航空专英1教案第3章 Forces in Flight

Ch3.ForcesinFlight

3.1Theforcesactingonanaeroplane

Figure2.1-2Dragsovercomearccatcrcsa

Lift(L)」、

Thrust(T)'—►Drag(D)

Weight(W)…

Figure2.1-3

Thefourmamforcesinbalance

weight重力，lift升力，drag阻力，thrust推力

3.2Weight重力

Gravityisthedownwardforceattractingallbodiesvertically

towardsthecentreoftheearth.Thegravitationalforceisweight.

Thetotalweightoftheloadedaeroplanemaybeconsideredasa

singleforceactingthroughthecentreofgravity.

thecentreofgravity重心（CG）

wingloading（翼载）

=theweightsupportedperunitareaofwing

=weightofaircraft/wingarea

Atypicaltrainingaeroplane：W=1220kg,S=20m2

wingloading=W/S=1220/20=61kg/m2

B-747wingloading=500kg/m2

ThepositionoftheCGis

shownindiagramswith

Weight▼acentroidsymbol:0

Figure2.1-4Weigh:acxscow

Throughthecentreofgravity（CG）

3.3Lift升力

Theproductionoftheliftforcebyanaerofoilisexplainedby

Bernoulli'sprinciple.

3.3.1Boundarylayer（边界层，附面层）

laminar层流

turbulent湍流

attachedflow附着流

separationflow分离流，separationpoint分离点(sp)

transition转振transitionpoint转振点

transitionregion转抿区

Allfluidshaveacertainstickinessandthereforearesistanceto

flow.Thisiscalledviscosity.Gasesarenothighlyviscousbutthere

isstilladegreeofstickiness.Inthecaseofawing,themoleculesof

airimmediatelyadjacenttothesurfacebecomeattachedtothe

surfaceandhavearelativevelocityofzero.Moleculesslightly

furtherawayfromthewingaredraggedalongbythe'attached5

moleculesbeneath.Thefurtherfromthewing,thelesstheairis

draggedalong,andhencethegreateristherelativevelocity.Alayer

isformed.Thelayersofairthatextendfromthesurfaceouttothe

freestreammakeuptheboundarylayer.

Thechangefromlaminartoturbulentflowtakesplaceatthe

transitionpoint,inthetransitionregion

aFreestream

aairflow

A，

-------------►Boundarylayer(afewmmthick)

----------►--------►affectedbyskinfrictiondrag-

----a--------------reducedrelativevelocity

AerofoiI-----------_____

00B6.EPS.Z--.—.....L..........

Figure2.1-7Boundarylayer

Transition

region

streamlineflow

——--------------..------------------------------------------

，一，♦------------------------------------————-----------

---------------•■------------------------------

006二ept

Figure2.1-8Sweamiineflow

Figure2.1-9S:reamhneflowisaesirao.eMOLTCarw

turbulentflow

Thin,laminar-TransitionTransmonSeparation

flowboundarypointpointpoint

layer

Slightlythicker,

luroulent

boundarylayer

Figure2.1-10Streamlineflowis

3.3.2Pressuredistribution（压强分布，压力分布）

Figure2.1-28

Distributionofstaticpressure

aroundacamberedaerofoil

a:apositiveangleofattack.

Pressuredistributionaroundacambered

aerofoilatvaryinganglesofattack

o

2

o

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a

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1-12Pressuredistribution

pressuredistributionchangeswithangleofattack.

a=4。，-4°,12°,20°

noliftforcebeyondthestallingangle

CL-CLMAXCt=acrit（临界迎角）

+4°

Figure2.1-30

Staticpressuredistribution

atvariousanglesofattack.

O

CCJ

a

m

s

s

e

i

d

q

巨

ITE

1“7Plotofpressurecoefficients(Cp)

atagivenangleofattack

3.3.3Liftfromatypicalwing

Thetotaleffectofthispressurepatternistoprovideanetupwards

force(lift)atpositiveangleofattacktogetherwithanetrearwards

force(drag).Thisactingpointisthecenterofpressure(cp).

Liftisacomponentofthetotalaerodynamicforceactingthrough

thecp,liftactsperpendiculartotheflightpath.

口,£reaction

/•

_也色line/—|:7.

Angleofr~(^-J^^Drag

aitacKI+.

RelativeaMow

Figure2.1-24Revivea-

Litt

LittL_________________盘

理

sag先W-

----_»，一■"-------------二--

------------------,aMorecamcer-morehh.

