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Aileron?Design
Chapter?12
Design?of?Control?Surfaces
From:?Aircraft?Design:?A?Systems?Engineering?Approach
Mohammad?Sadraey
792?pages
September?2012,?Hardcover
Wiley?Publications
12.4.1.?Introduction
The?primary?function?of?an?aileron?is?the?lateral?(i.e.?roll)?control?of?an?aircraft;?however,
it?also?affects?the?directional?control.?Due?to?this?reason,?the?aileron?and?the?rudder?are
usually?designed?concurrently.?Lateral?control?is?governed?primarily?through?a?roll?rate
(P).?Aileron?is?structurally?part?of?the?wing,?and?has?two?pieces;?each?located?on?the
trailing?edge?of?the?outer?portion?of?the?wing?left?and?right?sections.?Both?ailerons?are
often?used?symmetrically,?hence?their?geometries?are?identical.?Aileron?effectiveness?is?a
measure?of?how?good?the?deflected?aileron?is?producing?the?desired?rolling?moment.?The
generated?rolling?moment?is?a?function?of?aileron?size,?aileron?deflection,?and?its?distance
from?the?aircraft?fuselage?centerline.?Unlike?rudder?and?elevator?which?are?displacement
control,?the?aileron?is?a?rate?control.?Any?change?in?the?aileron?geometry?or?deflection
will?change?the?roll?rate;?which?subsequently?varies?constantly?the?roll?angle.
The??deflection??of??any??control??surface??including??the??aileron??involves??a??hinge
moment.?The?hinge?moments?are?the?aerodynamic?moments?that?must?be?overcome?to
deflect?the?control?surfaces.?The?hinge?moment?governs?the?magnitude?of?augmented
pilot?force?required?to?move?the?corresponding?actuator?to?deflect?the?control?surface.?To
minimize??the??size??and??thus??the??cost??of??the??actuation??system,??the??ailerons??should??be
designed?so?that?the?control?forces?are?as?low?as?possible.
In?the?design?process?of?an?aileron,?four?parameters?need?to?be?determined.?They
are:?1.?aileron?planform?area?(Sa);?2.?aileron?chord/span?(Ca/ba);?3.?maximum?up?and
down?aileron?deflection?(?±?dAmax);?and?4.?location?of?inner?edge?of?the?aileron?along?the
wing?span?(bai).?Figure?12.10?shows?the?aileron?geometry.?As?a?general?guidance,?the
typical?values?for?these?parameters?are?as?follows:?Sa/S?=?0.05?to?0.1,?ba/b?=?0.2-0.3,?Ca/C
=?0.15-0.25,?bai/b?=?0.6-0.8,?and?dAmax?=?±?30?degrees.?Based?on?this?statistics,?about?5?to
10?percent?of?the?wing?area?is?devoted?to?the?aileron,?the?aileron-to-wing-chord?ratio?is
about?15?to?25?percent,?aileron-to-wing-span?ratio?is?about?20-30?percent,?and?the?inboard
aileron??span??is??about??60??to??80??percent??of??the??wing??span.??Table??12.17??illustrates??the
characteristics?of?aileron?of?several?aircraft.
1
b
A
ba/2
Ca
Sa/2
bai/2
A
a.???Top-view?of?the?wing?and?aileron
dAup
dAdown
b.???Side-view?of?the?wing?and?aileron?(Section?AA)
Figure?12.1.?Geometry?of?aileron
Factors?affecting?the?design?of?the?aileron?are:?1.?the?required?hinge?moment,?2.
