Ch.4FlightPerformance

transportaircraftperformance：

take-offperformance起飛性能

climbperformance爬升性能

cruiseperformance巡航性能

descendingperformance下降性能

landingperformance著陸性能

turningperformance盤旋性能

engine-outperformance發(fā)動(dòng)機(jī)失效后性能

stallingperformance失速性能

4.1take-offperformance

Consideranairplanestandingmotionlessattheendofarunway.

Thepilotreleasesthebrakesandpushesthethrottletomaximum

take-offpower,andtheairplaneacceleratesdowntherunway.At

somedistancefromitsstartingpoint,theairplaneliftsintotheair.

4.1.1Forcesactingonanaircraftintake-off

Theforcesactingonanaircraftintake-offareweightW、liftL、

thrustT\dragDandarollingresistanceRcausedbyfriction

betweenthetiresandtheground.Thisresistanceforceisgivenby

thecoefficientofrollingfrictionandthenetnormalforce(W-L)

exertedbetweenthetiresandtheground.

Figure6.14Forcesactingonanairplaneduringtakeoffandlanding.

4.1.2take-offdistance

ThesumofSgandSaisthetotaltake-offdistancefortheairplane.

Figure6.12Illustrationofgrouncrollsg,airbornedistanceS0/andtotaltakeoffdistance.

TheSgiscalledthegroundroll(orsometimesthegroundrun)

whichiscoveredalongtherunwaybeforetheairplaneliftsintothe

air.TheSaisthetake-offdistanceinairborneovertheobstacle

whichisgenerallydefinedtobe50ftformilitaryaircraftand35ftfor

commercialaircraft.

ThegroundrollSgisfurtherdividedintointermediatesegments.

Thesesegmentsaredefinedbyvariousvelocities,asfollows：

o

Figure6.13Intermediatesegmentsofthegroundroll.

l,Vstaiistallingspeed失速速度

2,Vmcgminimumcontrolspeedontheground地面最小可操縱

速度

Thisistheminimumspeedatwhichenoughaerodynamicforce

canbegeneratedontheverticalfinwithrudderdeflectionwhilethe

airplaneisstillrollingalongthegroundtoproduceayawing

momentsufficienttocounteractthatproducedwhenthereisan

enginefailureforamultiengineaircraft.

3,Vmcaminimumcontrolspeedintheair空中最小可操縱速度

Iftheairplanewereintheair(withoutthelandinggearincontact

withtheground),theminimumspeedrequiredforyawcontrolin

caseofenginefailureisslightlygreaterthanVmcgFortheground

rollshowninFig.,VmCaisessentiallyareferencespeed-theairplane

isstillonthegroundwhenthisspeedisreached.

4,Videcisionspeed決斷速度

Thisisthespeedatwhichthepilotcansuccessfullycontinuethe

take-offeventhoughanenginefailure(inamultiengineaircraft)

wouldoccuratthatpoint.Thisspeedmustbeequaltoorlargerthan

Vmcginordertomaintaincontroloftheairplane.Ifanenginefails

beforeViisachieved,thetake-offmustbestopped.Ifanengine

failsafterViisreached,thetake-offcanbeachieved.

5,VRtake-offrotationalspeed起飛抬前輪速度

Atthisvelocity,thepilotinitiatesbyelevatordeflectionarotation

oftheairplaneinordertoincreasetheangleofattack,henceto

increaseCL.Clearly,themaximumangleofattackachievedduring

rotationshouldnotexceedthestallingangleofattack.

Actually,allthisisneededisanangleofattackhighenoughto

producealiftatthegivenvelocitylargerthantheweight,sothatthe

airplanewillliftofftheground.However,eventhisangleofattack

maynotbeachievablebecausethetailmaydragbytheground.

(Groundclearanceforthetailafterrotationisanimportantdesign

featurefortheairplane,imposedbytake-offconsiderations.)

6,Vmuminimumunstickspeed最小松桿速度

Iftherotationoftheairplaneislimitedbygroundclearancefor

thetail,theairplanemustcontinuetoacceleratewhilerollingalong

thegroundafterrotationisachieved,untilahigherspeedisreached

whereindeedtheliftbecomeslagerthanweight.Thisspeediscalled

theminimumunstickspeed.