，"-------------------------------------Figure2.118

1

--------w

9137^.eC.jacurve

Figure2”/

liftfromatypicalwing

L/(l/2p/s)

r(q=l/2pv)

Lift二L二qsCL4

Figure2.1-33

Coefficientofliftversusangleofattack.

EachangleofattackproducesaparticularC,value.

Liftdependson：

wingshape(aerofoilsection)；

angleofattack(AOA)；

airdensity；(p)

freestreamvelocity(trueairspeed)(V2)；

wingsurfacearea(S)

coefficientoflift,(CL),“liftingability^^ofwing

Forsteadystraightandlevelflight,lift=weight

liftequationlift=weight=L=W=l/2pv2sCb

1,Airfoil

1)Airfoilterminology翼型术语

a,chordline弦线，(MAC:meanaerodynamicchord)

b,leadingedge前缘

c,trailingedge后缘

d,chord弦长

e,meancamberline平均弯度线

f,maximumcamber最大弯度

g,locationofmaximumcamber最大弯度位置

h,maximumthickness最大厚度

i,locationofmaximumthickness最大厚度位置

j,leadingedgeradius前缘半径

2)Airfoilshapes翼型形状

a,typicalwellcamberedaerofoil(high-lift,low-speedwing)；

b,typicalhighspeedaerofoil；

c,typicallaminar-flowaerofoil；

d,symmetricalaerofoilo

Awell-camberedaerofoilAsymmetricalaerofoil

typicalhigh-lift,low-speedwing；（typicalHorizontalstabiliser）

LeadingecgeTrailingedgeLeadingedgeTrailingecge

Atypicalhigh-speedaerofoilAtypicallaminar-flowaerofoil

Figure2.1-16Variousaerofc:!cross-sections.

Atypicallaminar-flowaerofoil

Amorecamberedaerofoil«

Figure2.1-36

Comparisonofaerofoilcross-sections

•thelaminar-flowwing

littercamber,fairlysharpleadingedgeradius一agreater

distancelaminarflow—>lessprofiledrag（atlowangleof

attack）—>highercruisespeed（高巡航速度），lowerfuel

consumption（低油耗），greaterrange（大航程），

but—*lesslift（athighangleofattack）

一airflowseparationismoresudden

TowervalueofCLMAX-higherstallingspeed

Alaminarflowwingismoresusceptible（敏感）toasurface

condition.

•supercriticalwingsection超临界剖面（超临界翼型）

Supercriticalwinesectionsallowincreasedmiisingspeedbin.lisopermirgreater

rangetoragiven.lirtrame.enginemixbyallowingreducedfueldowin:herinse.Fig­

ure2-1shows.1supercrincalwingsection.

2-19Typicalsupercriticalwingcross-section

supercriticalwingsection：flattenthetopsurface

reflexcamber(反弯度)

toincreaseMCR(criticalMachnumber)一

delaytheformationofshockwave(duetotheflattentopsurface)

reflexcamberattherearundersurface—>increasedcruisingspeed

一thegreaterrange

2,Factorsaffectingthecoefficientoflift

1)Boundarylayer边界层，附面层

Aturbulentboundarylayerproducesmoredragandlessliftbut

actuallyremainsattachedtothewingathigherangleofattack,

separationisdelayed.

2)Angleofattack(AOA)迎角，攻角

1.24Effectolangleofattackonseparation

Atlowerangleofattack,thereisalinearincreaseinCLfora

givenincreaseinangle,butjustbeforethestallingangleis

reached,therateofincreaseofCLreduces.Atthestall,thereisrapid

reductionofCLbutnotethatthewingisstillproducingsomelift.

3)Aerofoilshapeandwingplanform翼型形状及机翼平面形状

a,leading-edgeradius前缘半径

Leading-edgeradiusaffectstheCLatornearthepointofthestall

withthesmallradiusproducingamoresuddenandmoresevere

effectontheCLcurveandthelargeradiusgivingahighervalueof

CLandamoreprogressivestallandgentlerflatteningoftheCL

curve.

b,camber弯度

asymmetricalaerofoil：a=0°CL=0

acamberedaerofoil：a=0°CL#0

Forthesameangleofattackthesymmetricalsectionhasalower

valueofCL,butthecamberedsectiongivesahighervalueofCLand

alsoproducesahighermaximumvalueofCLatthestallandalower

criticalangleofattack.