the?aileron?effectiveness,?3.?aerodynamic?and?mass?balancing,?4.?flap?geometry,?5.?the
aircraft?structure,?and?6.?cost.?Aileron?effectiveness?is?a?measure?of?how?effective?the
aileron?deflection?is?in?producing?the?desired?rolling?moment.?Aileron?effectiveness?is?a
function?of?its?size?and?its?distance?to?aircraft?center?of?gravity.?Hinge?moments?are?also
important?because?they?are?the?aerodynamic?moments?that?must?be?overcome?to?rotate?the
aileron.?The?hinge?moments?governs?the?magnitude?of?force?required?of?the?pilot?to?move
the?aileron.?Therefore,?great?care?must?be?used?in?designing?the?aileron?so?that?the?control
forces??are??within??acceptable??limits??for??the??pilots.??Finally,??aerodynamic??and??mass
balancing?deals?with?techniques?to?vary?the?hinge?moments?so?that?the?stick?force?stays
within?an?acceptable?range.?Handling?qualities?discussed?in?the?previous?section?govern
these?factors.?In?this?section,?principals?of?aileron?design,?design?procedure,?governing
equations,?constraints,?and?design?steps?as?well?as?a?fully?solved?example?are?presented.
12.4.2.?Principles?of?Aileron?Design
A??basic??item??in??the?list??of??aircraft??performance??requirements??is??the??maneuverability.
Aircraft?maneuverability?is?a?function?of?engine?thrust,?aircraft?mass?moment?of?inertia,
and?control?power.?One?of?the?primary?control?surfaces?which?cause?the?aircraft?to?be
steered?along?its?three-dimensional?flight?path?(i.e.?maneuver)?to?its?specified?destination
is?aileron.?Ailerons?are?like?plain?flaps?placed?at?outboard?of?the?trailing?edge?of?the?wing.
Right?aileron?and?left?aileron?are?deflected?differentially?and?simultaneously?to?produce?a
2
No
Aircraft
Type
mTO
(kg)
b
(m)
CA/C
Span?ratio
dAmax?(deg)
bi/b/2
bo/b/2
up
down
1
Cessna?182
Light?GA
1,406
11
0.2
0.46
0.95
20
14
2
Cessna?Citation
III
Business
jet
9,979
16.31
0.3
0.56
0.89
12.
5
12.5
3
Air?Tractor?AT-
802
Agriculture
7,257
18
0.36
0.4
0.95
17
13
4
Gulfstream?200
Business
jet
16,080
17.7
0.22
0.6
0.86
15
15
5
Fokker?100A
Airliner
44,450
28.08
0.24
0.6
0.94
25
20
6
Boeing?777-200
Airliner
247,200
60.9
0.22
0.321
0.762
30
10
7
Airbus?340-600
Airliner
368,000
63.45
0.3
0.64
0.92
25
20
8
Airbus?A340-
600
Airliner
368,000
63.45
0.25
0.67
0.92
25
25
rolling??moment??about??x-axis.??Therefore,??the??main??role??of??aileron??is??the??roll??control;
however?it?will?affect?yaw?control?as?well.?Roll?control?is?the?fundamental?basis?for?the
design?of?aileron.
Table?12.1.?Characteristics?of?aileron?for?several?aircraft
Table???12.12???(lateral???directional???handling???qualities???requirements)???provides
significant?criteria?to?design?the?aileron.?This?table?specifies?required?time?to?bank?an
aircraft?at??a?specified??bank??angle.??Since?the?effectiveness??of?control??surfaces??are??the
lowest?in?the?slower?speed,?the?roll?control?in?a?take-off?or?landing?operations?is?the?flight
phase?at?which?the?aileron?is?sized.?Thus,?in?designing?the?aileron?one?must?consider?only
level?1?and?most?critical?phases?of?flight?that?is?usually?phase?B.
Based?on?the?Newton’s?second?law?for?a?rotational?motion,?the?summation?of?all
applied?moments?is?equal?to?the?time?rate?of?change?of?angular?momentum.?If?the?mass
and?the?geometry?of?the?objet?(i.e.?vehicle)?are?fixed,?the?law?is?reduced?to?a?simpler
version:?The?summation?of?all?moments?is?equal?to?the?mass?moment?of?inertia?time?of
the?object?about?the?axis?or?rotation?multiplied?by?the?rate?of?change?of?angular?velocity.
In?the?case?of?a?rolling?motion,?the?summation?of?all?rolling?moments?(including?the
aircraft?aerodynamic?moment)?is?equal?to?the?aircraft?mass?moment?of?inertia?about?x-axis
multiplied?by?the?time?rate?of?change?(?/?t)?of?roll?rate?(P).
