双立柱堆垛机设计【含三维SW模型、CAD图纸和说明书】
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含三维SW模型、CAD图纸和说明书
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AileronDesignChapter12DesignofControlSurfacesFrom:AircraftDesign:ASystemsEngineeringApproachMohammadSadraey792pagesSeptember2012,HardcoverWileyPublications12.4.1.IntroductionTheprimaryfunctionofanaileronisthelateral(i.e.roll)controlofanaircraft;however,italsoaffectsthedirectionalcontrol.Duetothisreason,theaileronandtherudderareusuallydesignedconcurrently.Lateralcontrolisgovernedprimarilythrougharollrate(P).Aileronisstructurallypartofthewing,andhastwopieces;eachlocatedonthetrailingedgeoftheouterportionofthewingleftandrightsections.Bothaileronsareoftenusedsymmetrically,hencetheirgeometriesareidentical.Aileroneffectivenessisameasureofhowgoodthedeflectedaileronisproducingthedesiredrollingmoment.Thegeneratedrollingmomentisafunctionofaileronsize,ailerondeflection,anditsdistancefromtheaircraftfuselagecenterline.Unlikerudderandelevatorwhicharedisplacementcontrol,theaileronisaratecontrol.Anychangeintheailerongeometryordeflectionwillchangetherollrate;whichsubsequentlyvariesconstantlytherollangle.Thedeflectionofanycontrolsurfaceincludingtheaileroninvolvesahingemoment.Thehingemomentsaretheaerodynamicmomentsthatmustbeovercometodeflectthecontrolsurfaces.Thehingemomentgovernsthemagnitudeofaugmentedpilotforcerequiredtomovethecorrespondingactuatortodeflectthecontrolsurface.Tominimizethesizeandthusthecostoftheactuationsystem,theaileronsshouldbedesignedsothatthecontrolforcesareaslowaspossible.Inthedesignprocessofanaileron,fourparametersneedtobedetermined.Theyare:1.aileronplanformarea(Sa);2.aileronchord/span(Ca/ba);3.maximumupanddownailerondeflection(dAmax);and4.locationofinneredgeoftheaileronalongthewingspan(bai).Figure12.10showstheailerongeometry.Asageneralguidance,thetypicalvaluesfortheseparametersareasfollows:Sa/S=0.05to0.1,ba/b=0.2-0.3,Ca/C=0.15-0.25,bai/b=0.6-0.8,anddAmax=30degrees.Basedonthisstatistics,about5to10percentofthewingareaisdevotedtotheaileron,theaileron-to-wing-chordratioisabout15to25percent,aileron-to-wing-spanratioisabout20-30percent,andtheinboardaileronspanisabout60to80percentofthewingspan.Table12.17illustratesthecharacteristicsofaileronofseveralaircraft.1bAba/2CaSa/2bai/2Aa.Top-viewofthewingandailerondAupdAdownb.Side-viewofthewingandaileron(SectionAA)Figure12.1.GeometryofaileronFactorsaffectingthedesignoftheaileronare:1.therequiredhingemoment,2.theaileroneffectiveness,3.aerodynamicandmassbalancing,4.flapgeometry,5.theaircraftstructure,and6.cost.Aileroneffectivenessisameasureofhoweffectivetheailerondeflectionisinproducingthedesiredrollingmoment.Aileroneffectivenessisafunctionofitssizeanditsdistancetoaircraftcenterofgravity.Hingemomentsarealsoimportantbecausetheyaretheaerodynamicmomentsthatmustbeovercometorotatetheaileron.Thehingemomentsgovernsthemagnitudeofforcerequiredofthepilottomovetheaileron.Therefore,greatcaremustbeusedindesigningtheaileronsothatthecontrolforcesarewithinacceptablelimitsforthepilots.Finally,aerodynamicandmassbalancingdealswithtechniquestovarythehingemomentssothatthestickforcestayswithinanacceptablerange.Handlingqualitiesdiscussedintheprevioussectiongovernthesefactors.Inthissection,principalsofailerondesign,designprocedure,governingequations,constraints,anddesignstepsaswellasafullysolvedexamplearepresented.12.4.2.PrinciplesofAileronDesignAbasiciteminthelistofaircraftperformancerequirementsisthemaneuverability.Aircraftmaneuverabilityisafunctionofenginethrust,aircraftmassmomentofinertia,andcontrolpower.Oneoftheprimarycontrolsurfaceswhichcausetheaircrafttobesteeredalongitsthree-dimensionalflightpath(i.e.maneuver)toitsspecifieddestinationisaileron.Aileronsarelikeplainflapsplacedatoutboardofthetrailingedgeofthewing.Rightaileronandleftaileronaredeflecteddifferentiallyandsimultaneouslytoproducea2NoAircraftTypemTO(kg)b(m)CA/CSpanratiodAmax(deg)bi/b/2bo/b/2updown1Cessna182LightGA1,406110.20.460.9520142CessnaCitationIIIBusinessjet9,97916.310.30.560.8912.512.53AirTractorAT-802Agriculture7,257180.360.40.9517134Gulfstream200Businessjet16,0800.8615155Fokker100AAirliner44,45028.0425206Boeing777-200Airliner247,200210.76230107Airbus340-600Airliner368,00063.450.30.640.9225208AirbusA340-600Airliner368,00063.450.250.670.922525rollingmomentaboutx-axis.Therefore,themainroleofaileronistherollcontrol;howeveritwillaffectyawcontrolaswell.Rollcontrolisthefundamentalbasisforthedesignofaileron.Table12.1.CharacteristicsofaileronforseveralaircraftTable12.12(lateraldirectionalhandlingqualitiesrequirements)providessignificantcriteriatodesigntheaileron.Thistablespecifiesrequiredtimetobankanaircraftataspecifiedbankangle.Sincetheeffectivenessofcontrolsurfacesarethelowestintheslowerspeed,therollcontrolinatake-offorlandingoperationsistheflightphaseatwhichtheaileronissized.Thus,indesigningtheailerononemustconsideronlylevel1andmostcriticalphasesofflightthatisusuallyphaseB.BasedontheNewtonssecondlawforarotationalmotion,thesummationofallappliedmomentsisequaltothetimerateofchangeofangularmomentum.Ifthemassandthegeometryoftheobjet(i.e.vehicle)arefixed,thelawisreducedtoasimplerversion:Thesummationofallmomentsisequaltothemassmomentofinertiatimeoftheobjectabouttheaxisorrotationmultipliedbytherateofchangeofangularvelocity.Inthecaseofarollingmotion,thesummationofallrollingmoments(includingtheaircraftaerodynamicmoment)isequaltotheaircraftmassmomentofinertiaaboutx-axismultipliedbythetimerateofchange(/t)ofrollrate(P).Inboardaileron1Outboardaileron23Lcg=IxxPt(12.7)orP=LIxxcg(12.8)Generallyspeaking,therearetwoforcesinvolvedingeneratingtherollingmoment:1.Anincrementalchangeinwingliftduetoachangeinaileronangle,2.Aircraftrollingdragforceintheyzplane.Figure12.11illustratesthefront-viewofanaircraftwhereincrementalchangeintheliftduetoailerondeflection(DL)andincrementaldragduetotherollingspeedareshown.TheaircraftinFigure12.11isplanningtohaveapositiveroll,sotherightaileronisdeflectedupandleftailerondown(i.e.+dA).Thetotalaerodynamicrollingmomentinarollingmotionis:Mcgx=2DLyA-DDyD(12.9)Thefactor2hasbeenintroducedinthemomentduetolifttoaccountforbothleftandrightailerons.Thefactor2isnotconsideredfortherollingmomentduetorollingdragcalculation,sincetheaveragerollingdragwillbecomputedlater.TheparameteryListheaveragedistancebetweeneachaileronandthex-axis(i.e.aircraftcenterofgravity).TheparameteryDistheaveragedistancebetweenrollingdragcenterandthex-axis(i.e.aircraftcenterofgravity).Atypicallocationforthisdistanceisabout40%ofthewingsemispanfromrootchord.+dADDrightDLleftDLrightdyyyoyicgDDleftzyDyA+dAFrontviewFigure12.2.Incrementalchangeinliftanddragingeneratingarollingmotion4Inanaircraftwithshortwingspanandlargeaileron(e.g.fightersuchasGeneralDynamicsF-16FightingFalcon(Figure3.12)thedragdoesnotconsiderablyinfluenceontherollingspeed.However,inanaircraftwithalongwingspanandsmallaileron;suchasbomberBoeingB-52(Figures8.20and9.4);therollinginduceddragforcehasasignificanteffectontherollingspeed.Forinstance,theB-52takesabout10secondstohaveabankangleof45degreesatlowspeeds,whileforthecaseofafightersuchasF-16;ittakesonlyafractionofasecondforsuchroll.Owingtothefactthataileronsarelocatedatsomedistancefromthecenterofgravityoftheaircraft,incrementalliftforcegeneratedbyaileronsdeflectedup/down,createsarollingmoment.LA=2DLyA(12.10)However,theaerodynamicrollingmomentisgenerallymodeledasafunctionofwingarea(S),wingspan(b),dynamicpressure(q)as:LA=qSClbwhereClistherollingmomentcoefficientandthedynamicpressureis:(12.11)q=12rVT2(12.12)whereristheairdensityandVTistheaircrafttrueairspeed.TheparameterClisafunctionofaircraftconfiguration,sideslipangle,rudderdeflectionandailerondeflection.Inasymmetricaircraftwithnosideslipandnorudderdeflection,thiscoefficientislinearlymodeledas:Cl=CldAdA(12.13)TheparameterCldAisreferredtoastheaircraftrollingmoment-coefficient-due-to-aileron-deflectionderivativeandisalsocalledtheaileronrollcontrolpower.Theaircraftrollingdraginducedbytherollingspeedmaybemodeledas:DR=DDleft+DDright=12rVR2StotCDR(12.14)whereaircraftaverageCDRistheaircraftdragcoefficientinrollingmotion.Thiscoefficientisabout0.71.2whichincludesthedragcontributionofthefuselage.TheparameterStotisthesummationofwingplanformarea,horizontaltailplanformarea,andverticaltailplanformarea.Stot=Sw+Sht+Svt5(12.15)TheparameterVRistherollinglinearspeedinarollingmotionandisequaltorollrate(P)multipliedbyaveragedistancebetweenrollingdragcenter(SeeFigure12.11)alongy-axisandtheaircraftcenterofgravity:VR=PyD(12.16)Sinceallthreeliftingsurfaces(wing,horizontaltail,andverticaltail)arecontributingtotherollingdrag,theyDisinfact,theaverageofthreeaveragedistances.Thenon-dimensionalcontrolderivativeCldAisameasureoftherollcontrolpoweroftheaileron;itrepresentsthechangeinrollingmomentperunitchangeofailerondeflection.ThelargertheCldA,themoreeffectivetheaileronisatcreatingarollingmoment.Thiscontrolderivativemaybecalculatedusingmethodintroducedin19.However,anestimateoftherollcontrolpowerforanaileronispresentedinthisSectionbasedonasimplestripintegrationmethod.Theaerodynamicrollingmomentduetotheliftdistributionmaybewrittenincoefficientformas:DCl=DLAqSb=qCLACayAdyqSb=CLACayAdySb(12.17)ThesectionliftcoefficientCLAonthesectionscontainingtheaileronmaybewrittenasCLA=CLaa=CLadaddAdA=CLatadA(12.18)wheretaistheaileroneffectivenessparameterandisobtainedfromFigure12.12,giventheratiobetweenaileron-chordandwing-chord.Figure12.12isageneralrepresentativeofthecontrolsurfaceeffectiveness;itmaybeappliedtoaileron(ta),elevator(te),andrudder(tr).Thus,inFigure12.12,thesubscriptofparametertisdroppedtoindicatethegenerality.yCydy2CLawtdAyoIntegratingovertheregioncontainingtheaileronyieldsCl=Sbi(12.19)whereCLawhasbeencorrectedforthree-dimensionalflowandthefactor2isaddedtoaccountforthetwoailerons.Forthecalculationinthistechnique,thewingsectionalliftcurveslopeisassumedtobeconstantoverthewingspan.Therefore,theaileronsectionalliftcurveslopeisequaledtothewingsectionalliftcurveslope.Theparameteryirepresentstheinboardpositionofaileronwithrespecttothefuselagecenterline,andyotheoutboardpositionofaileronwithrespecttothefuselagecenterline(SeeFigure12.11).6TheaileronrollcontrolderivativecanbeobtainedbytakingthederivativewithrespecttoyCydydA:CldA=2CLawtyoSbi(12.20)t0.60.7Control-surface-to-lifting-surface-chordratioFigure12.3.ControlsurfaceangleofattackeffectivenessparameterThewingchord(C)asafunctionofy(alongspan)forataperedwingcanbeexpressedbythefollowingrelationship:C=Cr1+2yl-1b(12.21)whereCrdenotesthewingrootchord,andlisthewingtaperratio.SubstitutingthisrelationshipbackintotheexpressionforCldA(Equ.12.20)yields:1+2byydyCldA=2CLawtSbyoCyirl-1(12.22)or22l-13CldA=2CLawtCry2Sb+y3byiyo(12.23)ThisequationcanbeemployedtoestimaterollcontrolderivativeCldAusingtheailerongeometryandestimatingtfromFigure12.12.Gettingbacktoequation12.12,therearetwopiecesofailerons;eachatoneleftandrightsectionsofthewing.Thesetwopiecesmayhaveasimilarmagnitudeofdeflectionsorslightlydifferentdeflections,duetotheadverseyaw.Atanyrate,onlyonevaluewillentertothecalculationofrollingmoment.Thus,anaveragevalueofailerondeflectionwillbecalculatedasfollows:7dA=dAleft+dAright1(12.24)2ThesignofthisdAwilllaterbedeterminedbasedontheconventionintroducedearlier;apositivedAwillgenerateapositiverollingmoment.Substitutingequation12.9intoequation12.7yields:LA+DDyD=IxxPAsthenameimplies,Pisthetimerateofchangeofrollrate:(12.25)P=ddtP(12.26)Ontheotherhand,theangularvelocityaboutx-axis(P)isdefinedasthetimerateofchangeofbankangle:P=ddtF(12.27)Combiningequations12.26and12.27andremovingdtfrombothsides,resultsin:PdF=PdP(12.28)Assumingthattheaircraftisinitiallyatalevelcruisingflight(i.e.Po=0,fo=0),bothsidesmaybeintegratedas:fPdF=0PssPdP0(12.29)Thus,thebankangleduetoarollingmotionisobtainedas:F=dPPPwherePisobtainedfromequation12.25.Thus:(12.30)PssF=0IxxPLA+DDyDdP(12.31)Bothaerodynamicrollingmomentandaircraftdragduetorollingmotionarefunctionsofrollrate.Pluggingthesetwomomentsintoequation12.31yields:r(PyD)(Sw+Sht+Svt)CDRyDF1=Pss0qSClb+12IxxP2dP(12.32)Theaircraftrateofrollrateresponsetotheailerondeflectionhastwodistinctstates:1.Atransientstate,2.Asteadystate(SeeFigure12.13).Theintegrallimitfortherollrate(P)inequation12.32isfromaninitialtrimpointofnorollrate(i.e.winglevelandPo=0)toasteady-statevalueofrollrate(Pss).Sincetheaileronisfeaturedasaratecontrol,thedeflectionofaileronwilleventuallyresultinasteady-staterollrate(Figure12.13).Thus,unlesstheaileronsarereturnedtotheinitialzerodeflection,theaircraftwillnotstopataspecificbankangle.Table12.12definestherollraterequirementsintermsofthedesired8bankangle(F2)forthedurationoftseconds.Theequation12.32hasaclosed-formsolutionandcanbesolvedtodeterminethebankangle(F1)whentherollratereachesitssteady-statevalue.Rollrate(deg/sec)Psstsst2Time(sec)Figure12.4.AircraftrollrateresponsetoanailerondeflectionBankangle(deg)F2F1t1t2Time(sec)Figure12.5.AircraftbankangleresponsetoanailerondeflectionWhentheaircrafthasasteady-state(Pss)rollrate,thenewbankangle(Figure12.14)afterDtseconds(i.e.t2-tss)isreadilyobtainedbythefollowinglinearrelationship:F2=Pss(t2-tss)+F1(12.33)Duetothefactthattheaircraftdragduetorollrateisnotconstantandisincreasedwithanincreasetotherollrate;therollingmotionisnotlinear.Thisimplies9thatthevariationoftherollrateisnotlinear;andthereisanangularrotationaboutx-axis.However,untiltheresistingmomentagainsttherollingmotionisequaltotheailerongeneratedaerodynamicrollingmoment;theaircraftwillexperienceanangularaccelerationaboutx-axis.Soonafterthetworollingmomentsareequal,theaircraftwillcontinuetorollwithaconstantrollrate(Pss).Thesteady-statevalueforrollrate(Pss)isobtainedbyconsideringthatthefactthatwhentheaircraftisrollingwithaconstantrollrate,theailerongeneratedaerodynamicrollingmomentisequaltothemomentofaircraftdragintherollingmotion.LA=DDRyD(12.34)Combiningequations12.14,12.15,and12.16,theaircraftdragduetotherollingmotionisobtainedas:DR=12r(PyD)2(Sw+Sht+Svt)CDR(12.35)Insertingtheequation12.35intoequation12.34yields:LA=12r(PyD)2(Sw+Sht+Svt)CDRyD(12.36)Solvingforthesteady-staterollrate(Pss)resultsin:Pss=2LAr(Sw+Sht+Svt)CDRyD3(12.37)Ontheotherhand,theequation12.32issimplyadefinitemathematicalintegration.Thisintegrationmaybemodeledasthefollowinggeneralintegrationproblem:y=k2xdxx+a2Accordingto20,thereisaclosedformsolutiontosuchintegrationasfollows:(12.38)y=k12ln(x2+a2)(12.39)Theparameterskandaareobtainedbycomparingequation12.38withequation12.32.ry(Sw+Sht+Svt)CDRk=3D2Ixx(12.40)a2=(12.41)(Sw+Sht+Svt)CDyDV2SClb3RHence,thesolutiontotheintegrationinequation12.32isdeterminedas:11lnP2+3F1=IxxryD3(Sw+Sht+Svt)CDRPssV2SClb(Sw+Sht+Svt)CDRyD0(12.42)Applyingthelimits(from0toPss)tothesolutionresultsin:ry(Sw+Sht+Svt)CDRF1=3DIxx2ln(Pss)(12.43)Recallthatwearelookingtodetermineaileronrollcontrolpower.Inanotherword,itisdesiredtoobtainhowlongittakes(t2)tobanktoadesiredbankanglewhenaileronsaredeflected.Thisdurationtendstohavetwoparts:1.Theduration(tss)thattakesanaircrafttoreachthesteady-staterollrate(Pss),2.Thetime(DtR)torolllinearlyfromFsstoF2(SeeFigure12.14).t2=tss+DtRwhere(12.44)DtR=F2-F1Pss(12.45)F1=Fo+12ComparingFigures12.13and12.14indicatesthatt1=tss.Thetime(tss)thattakesanaircrafttoachieveasteady-staterollrateduetoanailerondeflectionisafunctionofangularacceleration(P).Basedonclassicaldynamics,thisacceleratedrollcanbeexpressedas:Ptss(12.46)2Itisassumedthattheaircraftisinitiallyatawing-levelflightcondition(i.e.Fo=0).Hence:t1=tss=2F1(12.47)PwhereF1isdeterminedfromequation12.43.Inaddition,inanacceleratedrollingmotion,therelationshipbetweenfinalrollrate(P1)andinitialrollrate(Po)isafunctionoftherateofrollrate(P)andthefinalbankangle(F1).Basedonclassicaldynamics,anacceleratedrollingmotioncanbeexpressedas:P12-Po2=2PF1(12.48)Itisassumedthattheaircraftisinitiallyatawing-levelflightcondition(i.e.Po=0)andthenewrollrateisthesteady-staterollrate(i.e.P1=Pss).Thus:P=Pss22F1(12.49)wherePssisdeterminedfromequation12.45.11Bankangle(deg)freqtreqTime(sec)Figure12.6.BankangleversustimeForaGAandtransportaircraft,thetimetoreachthesteadystaterollingmotion(t1)islong(morethantenseconds).Thus,theapplicationofequations12.48and12.49isoftennotneededforailerondesign,sincetherollrequirementiswithinafewseconds.However,forafighteraircraftandmissile,therollingmotion(SeeFigure12.15)isveryfast(thetimet1iswithinafewseconds),sotheapplicationofequations12.48and12.49isusuallyneededforailerondesign.Forthisreason,whenthebankangle(F1)correspondingtosteadystaterollrate(Pss)isbeyond90degrees,theequation12.46servesastherelationshipbetweentherequiredtimetoreachadesiredbankangle.Therefore,thedurationrequired(treq)toachieveadesiredbankangle(Fdes)willbedeterminedasfollows:t2=2Fdes(12.50)PTheequationsandrelationshipsintroducedanddevelopedinthissectionprovidethenecessarytoolstodesigntheailerontosatisfytherollcontrolrequirements.Table12.12addressesthemilitaryaircraftrollcontrolrequirements;foracivilaircraft,itissuggestedtoadoptasimilarlistofrequirements.Tohavethegreatestrollcontrolbyailerontoproducearollingmoment,considertheaileronoutboardofthewingtowardwingtip.Thereforeflapwillbeconsideredattheinboardofthewing.Thisapproachwillresultinthesmallest,lightestandmosteconomicalaileronsurfaces.TheailerondesigntechniqueandthedesignprocedurewillbepresentedinSection2.4.3.