
30、r networking permitted without license from IHS-,-,-.MICATN2555 7tothetheoreticalvalueof fora sweptwingcanbeobtained.pCLForexample,whenthevalueof Cy duetotipsuctionfortheunsweptpCLwingwith0.5taperratioforthe45sweptwingofbedetermined.Whenthis(0.28fromfig.8)isassuredtobethesame0.5taperratio,a correcti
31、onto canPmvalueof Cy ismultipliedby-1.01,theCLlongitudinaldistancebetweenthemountingpoint(quarterchordofthemeanaerodynamicchord)andthe50-percentpointofthetipchord(wherethesuctionforceisassumedtoact),andwhentheresultisdividedbythespan3.04,a valueof CL duetotipsuctionisdetermined;inthiscase,theadditio
32、nto is-0.093. ThefinalvalueofCL % CListhenthesumofthetheoreticalvalue(-0.065) andthetip-suctionincrement(-0.093).Thisvalue(-0.158)isincloseagreementwiththeactualexperimentalvalueof-0.160.Theorypredictstheeffectofachangeintaperratioon (%)%=0 d cnpcLnmreaccuratelythanitdoestheeffectofsweep.Theapparent
33、closeagreementbetweenthe theoreticalandexperimentalvaluesof Cy forthesweptwingsispCLactuallyduetotheoverpredictionofthetheorywhichyinthiscase,compensatesfortheunaccounted-fortip-suctioneffect.Astheaspectratioofthewingincreases,thevalueof Cy dueto.thetipsuctionwouldbeexpectedtobecomesmaller.Theerrors
34、associatedwiththeneglectofthetipsuctioninthetheoreticalanalysisshouldthenbequitesmallforwingsofhighaspectratio.Thetheoretic-valuesof Czp atzeroliftasobtainedbythemethodofreference6showthesameeffectofa changeintaperratioreference5.CONCLUSIONSasdidthetheoryofResultsoftestsmadeinthe6-foot-diameterrolli
35、ng-flowtestsectionoftheIngleystabilitytunnelinstraight”androllingflowona seriesoftaperedsweptwingsindicatethefollowingconclusions:1.A decreaseintarratioofa sweptwingcauseda smalldecreaseindampinginroll,atlowandmoderateliftcoefficients;athighliftcoefficients,decreasingthetaperratiocausedalargereducti
36、oninthedampinginrollandgreatlyreducedtheincreaseobtainedfortheuntaperedwingpriortomaximumlift.Foranunsweptwing,a decreaseintaperratio.-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 NACATN2555causeda smalldecreaseinthedampinginrollthroughoutthelif
37、t-coefficientrange.2.AtlowHft coefficients,adecreasefitaperratiocauseda s?nallldecreaseintherateofchengeoftheyawingmomentduetoro andthelateralforceduetorollwithliftcoefficient.3.Availabletheorypredictstheeffectofchangeontherateofchangeofthe_ momentduetorollefficientandonthehnpinginrollatzeroliftmmed
38、oestheeffectofsweep.intaperratiowithft CO-accuratelythanit,4. Tip suctionmaycauselargeerrorsintheavailabletheoreticalvdhzesoftieya*gant duetorollandtielateral.forceduetoroll;theyawingmmmntduetoro ofa sweptwingcanbeestimatedquiteaccuratelyapplginga sle correctiontotheavdlabletheorybyutiHzingtheexpe-n
39、tal valueofthelateralforceforenunsweptwingofthesme aspectratioandtaperratio(thetip-suctionforce)andthegeometriccharacteristicsofthewing.LangleyAeronautic-LaboratoryITationelAdvisoryCttee forAeronauticsLangleyField,Va.,August24,1948 “,.*-. _. - Provided by IHSNot for ResaleNo reproduction or networki
40、ng permitted without license from IHS-,-,-2.NACATN2555 9REFERENCES1.BirdjJohnD.,Jaquet,ByronM.,andCowan,JohnW.: EffectofFuselageandTailSurfacesonLow-speedYawingCharacteristicsofaSwept-WingModelasDeterminedh Curved-FlowTestSectionofLangleyStabilityTunnel.NACATN2h83,1951. (FormerlyNACARML8G13.)2.MacLa
41、chlan,Robert,andLetb,William:CorrelationofTwoE2cperbnentalMethodsofDeterminingtheRolldngcharacteristicsofUusweptWings.NACATN1309,1947.3.Lelilm,William,andCowan,JohnW.: EffectofTaperRatioonIaw-speedStaticandYawingStabilityDeti-vativesof45Swept-backWingsofAspectRatioof2.6.1.NACATN1671,1948.4.Goodman,A
42、lex,sndBrewer,JackD.: IiweatigationatLowSpeedsoftheEffectofAspectRatioandSweeponStaticandYawingStabilityDerivativesofUntaperedWings.NACATN1669,1948.5.Toll.,ThomasA.,andQueio,M.J.: Approte RelatimsandChsrtsforLow-Speed.StabiHtyDerivativesofSweytWings.NACATN1581,1948.6.Weissinger,J.: TheLiftDistributi
43、onofSwept-BackWings.NACA!I!M1120,1947.(, .-. - .-. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10Figure1.-SystemofTzJ2ec7iuoB-B -.axesused.Arrowsindicatepositivedirectionofangles,forces,andmoments. Provided by IHSNot for ResaleNo reproduction or
44、networking permitted without license from IHS-,-,-,1IIiIIII. Mgure 2.- PleafOITtlEof -S tested. NACA A = 2.61.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Iljio, O.Y*Provided by IHSNot for ResaleNo reproduction or networking permitted without lice
45、nse from IHS-,-,-NACATN2555,.22?/?4(9-A?13Figure4.- Effectoftaperontheaerodynamiccharacteristicsofthesweptwings.A = 45;A = 2.61. . .- - .-. . . _.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1428/?420.A = 2.61.u.- . . Provided by IHSNot for Resale
46、No reproduction or networking permitted without license from IHS-,-,-16.4.qoP-.4NACATN2555I Lu+l-LM II 1 1 t ,1 , 1I I I I7 I I I I I I I I ! ! / . I.AI I I I I I I I I I Vlu 3I 1 , ,I 1 I I I I al I I-z O .2 .4 .6 .8 /ff c and (“P)%- it “W ratio” qProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