Inboard?aileron??1
Outboard?aileron???2
3
??L
cg
=?I?xx
?P
?t
(12.7)
or
·
P?=
??L
I?xx
cg
(12.8)
Generally?speaking,?there?are?two?forces?involved?in?generating?the?rolling?moment:?1.
An?incremental?change?in?wing?lift?due?to?a?change?in?aileron?angle,?2.?Aircraft?rolling
drag?force?in?the?yz?plane.?Figure?12.11?illustrates?the?front-view?of?an?aircraft?where
incremental?change?in?the?lift?due?to?aileron?deflection?(DL)?and?incremental?drag?due?to
the?rolling?speed?are?shown.
The?aircraft?in?Figure?12.11?is?planning?to?have?a?positive?roll,?so?the?right?aileron
is?deflected?up?and?left?aileron?down?(i.e.?+dA).?The?total?aerodynamic?rolling?moment?in
a?rolling?motion?is:
??M
cgx
=?2DL?×?y?A??-?DD?×?yD
(12.9)
The?factor?2?has?been?introduced?in?the?moment?due?to?lift?to?account?for?both?left
and?right?ailerons.?The?factor?2?is?not?considered?for?the?rolling?moment?due?to?rolling
drag?calculation,?since?the?average?rolling?drag?will?be?computed?later.?The?parameter?yL
is?the?average?distance?between?each?aileron?and?the?x-axis?(i.e.?aircraft?center?of?gravity).
The?parameter?yD?is?the?average?distance?between?rolling?drag?center?and?the?x-axis?(i.e.
aircraft?center?of?gravity).?A?typical?location?for?this?distance?is?about?40%?of?the?wing
semispan?from?root?chord.
+dA
DDright
DLleft
DLright
dy
y
yo
yi
cg?????????????????????????????DDleft
z
yD
yA
+dA
Front?view
Figure?12.2.?Incremental?change?in?lift?and?drag?in?generating?a?rolling?motion
4
In??an??aircraft??with??short??wingspan??and??large??aileron??(e.g.??fighter??such??as??General
Dynamics?F-16?Fighting?Falcon?(Figure?3.12))?the?drag?does?not?considerably?influence
on?the?rolling?speed.?However,?in?an?aircraft?with?a?long?wingspan?and?small?aileron;
such?as?bomber?Boeing?B-52?(Figures?8.20?and?9.4);?the?rolling?induced?drag?force?has?a
significant?effect?on?the?rolling?speed.?For?instance,?the?B-52?takes?about?10?seconds?to
have?a?bank?angle?of?45?degrees?at?low?speeds,?while?for?the?case?of?a?fighter?such?as?F-
16;?it?takes?only?a?fraction?of?a?second?for?such?roll.
Owing?to?the?fact?that?ailerons?are?located?at?some?distance?from?the?center?of?gravity?of
the?aircraft,?incremental??lift?force?generated??by?ailerons??deflected?up/down,??creates?a
rolling?moment.
LA?=?2DL?×?yA
(12.10)
However,?the?aerodynamic?rolling?moment?is?generally?modeled?as?a?function?of?wing
area?(S),?wing?span?(b),?dynamic?pressure?(q)?as:
LA?=?qSClb
where?Cl?is?the?rolling?moment?coefficient?and?the?dynamic?pressure?is:
(12.11)
q?=
1
2
rVT2
(12.12)
where?r?is?the?air?density?and?VT?is?the?aircraft?true?airspeed.?The?parameter?Cl?is?a
function?of?aircraft?configuration,?sideslip?angle,?rudder?deflection?and?aileron?deflection.
In??a??symmetric??aircraft??with??no??sideslip??and??no??rudder??deflection,??this??coefficient??is
linearly?modeled?as:
Cl?=?CldA?d?A
(12.13)
The??parameter??Cld
A
is??referred??to??as??the??aircraft??rolling??moment-coefficient-due-to-
aileron-deflection?derivative?and?is?also?called?the?aileron?roll?control?power.?The?aircraft
rolling?drag?induced?by?the?rolling?speed?may?be?modeled?as:
DR?=?DDleft?+?DDright?=
1
2
rVR2?StotCDR
(12.14)
where??aircraft??average??CDR??is??the??aircraft??drag??coefficient??in??rolling??motion.??This
coefficient?is?about?0.7?–?1.2?which?includes?the?drag?contribution?of?the?fuselage.?The
parameter?Stot?is?the?summation?of?wing?planform?area,?horizontal?tail?planform?area,?and
vertical?tail?planform?area.
