1、C43 ,-).-INATIONALADVISORYCOMMITTEEFORAERONAUTICSTECHNICAL NOTE 3245CALCULATED SUBSONICSPAN LOADS AND RESULTING STABIUTYDERIVATIVES OF UNSWEPT AND 450SWEPTBACK TAILSURFACES INSIDESLIPAND INSTEADY ROLLByM. J.QueijoandDonaldR.RileyLa.ngleyAeronauticalLaboratoryLangleyField,Va.vWashingtonOctober1954k=w
2、i b _.- -/L I . . . - . .- . . - - . . . . +.-.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-lLIECHLIBRARYK#B,FJPuIIl!lllllllilul!l!uuWIONAL ADVISORYCNITTEEFORAERONAUTICS UObb28DTECHNICALNOTE3245CAWULMEDSUBSONICSPANLOUXSANDRESULTINGSTABILITYDERIVAT
3、IVESOFUNSWEPTAND450swEmwx NmSURFACESINSIDESLIPANDINSTEADYROILByM.J.QueijoandDonaldR.RileyslJMMARYSubsonicspsmloadsandtheresultingbeencalculatedfora systematicseriesofstabiliity derivativeshavevertical-andhorizontal-tailcombinationsinsideslipandinsteadyrollinordertoprovideinforma-tionembracinga wider
4、angeofprobabletailconfigurations.Allcal-culationsweremadebyapplicationofthediscrete-horseshoe-vortexmethodtotheproblemofestimatingloadsonintersectingsurfaces.Theinves-tigationcoveredvariationsinvertical-tailaspectratio,theratioofhorizontal-tailaspectratiotovertical-tailsspectratio,theeffectsofhorizo
5、ntal-taildihedralangle(forthesideslipcase),andtheeffectsofverticalpositionofthehorizontal”tailforsurfaceshavingtheir. quarter-chordlinessweptback0and45. Theresultsoftheinvestiga-tionarepresentedinchartsfrm whichthespanloadsforthevariousconditionscanbeobtained.Theresultingstabilityderivativesarepre-s
6、entedasvertical-andhorizontal-tailcontributionsaswellastotal-tail-assemblyderivatives.Theresultsofthisinvestigation,whichwasmadeforawiderrangeofgeometricvariablesthanpreviousstudies,showedtrendswhichwereingeneralagreementwiththeresultsofpreviousinvestigations.Alsopresentedinthispaperandusedinthecqut
7、ationsisanextensivetableofvaluesofsidewashduetoarec vo=.AccuratetionofthesedesignerasaINTRODUCTIONinformationregardingtailloadsandthespanwisedistribu-loadsduringvariousmaneuversisrequiredbytheaircraftbasisforstructuhowever,somecalculationsmadeinconjunctionwiththetivestigationofreference4 indicatedit
8、sappli-cabilitytothecalculationofloadsonintersectingsurfaces(tailsur-faces)insideslip.Sincethebasicmethodisexplainedindetailtireference5,onlythepertinentdetailssreincludedherein(seeappen-d3xA). Thediscrete-horseshoe-vortexmethodwasusedinthepresentinvestigationtoobtainsubsonicspanwiseloaddistribution
9、sandresultingaerodynamicderivativesfora systematicseriesoftailconfigurationsinsideslipandinsteadyroll.Also,theadditionalspanloadingsduetothedihedrangleofthehorizontal-tailsurfacesweredeterminedforthesides13pcase.Calculationsweremadeforsurfaceshavingunsweptand45sweptbackquarter-chordlinesandataperrat
10、ioof0.5. Thegeometricvariablescoveredinthisinvestigationincludedvertical-tailaspectratio,ratioofhorizontal-tailaspectratiotoverticsl-tailaspectratio,andverticallocationofthehorizontaltail.ThecontributionofMr.M.J.Queijotothepresentpaperwassub-mittedtotheUniversityofVirginiainpsrtialfulfillmentofthere
11、quirementsfora degreeofmasterofscience.Theresultspresentedhereinsrereferredtothestabilitysystemofaxeswiththeoriginatthequarterchordoftheverticsl-tailrootchord(seefig.1). “A aspectratio,b2/Sb span,fts area, sq ftc localchord,ftProvided by IHSNot for ResaleNo reproduction or networking permitted witho
12、ut license from IHS-,-,-NACATN3243 3.zdKPvvwvu3c/4ABrX,y,zXjy,zNPf(x,y,z)F(x,y)F(x,y,z),. claveragegeometricchord,ftsemispanofrectangularhorseshoevortex,ftcirculationstrength,sqft/secrateofroll,radians/seesidewash-velocityrelativetostabilityaxes,ft/secsidewashvelocityrelativetohorseshoevortex,ft/sec
