Aileron Sizing ProAdvice

7/27/2019 Aileron Sizing ProAdvice

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ProAdvice3 AILERONSIZING Copyright2011GreatOwlPublishing 1NOTFORRESALE

ProAdvice 3: AILERON SIZING

Introduction

Thepurposeoftheailerons istoprovidecontrolabouttheairplanesrollaxis.Therearethreecommontypesof

aileronsusedinmodernairplanes;PlainFlapAilerons,FriseAilerons,andSpoilerFlapAilerons.Schematicsofthese

areshowninFigure1.OtherailerontypesincludetheFlaperon(acombinationofflapsandailerons)andElevon(a

combinationofelevatorsandailerons).

Figure1:Threecommontypesofailerons;PlainFlap(top),Frise(middle),andSpoilerFlap(bottom).

PlainFlapAilerons

The plain flap is the most common type of aileron configuration. They are very effective and inexpensive to

manufacture.For this reason, theycanbe foundonawide rangeofaircraft, ranging fromprimary trainers to

commercialaircraft.Ascanbeseen inFigure1theaileronontheupgoingwingisdeflectedTrailingEdgeDown

(TED)andthedowngoingwingisdeflectedTrailingEdgeUp(TEU).

FriseAilerons

TheFriseaileronwasinventedbythefameddesignerLeslieGeorgeFriseBScFRAeS(18971979)1.Theirpurposeis

toreduceoreliminateadverseyaw(seeSection22),butalsotoreducehingemoments.Thiscanbeaccomplished

inseveralways,ofwhichoneisshowninFigure1.Allrequirethehingetobeoffsettothelowersurfaceasshown

inthefigure.

The geometry of the aileron forces the leading edge of the aileron that is deflected Trailing Edge Up (TEU)

downwardandoutsideoftheregularOutsideMoldLine(OML).Thisexposesittotheairstreamandincreasesthe

drag on that side of the wing (the downgoing side). The drag generates a yawing moment and reduces the

1 Amongwellknowaircraftwhosedesignhecontributed to inare theBristolFighter,BristolBulldog ,BristolBeaufighter,and theHunting

PercivalJetProvost.


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Figure2:Changeinliftduetoailerondeflection.

Thesteadystaterollrateisdeterminedfrom:

a

pl

al

C

C

V

pb

2 (1)

Notethatthesteadystaterollratecanbedeterminedfrom:

b

V

C

Cp a

pl

al 2

(2)

Rollauthorityandrolldampingfortwospecialbutcommonwingplanformshapes.

CASE1:StraightTaperedWingwithTaperRatio:

Rollauthority:

3

1

3

2

2

1

2

23

14bb

bbb

Sb

CcC

Ra

l

al (3)

Rolldamping:

3124S

bCccC

Rdol

pl (4)

Unitsforboth: perradianorperdegree

CASE2:RectangularWing(=1):

Rollauthority:2

2

1

2

2

b

bbcC a

l

al

(5)

Rolldamping:6

dol

pl

ccC (6)

DERIVATION:

Assumethewingisrigidandtherollingmotioniscausedbydeflectingtheaileronstoananglea.Furtherassumethe roll rate p is impeded by the roll damping due to a local change in AOA along the wing (with a minor

contribution from the vertical tail). Thereforewe canwrite the equation of rolling motion for the aircraft as

follows:


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a

a

XX

L

V

pb

p

LpI

2 (i)

Where IXX is theaircraftsmomentof inertia (inslugsftorkgm) p is the rollacceleration in rad/s,L is the

rollingmomentinftlbforNm,andaistheailerondeflectionindegrees.

aa

a

a

a

a pL

L

V

pbL

V

pb

p

LL

V

pb

p

L

2220

Intermsofstabilityderivativeswecanwrite:

a

pl

al

C

C

V

pb

2

(ii)

So,theproblemboilsdowntothedeterminationofthetwoderivativesClaandClp,butthiswillbeshown ina

futureProAdvice.

