AircraftSchoolofAeronauticsandAstronauticsShanghaiJiaoTongUniversityOverviewof RefinedweightThrust/WeightratioandwingLandinggearandAircraftPowerStabilityandLoads,materialsandstructures14\15Performance(a,b)AviationMilitaryaircraftdesign–DesignAdvanceddesigntopics(flighttests,retrofit,RoleofperformanceBasicconceptsandPerformanceanalysisfordifferentsegmentsinatypicalflightmission,includingTakeoffSteadylevelSteadyclimbinganddescendingLevelturningGlidingLandingAircraftperformanceanalysistreataircraftasapointmass,notarigidbodyasisdoneinaircraftstabilityAircraftperformancecalculationformsanimportantpartofconceptualdesign,whichlinksdesignparameterswithperformancerequirementsAerodynamicAerodynamicEngineRoleofPerformanceThroughouttheaircraftlifecyclefrommanufacture,flighttesttoProjectdesignstage→requirementanalysis,enginedata(thrust,SFC),etcDetaileddesign→windtunneldata,CFD,CADdrawings,certificationdata,operationalmanual,flighttestplanManufacture→validationofdesign,fullsetoftechnicalmanualsFlighttests→Crossvalidationwithwindtunneldata,certificatedocuments,faultanalysisInputs/OutputsforPerformanceCalculationsAerodynamicforcesfromengineeringestimationmethods/CFD/wingtunneldataEnginedatafromengineWeightestimationincludingC.G.locationsfrominitialsizingTakeoffandinitialClimbtooperatingApproachandPayloadrangeBasicBasicConcepts–????:Groundspeed,theaircraftspeedrelativetotheground.ItcalculatedfromTASandwindspeedFortakeoffandlanding,headwindtakeForclimb,cruise,anddescend,headwindtake----Groundspeed,trueairspeedand AirspeedasafunctionofBasicConcepts– In±±??????????????????????????= ±????????????????????????±??????????????????????≡???????????????????????????????????????????BasicConcepts–(Geometry)altitude(??)–theabsolutealtitudeaboveseaPressurealtitude(????),theISA(geometry)altitudewiththesamepressurelevelForahotday,lowerthangeometryForcoldday,higherthangeometry??=??=???????=???????=

1?2.25577× ??1?6.87559× ????

11

?????????BasicEquationsofXd,Yd, yrxzBasicEquationsofMotionEquationsofmotioninflightpathcoordinateBody γDHorizontal TypicalFlightProfileofaCivilJet

10000

15001500

M= 20000

爬 爬 巡

進場與滑降

輪檔時間Take-offTakeoffVs:stallspeed(intake-offV1:criticalpowerfailureVR:rotationspeed,thiscanequalVmu:minimumunstickspeed,VRmaynotbesufficienttoliftoffduetolimitonrotationangleVLOF:lift-offspeed,theaircraftbecomesV2:take-offclimbspeed,achievedat35ftscreenTake-off Availabletake-offTake-offOptionswithEngineTake-off-allenginesoperatingTDMdVdt RMgTD(MgTake-off-allenginesoperatingGroundrolldistancecanbecomputedbyApproximationcanbeassumedT

5 5VWstatic40.020.01cL,max,t

DW

??isBPRoftheturbofanTake-offallenginesoperatingTransitionflightTake-off-allenginesoperating TransitiontoAircraftacceleratefromVLOFtoSimpleestimationcanbemadebyassumingFlyingalonganLMgcosMV rV

/[g(n ScreenheightTake-offDistance-allenginesoperating(IV)Take-offdistance-allenginesoperating(V)ClimbaftertransitiontoscreenClimbdistance:thegrounddistancefromtheendoftransitiontothescreenheightwhere,htistheheightattheendoftransition,γcisthebestclimbangleTotaldistancefortake-offisthesumofgroundroll,transition,andclimbdistanceTake-offdistance–withoneenginefailedBalancedfieldDefinition:thefieldlengthwhen“accelerate-go”distanceisequaltothe“accelerate-stop”SteadyClimb&DescendTypicalClimbProfileandZ0

constantMachnumberairspeedclimbairspeedclimb ClimbcarriedoutmainlyatconstantequivalentairspeedInitialClimbto1500ftafterTakeoffInitialclimbistypicallydividedintofourAirworthinessdemandscertainclimbgradientwithoneenginefailurefortwinengineorfourengineaircraft–refertocertificationcodeTake-offclimbperformanceisusuallydefinedbysecondsegmentperformancerequirementwhichisthemostcriticalInitialClimbto1500ftafterTakeoffClimbrate(verticalvelocity)canbeobtainedbyanalyzing WTherefore,theclimbrateisrelatedtothrust,drag,andweightoftheaircraftThrustis85%ofthestaticDragofthebasicTheasymmetricdragduetoafailedwindmilldrag,Additionaltrimdrag,5%ofthebasicprofileClimbPerformance:furtherGivenaclimb

=????????+?????????1+

?? BestrateofclimbandBestangleofBestrateofclimbprovidesthemaxclimbBestangleofclimbprovidesthemaxclimbTimetoclimbandfueltoTimetoclimeacertaindistanceandcorrespondingfuelusedcanbecalculatedas????