13、downwashvelocity,ft/secfree-streamvelocity,ft/seccomponentoffree-stresmvelocitynormal.tosurfaceatcontrolpoint,ft/sechowever,a cmparisonoffigures4 and5showsthatsweepdoesreducethemagnitudeofthespanloadcoefficientssghtlyandalsoreducestheeffectoftheratio/1+ onboththevertical-andhorizontal-tailloaddistri
14、bution.Forthesweptbacktailconfigurationstheloadonthehorizontaltailwhenatthemidpositionis-. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2LNACATN3245 9almostnonexl.stantforallthreevaluesof Av considered.lhaddition,forthelargervertical-tailaspectra
15、tioconsideredAv= 3.0,sweep(iappearstoreversetheusualspaneffectontheverticsl.-tailoaddis-tributionintheregionnearthehorizontaltailforthehighandlowhorizontal-taillocations.Sideslipofhorizontaltailwithdihedral.-Aspointedoutpre-viously,theseloadswerecalculatedfortheconditionwhereahorizontaltailhati dihe
16、dralwasinsidesl.ipwhiletheverticaltailremainedalinedwiththerelatinwind.Sucha conditionpermitsanevaluationoftheadditionalloadduetohorizontal-taildihedralangle.Resultsofcalculationoftheadditionalspanloaddistributionontheverticalandhorizontal.surfacesofunswepttailconfigurationsresultingfromsideslipofth
17、ehorizontal.tailwithdihedralarepresentedinfigure6.Theinducedloadinbutas Av isincreasedto3.0,forexsmple,themax3mumavailableend-plateeffectforhighhorizontal-taillocationsisonlyabouttwo-thirdsofthatindicatedforthelowposition.Shilarcomparisonsoftherestsforthesweptconfigura-tionscamnoteffectivelybemadesi
18、ncethenecessarydifferentiationbetweensweepangleandvertical-tailtaper-ratioeffectsis+lmosthpossibletoperformforthelimitedrangeoftail.configurationspre-sentedherein.Theesttitedrolling+momentderivatives(c%): (Cl$hm c%exepresentedinfigures16,17,and18,respectively,fortheunswepttailconfigurations,andinfig
19、ures19,20,snd21forthe450swept-backconfigurations.TheresultsshuwthatthehorizontaltailateitherextremityoftheverticaltailcontributestothetotalroU_ing-momentcoefficientintwoways.First,thehorizontaltailactsasanendplateontheverticaltail,andthusincreasesthevertical-tallloadand.itsresultsntmment. Second,the
20、horizontaltailhasonit/L! . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN3245 / 13,.,aninducedloadwhichresultsinarolg mcunentoflargemagnitudewhentheaspectratio(orspan)islarge.Thedirectionaswellasthems.-tudeoftheloadsonthehorizontaltaildepend
21、sontheverticalpositionofthehorizontaltail.Thus,whentbehorizontaltailisinthehighpositionthevertic-andhorizontal-tailrolJi.ngmomentsareaiklltive,whilethemomentssubtractwhenthehorizontaltsilisinthelowposi-tion.Theinducedloadandrolling-mmentcontributionofthehorizontaltailissmaXlwhenthehorizontaltailisat
22、thecenteroftheverticaltail.Theeffectsof.sweeponthetailrollingmomentsappesrtoberathersmall,particularlywhenthetailsconsideredareoflowaspectratio.ThemomentsofthesurfaceshavingIxhowever,for Av= 3.0 theoppositetrendisobservedfortailsatthetidandhighpositions. Steadyroll.-Theresultsobtainedforlaterslforce
23、duetorollareshowninfigures32and33forunsweptand45sweptbacktails,respec-tively.Theresultsshowthat Cyp,whichiscontributedonlybytheverticaltail.,islargelyaffectedbyhorizontal-tailaspectratioifthehorizontaltailisateitherextremityoftheverticaltail.limreasingtheaspectratioofthelowhorizontaltailcausesCy tod
24、ecreaseinP_tude, where=theoppositeiStrueforthehighhorizontaltail.Thiseffectis,ofcourse,a consequenceofthechangesinvertical-tailspanloadcausedbythehorizontal-tailload.(Seefigs.10and12.)ThecalculatedresultsforthedampinginrolJ_contributedbytheunsweptverticaltail.,horizontaltail,andccmpletetdl assemblie