QED

STEP-BY-STEP: Aileron Sizing

STEP1: EstablishinitialdimensionsbasedonFigure3.Alsodeterminethelikelyailerondeflectionangle,a.Notethatthecontrolsystemwillstretch inflightreducingthemaximumgrounddeflection.This

meansthatacontrolsystemdesignedforamaximumdeflectionof,say,15ontheground,may

onlydeflectasmuchas75%ofthat inflight.Somecontrolsystemsaresopoorlydesigned3that

theymayonlyachieve25%of themaximumdeflection.Atany rate,75% isa reasonable first

stabestimateforanaveragecontrolsystem.Thiswouldmeanthatamaximumdeflectionof15

iscloserto11.3inflight.

STEP2: Using the geometry from STEP 1, estimate roll damping,pl

C .Use Equation (4) for a straight

taperedwing,andEquation(6)foraHersheybarwing.

STEP3: UsingthegeometryfromSTEP1,estimatetherollauthority,a

lC .UseEquation(3)forastraight

taperedwing,andEquation(5)foraHersheybarwing.

STEP4: DetermineadesiredtargetrollhelixangleperSection23.5.2usingEquation(1).Ifthecalculated

value is lessthantheselectedtargetenlargeb1orb2,orboth.Notethatb2canneverbe larger

thanb/2and0


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Figure3:Definitionoftheailerongeometry.

Special Case Aileron Sizing: Constant Chord Wing

Thefollowingexpressioncanbeusedtodeterminethespanwiselocationoftheinboardedgeoftheaileron,fora

givenoutboardedge.Itonlyappliestoconstantchord(Hersheybar)wings.

Physicaldimension:2

2

2

12

bbc

C

V

pbb

aa

l

pl

(7)

Fractionaldimension:

2

11

2

b

b

c

C

V

pb

b

b

aa

l

pl

(8)

Where; b1=Spanwisestationfortheinboardedgeoftheaileron,inftorm.

b2=Spanwisestationfortheoutboardedgeoftheaileron,inftorm.

DERIVATION:

BeginwithEquation(1)andsolveforCla:

a

pl

ala

pl

al C

V

pbC

C

C

V

pb

22 (i)

Rollauthorityforarectangularwingcanbeshowntobe:

22

1

2

2

2 b

bbcC

VpbC al

a

pl

al

(ii)

Sinceourtargetistodeterminetheinboardstation,b1,fortheaileronwesolveforitusingEquation(ii):

2

2

2

12

bc

bC

V

pbb

ala

pl

(iii)

QED


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EXAMPLE1:

AUAVisbeingdesignedwithaHersheybarwingwhosedimensionsareshowninFigure4.Themaximumaileron

ground deflection is 20. Assuming that 75% of that will be achievable in flight, determine the roll rate for

maximumailerondeflectionatV=100KTASifchangeinliftwithailerondeflection,cla,hasbeenfoundtoequal

3.165perradianandtheairfoilsliftcurveslopeiscl=5.322perradianandsectiondragcoefficientistakenascdo

=0.010.Compare the results to thatobtained from theVortexLattice code SURFACESpresented in the same

examples.

Figure4:Examplegeometry.

SOLUTION:

DeterminethederivativeCla

/01036.0/rad5936.0211212

165.3226

3

22

1

ydyyc

Sb

c

d

dCC

b

b

al

a

l

al

STEP2:DeterminethederivativeClp

/rad8887.06

010.0322.5

6

dol

pl

ccC

STEP3:Determinetherollhelixangle

Basedonthistherollrateat100KTAScanbefoundfromEquation(1),wherethemaximumachievabledeflection

amountsto20x0.75=15:

deg02.10180

158887.0

5936.0

2

a

pl

al

C

C

V

pb

STEP4:

Determine

the

roll

rate

p

/s9.28212

8.168215

8887.0

5936.02

b

V

C

Cp

a

pl

al

AmodelofthiswingwasconstructedinSURFACES.Oncecomplete,theTasks>StabilityDerivativeswasselected

on theVLMConsoleandthe twooptionscheckedasshown in the imagebelow.Theaileronauthorityand roll

dampingwherethendeterminedandfoundtoequal:


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ProAdvice3 AILERONSIZING Copyright2011GreatOwlPublishing 7

NOTFORRESALE

rad/6336.0/rad4134.0pla

l CandC

Therefore,SURFACESpredictsthefollowingrollrateforthewing:

/s3.27512

8.168215

0.6336-

0.41342

b

V

C

Cp a

pl

al

Ascanbeseen,thesolutionfromSURFACESaccountsfortipeffectsbothfortherootandtipoftheaileron,aswell

asthat

of

the

wing.