7,VLOliftoffspeed起飛速度，離地速度

Forincreasedsafety,theangleofattackafterrotationisslightly

lessthanthemaximumallowablebytailclearance,andtheairplane

continuestoacceleratetoaslightlyhighervelocity,calledtheliftoff

speed,denotedbyVLO.Thisispointatwhichtheairplaneactually

liftsofftheground.Thetotaldistancecoveredalongthegroundto

thispointisthegroundrollSg.

4.1.3Factorsaffectingtake-offperformance

Thedesignparametershaveanimportanteffectontake-offground

roll.SgdependsonwingloadW/S,thrust-to-weightT/Wand

maximumliftcoefficient(CL)max,theambientdensitypco,wind

andgroundconditions.

SgincreaseswithanincreaseinW/S.

Sgdecreaseswithanincreasein(CL)max.

SgdecreaseswithanincreaseinT/W.

Sgincreaseswithadecreaseinpg.

Sgincreaseswithatailwind,anddecreaseswithaheadwind.

4.2Climbperformance

zooming急躍升

powerrequired需用功率thrustrequired需用推力

poweravailable可用功率thrustavailable可用推力

excesspower富裕功率excessthrust富裕推力

Aclimbisanascendingflightpathatconstantspeed.

Itisusuallyastraightpathbut,sometimes,aclimbingturnis

necessary.

?azoom,whichexchangesspeedforheight.

Anaircraftflyingathighspeed/lowaltitudecanrapidlyconvert

thekineticenergytopotentialenergybyraisingthenoseand

“zooming”.

Inanormalclimbtocruisealtitude,suchtechniquesare

inefficient.Fuelburntintheengineisconvertedintoincreasing

potentialorkineticenergy.

Figure2.3-11Asteadyclimbamia7o°m.

Azoomisanincreaseinaltitudethatexchangingthekinetic

energyofmotionforpotentialenergy,i.e.byconvertingexcess

velocityVtoincreasedaltitude.Azoomisonlyatransientprocess.

?aclimbwheretheaircraftisdrivenupwardbyexcessthrustfrom

theengineandsustainsitsspeedthroughout.

ceiling升限absoluteceiling絕對(duì)升限，理論升限

serviceceiling實(shí)際升限，使用升限

Asteadyclimbisachievedbyconvertingpropulsiveenergy

(thrust)togivealtitude.

Aclimbcanbemaintaineduntilthereductioninthrust,dueto

increasingaltitude,eventuallyreducestherateofclimbtozero.This

isknownastheabsoluteceilingoftheaircraft.Theserviceceilingis

thealtitudewherethemaximumrateofclimbisreducedto100feet

perminute.

typesofclimb

Therearethree(orfour)typesofclimb：

?maximumangleclimb

?maximumrateclimb

?normalclimb

?cruiseclimb

4.2.1Forcesactingonanaircraftinclimb

Figure2.3-12fourforcesinasteadyclimb.

Ifyoumaintainasteadyclimbataconstantindicatedairspeed,the

engine-propellermustsupplysufficientthrusttoovercome：

?thedragattheclimbairspeed;and

?thecomponentoftheweightthatactsnegativelyalongtheclimb

path.

Inaclimbthereisnoacceleration.Theforcesareinequilibrium

andconsequentlytheresultantforceiszero.

Inaclimbthrustisgreaterthantotaldrag;totalliftisslightlyless

thanweight.

???T=D+WxsinQ,L=WxCos0

Astheclimbbecomessteeper,moreandmorethrustisrequired

andlessandlesslift.Inaverticalclimb,whichsomefighterscan

achieve,thethrustbalancesthedragandalloftheweight,thereisno

liftatall.

Wenormallyclimbat5°orless,sothedifferencebetweenliftand

weightissmall.(cos5°=0.996)

4.2.2Maximumrateclimb

Verticalspeediscalledrateofclimb.Rateofclimbisshownin

thecockpitontheverticalspeedindicator(VSI).