Stot?=?Sw?+?Sht?+?Svt
5
(12.15)
The?parameter?VR?is?the?rolling?linear?speed?in?a?rolling?motion?and?is?equal?to?roll?rate
(P)?multiplied?by?average?distance?between?rolling?drag?center?(See?Figure?12.11)?along
y-axis?and?the?aircraft?center?of?gravity:
VR?=?P?×?yD
(12.16)
Since?all?three?lifting?surfaces?(wing,?horizontal?tail,?and?vertical?tail)?are?contributing?to
the??rolling??drag,??the??yD??is??in??fact,??the??average??of??three??average??distances.??The??non-
dimensional?control?derivative?Cld?A?is?a?measure?of?the?roll?control?power?of?the?aileron;?it
represents?the?change?in?rolling?moment?per?unit?change?of?aileron?deflection.?The?larger
the??Cld?A?,?the?more?effective?the?aileron?is?at?creating?a?rolling?moment.?This?control
derivative?may?be?calculated?using?method?introduced?in?[19].?However,?an?estimate?of
the?roll?control?power?for?an?aileron?is?presented?in?this?Section?based?on?a?simple?strip
integration?method.?The?aerodynamic?rolling?moment?due?to?the?lift?distribution?may?be
written?in?coefficient?form?as:
DCl?=
DLA
qSb
=
qCLA?Ca?y?Ady
qSb
=
CLA?Ca?y?Ady
Sb
(12.17)
The?section?lift?coefficient?CLA??on?the?sections?containing?the?aileron?may?be?written?as
CLA?=?CLa?a?=?CLa
da
dd?A
d?A?=?CLa?t?a?×?d?A
(12.18)
where?ta?is?the?aileron?effectiveness?parameter?and?is?obtained?from?Figure?12.12,?given
the?ratio?between?aileron-chord?and?wing-chord.?Figure?12.12?is?a?general?representative
of?the?control?surface?effectiveness;?it?may?be?applied?to?aileron?(ta),?elevator?(te),?and
rudder?(tr).?Thus,?in?Figure?12.12,?the?subscript?of?parameter?t?is?dropped?to?indicate?the
generality.
òy?Cydy
2CLaw?td??A yo
Integrating?over?the?region?containing?the?aileron?yields
Cl?=
Sb
i
(12.19)
where??CLaw??has?been?corrected?for?three-dimensional?flow?and?the?factor?2?is?added?to
account?for?the?two?ailerons.?For?the?calculation?in?this?technique,?the?wing?sectional?lift
curve?slope?is?assumed?to?be?constant?over?the?wing?span.?Therefore,?the?aileron?sectional
lift??curve??slope??is??equaled??to??the??wing??sectional??lift??curve??slope.??The??parameter??yi
represents?the?inboard?position?of?aileron?with?respect?to?the?fuselage?centerline,?and?yo
the?outboard?position?of?aileron?with?respect?to?the?fuselage?centerline?(See?Figure?12.11).
6
The?aileron?roll?control?derivative?can?be?obtained?by?taking?the?derivative?with?respect?to
òy?Cydy
dA:
Cld?A??=
2CLaw?t??yo
Sb
i
(12.20)
t
0.8
0.6
0.4
0.2
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Control-surface-to-lifting-surface-chord?ratio
Figure?12.3.?Control?surface?angle?of?attack?effectiveness?parameter
The?wing?chord?(C)?as?a?function?of?y?(along?span)?for?a?tapered?wing?can?be?expressed
by?the?following?relationship:
C??=?Cr?ê1?+?2?
÷?yú
é ??l?-1???ù
? è???b???????
(12.21)
where?Cr?denotes?the?wing?root?chord,?and?l?is?the?wing?taper?ratio.?Substituting?this
relationship?back?into?the?expression?for?Cld?A?(Equ.?12.20)?yields:
ê1?+?2? b ÷?yú?ydy
Cld?A??=
2CLaw?t
Sb
yo
ò?C
yi
r
é?????????l?-1???ù
????????è?????????????
(12.22)
or
???2
2???l?-1? 3?ù
Cld?A
=
2CLaw?tCr?é?y?2
ê
Sb
+?????????????÷?y??ú
3?è???b??????????yi
yo
(12.23)
This?equation?can?be?employed?to?estimate?roll?control?derivative??Cld?A?using?the?aileron
geometry?and?estimating?t?from?Figure?12.12.?Getting?back?to?equation?12.12,?there?are
two?pieces?of?ailerons;?each?at?one?left?and?right?sections?of?the?wing.?These?two?pieces
may?have?a?similar?magnitude?of?deflections?or?slightly?different?deflections,?due?to?the
adverse?yaw.?At?any?rate,?only?one?value?will?enter?to?the?calculation?of?rolling?moment.
Thus,?an?average?value?of?aileron?deflection?will?be?calculated?as?follows:
7
[ ]
d??A??=
d??Aleft +?d??Aright
1
(12.24)
2
The?sign?of?this?dA?will?later?be?determined?based?on?the?convention?introduced?earlier;?a
positive??dA??will??generate??a??positive??rolling??moment.??Substituting??equation??12.9??into
equation?12.7?yields:
·
LA?+?DD?×?yD?=?I?xx?P
·
As?the?name?implies,?P??is?the?time?rate?of?change?of?roll?rate:
(12.25)
·
P?=
d
dt
P
(12.26)
On?the?other?hand,?the?angular?velocity?about?x-axis?(P)?is?defined?as?the?time?rate?of
change?of?bank?angle:
P?=
d
dt
F
(12.27)
Combining?equations?12.26?and?12.27?and?removing?dt?from?both?sides,?results?in:
·
P?dF?=?PdP
(12.28)
Assuming?that?the?aircraft?is?initially?at?a?level?cruising?flight?(i.e.?Po?=?0,?fo?=?0),?both
sides?may?be?integrated?as:
f??·
ò?P?dF?=
0
Pss
ò?PdP
0
(12.29)
Thus,?the?bank?angle?due?to?a?rolling?motion?is?obtained?as:
F?=?ò ·??dP
P
P
·
where?P??is?obtained?from?equation?12.25.?Thus:
(12.30)
Pss
F?=?ò
0
I?xx?P
LA?+?DD?×?yD
dP
(12.31)
Both?aerodynamic?rolling?moment?and?aircraft?drag?due?to?rolling?motion?are?functions?of
roll?rate.?Plugging?these?two?moments?into?equation?12.31?yields:
r(P?×?yD?)?(Sw??+?Sht??+?Svt?)CDR??×?yD
F1?=
Pss
ò
0?qSCl?b?+
1
2
I?xx?P
2
dP
(12.32)
The?aircraft?rate?of?roll?rate?response?to?the?aileron?deflection?has?two?distinct?states:?1.?A
transient?state,?2.?A?steady?state?(See?Figure?12.13).?The?integral?limit?for?the?roll?rate?(P)
in?equation?12.32?is?from?an?initial?trim?point?of?no?roll?rate?(i.e.?wing?level?and?Po?=?0)?to
a?steady-state?value?of?roll?rate?(Pss).?Since?the?aileron?is?featured?as?a?rate?control,?the
deflection?of?aileron?will?eventually?result?in?a?steady-state?roll?rate?(Figure?12.13).?Thus,
unless?the?ailerons?are?returned?to?the?initial?zero?deflection,?the?aircraft?will?not?stop?at?a
specific?bank?angle.?Table?12.12?defines?the?roll?rate?requirements?in?terms?of?the?desired
8
bank?angle?(F2)?for?the?duration?of?t?seconds.?The?equation?12.32?has?a?closed-form
solution?and?can?be?solved?to?determine?the?bank?angle?(F1)?when?the?roll?rate?reaches?its
steady-state?value.