That

interaction

is

quite

complicated

and

it

is

an

important

detail

to

capture

so

that

one

does

notoverestimatetherollrate.


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Maximizing Responsiveness

Some airplanes require flap span to bemaximized tomeet requirements for stall speed. Thismeans that the

aileronspanislessthanideal.Thedesignercanattempttoimprovetheeffectivenessoftheremainingaileronsby

positioningthecentroidoftheaileronplanformascloseaspossibletothelocationwheretheirspanwisesection

momentreachesmaximum.

Considerthetaperedwingplanform(halfspan)below:

Figure5:DefinitionofaninfinitesimalsegmentSonthewing.

Spanwisesectionmoment(analogoustosectionliftorsectionliftcoefficient)isdefinedasfollows:

SCqyMCyC lXlm

Where; Cm=SpanwisemomentcoefficientCl=Sectionliftcoefficient

MX=Elementalrollingmomenty=Spanwisestation

q=Dynamicpressure

S=Areaofelementalstrip

Considerthewingshownbelow,whichshowthedistributionofsectionliftcoefficients:


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Figure6:

Distribution

of

section

lift

coefficient

along

the

wing4.

Letszoominandshowthesectionmomentsforastrip:

Figure7:Generationofspanwisesectionmoment.

Letsplotthesectionmomentsforeachstrip.

4GeneratedwiththeVortexLatticecodeSURFACES.

Si

yi


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Figure8:Distributionofsectionmomentsalongthewing.

TheeffectofdeflectingaileronsonthedistributionofsectionliftcoefficientscanbeseeninFigure9below.The

aileronsaredeflectedsome15andthewingsAOAamountsto8at100KCAS.

Figure9:Typicalimpactofdeflectingaileronsonthesectionliftcoefficients5.


Maximum section moment. This is where

weshould trytoplacethecentroidof the

aileron. This will achieve maximum

responsiveness.


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Figure10:Impactofailerondeflectionontheflowfieldbehindtheaircraft.Notethedifferenceinthewingtip

vortices6.

Aileron Stick Forces

Inaconventional,humanoperatedaileroncontrolsystem,thepilotmustreactthehingemomenttheresultsfrom

deflectingthecontrolsurface.Thisisdonebyapplyingaforcetothepropercontrol(astick,yoke,orasteering

wheel).

Figure11:Thehingemoment(HM)isreactedasaforce,eitherdirectlybythepilotorbyacontrolsystem

(typicallyhydraulicorelectric).

Hingemomentsarehighlyaffectedbythegeometryofthecontrols,includingthehingelocationandshapeofthe

control.Ageneralexpressionforthehingemomentisgivenbelow:

hff CSCVHM2

2

1 (9)

Where; Cf=Flapchord(aftofhingeline)

Ch=Hingemoment



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Sf=Flaparea(aftofhingeline)

V=Airspeed,

=Densityofair

Figure12:Geometrydefinitions

Thehingemomentcoefficientisgivenby:

tt

hhhhh CCCCC 0 (10)

WHATISProAdvice?

ProAdvicesareshortandsimplifiedexcerptsfromProfessorGudmundssonsdesignhandbookAircraftPreliminary

DesignHandbook

and

are

intended

to

provide

the

aircraft

designer

with

clear

and

concise

analysis

methods

for

the

aircraftdesigner.Thishandbook is currently indevelopment. SnorriGudmundsson isanAssistantProfessorof

Aerospace Engineering at EmbryRiddle Aeronautical University in Daytona Beach, Florida, where he teaches

AircraftPreliminaryDesigntoseniorengineeringstudents.

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