1、QJmii-”53mt I 1!NATIONALADVISORYCOMMITIEEFORAERONAUTICSTECHNICAL NOTE 3748XLCULATIONAND COMPILATIONOFTEEUNSTEADY-LIFTFORA RIGIDWINGSUBJECTEDTOSINUSOIDALGUSTSANDTOSINUSOIDALSINKINGOSCILLATIONSByJosephA.DrischlerLangleyAeronauticalLaboratoryLangleyField,Va.WashingtonOctober1956FUNCTIONE-II.-. ._ . . .
2、 . . . . . . . . . - - . . . . . . . - .-,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-lW lllllllllMluulllllllllllNATIONALlmTIsoRYco K)RAEROIWYJZCS Otlhbz.?!J!ECBNICALmmCAK!ULATIOI?ANDCOMP=ON OFTHE3748UJ.vsmxm-mmFUNCTIONSlK)RARIGIDWR?GSUBJECTEDIY)
3、SINUSOIDALGUSLE3ANDSINUSOIDALSINKINGOSCILLATIONSByJosephA.Drischler.Thetotalliftresponsesofwingstosinusoidalgustsandtostnus-oid.alverticaloscillationsarecalculatedfromtheresponsetogustpenetrationandtoasuddenchangeinsinkingvelocitythroughuseofthewell-establishedreciprocalrelationsforunsteadyflow.Thec
4、asescon-sideredaretwodimensionalwingsinincompressible,subsoniccompressible,sonic,andsupersonicflow;ellipticalandrectangularwingsinincom-pressibleflow;widerectangularanddeltawingsinsupersonicflaw;enddeltawingsofvsnishinglylowaspectratioinincompressibleandcom-pressibleflow.Formostofthecasesconsidered,
5、closed-formexpressionsaregivenandthefinalresultsarepresentedintheform.ofplotsofthesquareofthemcdulusoftheW% “coefficientforwingsinasimsoidallyoscillatinggustandintheformoftherealandimaginarypartsoftheliftcoqonentforwingsundergoingsinusoidalsinkingoscillations.Asummarytableispresentasaguidetothescope
6、endresultsofthispaper;thistablecontainsthefigureandequationnunibersforthetypesoffluwandplanformsconsidered.INTRODUCTIONTwoofthefactorsrequforellipticalshdrectangularWLWSb incompressibleflow;forwiderectangularanddeltawingsinsupersonicflow;andforverynarrowdeltawingsinincompressiblesmdcompressibleflow.
7、Calculationsoftheunsteady-ld.ftfunctionsassociatedwithrigidrestrslndwingsinsinusoidalgustsseemtobenonexistent,withtheexceptionoftheworkbyJones(ref.6)forel.Mpticalwingsin- . . . . .-. . . . - . . . .-. . . -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-
8、,-,-2 MICATN3748incompressibleflowandbyGarrick(ref.U.)andSears(ref.W) forwingsintwo-dimensionalincompressibleflow.Thepurposeofthisreportistwofold-toccmpil.etheunste-liftfunctionsassociatedwithsinusoidal.sinkingoscilhtionsandtoderivetheunsteady-liftfunctionsassociatedwitharigidrestrainedwinginasinuso
9、idalgust.Theselatterfunctionsaxederivedhereinfromexistingunsteady-llftfunctionsforawingpenetratingashq-edgedgustbymeanEofthereciprocalrelationbetweehthefunctionforawinginasinusoidalgustandthefunctionforawingpenetratingaunitsharp-edgedgust. Thereciprocalrelationusedwasofthesametypeasthatreportedinref
10、erenceU. -Theunstesdy-Mftfunctionsassociatedwitharigidrestrainedwinginasinusoidaloscillatinggustarerivedfortwo-dimensionalwingsinincompressible,subsoniccompressible,sonic,andsupersonicflow;forel13.pticalandrectangularwingsinincompressiblefluw;andforwiderectangularanddeltawingsinsupersonicflow.Inaddi
11、tion,theindicial.lift functionforawingpenetratingasharp-edgedgustandthecorre-spondingoscillatoryliftfunctionarederivedforadeltawingofvani-shingaspectratioincompressibleflow.ThefunctionspresentedinthispaperaretotalMft functions-whichincludethecirculatoryandnoncirculat.orycomponents.b studiesoftheairp
12、laneresponsetoatmosphericturbulence(seeref.u, forinstance),theunsteady-liftfunctionsforaYigidwinginasinusoidalgustusu appearintheformofthesquareofthemodulus ofliftcoefficient,whereastheunsteady-liftfunctionsforawingunder-goingsinusoidalsinkingoscillationsaearintheformoftheindividualin-phaseendout-of
13、-phase(realandimnary,respectively)componentsoflift.!llherefwe,onthisbasis,alltheresultsinthisperarepresentedinthefiguresintheformsmentioned.Anindextothefiguresandequationsorotkrsourcesofinfomnationfortheunsteady-liftfunc-tionsforthepesofflowandwingplanformsconsideredhereinispre-sentedasatable.SYMBOI