Increasingcamber

Symmetrical

/section

A

Angleofatuck

V26EffectofcamberonCL/(icurve

c,aspectratio展弦比

Theliftofalowaspectratiowingwillincreaseata

lowerratewithincreasingangleofattackthanthelift

onahighaspectratiowing.

d,sweepback后掠角

e,surfacecondition表面状态，表面条件

Roughnessofthewingsurfacewilleffecttheconditionofthe

boundarylayerandthusabilityofthewingtogeneratelift.

4)ReynoldsNumber雷诺数Re,R,

R=pvL/]ip=density密度

V=TAS真空速

L=chordlength弦长

「viscosity粘性系数

ReynoldsNumber(RI

Rswherep=density

V=TAS

L=chordlength

|i=viscosity

IfVisincreased,ReynoldsNumberwillincreaseandsotheair

flowhasmoreenergy,givingahighervalueofCtmax-Thisisbecause

athigherspeeds,forsameangleofattack,theboundarylayerwill

receivemorekineticenergywhichwillresultindelayedseparation

andconsequentlyahighermaximumvalueofCL.

AreductionofindensityathighaltitudewillreduceReandhence

reduceCtmax.Againthereasonislinkedwiththeenergyofthe

boundarylayer.Alowerdensitygiveslowermassandhencelower

kineticenergysincekineticenergyisafunctionofmassaswellas

speed.(KE=l/2mv2)

5)Machnumber马赫数M=v/av：truespeed真空速

a：localspeedofsound音速

ThecoefficientofliftwillincreasewithincreasingMachnumber

atlowairspeed.

3,Thecentreofpressure(CP)压力中心，压心

:Angleofattackincreasesasairspeedreduces

togeneratethesamelift

Figure2.1-32Movemen!ofthecentreofpressure-camberedaerofoil.

af—>CLT(increasingtheliftingabilityofwing)一CPmoves

forward,

a=acritCPmovesback

1-18CPmovementwithincraasing«

donotconfusethepitchattitudeofaircraft(thelongitudinalaxis

relativetothehorizon)withtheangleofattack(thelongitudinalaxis

relativetotheairflow)andwiththeangleofincidence(the

longitudinalaxisrelativetothechordline).

Figure2.1-27

Theangleofincidenceisfixed

Longitudinalaxisduringdesignandconstruciion

ofaeroplaneOITBEPS

theangleofincidence安装角longitudinalaxis纵轴

3.3.4Highliftdevices

highliftdevices高升力装置，增升装置

k'

Figure21-38

Cessnaelectricflapsystem.

1,Usinghigh-liftdevicespurpose

forexample：cruisespeedVeru-120knots,

stallingspeedVs=60knots,CLTfourtimesthe

coefficientoflift.

Usinghigh-liftdevices,togivetherequiredadditionalliftata

lowerspeed.

Lift=weight=CLxv2pV"xS

FinewingWell-camberedwino

Figure2.1-39SameaspeedCMana-faosrgne：，,：

InstraightandlevelflightL=W=l/2pv2sCt

40KIAS

Stallspeedwithfullflap

Figure2.1-40Flapslowerthestallingspeedandnoseauitude

H=const.—>p=const.,s]andchangingaerofoilshape一Cj,

Therequiredliftcanbegeneratedatmuchlowerspeeds.Thisis

thepurposeofthehigh-liftdevices.

2

L=W=l/2pvssCLmaxVS=^2W/(psCLmax)CimaxT-^Vs]

2,thetypesofhigh-liftdevices

Figure5.29Varioustypesofhigh-liftdevices.

1)leadingedgedevices前缘装置

•slats缝翼：increasingtheliftcoefficientatveryhighangleof

attack.

Figure2.1-44Siorsaeiaythestall.

Slatscausesomeofthehighenergyairflowbeneaththewingto

flowthroughaslotandovertheuppersurfaceofthewing,thereby

delayingseparationandthestall,allowingtheaeroplanetoflyata

higherangleofattackandalowerairspeed.

Figure2.1-42Fu；l-spans(a*:1,

•leadingedgeflaps前缘襟翼：changingtheeffectivecurvature

oftheleadingedge,controllingtheflowathigherangleofattack.

•Krugerflaps克鲁克襟翼：improvingleadingedgeflow

condition,delayingleadingedgeseparation.