Power=workdone/persecond=forcexdistance/persecond

=forcexvelocity=thrustxTAS

VsinO=Vy=V(T-D)/W=(Pa-Pr)/W=富裕功率/W

Papoweravailable(Pa=TxV),

Prpowerrequired(P「=DxV)

Pa-Prexcesspower

IfW=COnSt.,(Vy)max=(Pa-Pr)max/W

Climbingformaximumrateisachievedataspeedwherethereis

maximumexcesspower.

Power

available

Power-Power

required

power

3-3Maximumofclimb

Thegreatertheexcesspower,thelowertheweight,thelowerthe

drag,andthegreaterrateofclimb.

4.2.3Maximumangleclimb

Vsin0=(T-D)/WT-D：excessthrust富裕推力

/.Theangleofclimbdependsdirectlyontheamountofexcess

thrustandtheweight.

?thelowertheweight,thegreatertheangleofclimb.

?thegreaterthethrust,thegreatertheangleofclimb.

?thelowerthedrag,thegreatertheangleofclimb.

Formaximumclimbgradient,theaeroplaneshouldgenerallybe

keptinalow-dragconfiguration.

Cleanlake-oil

(nnflaps).

Figure2.3-13

Climbgradieinrnaybe

lesswiih(lapsextended

Take-ofl

withflaps

extended

Thespeedforthemaximumrateofclimb(Vy)usuallyoccursata

speedsomewherenearthatforthebestlift/dragratio,andis

thereforefasterthanthespeedforthemaximumangleofclimb.

dh=Vydt=Vxsin0dt

dL=VxcosQdt

4.2.4Factorsaffectingclimbperformance

Performanceintheclimb,eitherangleorrateofclimb,will

reducedueto

?reducedthrustandpower;

?increasedweightordrag;

?lowairdensityduetohightemperatureorhigheraltitude;

?inaccurateairspeed(eithertoofastortooslow).

1,temperature

Highambienttemperaturesdecreaseclimbperformance.Ifthe

temperatureishigh,thentheairdensity(p)isless.The

engine-propellerandtheairframewillbothbelessefficient,sothe

performancecapabilityoftheaeroplaneislessonahotday.

2,altitude

Figure2.3-15ClimbperformancedecreaseswithaltitudeuntilzeroROC.

Increasingaltitudedecreasesclimbperformance.Poweravailable

fromtheengine/propellerdecreaseswithaltitude.Theclimb

performance,boththerateandtheangleofclimb,willdecreaseat

altitude.

MAXIMUMRATEOFCLIMB

CONDITIONS:FlapsUpNOTE：Mixtureleanedabove3,000feet(ormaximumrpm.

FullThrollle

PRESSCLIMBRATEOFCUMB-FPM

W日GHT，

ALT1SPEED

LBS

FTKIAS-20?C0℃2t)?C40℃

1,670S.L.67835765700,630

2.OQ066735670600535

4.OOP65635570505445

6,00063535475415355

8.00062440380320265

10,00061340285230175

12；0006024519019585

iisoers

ClimbingIAS(orbestRateofclimbRateo(climb

raleofclimbdecreasesdecreaseswithdecreaseswith

withaltitude."altitudeincrease.temperatureincrease.

Figure2.3-16Atypicalclimbperformancetable.

(mixtureleaned貧油)

3,airspeed

1)flyingtoofast

Ifyouflyfasterthantherecommendedspeed,thereislessexcess

thrustandlessexcesspower.

Correctspeed

Toofast

->Tooslow

Figure2.3-17

Thecorrectclimbspeedforthebestperformance.

2)flyingtooslow

Ifyouflyslowerthantherecommendedspeed,theexcesspower

isreducedand,therefore,therateofclimbisdirectlyreduced.

4,theeffectofwindonclimbperformance

Whenairmoves,theaircraftwilltravelalesserorgreater

horizontaldistance(headwindandtailwindrespectively)inthattime.

Theangleofclimbrelativetotheterrain,issteeperinaheadwind

andisreducedbyatailwind.

4.3Cruiseperformance

4.3.1Forcesactingonanaircraftincruise

36Forcesandmomtnttinlevelflight

liftproducedbythemainplane(wing)CP

weightofthetotalaircraftCG

dragwhichactsrearwardoppositetotheflightpath

thrustproducedbytheengines

Insteady(unaccelerated),straightandlevelflighttheaircraftis

travelinginastraightlineataconstantaltitudeandataconstant

airspeed,totalliftequalstotalweight,andthrustequalstotaldrag.

