1、I.1MAR19489NATIONALADVISORYCOMMITTEE FORAERONAUTICSTECHNICALNOTENo. 1506AN APPLICATIONOF FALKNERSSURFACE-LOADINGMETHODTO _PREDICTIONSOF HINGE-MOMENTPARAMETERSFORSWEPT-RACKWINGSByArthurL. JonesandLomaSluderAmes AeronauticalLaboratoryMoffettField, Calif.glWashingtonFebruary1048FORRE!TRIWgE - _$% N(3TT
2、O BE TAKENI%3M THIS ROOM *N A CA-LIBRARYthe ocmpdnent3sappliedasapercentageoorrectlmntothesectiondataandthesta?esmltnecurvaturecomponentisappliedasanadditivecorrection.Inviewofthisanalysis and Chb canbewritten(neglectingthespaxmrisevariations),(chJL*a=Ckt.* Chencethepredictionof C9 directlybytheuseo
3、ftheFalknermethodappearstobeimpraotcal.Asimplifng assumptionconcerningthemmponentsofthecontrol-defleotedl=ding,however,providedtheapprote predictionfor presentedinthediscussionoftheresults.Forthepredictionsoftheangl=f-attackparamtersthedesireddifferenoebetweenthestiip-theayloadingandtheFaber liftlng
4、tiaceloadingfora givenangleofattackisfounddirectlybysubtraction.Consequentlythedifferenceinloadlngdoesnotappearintheconvenienttwo-caponentfOr& Thephysicalinterpretationassociatedwiththetwocomponentsoftheinducedleadan&theequationeressingthefinites- metersasfunctionsofthesecomponentsarewellestablishe
5、d.Itisdesirable,therefore,toresolmtheZnducedloadbasedcmtheFalknermethodcalculationsintothetwocomponentstherthantoattemptanana4eisusingthetotalinducedleadasoneunit.ToseparatetheInduoedangle-ofdttackeffectcontainedintiesecondterrorofequation(1)fromthestreamlinecurvatureo-ponentformingthethirdtermofequ
6、ation(1)thefactoraj/umustbedeterminedsomewhatarbitrarily.Itwasfoundthatthemostsulblearrangezmmtwastoderbermlneafactoraj/CLbasedontieFalknerpredictedvaluefor C% whichsubsequentlycouldbetransfommdto /a. Sincethelif-urveslopecm beeqressedintermof and ()Scc. inthefollowingmnner(neglectingthespanwiseinte
7、gmtione)(3)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.-8 “” I?AC.ATNNo. 1506(Lw) .where sa71 IScomposedof all the elemntalleadsofthechordwiseleaddistributionexcepttheadditionalt loadingelentrepresentedbythe cotf3/2terminFalhertsseriethenwherez
8、istheFaUsnerresultand Cza=%.Thedesiredformfor isfinallyobtainedfromwherethe Ch tobeusedhasbeenadjustadtothepropmeectionCla bymoansofequation(3).Thisvalueof /a isappliedintheseaondtermofthehinge+mmentequation(1).Thethirdtermofequation(1)Eh -(J.-T .C.oanbe“co&dromthel“a”dingelementsmakingupthe%.C. loa
9、dplustheintegrationofthespanwisevariationufthethe cot0/2 loadrelativetotheaverageoot(3/2load.Theaverageclot0/2 loadcorrespondstothe q/a factordiscussed.DIX3CUSSIONCl?THEXHTICALANDEXPERIMENTALRESULTSTheoreticalCheckofFalknerSolution-.,_ThepcmsibilitythattheFalbermethodmightnotPovideamfficientlyaccura
10、tetheoreticalsolutionfa theloaddistrib-tionatfairlylargeanglesofsweepledtoa theoreticalinvesti-gationtocheckaFal.knersolutionfora 45swepck wingbymeansoftheCohensemigraphicalmethod.Thecalculatedinducedvelocitiessmdtheirlooationsaregiveninfigure1alcmgwiththeproperboundaryvalue.Theboundaryoonditionesta
11、blishedbythe flatplateatanangleoflatckwasnotreciselysatiefiedatanyofthepointsinvestigated.Theestimatedleadsneoessarytoremcwethedismepanciesbetweentheinducedvelocitiesandthe -.-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TWXTNFJO.1506 9boundarycon
12、ditions,however,yieldedaerysnmllckingeinhent coefficient,approximately =0.0002.ThisresultindicatesthatanysizeableerrorInthehinge-mcnmntter%? predictedbytheFalJmermethodwouldbeduetotheeffects viscosityratherthantheinabilityoftheFalknernwthodtoprovidea sufficientlyaccuratesolutionfcwpotentialflow.Sour