Roll?rate
(deg/sec)
Pss
tss t2
Time?(sec)
Figure?12.4.?Aircraft?roll?rate?response?to?an?aileron?deflection
Bank
angle
(deg)
F2
F1
t1
t2
Time?(sec)
Figure?12.5.?Aircraft?bank?angle?response?to?an?aileron?deflection
When?the?aircraft?has?a?steady-state?(Pss)?roll?rate,?the?new?bank?angle?(Figure?12.14)?after
Dt?seconds?(i.e.?t2-tss)?is?readily?obtained?by?the?following?linear?relationship:
F2?=?Pss?×?(t2?-?tss?)?+?F1
(12.33)
Due??to??the??fact??that??the??aircraft??drag??due??to??roll??rate??is??not??constant??and??is
increased?with?an?increase?to?the?roll?rate;?the?rolling?motion?is?not?linear.?This?implies
9
that?the?variation?of?the?roll?rate?is?not?linear;?and?there?is?an?angular?rotation?about?x-
axis.??However,??until??the??resisting??moment??against??the??rolling??motion??is??equal??to??the
aileron?generated?aerodynamic?rolling?moment;?the?aircraft?will?experience?an?angular
acceleration?about?x-axis.?Soon?after?the?two?rolling?moments?are?equal,?the?aircraft?will
continue?to?roll?with?a?constant?roll?rate?(Pss).?The?steady-state?value?for?roll?rate?(Pss)?is
obtained?by?considering?that?the?fact?that?when?the?aircraft?is?rolling?with?a?constant?roll
rate,?the?aileron?generated?aerodynamic?rolling?moment?is?equal?to?the?moment?of?aircraft
drag?in?the?rolling?motion.
LA?=?DDR?×?yD
(12.34)
Combining?equations?12.14,?12.15,?and?12.16,?the?aircraft?drag?due?to?the?rolling?motion
is?obtained?as:
DR?=
1
2
r(P?×?yD?)2?(Sw?+?Sht?+?Svt?)CDR
(12.35)
Inserting?the?equation?12.35?into?equation?12.34?yields:
LA?=
1
2
r(P?×?yD?)2?(Sw?+?Sht?+?Svt?)CDR?×?yD
(12.36)
Solving?for?the?steady-state?roll?rate?(Pss)?results?in:
Pss??=
2?×?LA
r(Sw??+?Sht??+?Svt?)CDR??×?yD3
(12.37)
On?the?other?hand,?the?equation?12.32?is?simply?a?definite?mathematical?integration.?This
integration?may?be?modeled?as?the?following?general?integration?problem:
y??=?k?ò 2
xdx
x???+?a?2
According?to?[20],?there?is?a?closed?form?solution?to?such?integration?as?follows:
(12.38)
y?=?k
1
2
ln(x?2?+?a?2?)
(12.39)
The?parameters?k?and?a?are?obtained?by?comparing?equation?12.38?with?equation?12.32.
ry??(Sw??+?Sht??+?Svt?)CDR
k??=
3
D
2I?xx
(12.40)
a?2??= (12.41)
(Sw??+?Sht??+?Svt?)CD
yD
V?2?SCl?b
3
R
Hence,?the?solution?to?the?integration?in?equation?12.32?is?determined?as:
11
ln??P?2??+
è
?ù
3?÷÷ú
é
F1??=?ê
ê?
I?xx
ryD3?(Sw??+?Sht??+?Svt?)CDR
?
?
Pss
V?2?SCl?b
(Sw??+?Sht??+?Svt?)CDR?yD?????ú??0
(12.42)
Applying?the?limits?(from?0?to?Pss)?to?the?solution?results?in:
ry??(Sw??+?Sht??+?Svt?)CDR
F1??=
3
D
I?xx
2
ln(Pss?)
(12.43)
Recall?that?we?are?looking?to?determine?aileron?roll?control?power.?In?another?word,?it?is
desired?to?obtain?how?long?it?takes?(t2)?to?bank?to?a?desired?bank?angle?when?ailerons?are
deflected.?This?duration?tends?to?have?two?parts:?1.?The?duration?(tss
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