Theaircraftisinequilibrium.thrust=drag,lift=weight.

Thismeansthatallforcesandmomentsareinbalancethereisno

resultantforcetoaccelerateordecelerateit-norresultantmomentto

changeitsattitudeinpitch,roll,oryaw.

1,pitchingmomentsofthefourforces

,L

CG-J--^?D

T4----------hCP什=^

▼

—Balancing

Rerodynamic

force(moment)

Figure2.3-2

Thetailplanepiovidesthefinalbalancingmomein

couple力偶(thrust/drag,lift/weight)

WheretheCPisbehindtheCG,thelift-weightpairproducesa

nose-downpitchingmoment.

Thethrust-dragpairproducesanose-upornose-downpitching

moment.Thesizeofthismomentissignificantlylessthanthelift-

weightmomentbecauseofasmallmomentarmandsmallforce.

nose-downpitchingmoment低頭俯仰力矩(-)

nose-uppitchingmoment抬頭俯仰力矩(+)

2,balancingmoment-thetailplane

howbalancingthefourforcestoachievepitchingequilibrium

?Highthrustline,

lowdragline;

-nose-downmoment.

?ForwardCG;

-nose-downmoment.

?Tailplanemusthave

downloadtocounteract.

Weight

?Lowthrustline.

highdragline;

-nose-upmoment

?AftCG;

-nose-upmoment.

Drag?Tailplanemusthave

uploadtocounteract.

AGK

Weight

3-7Differingarrangementofforces

Theconventionalaircraftisfittedwithatailplanethatprovidesa

meansofbalancingtheresultsofthefourmainforces.

Thelargedistanceofthetailplanefromthecentreofgravity

(largetailmomentarm)allowstheuseofrelativelysmalltailplane

forcestoachievethenecessaryrestoringmoments.

Thetailplanemaybefixedorvaried.

Mostlargeaircraftshaveavariable-incidencetailplanewithan

attachedelevatorwhichprovidesamuchwiderrangeoftrim

capabilityandgreatercontrolpower.

Variable-incidencetailplanearecommonlyfoundonaircraftsthat

havealargeCGrange,alargespeedrangeandvaryingpitch

moments.

variable-incidence變安裝角，trim配平

3,variationinthebalanceofforcesandmoments

1)variationofspeedinthecruise

Areductionincruisespeedwillrequireanincreaseinangleof

attacktomaintainliftequaltoweight,whichwillresultinaforward

movementoftheCP.

AforwardmovementofCPpositionforaconstantliftwillreduce

themagnitudeofthenose-downpitchingmoment.Sincethedrag

thatresultsfromalowerspeedwillalsochange,thenthetotal

balanceofforceswillchange,requiringanewbalancingmoment

fromthetailplane.

Theresultofchangingspeedinthecruiseistovarythemagnitude

ofthetailplaneforce.

2)variationofweightinthecruise

Inanormalflight,theweightgraduallyreducesasfuelis

burned-off.Iftheaeroplaneistoflylevel,theliftproducedmust

graduallydecreaseastheweightdecreases.Ifthereisasudden

decreaseinweight,say,byhalfadozenparachutistsleapingout,

thentomaintainstraightandlevelflight,theliftmustreducebya

correspondingamount.TheCL(angleofattack)ortheairspeed

mustbereducedsothatlessliftisgenerated.

4-----------------------------------------

Heavy1Lighter

fasteratsamesloweratsameangleo(attack

angleofattack1(reducepowergradually)

W|_---------------_”--

________________________

Figure2.3-3Forthesameangleolattack,alighteraeroplaneinusiUyslower

----------------------.___

L—

tL|

二____----

Heavy-fast1Lighlandsamepower1

lefton-faster

wf_______________

…一W___一-----__________

__---__

Figure2.3-4Samepower-lighteraeroplanehaslowerangleofattackand(lies(aster.