13、ceofErlmen*lResultsTheerinwntal*&dimensionalandfinl-pan YELIUSSoftheP=*rs ticlutidinb 1wereobalned fromtestsof a tm-dimensilmodel,twounsweptsemispanmodels,andtwosweptsemi-spanmodels,inthe7- byl&footwindtunnelsatthe-s Aernauticallaboratory.Theairfoilseconwasan 6&o1oandonthesweptplanformsthissecticmwa
14、slocatedperpendiculartothequarte=hordline.Allthefinite-spanmedalshadtaperratioscd0.5andlvid3rcent+hordfullspan,sealedgapele=torswithnoseradiusbalances.BoththetwcALinwnsionalandthreedimensionaltestswere=de ataReynoldsnumberofapproimately3.0by1.Ccanparisonof Theoretical andExperimentalRemiltsThevalues
15、oftheters predictedbytheSuansonthdandpresentedIntibleIwerecalculatedbytieopmationsout-linedInreference2. Tncludedintheseoperatkmswerea vis-oosltyfactorforthestreamlinecurvatureloadanda compressi-bilityfactor.Thecomputationsofthevalues attributedtotheFalknermethode basedontheFallmerloadingsolutionsfc
16、a?fourellipticalplanform4,twosweptandtwounswept aspectratios3 and4.5. Thesweepangleof35 wasreferredtothqone-quarterchordline,whichwaskeptstraightonthesePM fams.TheeQress50nsforpredictingtieaerodynamicters cc9asl&eredaregiveninthediscussionoftheindividualparameters%Theclifferenceintheplanf am usedtoo
17、btaintiepredictedanderimentalresults(respectively,anellipticalanda 0.5-per ratioplanfomn)leftthepossibilitythatanydiscrepsaciesarising%etueentheedictedanderntal resultsmtghtbeduetoagreatlyIncreasedeffectof&per ratiochangesonthesurfaceloaddistributionatappreciablesweepbackangles.Forunsweptwingstheapp
18、licationofellipticalplanfmm resultstoProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 .“kACATN ITO.506 “” .thepredictionofaerodynamicparamtersforvarioustypesoftaperedplanformshasbeenfoundtobereasonablyacourateaswellaspractical.Theaddedeffectsofswee
19、p,however,madeit .desirabletoanalyzea 0.5taperratioswept-backplanformofaspectratio$andcomparetheresultswiththeresultsbasedontheanalysisoftheellipticalplanforms.Thecomparisonshowedthatthedifferencebetweenthepredictedresultsfortheell-ticaland0.5taperratioplanforms,giveninthefolluwingable,wassmallenoug
20、htobeoflittleconsequenceinthiscase.lhperratio0.5Elliptical-0.0022 -0.0023-.0093 -.0093,054 .055a71 032 .033.60 .60IThepredietadvaluesfortheunsweptwingsarenottitendedasa comparisonbetweenexperimentandtheoryinordertocheckthevalidityofthepredictionsbyreference2. mh mthodhaSalreadybeenestablishedasgener
21、allysatisfactorybyerimsntalverificationm alargenumberofwings(approximately30).Theunswept“wingresultsarepresen-dtoIndicatetktexcluei?eOf .theincidentalcompressibilityandviscosityfactorstheFalknermethodprovidesessentiallythesamecorrectioninmagnitudeanddirectionthattheestablishedmethodofreference2provi
22、des.(Forprofiletrailing+dgeanglesof140orledsthevfscosityfactorreducesthestreamlinecurvaturecomectionbylessthan10percent.)c .-i?TheexpressionusedtocalcuteC% Isequatdon(1)whichasbeendiscussedpreviouslyinthesectiononapplicationofthemsthodtohingeammentcorrections.Thediscrepanciesbetweenpredictedandexper
23、imentalvaluesfortheunsweptwingsarelargerthanexpected.Theutilityof., -: .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN NO.1506 Uthesepredictions,consequently,couldbequestioned.Itshouldbenoted,however,thatfortheeaunsweptplanformsthestream-line
24、curvaturecori?ectionsamountto Mb = 0.0018 and =O.0011fortheaspectratios3 andL5, respeotivelyoThelifting-line-theorypredictionswhichwouldbeequivalenttothelifting-surface-theorypredicticmsminusthestreamlinecurvaturecorrectionswouldbeinerrorby2-1/2to4tiumsasmuchastheItiting+urface-theorypredictions.Rev