25、sareshowninfigures, 35,and36,respectively.Asexpected,theresultsoffigure36ticate thathorizontal-tailaspectratioorspan,asindi-catedbytheratioAh/ foragivenvalueof Av,hasanappreciable AinfluenceontheresultingCzp ofthetailassenibly.Whatisofinter-est,however,isthatforthelowandmidhorizontal-tailpositionsth
26、eratioAh/. hassminfluenceonlywhenthehorizontaltailislargerthantheverticaltail.Fortheramgeofvsluesof 1 fromOto1.0forthelowandmidlocations,thealmostconstantvalueof Czp appearstobeessentiallytheresultoftwoopposingeffects.Consider,forexample,thehorizontal-tailcontributionforthelowhorizontal-tailposition
27、asindicatedtifigure35. Aninducedloadexistsonthehori-zontaltailsimilartothesidesliploadshowninfigure4,aresultofthepresenceofthehorizontal.tailatthebaseoftheverticaltailthatiscarryingaload.Superimposedonthisloadisaloadduetosteadyrolling(fig.n). Thesetwoloadsopposeoneanotherandtendtocm-cel.Whenthehoriz
28、ontaltailisoflowsspectratio,theresultantmmnentfromtheaforementionedloadsisverymall. Fortailcombina-tionswithhigh-aspect-ratiohorizontaltails,therollingmomentduetoro13dngpredominates.A shilareffectoccursonthevertical.tailinthattheend-plateeffecttendstoincreasetherolngloadonthever-ticsltail,andtherolg
29、 loadonthehorizontaltailinducesa side-washwhichtendstodecreaseit. Thetiteractionoftheseloadsissuch()that C2Pv isonlyskl.ghtlyinfluencedbythehorizontal-tailaspectratio,atleastfort- rangeofsizepresentedhere.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,
30、-,-ljNACATN3245Forthehighhorizontal-taillocationsimilareffectson Cl()Pva (CZP)h occur;however,forthisconfigurationtheloads e-”inthe same direction as the rollingloads.Theresultsfor C(Qv (“h d fortieinducedend-plate45sweptbacktailconfigurationsm?epresentedinfigures37, and39,respectively.Acomparisonof
31、theresultsfortheunsweptandswepttollstidicatestheusandtheboundaryconditionissatisfiedateachbyequatingthe Jnormal”velocityarisingfromthecompletevortexsystemtothecomponentofthefree-streamvelocitynormaltothesurfaceatthatpoint.This.methodyieldsa setof N simultaneousequationswithoneequationfor reachofthe
32、N controlpoints.TheseequationsareoftheformNKn f (x,y,z)7J3c/41 n (1)Thenormalvelocitycomponentatanycontrolpointresultingfromasystemofhorseshoevorticesrepresentingtwointersectingsurfacescon-sistsofthedownwashcontributedbyallhorseshoevorticescontainedinthesameplaneasthecontrolpointplusthesidewashgener
33、atedbyall horseshoevorticeslocatedintheintersectingplane.Reference7pre-sentsgeneralexpressionsforthedownwashandsidewashvelocitycom-ponentsduetoa singlerectangularhorseshoevortexreferredtoa setofCartesiancoordinatestiththeoriginlocatedatthemidpointoftheboundvortex.Nondimensionalizthethreecoordinatedi
34、stancesappearingintheequationswithrespecttothevortexsemispanandrearrangingthetermsyieldsthefollowingexpressions:Forthedownwashvelocitywintheplaneofa rectangularhorseshoevortex(z= O),Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3245 171Y-l1
35、+I1ti+ 1y+11+1x I(2)andforthesidewashvelocityvatanypointonanintersectingplane,kfid zT=r1Z2+ (y+ 1)2Lz122+ (Y - 1)2Theright-handsideofeqxation(2)-1x I+.-2f2 + zz+ (y + 1)x-1-1(3)2Xiz+ 212+ (y-1)isdefinedhereinas F(x,y).Tabulatedvaluesofthisfunctionareavailableinvariouspublicationsforawiderangeof x an
36、d y values.(Forexsmple,seeref.8.)TablesofthecorrespondingfunctionF(x,y,z)ofequation(3)werenotavailableand,consequently,thefunctionwasevaluatedandtabulatedforthe x, y,and z valuesapplicabletothepresentinvestigation.(SeeappendixB.)Inthepresentinvestigationtheverticaltailisrepresentedbyasystemofsixandt