Supposethattheaeroplaneiscruisingataparticularangleof

attack,say,forthebestL/Dratio.Tomaintainthismostefficient

angleofattackastheweightreduces,theairspeedmustbe

reducedtoreducetheliftsothatisstillbalancetheweight.So,ifthe

heightandtheangleofattackaretobekeepconstant,thenthe

airspeedwillhavetobereduced.Thepower(thrust)willbeadjustto

balancethereduceddrag.

adozen一打』2丁parachutist降落傘

leapingout放出

Ifyouwishtokeepthepowerconstantandyouwanttomaintain

heightastheweightdecreases,theliftmustbedecreasedby

reducingtheangleofattack(decreasingtheCL).Thereforethespeed

willincrease.

Ifyouwanttokeepthespeedconstantandmaintainheight,then

astheweightreducesyoumustreducetheliftproduced,andyoudo

thisdecreasingtheangleofattack.

H=const.W[一L1W=L=(1/2)pV2SCtp=const.

a=const.一CL=const.一V](一DJ—T1D=T)

T=const.一a](CLp-Vf(D=T)

V=const.—(CJ)

Sometimestheweightincreasesinflightby,forinstance,the

formationoficeonthestructure.Anincreasedweightwillmeanthat

increasedliftisrequiredtomaintainlevelflight-andonceagainthe

abovediscussionapplies,butinreverse.

Iceonthewings,especiallyontheuppersurfaceneartheleading

edgewillcauseadrastic(急居ij的)decreaseintheefficiency(CL)

ofthewingandasignificantincreaseindrag.

Tomaintaintherecommendedangleofattackfortherequired

cruisemode,alowerspeedmustbeflownforthelower

weight-alternatively,theaircraftmaybeallowedtoslowlyclimb

(cruiseclimb).

3)variationofcentreofgravityposition

DifferentCGpositionwillresultinvariationtothebalanceof

momentsabouttheCG.

AchangeinCGpositionresultsadifferenttailplaneforce.

3-8Changingtailplaneloadwith

momentofcentreofgravity

4)attitudeinlevelflight

Toobtaintherequiredliftatlowspeed,ahighangleofattack

(highCL)isrequired,whileathighspeed,onlyasmallangleof

attack(lowCL)isneeded.

4.3.2Performanceinlevelflight

Thethrustrequiredforsteady,straightandlevelflightisequalto

thedrag(D=T),andsothethrust-requiredcurveisidenticaltothe

dragcurve.

Figure2.3-5

Thrusi-iequiiedcurve(orIliedragcu;vei

Highthrustisrequiredathighspeedstoovercomemainlyparasite

drag(lowangleofattack,lowinduceddrag).

Figure2.3-6Thepowercurve

?Minimumthrustisrequiredatminimumdragspeed(whichisalso

thebestL/Dratiospeed,sinceLisconstantinstraightandlevel

flightandDisatitsminimum).

?Increasedthrustisrequiredatlowspeeds(highangleofattack)

toovercomemainlyinduceddrag.

Power=thrustxtrueairspeed

Wecandevelopapowerrequiredcurvefromthrustrequiredcurve

bymultiplyingthethrustrequired,atanypointonthecurve,byTAS

anythatpointandthenplottingtheresultagainstthesamespeed

scale.Thiswillgiveusthepowerrequiredtomaintainlevelflightat

thatspeed.

1,whatdoesthegraphshow?

，

怎

M

o

d

s

s

<

SlowiAl厚?臂dFast8

曄):-

Figure2.3-7Maximumlevelflightspeed.

?maximumlevelflightspeed

Maximumlevelflightspeedoccurswhenthepoweravailable

fromtheengine-propellermatchesthepowerrequiredtoproduce

enoughthrusttobalancethedragatthehighspeed.

?minimumlevelflightspeed

Theminimumlevelflightspeedisusuallynotdeterminedbythe

powercapabilityofthepowerplant,buttheaerodynamiccapability

oftheaeroplane.

Insteadystraightandlevelflight,theliftmustbalancetheweight.

2

W=L=l/2pVSCL

Lessdenseair

IAS125kil

TAS150ktJ

Figure2.3-9SameIAS(andli(0alahigheraltituderequireshigherTAS.

Asaltitudeisincreased,airdensity(p)decreases.

Onewaytogeneratetherequiredliftandcompensateforthe

decreaseddensity(p)isforthepilottoincreasethetrueairspeedV

sothatthevalueofl/2pV2remainsthesameasbefore.