Functionofleadingedgedevicesisfollowing：

①usingthegapflow(slat-fixedslotsandautomaticslats)

②droopingthefrontsectionofwing(leadingedgeflaps)

(3)usingKrugerflapswhichfoldout(折叠)fromunderthe

leadingedge

1-slat2-wingtip3-aileron4-flap

2)trailingedgedevices后缘装置

•simpleflaps(plainfliips)简单襟翼

•splitfliips开裂式襟翼

•slottedflaps开缝襟翼(asingleslotormultipleslots)

•Fowlerflap富勒式襟翼(后退开缝襟翼)

Figure2.1-41FullflapontheCessna172

Figure2.1-45

Efiec:ofleading-edgeandrailing-edgeflapsonCLmax

Thetrailingedgeflapsincreasethecamberoftheaerofoilsection,

orwingareaorusinggapflow.

Thegreaterthemeancamberline,thegreatertheliftcapability

(themaximumCLpossible)ofthewing.

3,effectsofflaps

1)increasedlift"aballoon"Tiftflaps”

Balloon

Traihng-edgeflaps

extendedhere

—一—一

Trailing-edgeflapsextendedalong

withachangeinthepitchattitude

Figure2.1-47Loweringflapcancauseaballoonunless:hepilotadiusisthepitchauitude

2)pitchingmoment

CPmovesaft—>longermomentarm一nose-downpitching

moment

L

A

Longermomentarmwfr«»$

Figure2.1-48•.：•..-^jse:ne-icDHCH(downinthiscase).

3)decreasedlift/dragratio

Thedragincreaseisgreaterthantheliftincreases,soL/D1.

4)increaseddrag“dragflaps”

IAS70ktIAS55kt

WW

Clean

Figure2,1-49

Expendingflap-eithermorethrustorasleeper

descen：isrequirediooalancetnemcreasecdrag

5)lowerstallingangle

Figure2.1-50Flapextensionlowersthestallingangle

flapsdown一lowerstallingangle一flatterattitude

Figure2.1-51Sameaircraftpitchaunudesbutdifferemanglesofattack.

4,flapsfortake-off

Cleantake-off

(noflaps)、

Take-off

withflaps

extended

MfBIPS

Figure2.1-52Facsaiiowashonertake-offgrourarun

attake-offpositionbypartiallyloweringtheflaps

—>CLT，CDT(asmallpenalty)一lowerspeed-ashorter

take-offgroundrun

Whenretracttheflaps：

一CL1—>aircraftsinks(needtorisethenose,af)

一reductionofthecamberattherearofthewing

一movingthecentreofpressureforwards一thenose

topitch一retrimming

一CD1

5,flapsforapproachandlanding

atapproachandlandingbyloweringtheflaps-CJ,CDTT一a

lowerspeed

ballooning-CLT

pitchattitude-movingthecentreofpressure

•flapsincreasethepilotforwardview(视里子)

Withtrailingedgeflapsextended,theaeroplane'srequired

noseattitudeislower一Theimprovesforwardviewforthepilot.

Figure2.1-53Extendedflapsimorovethepile:sforwarc,viewandincreasedrag

3.4Drag阻力

Dragactsintheoppositedirectiontotheaircraft'smotionthrough

theair.Thethrustistoovercomedrag.

Thelowerthedrag,thelessthethrustrequired.

Thrustaboveandbeyondthatrequiredtoovercomedragisused

toclimb,accelerateandmanoeuvretheaircraft.Itiscalledexcess

thrust（富裕推力）

Figure2.1-54:•：：:J-

Totaldragisthesumofallforcesactingparalleltoflight-pathof

theaircraft.

Figure2.1-55Tote：cracsthe:o:a'airresisrance：c-notion

Atsubsonicspeedsitisnormaltosubdividedragintotwomain

types

▲parasitedrag废阻，寄生阻力Cdo

（alsoknownaszero-liftdrag零升阻力）

▲induceddrag诱导阻力，Cdi

（sometimesreferredtoaslift-dependentdrag升致阻力）

Cd=Cdo+Cdi

3.4.1Parasitedrag

Parasitedragincludessurfacefrictiondrag,formdragand

interferencedrag.

1,surfacefrictiondrag表面摩擦阻力，摩阻

1)Surface(orskin)frictiondragislargelydeterminedbythetotal

areaoftheaircraftthatisexposedtotheairflowingpastit.(wetted

area浸润面积)

2)Thetypeofboundarylayerpresentalsohassignificanteffectwith

laminarflowcreatinglesssurfacefrictiondragthantheturbulent

flow.

3)Thethirdfactoraffectingsurfacefrictiondragisthecoefficientof

viscosityoftheair.Thegreatertheviscosity,thegreaterthedragging

effectoftheair.