14、S.A aspectratioa velociofsoundb(x) spanwisecoothetotallift forelP*ic rectwingsinincompressibhflow(figs.3to6);forwidedeltaandrectan-gularwingsinsupersonicflow(figs.15to20);audfordeltawingsofvanishingaspectratioinincompressibleandcompressibleflow(figs.9allalo).The C(k)functions,althoughderivedbyothera
15、uthorsforallthe_ considerdherein,wererecalculatedbymeansofequation(5) fromexistingkl(s) functions. ThefunctionsC(k)asderivedbyuseofequation(5)are 6 agreanent withthefunctionsderivedbyotherauthors.TheresultsaxegivenbytheequationsinappendixA andthefigureswhichcontainplotsofthemcdulussquaredforthefunct
16、ion(k)(that)qk)12andthesearatedrealandimaginarypartsofthefuncforelliptical.sndrectangularwingsinincompressiblefldw;forwiderectangularanddeltawingsb supersonicflow;andfordeltawingsofvauishinglylowaspectratioinincompressibleandcompressiblefluw.Formostofthecasesconsidered,closed-fomnexpressionsme given
17、- thefinalresultsarepresentedtntheformofplotsofthesq.mreofthemodulusoftheliftcoefficientsforawhg ina sinusoidal.gust,andthein-phaaesndout-of-phaseliftcomponmtssrepresentedforawingunderg-oingSinusoidalsinkingoscillations.Certaingapsstill exist in the lmuwledge oftheunstesdy-13ftproblem.Forinstance,th
18、ereseemstobelittleornoinformationavailableforthesweptwing. Forrectangularwingsh mibsonicflow,andinsupersonicflawforwhichthecharacteristicMachlinesfitersectthesideedgesofthewing,theunsteady-liftproblemremainsunsolved,asitisforthedeltawingforsubsoniccompressibleandincompressibleflow.Informationonother
19、wingswithsubsoniclest.l(k)l2u(k1.0) (63) ,4A2WideDeltaWinginSupersonicFlawForawidedeltawinginsupersonicflow,thefollowingetionshavebeenkl(s)=q(s)=kl(s)=derivedfrcmreferences22andd:(),.kJs) = thesub-scriptsrepresenttheregionunderconsideration.($)T1 =-W.(QJ) -”-F=ZT2=YCI()3 2W0=T -al t=-l.1 b(x)+y +tan
20、-lJ 1b(x)-y -T- b(x)-y T- b(x)+y 2(82)(83)(m)_._. . . . . - . . - - . -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. .-24and,forlargesketch(c),valuesof T (thatiS,forthehigherINAOATN3748numberregionsinHwhere an integral equationfor ftogetherwithat
21、abulationofb(x)thisfunctionisgiveninreferen;e19:soLwingequations(82)to(85)forthevelocitypotential$ andsubstitutingtito,equation(79)yieldsthefollowingloadingcoeffi-cientsforthevariousregions:.(85)4P()T*2b(x)()4% .()fal(a3=ql/zjy7i-Thecorrespondingliftcoefficientperunitlengthis1“zb+=1z=b(x)1ZJ-=b(x)(8
22、6)(87).(88) .2 if-qf-b(x) b(t)(;)(T2b(x) (90). - - .-. . _ . - . . . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACATN37k8aocontainsessentialmaterialfrcmTN2763 TN2897.). Wagner,Herbert:be?dieEntstehungdesdynamischenAuftriebeswgflcontainsmate
23、rialfromTN2256byIomax,Heaslet,Fuller.)20.Heaslet,Max.A.,and.Iamax,Harvard:!l!wo-DimensionalUnsteadyLiftWoblemsinsUp131%301dCFlight.NACARep.945,1949.(SupersedesNACATN1621.)21.Euckel,Vera:Tslxilationofthe f FunctionsWhichOccurintheAerodynamicTheoryofOscillatingWingsinSupersonicFlow.NACATN3606,1956.22.
24、1-es,JohnW.: TransientIoadingofWideDeltaAirfoilsatSuper-sonicSpeeds.Jour.Aero.Sci.,vol.18,no.8,Aug.1951,PPa71 543-554= “23.Miles,Johnw.: TransientJailingofSupersonicRectangularJour.Aero.Sci.,vol.17,no.10,Oct.1956,pp.7-652.Airfoils .-. - - .Provided by IHSNot for ResaleNo reproduction or networking p
25、ermitted without license from IHS-,-,-.29.IypeOfflew Wingplanfoml C(k) q(k) C(k):F= IG(k) J4K#Btlibb m dimansimlalEq. (u) Eq. (12) 2mmLlp7mib18 ” $:l m , ,TImOhaMmna “M50.6: :Raf.3 1 r8M=o. Eq: 43)cCqraEidblaallaBEibk:M=o w= Eta m. (47)R.(Wy -0.1 Raf.10 (b) “ 9 10Solllc - *.(*) a.(55) U 12-:q2,y,2,d
26、$2 m icmal R.(59)m.(60) u 3.4Slqmralmic:M=+$+2,aud?$ widedelta E!q.(66)Eq.(67) 15 3.6m=c: WI*yyyulex: I17(a) If3(a)M.3Q,2,alla4Q7 3 A=2 f17) la)A=4 17c) rlac)M=?m.(m m.(72) Ig(a) 20(a)M.2 A-1,2,4,-= W(b) 20(b)M=? 19(c) a(c)%il.ydrdatmycqpnantaellftphtt%a.%amllataaIlmarlcallyflcall (s) nnlcucmgiventiappnaixc.- - - - - -. . . - -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