2,speedstabilityandthedragcurve

1)higherspeeds

Dragor

power

required

straight；

and

level

Airspeed(TAS)18g

Figure2.3-10Speedstability.

Aboveminimumdragspeed,anyminorspeedfluctuationisself

correcting.Thisiscalledspeedstability.

Intheregime,anincreaseinairspeedincreasesthetotaldrag,due

toanincreaseinparasitedragcausingtheaircrafttoslowdown.A

decreaseinairspeeddecreasesthetotaldrag,duemainlytoan

decreaseinparasitedragcausingtheaeroplanetoacceleratebackto

itsoriginalspeed.

Inthenormalairspeedregime,abovetheminimumdragspeed,

thepilotdoesnothavetobeactivewiththethrottlesincethe

aeroplaneisspeedstableand,followinganydisturbance,will

tendtoreturntoitsoriginaltrimmedairspeedwithoutpilotaction.

2)lowerspeeds

Atlowerspeeds(belowminimumdragspeed)itisadifferent

matter.Ifagustcausesairspeedtodecrease,thetotaldragincreases.

Totaldragnowexceedsthrust,causingtheaeroplanetoslowdown

further.

Ifagustcausesairspeedtoincrease,thetotaldragdecreases.Drag

isnowlessthanthrust,causingtheaeroplanetoacceleratefurther

awayfromtheoriginalspeed.Thisiscalledinstability.

4.3.3Maximumrangecruise

Maximumrangeisthegreatestdistancethatcanbeachievedfrom

thefuelavailable.Itshowshowfartheaircraftcantravel

irrespectiveofthetimetaken.

irrespective與...無關(guān)

比航程specificairrange(SAR)

Specificairrange(SAR)isaratioofdistancetofuel

consumption.

SAR=distance/fuelused

=(distance/time)/(fuelused/time)

=TAS/fuelflow

耗油率specificfuelconsumption(SFC)

Specificfuelconsumption(SFC)isaratiooffuelflowto

thrust.

SFC=fuelflow/thrustfuelflow=SFCxthrust

JSAR=TAS/(thrustxSFC)

(SAR)max=(TAS/drag)max/(SFC)min

SARofanaircraftisdependentontwoseparatefactors,an

airframeconsiderationandaseparateengineconsideration.

1,airframeconsideration(max.TAS/drag)

TAS/drag=(TAS/IAS)x(lAS/drag)

FormaximumvalueofTAS/drag,weneedamaximumvalueof

TAS/IAS,togetherwiththemaximumvalueoflAS/drag.

ThemaximumIAS/dragratioisachieved,whenalinefromthe

originindrawnatatangenttothedrag0°IAScurve,thisIAS

being1.32timestheIASforminimumdrag(VIMD).Thisspeedis

validatallaltitude,(forthejetaircraft)

Powerrequired=thrustrequiredxTAS

Powerrequired/TAS=thrustrequired=drag

(Powerrequired/TAS)min=(drag)min

p

￡

n

oa-

」

①」

M

o

d

Airspeed

-------------------?(TAS)

Maximum、—Maximumrange

endurancespeedspeed(bestL/D,

(speedforminimumpower)minimumdrag)

Figure2.3-8Maximumrangeandendurance

2,engineconsideration(minimumSFC)

3-14VariationofSFCwithchangeinenginerpm

ForminimumSFC,wewanttheenginetousetheleastfuelfora

givenamountofthrustproduced.

OneofthemainfactorthathasreducedSFCisachangeinengine

designandconfiguration.

OfthevariablethateffectsSFC,andcontrollablebythepilot,

engineRPMhasthemostaffect.

EnginesaredesignedtohaveabandofrpmsoverwhichSFC

doesnotchangesignificantly.Withinthisoperatingbandtherewill

beonespecificsettingthatprovidesthelowestSFC.Thisiscalled

thedesignrpm.

cruiseclimb：

Onceaircraftweighthasreducedfromtheinitialcruisefigure,the

aircraftisclimbedwithdesignrpmsuchthatIASreducesto

maintainbestrangeangleofattack.

3-17Effectonmaximumrangeofvariouscruiseprofiles

stepclimb：