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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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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.
5GeneratedwiththeVortexLatticecodeSURFACES.
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
6GeneratedwiththeVortexLatticecodeSURFACES.
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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.