Forminimumsurfacefrictiondrag,thetransitionfromlaminarto

turbulentmustbedelayedaslongaspossible.

2,formdrag型阻

pressuregradient压强梯度

adversepressuregradient逆压梯度，反压梯度

reversepressuregradient逆压梯度，反压梯度

favorablepressuregradient顺压梯度

1-31Effectofadversepressuregradient

Whentheboundarylayerfinallyseparates,theseparatedflow

stillimpactsagainstsurfacecausingdrag.Thisisformdrag.

Effectsaremadetodelayseparationoftheboundarylayerinan

attempttoreduceformdrag.

Withgreaterkineticenergy,theboundarylayercanresistthe

effectsoftheadversepressuregradientforlonger,thedelaying

separationandreducedrag.

->Skinfcchondrac

0?6AEPS

Figure2.1-56Skinfricnondragandformdrag

SeparationpointSeparationpoint

Figure2.1-59

Icewillr.crease

drag(ancweicn*)

wake尾迹，protuberance突起物，fineness长细比

fairing整流罩，iceaccretion冰生成，

frontalarea迎风面积（最大横截面积）

Figure2.1-60Streamlining,especiallybenmdtheshaoe.reaucesformdragsubsiantially

3,interferencedrag干扰阻力

Thetotalparasitedragofanaeroplaneisgreaterthanthesumof

surfacefrictiondragandformdrag.Theadditionaldragiscausedby

mixing,orinterferenceoftheboundarylayerairflowatthejunction

ofvarioussurface,suchasatthewing/fuselagejunction,thetail

section/fuselagejunctionandthewing/enginenacellejunction.

Suitablefilleting（倒角）,fairing,streamliningofshapes

minimizethisinterferencedrag.

4,summaryofparasitedrag

3Parasite-

Pdrag0cTAS2

9

M

CD

0』

d

«SlowIASFast

1-33EffectofIASonparasiticdrag

Parasitedragincreaseswithairspeed,atveryhighspeedsnearly

allthetotaldragiscausedbyit.

Thepredominanceofparasitedragathighspeedsshowstheneed

foraerodynamic“cleanness“toobtainmaximumperformance.

ParasitedragisdirectlyproportionaltothesquareofTAS,and

doublingthespeedwillquadrupletheamountofparasitedrag.

3.4.2Induceddrag

1,Howinduceddragiscaused?

vortex—>vortices,vortexes（复数）旋涡

wingtipvortex翼尖涡

downwash下洗

induceddownwash诱导下洗

downwashangle下洗角

remoteflow远前方耒流

Induceddragisadirectresultoftheaircraftproducinglift.

Thedifferenceinpressurebetweentheupperandlowersurfaceof

thewingcausesairtospillaroundthetip,deflectingtheupper

surfaceflowtowardsthefuselageandthelowersurfaceflowtoward

thetips.

Asthetwoflowsmeetatthetrailingedgeaseriesofvorticesis

formed,whichaccumulateatthetiptoformalargewingtipvortex.

Whenthepressuredifferencebetweentheupperandlowersurface

isincreased(morelift),thenthesizeofthevortexwillincreasealso.

Induceddrag

a=angleofattack

toeffectiveflow

5=angleofinduced

downwash

Notes:1.'Lift'producedis90°

toeffectiveflow,but

thismustbeincreased

togive^desiredlift*at

90°toremoteflow.

2.AmountofInduceddrag

islargelydetermined

byangleofInduceddown­

wash.U1.i.e.sizeofvortex.

1・37Effectofdownwashangleonamountofinduceddrag

CCLwithA=aspectratio

D|-«An=pi(3.1416)

Productionoflift—*wingtipvorticesandtrailingedgevortices

fbrm一downwash一localrelativeairflowdirectionchanges一

liftisinclinedbackward一induceddrag(paralleltotheremote

relativeairflow)

2,Factorsaffectinginduceddrag

1)planform机翼平面形状

elliptical那青园的

ellipticalplanform：Cdi=CL2/7rAA=aspectratio

Theellipticalplanformhasminimuminduceddrag.

1-38Spanwiseliftdistribution

2)aspectratio展弦比

A=b?/sb=spanlengthsowingarea

A=b/cc=meanchord

Atthesameareaofwing,anarrowwingofhighaspectratio(a

smallwingtips)hasweakerwingtipvortices,lessinduceddownwash

andlessinduceddrag.

Chord*