AileronDesignConstraintsAnydesignproblemintheengineeringdisciplineisusuallylimitedbyvariousconstraintsandtheailerondesignisnoexception.Inthissection,anumberofconstraintsontheailerondesignwillbeintroduced.1.AileronReversalAnumberofaircraftwhenflyingneartheirmaximumspeedaresubjecttoanimportantaero-elasticphenomenon.Norealstructureisideallyrigid;andithasstaticanddynamicflexibility.Wingsareusuallyproducedfromaerospacematerialssuchasaluminumandcompositematerialsandhavestructureswhichareflexible.Thisflexibilitycausesthewingnottobeabletomaintainitsgeometryandintegrityespeciallyinhighspeedflightoperations.Thisphenomenonwhichisreferredtoasaileronreversalnegativelyinfluencestheaileroneffectiveness.Considertheright-sectionofaflexiblewingwithadownwarddeflectedailerontocreateanegativerollingmoment.Atsubsonicspeeds,theincrementaerodynamicloadduetoailerondeflectionhasacentroidsomewherenearthemiddleofthewingchord.Atsupersonicspeeds,thecontrolloadactsmainlyonthedeflectedaileronitself,andhencehasitscentroidevenfarthertotherear.Ifthisloadcentroidisbehindtheelasticaxisofthewingstructure,thenanose-downtwist(atwist)ofthemainwingsurface(aboutyaxis)results.Thepurposeofthisdeflectionwastoraisetheright-wingsection.However,thewingtwistreducesthewingangleofattack,andconsequentlyareductionoftheliftontheright-sectionofthewing(Figure12.16).Inextremecases,thedown-liftduetoaero-elastictwistwillexceedthecommandedup-lift,sotheneteffectisreversed.Thischangeintheliftdirectionwillconsequentlygenerateapositiverollingmoment.Thisundesiredrollingmomentimpliesthattheaileronhaslostitseffectivenessandtherollcontrolderivative;CldAhaschangeditssign.Suchphenomenonisreferredtoasaileronreversal.Thisphenomenonposesasignificantconstraintonailerondesign.Inaddition,structuraldesignofthewingmustexaminethisaeroelasticityeffectofailerondeflection.Theaileronreversaloftenoccursathighspeeds.Mosthighperformanceaircrafthaveanaileronreversalspeedbeyondwhichtheaileronslosetheireffectiveness.TheF-14fighteraircraftexperiencesaileronreversalathighspeed.atwistdAa.Anidealanddesiredaileronb.AnaileronwithaileronreversalFigure12.7.Aileronreversal13dAClearly,suchaileronreversalisnotacceptablewithintheflightenvelope,andmustbeconsideredduringdesignprocess.Anumberofsolutionsforsuchproblemare:1.Makingthewingstiffer,2.Limittherangeofailerondeflectionsathighspeed,3.Employingtwosetsofailerons;onesetatinboardwingsectionforhighspeedflight,andonesetatoutboardwingsectionforhighspeedflight,4.Reducetheaileronchord,and5.Usingspoilerforrollcontrol,6.Movingtheaileronstowardwinginboardsection.ThetransportaircraftBoeing747hasthreedifferenttypesofrollcontroldevice:inboardailerons,outboardailerons,andspoilers.Theoutboardaileronsaredisabledexceptinlow-speedflightswhentheflapsarealsodeflected.Spoilersareessentiallyflatplatesofabout10-15%chordlocatedjustaheadoftheflaps.Whenspoilersareraised,theycauseaflowseparationandlocallossoflift.Thus,toavoidrollreversalwithintheoperationalflightenvelope,thewingstructuremustbedesignedwithsufficientstiffness..AdverseYawWhenanairplaneisbankedtoexecuteaturn,itisdesiredthataircraftyawsandrollssimultaneously.Furthermore,itisbeneficialtohavetheyawingandrollingmomentsinthesamedirection(i.e.botheitherpositiveornegative).Forinstance,whenanaircraftistoturntotheright,itshouldberolled(aboutx-axis)clockwiseandyawed(aboutz-axis)clockwise.Insuchaturn,thepilotwillhaveahappyandcomfortablefeeling.Suchyawingmomentisreferredtoaspro-verseyaw,andsuchturnisaprerequisiteforacoordinatedturn.Thisyawkeepstheaircraftpointingintotherelativewind.Ontheotherhand,iftheaircraftyawsinadirectionoppositetothedesiredturndirection(i.e.apositiveroll,butanegativeyaw);pilotwillnothaveadesirablefeelingandaircraftturnisnotcoordinated.Thisyawingmomentisreferredtoasadverseyaw.Whenaturnisnotcoordinated,theaircraftwilleithersliporskid.Toseewhyandhowtheseturnsmayhappen,seeFigure12.17wherethepilotisplanningtoturntotheright.Forsuchagoal,thepilotmustapplyapositiveailerondeflection(i.e.left-ailerondownandright-aileronup).Theliftdistributionoverthewinginacruisingflightissymmetric;i.e.theright-wing-sectionliftandtheleft-wing-sectionliftarethesame.Whentheleftaileronisdeflecteddownandrightaileronisdeflectedup,theliftdistributionvariessuchthattheright-wing-sectionliftismorethanleft-wing-sectionlift.Suchdeflectionscreateaclockwiserollingmoment(Fig.12.17a)asdesired.However,theailerondeflectionsimultaneouslyalterstheinduceddragofrightandleftwingdifferently.Recallthatwingdragcomponentsoftwoparts:zero-liftdrag(Do)andinduceddrag(Di).Thewinginduceddragisafunctionofwingliftcoefficient(2CDi=KCL).Sincetheright-wing-sectionlocalliftcoefficientishigherthantheleft-wing-sectionlocalliftcoefficient,theright-wing-sectiondragishigherthantheleft-wing-sectiondrag.Thedragisanaerodynamicforceandhasanarmrelativetothe14aircraftcenterofgravity.Thedragdirectionisrearward,sothiswing-drag-coupleisgeneratinganegative(SeeFig.12.17b)yawingmoment(i.e.adverseyaw).Thus,iftherudderisnotdeflectedsimultaneouslywithailerondeflection,thedirectionoftheaileron-generatedrollingmomentandthewing-draggeneratedyawingmomentwouldnotbecoordinated.Thus,whenapilotdeflectsaconventionalailerontomakeaturn,theaircraftwillinitiallyyawinadirectionoppositetothatexpected.DLright+dADDrighta.Frontview(positiveroll)VcgDLleft+dADDleftb.Down-view(negativeyaw)Figure12.8.AdverseyawduetowingdragThephenomenonofadverseyawimposesaconstraintontheailerondesign.Toavoidsuchanundesirableyawingmotion(i.e.,adverseyaw),thereareanumberofsolutions;fourofwhichareasfollows:1.Employasimultaneousaileron-rudderdeflectionssuchthattoeliminatetheadverseyaw.Thisrequiresaninterconnectionbetweenaileronandrudder.2.Differentialailerons;i.e.up-deflectionoftheaileroninonesideisgreaterthanthedown-deflectionoftheotheraileron.Thiscausesequalinduceddraginrightandleftwingduringaturn.3.EmployFriseaileroninwhichtheaileronhingelineishigherthantheregularlocation.4.Employspoiler.BothFriseaileronandspoilerarecreatingawingdragsuchthebothwing-sectionsdragsarebalanced.MostCessnaaircraftuseFriseailerons,butmostPiperaircraftemploydifferentiallydeflectedailerons.Thecriticalconditionforanadverseyawoccurswhentheairplaneisflyingatslowspeeds(i.e.highliftcoefficient).Thisphenomenonmeans15thatdesignermustconsidertheapplicationofoneorcombinationoftheabove-mentionedtechniquestoeliminateadverseyaw..FlapThewingtrailingedgeinaconventionalaircraftisthehomefortwocontrolsurfaces;oneprimary(i.e.aileron),andonesecondary(i.e.trailingedgehighliftdevicesuchasflap).Astheaileronandtheflaparenexttoeachotheralongthewingtrailingedge,theyimposeaspanlimitononeanother(Fig.12.16).Thebalancebetweenaileronspan(ba)andflapspan(bf)isafunctionofthepriorityofrollcontroloverthetake-off/landingperformance.Toimprovetherollcontrolpower,theaileronsaretobeplacedontheoutboardandtheflapontheinboardpartofthewingsections.Theapplicationofhighliftdeviceappliesanotherconstraintontheailerondesignwhichmustbedealtwithintheaircraftdesignprocess.Thespanwiseextentofailerondependsontheamountofspanrequiredfortrailingedgehighliftdevices.Ingeneral,theouterlimitoftheflapisatthespanwisestationwheretheaileronbegins.Theexactspanneededforaileronsprimarilydependoftherollcontrolrequirements.Alowspeedaircraftusuallyutilizesabout40%ofthetotalwingsemispanforailerons.Thismeansthatflapscanstartatthesideofthefuselageandextendtothe60%semispanstation.However,withtheapplicationofspoilers,theaileronsaregenerallyreducedinsize,andtheflapsmayextendtoabout75%ofthewingsemispan.Furthermore,ifasmallinboardaileronisprovidedforgentlemaneuvers,theeffectivespanoftheflapsisreduced.Ifthetake-off/landingperformanceisofhigherimportanceintheprioritylist,trytodevoteasmallspantoaileron;sothatalargespancanbeoccupiedbypowerfulflaps.Thisinturnmeanslowerstallspeedandmoresafety.Ontheotherhand,ifrollcontrolhashigherprioritythanthetake-off/landingperformance,theaileronsshouldbedesignedbeforetheflapsaredesigned.Duetooftheimportanceoftherollcontrolinafighteraircraft,spanoftheflapsmustbeselectedasshortaspossible,sothatthespanoftheaileronislongenough.Therefore,inafighteraircraft,itisadvisedtodesigntheaileronpriortoflapdesign.Ontheotherhand,inthecaseofcivilGAandtransportaircraft,itisrecommendedtodesignflapfirst,whileinthecaseofafighteraircraft,designaileronfirst..WingRearSparAnotherailerondesignconstraintinaconventionalaircraftisappliedbythewingrearspar.Aileronneedsahingelinetorotateaboutandtoprovidetheaileronwithasufficientfreedomtooperate.Tohavelighterandalesscomplicatedwingstructure,itisadvisedtoconsiderthewingrearsparasthemostforwardlimitfortheaileron.Thismaylimittheaileronchord;butatthesametime,improvesthewingstructuralintegrity.Inaddition,it16isstructurallybettertohavethesamechordforaileronandflaps.Thisselectionresultsinalighterstructureandallowstherearspartoholdbothflapandaileron.Thereforetheaileron-to-wingattachmentthroughtherearspar(SeeFig.12.18)isconsideredasbothaconstraint,andatthesametime,anattachmentpoint.MainSparRearSparAWingFlapAileronTipWingtrailingedgebf/2Abai/2SectionA-ATop-viewofthewingFigure12.9.Flap,aileronandrearspar.AileronStallWhenaileronsaredeflectedmorethanabout20-25degrees,flowseparationtendstooccur.Thus,theaileronswilllosetheireffectiveness.Furthermore,closetowingstall,evenasmalldownwardailerondeflectioncanproduceflowseparationandlossofrollcontroleffectiveness.Topreventrollcontroleffectiveness,itisrecommendedtoconsidertheaileronmaximumdeflectiontobelessthan25degrees(bothupanddown).Hence,themaximumailerondeflectionisdictatedbytheaileronstallrequirement.Table12.19providesatechniquetodeterminethestallangleofaliftingsurface(e.g.wing)whenitscontrolsurface(e.g.aileron)isdeflected..WingtipDuetoaspanwisecomponentofairflowalongthewingspan,thereisatendencyfortheflowtoleakaroundthewingtips.Thisflowestablishesacirculatorymotionthattrailsdownstreamofthewing.Thus,atrailingvortexiscreatedateachwingtip.Toconsidereffectsofvortexflowatthetipofthewing,spanoftheaileronsmustnotruntowardwingtip.Inanotherword,somedistancemustexistbetweenouteredgeoftheaileronandtipofthewing(SeeFig12.16).1712.4.4.StepsofAileronDesignInSections12.4.1through12.4.3,aileronfunction,designcriteria,parameters,governingrulesandequations,formulation,designrequirementshavebeendevelopedandpresented.Inaddition,Section12.3introducestherollcontrolandlateralhandlingqualitiesrequirementsforvariousaircraftandflightphases.Inthissection,ailerondesignproceduresintermsofdesignstepsareintroduced.Itmustbenotedthatthereisnouniquesolutiontosatisfythecustomerrequirementsindesigninganaileron.Severalailerondesignsmaysatisfytherollcontrolrequirements,buteachwillhaveauniqueadvantagesanddisadvantages.Basedonthesystemsengineeringapproach,theailerondetaildesignbeginswithidentifyinganddefiningdesignrequirementsandendswithoptimization.Thefollowingistheailerondesignstepsforaconventionalaircraft:1.Layoutdesignrequirements(e.g.cost,control,structure,manufacturability,andoperational)2.Selectrollcontrolsurfaceconfiguration3.Specifymaneuverabilityandrollcontrolrequirements4.Identifytheaircraftclassandcriticalflightphaseforrollcontrol5.Identifythehandlingqualitiesdesignrequirements(Section12.3)fromresourcessuchasaviationstandards(e.g.Table12.12).Thedesignrequirementsprimarilyincludethetime(treq)thattakesanaircrafttorollfromaninitialbankangletoaspecifiedbankangle.ThetotaldesiredbankangleisdenotedasFdes.6.Specify/Selecttheinboardandoutboardpositionsoftheaileronasafunctionofwingspan(i.e.bai/bandbao/b).Iftheflapsarealreadydesigned,identifytheoutboardpositionoftheflap;thenconsidertheinboardlocationoftheailerontobenexttotheoutboardpositionoftheflap.7.Specify/Selecttheratiobetweenaileron-chordtothewing-chord(i.e.Ca/C).Aninitialselectionfortheaileronleadingedgemaybeconsideredasthenexttothewingrearspar.8.Determineaileroneffectivenessparameter(ta)fromFigure12.12.9.Calculateaileronrollingmomentcoefficientderivative(CldA).Youmayusereferencessuchas19orestimatethederivativebyemployingequation12.23.10.Selectthemaximumailerondeflection(dAmax).Atypicalvalueisabout25degrees.11.Calculateaircraftrollingmomentcoefficient(Cl)whenaileronisdeflectedwiththemaximumdeflection(equation12.13).Bothpositiveandnegativedeflectionswillservethesame.12.Calculateaircraftrollingmoment(LA)whenaileronisdeflectedwiththemaximumdeflection(equation12.10)13.Determinethesteady-staterollrate(Pss)employingequation12.37.14.Calculatethebankangle(F1)atwhichtheaircraftachievesthesteadystaterollrate(equation12.43)1815.Calculatetheaircraftrateofrollrate(P)thatisproducedbytheaileronrollingmomentuntiltheaircraftreachesthesteady-staterollrate(Pss)byusingequation12.49.16.Ifthebankangle(F1)calculatedinstep14isgreaterthanthebankangle(Freq)ofstep5,determinethetime(t)thattakestheaircrafttoachievethedesiredbankangleusingequation12.50.Thedesiredbankangleisdeterminedinstep5.17.Ifthebankangle(F1)calculatedinstep14islessthanthebankangle(Freq)ofstep5,determinethetime(t2)thattakestheaircrafttoreachthedesiredbankangle(F2orFreq)usingequations12.44and12.45.18.Comparetherolltimeobtainedinstep16or17withtherequiredrolltime(treq)expressedinstep5.Inorderfortheailerondesigntobeacceptable,therolltimeobtainedinstep16or17mustbeequalorslightlylongerthantherolltimespecifiedinstep5.19.Ifthedurationobtainedinstep16or17isequallongerthantheduration(treq)statedinstep5,theailerondesignrequirementhasbeenmetandmovetostep26.20.Ifthedurationobtainedinstep16or17isshorterthantheduration(treq)statedinstep5,theailerondesignhasnotmettherequirement.Thesolutionis;eithertoincreasetheaileronsize(aileronspanorchord);ortoincreasetheaileronmaximumdeflection.21.Iftheailerongeometryischanged,returntostep7.Iftheaileronmaximumdeflectionischanged,returntostep10.22.Incasewhereanincreaseinthegeometryofailerondoesnotresolvetheproblem;theentirewingmustberedesigned;ortheaircraftconfigurationmustbechanged.23.Checkaileronstallwhendeflectedwithitsmaximumdeflectionangle.Ifaileronstalloccurs,thedeflectionmustbereduced.24.Checkthefeaturesofadverseyaw.Selectasolutiontopreventit.25.Checktheaileronreversalathighspeed.Ifitoccurs;eitherredesigntheaileron,orreinforcethewingstructure.26.Aerodynamicbalance/massbalanceifnecessary(Section12.7)27.Optimizetheailerondesign28.Calculateaileronspan,chord,area,anddrawthefinaldesignfortheaileron12.8.1.AileronDesignExampleExample12.4Problemstatement:Designtherollcontrolsurface(s)foraland-basedmilitarytransportaircrafttomeetrollcontrolMIL-STDrequirements.Theaircrafthasaconventionalconfigurationandthefollowinggeometryandweightcharacteristics:mTO=6,500kg,S=21m2,AR=8,l=0.7,Sh=5.3m2,Sv=4.2m2,Vs=80knot,CLaw=4.51/rad,Ixx=28,000kg.m219ClassFlightphaseLevelofacceptabilityIIC1Furthermore,thecontrolsurfacemustbeoflowcostandmanufacturable.Thehighliftdevicehasbeenalreadydesignedandtheoutboardflaplocationisdeterminedtobeat60%ofthewingsemispan.Thewingrearsparislocatedat75%ofthewingchord.Solution:Step1:Theproblemstatementspecifiedthemaneuverabilityandrollcontrolrequirementstocomplywithmilitarystandards.Step2:Duetotheaircraftconfiguration,simplicityofdesign,andadesireforalowcost,aconventionalrollcontrolsurfaceconfiguration(i.e.aileron)isselected.Step3:Hence,Table12.12willbethereferencefortheailerondesignwhichexpressestherequirementasthetimetoachieveaspecifiedbankanglechange.Step4:BasedonTable12.5,aland-basedmilitarytransportaircraftwithamassof6,500kgbelongstoClassII.Thecriticalflightphaseforarollcontrolisatthelowestspeed.Thus,itisrequiredthattheaircraftmustberollcontrollableatapproachflightcondition.AccordingtoTable12.6,theapproachflightoperationisconsideredasaphaseC.Todesigntheaileron,levelofacceptabilityof1isconsidered.Therefore:Step5:TherollcontrolhandlingqualitiesdesignrequirementisidentifiedfromTable12.12-bwhichstatesthattheaircraftinClassII,flightphaseCforalevelofacceptabilityof1isrequiredtobeabletoachieveabankangleof30oin1.8seconds.Step6:Accordingtotheproblemstatement,theoutboardflaplocationisat60%ofthewingspan.Sotheinboardandoutboardpositionsoftheaileronasafunctionofwingspan(i.e.bai/bandbao/b)aretentativelyselectedtobeat70%and95%ofthewingspanrespectively.Step7:Thewingrearsparislocatedat75%ofthewingchord,sotheratiobetweenaileron-chordtothewing-chord(i.e.Ca/C)istentativelyselectedtobe20%.Step8:21Theaileroneffectivenessparameter(ta)isdeterminedfromFigure12.12.Sincetheaileron-to-wingchordratiois0.2,sotheaileroneffectivenessparameterwillbe0.41.Step9:Theaileronrollingmomentcoefficientderivative(CldA)iscalculatedemployingequation12.22.2l-13CldA=2CLawtCry2Sb2+y3byiyo(12.23)Wefirstneedtodeterminewingspan,wingmeanaerodynamicchord,andwingrootchord.AR=b2Sb=SAR=2110b=14.49m(5.19)AR=bCC=bAR=14.4910C=1.449m(5.18)1.449=CrCr=1.604mC=23Cr1+l+l21+l231+0.8+0.821+0.8(5.26)Theinboardandoutboardpositionsoftheaileronasafunctionofwingspanareselectedtobeat70%and90%ofthewingspanrespectively.Therefore:yi=0.7b2=0.714.492=5.072myo=0.95b2=0.9514.492=6.883mPluggingthevaluesfortheparametersinequation12.23isasfollows:20.8-135.0722CldA=24.50.411.6046.88322114.492+6.883-314.492+5.072314.4920.8-13whichyields:CldA=0.1761radStep10:Amaximumailerondeflection(dAmax)of20degreesisselected.Step11:Theaircraftrollingmomentcoefficient(Cl)whenaileronisdeflectedwiththemaximumdeflectionis:21Cl=CldAdA=0.1762057.3=0.061(12.13)
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