??????=Integrationorapproximationcanbeusedtocalculatefrom??1toSteadyLevelEquationsforLevelLαLαVDHorizontal TW RateofchangeofaircraftT=D+Wsinγ=DL=Wcosγ=W

dW

SteadyLevelCruiseAnalysisforunacceleratinglevel

??=??= ??=??= ?? and

=

=

TheseequationscanbeusedinfurtherMinimumcruisethrustrequirementforjetMinimumcruisepowerrequirementforpropellerThrustrequiredforlevelflightjetMinimumthrustforgivenaircraftweightcanbefoundfrom

?? =????????0? = ??12??min??????????? and?????????????????????AtAtanygivenweight,theaircraftcanbeflownattheoptimalliftcoefficientforminimumdragbyvaryingvelocityorairdensityQuestionQuestionone:WhatisformulafortotalThrustrequiredforlevelflightpropellerMinimumpowerrequiredforpropelleraircraftcanbederivedbyfirstcalculatethepower??=????= ????3??????0+

?? 2 2Similartothederivationonprevious

22 ????2??????0? =22

????2= and=Questionone:WhatisformulafortotalQuestionQuestiontwo:Willthetotaldragbehigherthanflyingatminthrust?CalculationsonprevioustwoslidesareCalculationsonprevioustwoslidesarebasedontwoassumptions????0and??areconstantwith??BreguetRangeRateofweight dW

SFCTSFCDWsin

SFC

SFC

L dW

R L aML R dx0

SFC1

<<1,becauseBreguetEquations-DuringSFCremainsroughlyconstant(0.5ConstantL/DalsoroughlyCruisingintropopause,a= W2aMLD WR dx

RaMLD 1

2PayloadRange Rangeisrelatedtofuel/weightaML

W aML

WFR

logW2

log1W 1

1MaximumMaximumMaximumfuel MaximumtakeoffRangeMoreAnalysison Minimumthrustlevel= and=??=???? + =???? +Minimumpowerlevel= and=??=???? + =???? +Thevelocityforminimumpoweris~0.76timesthevelocityforminimumthrustcruise,whileliftcoefficientis~73%higherThevelocityforminimumpoweris~0.76timesthevelocityforminimumthrustcruise,whileliftcoefficientis~73%higherforminimumpowerflight.Buttotaldragforminpowerisnottwicethatformindrag!LevelTurningAnalysisofLevel Turningrateorrateofturning(ROT)DefinedasradialaccelerationdividedbythevelocityAngularForceVerticalliftcomponentequalsLoadfactorisThereforeturning= =?? ?? AnalysisofLevelTurningTurning??

–SmallerVandhighergivessmallerTwotypesofturning,dependsontimeperiodInstantaneous,forshortperiodoftimeSustainedturning,foranextendedperiodoftimeInstantaneousInstantaneousturn–aircraftisallowedtoslowdownduringtheturnTheloadfactor??willonlybelimitedbythemaximumliftcoefficient(stall)orstructuralstrengthCornerspeedisimportantfordogfightDragisgreaterthanthrusthigherthanInsustainedturning,theaircraftisnotallowedtoslowdownorlosealtitude,whichimpliesthat??=??and??=??=??=

with????

tosolvethisasKandnarebothfunctionsoftheCLtosolvethisasKandnarebothfunctionsoftheCL??ThisgivestheloadfactorSustainedTurningInasustainedturninggivenflightconditions(speed,altitude,payload),nMaximumnMaximumncanbeachievedwithminFromminimumdraglevelflightanalysis,there??min and?????????? Themaximumsustained-turnloadfactorcanbesolved??=????=

??

??=

GlidingStraightGliding ConditionsforstraightglidingThethrustissettoThedirectionoftheglidingangleis??= ??= =ctan?? HorizontalαGlideGlideratioisdefinedastheratiobetweenhorizontaldistancetravelledandaltitudelostGlideratioisequaltothelift-to-dragMaxglideratiogivesthemaximumrangeforglidingflight,thereforerequiresflyingatmaxL/D–minCD??min and?????????? SinkAnotherparametersofinterestforglidingDeterminethetimethataglidermayremaininthe??2cos3??2cos3??=Vsinγ=sin ????Minimumsinkratecanbeobtainedbyminimizing whichleadsinin=3=00SinkRateandGlide DifferencebetweensinkrateandglideLandingApproachandLandingThelandingphaseissplitintoseveralGroundLandingdistanceisthesumofdistancesrequired Theapproachpathistypicallymadeat3°totheFARcertificationspecifiestheapproachstartsatascreenheightof50ftandendsattheflareheighthFApproachspeedisSAobstacleheighthF/tanhFrAA/Flare–AirAsimplifiedapproachassumesthattheangularaccelerationmaybeignoredTT–D+Wγ=mVdV/dx=(W/2g)dV2/dxL–W=0SaSa=[(W/S)l/(4gρslбCL,lmax)]/[–(D/L)eff+RotationtoTouchGroundRunlOnthesimplestlevel,assumingconstantdeceleration(-a),thedistancecoveredfromVl2to0is V2/2alOnthenextddV/dt=(1/2g)dV2/dx=(T/W)l–(D/W)l–((D/W)l((Fbrake/W)l=mbrake(1-L/W)=mbrake[1–GrounddistancecanbecomputedfromOtherAircraftPerformanceCommonsetofperformanceTurnrate,cornerspeed,loadfactorOtherperformancemeasuresofControlspeedandaltitudePoststallbehavior,60-degreeAOAoperations,forexamplearetypicalfor4thgenerationfightersPerformancewithThrustStoreDynamicMostImportantAircraftPerformanceCharacteristicsCapabilitiesofaircraftcanbemostlyrepresentedMaximumStallingBestingclimbingBestglideRateofMa