25、iousevidencef(references2and6)indicatethatforapplicationsofthelifturface-theorycomectionerrorsof0.0006and0.0008forthepredictedvaluesof C areexcepticmalbutnotunreasonable.Thediscrepanciesintheprediatedwluesof forthesweptiaakwings,however,arebeyondthelimitsofrationaliz-ticmbyconsiderationasrandomaases
26、Thestreamlinecturecorrectionfortheseswep%backwingsare =0.0007andZX& =-0.0003fortheaspectmtios3 and4.39 smctm=us thelifting-line-theoryvalueswouldbeonlysl-ightlyimprovedupm inonecaseandwouldbeslightlysuperiorintheother.AsshownpreviouslytheFalknermethodgivesa sufficientl.yaocuratetheoreticalloaddistr
27、ibutionfcminviscfdflow,hencethedeteriorationofthelifting-eurfaae-theorypredicationsinthesweptiaakoasesapparentlyisduetotheinareasedviscouseffects.c .-+?The C% valuesattributedtothel?allmernmthcdhavebe& a ustedtothepropersectionlift-curveslopebys ofequaticm(3).ThereliabilityoftheSwansonandFallmermeth
28、odsfcirpredictionsof forunsweptwingshasbeeninvestigatedanddiscussedpreciouslyinreferenaes2and4. W bothofthepresentappliaaticns.tounsweptwingstheprediatedvalwswereslfghtlyhigh.Thepredictedvaluesof Cb forsweptwingsbytheFa.lknermethodwerealsohigherthantheexperlnemtal.values.- TheinabilltyoftheFalknermt
29、hodtoyielddireatlysurfacel-dingsolutionsfordeflectidcontrolsurfaceshasbeendiscussedpreviously.Althoughthisresizrlaticnpreventsaneliait=nati & Ch$bytheFallmer?mthod,aaeqnw+sianfor C9 canbedevelod ipvolvingreQ tiesectionC%andapartiaevaluationoftheinductioneffects.Provided by IHSNot for ResaleNo reprod
30、uction or networking permitted without license from IHS-,-,-12indicatesthattheloadingforaucmtroldeflectiona canbeccndderedaecomposedoftwoconstituentNACATN NO.ataccmstantparts,a Wd-IngConespondingtotheV&iationofthehi-ent wiihcontroldeflectionforaconstantcl,(ch)cz,andaloadingcorrespondingtothevariatio
31、nofhingemmmntwithangleofattackforaccmstantcontroldefleotion,(Q5 a71 Theinductioneffectsmethod.,Sideredbecansscm bedeterminedforonlythesecondtermbytheFalkmerbutiftheinductiaeffectsofthefirstrm arecon-tobenegligibletheexpressfcmforthefinibsx Chbc%=(%Ja+ C%)czc%- (%)%(%JLo. “Thisemsion wasusedtodetermi
32、nethedictedvaluesatt&f-bwtedtoFalknerthatarepresentedintableI. Anexcellentcheckonthisexpression,canbemde bysubstitutingerimnlresultsfcmthetermsontheright-handsideoftheequation.Thusfortheaspmtratio3unsweptwtng1506. .-Cha= 4.0XL4 + (-0.602) (-0.0057) - (e70) (.lo) = *.andf$a?c% =asyeotratio!h5unsweptw
33、ing-0.0114 + (-0.602) (-0.0057) - (0.68) (4.0020) = -0.0094.=.=almostthe)precisemasuredvalues.Fortheunsweptcasesthisexpressionappliedtotheseotlondatayieldedverygoodpredictions CE5.Inthesweptcases,however,theviscouseffectsandpossiblytheneglectedinducedeffectsem apparentlyquiteimportantandtheFallmermt
34、hoddms notappeartobeapplicableevenIntheapproximatefcm ofexpression.zi”- Byusingthesamedivisionoftheloadingdelectialthatwasanalyzedfor Chb ud by* duetoflapthesem.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATNNO.1506 13assumptionsconcerningthei
35、nducedeffects,a simplifiedexpree-slonfor C% canbewrittenThe=h.OS for CL thatareattributedtotheFal.knermethodwerecalculatedusingtiaewression.Comparisonofthepedicada-derimentalvaluesfm C% leadstoGouclazsZaussimX!&xtothosefr Cha. Thepredictedvaluesfortheunsweptwingsaresatis-factoryand3ustifytheassumpti
36、onsthatwerede. Thee-dict&s for-theerrorindicatingareimportant.swepackwings,huwever,thattheneglectedinducedCONCLUDIM2REMARKSareandComparisonoftheprediotedvaluesof C&appreciab-inviscouseffectswiththeexperi-mentalvaluesf% thetwounsweptwingsindic=tidthatnotwt&s-ding incidentalviscosityandcompressibility