37、hehorizontaltailby12equispanrectangularhorse-shoevortices.Eachofthethreebasictypesofloadinginvestigatedforeachtailconfigurationleadstoantisymmetricalloaddistributionsonthehorizontaltail.Theloadscarriedoneachsemispanofthehorizontaltailhavethesamemagaitudeanddistributionbutareoppositeinsign.(Forexampl
38、e,infig.2, K1= -Ku, = -KU, etc.) Sincethisparticu-larconditionexistsandsincesixhorseshoevorticeswerelocatedoneachsemispanofthehorizontaltail,thenumberofequationstobesolvedcanbereducedfrom18toI-2.Ifthecirculationstrengths areassumed. - - - - - - . . - .- . - _ -Provided by IHSNot for ResaleNo reprodu
39、ction or networking permitted without license from IHS-,-,- -.18 NACATN3245tobepositivefortherepresentationshowninfigure2,theformofthestiultaneousequationsbecomesn=6 %1u3c/4 4ycdhfn(x,y,z)-In=18f13-n(X,y,z) *-5 fn(x,y,z) (4)n=lj4fiThesummationfrom n = 1 to n = 6 representsthehorizontal-tailcontribut
40、ion,andthesummationfrom n = 13 to n = 18 representsthevertical-tailcontribution.Thesignprecedingthesecondsummationdependsonwhereu3c/4 isbeingcomputed.Theplussignisforhorizontal-tailcontrolpointsandtheminussignforvertical-tailcon-trolpoints.Theterm U3C/4representstheboundaryconditionsatagivencontrolp
41、ointandisusuallyreplacedbyamoreappropriateformdepending,ofcourse,onthetypeofmaneuverunderconsideration.Theboundaryconditionsassociatedwithtailcombinationsinsidesl.ipandsteadyrollareasfollows:Boundaryconditions,u3c/4Case TypeofmaneuverHorizontaltailVerticaltail(1) Sideslip,r = O 0 VPSideslipofhorizon
42、taltails,(2) verticaltailat f3= O, nr or+o(3) Roll P% v P% vv% VbvIncase(3),the y and z coordinatesappearingintheboundarycon-ditionsrepresentdistancesmeasuredtoeachcontrolpointundercon-siderationrelativetothestabilitysystemofaxesforthecompletetailconfigurationandshouldnotbeconfusedwiththeprimedvalue
43、susedpreviously.Substitutingtheseboundaryvaluesintoequation_(4)fortheappropriatecontrolpointsanddividingthroughby V13,ViP,.-. ._ _ Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3245 19()pbvand V forcases(l),(2),and(3),respectively,yield12si
44、mul-Vtaneousequationswith12unknowns.Asanillustrativeexample,case(1)inamorereducedformcan%eexpressedinthefollowingmanner:Forcontrolyointslocatedonthehorizontaltail,thatis,points1to12 (see fig.2),n=6 Ko= 1Fn(x,y)-F15n(xjY)+n=l4fidhVn=18E % Fn(x,y,z)n.134fiVForcontrolpointsonthen%zicdtail(13to18),Fn(x,
45、y,z)-F15-n(x)Yz)n=18E k Fn(x,y)n=1341fV(5)(6)Thesimultaneousequationsofthistypeobtainedforthevariousflowconditionscanbesolvedfortermswhichyieldthespanloads.Now,ifthetermcontainingtheunknowncirculationstrengthsandboundarycon-ditionsisdesignatedasloadcoefficient,thentheloadcoefficientforthethreecasesc
46、onsideredhereincanbeobtainedasfollows:Forcase(l),Forcase(2),- ._. . - . . . , - z. - - - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-20Forcase(3),K and4fidpbvhThetwoloadcoefficientsrepresentedNACATN3245r“.Kdifferonlyinthetesdh and appearinginthed
47、enominator.Thisdifferenceistheresultofusinghorseshoevorticesofdifferentspanstorepresenttheverticalandhorizontaltails.A moreconvenientandusefulformoftheloadcoefficientscanbederivedbyutilizingthewell-knownKutta-Joukowskiequation2=pvKwhere 1 istheloadperunitspan.Byuseofthisequation,thefol-lowingrelatio
48、nshipscanbeobtained:cc()z Kn= 1.0472Ah6P h 41tdhV()cc_y Kn= 2.0944E$rv 4Ycdvvpr(7) . _ -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN3245 21Propersummationofthesespanloadcoefficientsyieldsseveralofthemoreimportantaerodynamicderivatives.Thesederivativesandtheircorrespondingsummations