37、factorstheFalknermethodprovidedessentiallythesam correctionstothelifting-llne-theoryhing ntandliftparanmtersthatwasprovidedbytheprocedureoutlinedin No.1175bySuaneonandCrandall. Althoughneither eetofpredictedC values fortheunsweptwingecheckedtheerimentalresulteaswellasecd,thepredictedltftingurface-th
38、eoryvaluesweregreatimyrove-menteovertheItfting-line-theorypredlctfone.Thevalueeof C fa theswept-backwingspredictedbyanapplicationofFalhersslifting-surfacetheorywereinerrortoeuchanextentaetobe impractical.Thesevalues ehcwednonetilgproventoverthellfthg-ldne-theoryvaluee.Theotherhlnge-momentpammeterC*
39、estfmtedbyueeoftheFalknerpredictedsurfaceleadingwaeappreciablyinerroralso.Theunreliabilityoftheaerodynamicpaz%mterepredictedforthesweptAackwingeisnotdirectlychargeabletothepotentialtheoryeurfacebadlngepredictedbytheFallmermethodfortheeeplanforms.Thepredictedloadfngfora 45swepkbackwingwascheckedandfo
40、undtosatisfytheboundaryconditlonereasonablywell.Thueitisprobablethatthedfecrepanciesbetweenthepredictedandexperimentalreeultefortheewep=ackwingsareProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 NACA NO.1506.duetoviscouseffeotswhichwerenotincluded
41、intheFallmermethodmnalyeisappliedInthisinvestigation.AnUMIAeronauticalIabaratory,IWtlcmdAdtilsaryCommitteeforA!StrOW3UtiCB,MoffettField,Calif. -TamRmoEs1. Swanson,RobertS.,andGillls,ClarenceL.: LimitationsofLifting-LineTheoryforEstimmtbnofAileronHin&4wntOharaoteristics.NACA NO.3L02,1943a712. Swanson
42、RobertS.,andCrandall,StewartM.: Lifting-SurfaOe-TheoryAspectioCorrectlcmstotheLiftandntParametersforFulkSpaaElevatorsonHorizontalilSwfaoes.NACATNNO.2175,1947.3. Cohn,Doris:A Methodfarlle theCamberandTwistofaSurl?acetoSupporta GivenDistributionofLift.HAOATHNo.855, 1942.-k. Fallmer,V.M.: TheOalculati
43、and?AerodynamicLoadingmSurfacesofhy Shape.R.&M. ITO.1910,BritishA.R.C.S1943a715. Swanson,RobertS.,andCranWl, Wmart M.: AuEl.eatro-gnetllogy MethodforSolvingL3ftlng-Surfaoe-!EWacyR)oblems. NAOA_ NO.L5D23,1945.6. Jones,ArthurL.,Flanagan,MildredG.,andSluder,Loma: AnApplioatiopofLifting-aceTheorytothePr
44、edictionoflhQ&ofAttackHfnge-MomentParametersforAspeotRatfo4.5Wings.NACATNNo.1420,1947. -. . . - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATKUM MW5C+IYCnnml-m m AfncwuTlcsTABLEI.-CCUPARISOllOFPREOICI!SDMD EXPEWMl?WULVALUESSection A=3.o A=4.FIl
45、eer-APied Refet- AppliedPara- gxperi- enoe FdklMr Erperi- enae Falbmr lgrperi-neter Iwltal 2 method mental 2 method mentalunsweptCha 4.006V-0.0017 -000016 -040010 -0.0029 -0.0028 -0.0020ch8 -.0114 -.0064 -.0089 -.0067 -.009s -.0067 -.0096%a a711OS .056 .057 .053 .071 .(Y7O .066%/j a71W .036 .0s5 .03
46、7 .044 ! .042 .046a .608 .640 .610 a717W .626 .600 .660tsweptIc% -.00s7 - -.0023 -.001!3 - -.0039 -.0021%6 -.0114 - -.0093 -.0072 - -.0105 -.0069%a. .108 - .055 .063 - .057 .0s1%8 “* - I .033 .028 - .040 I .032a .602 - .600 .520 - a71600 .520Provided by IHSNot for ResaleNo reproduction or networking
47、 permitted without license from IHS-,-,-.,.- .-.1. . .-.-.- .,=-. . - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.L2 - - - - - - - -.&.6.4 #/=Q.5 y/b/2.Qd.2I I I INATIWL ADVISORYlTTEE FWl MiWNAUTICS00 ,/ .2 ,3 .4 .5 .6 .7 .8 .9 0Chofdw/3e /DOS/?/d7, X/Cfigure k- Aduced wkcifkv cakwhfed fhe C&n method for h%hodng predicted Ay /k /l%2ner mefhod m u 45swepfhck wl+p.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
