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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
å L
cg
= I xx
¶P
¶t
(12.7)
or
·
P =
å 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:
å 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 + 2ç
÷ yú
é æ l -1ö ù
ë è b ø û
(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 + 2ç b ÷ yú ydy
Cld A =
2CLaw t
Sb
yo
ò C
yi
r
é æ l -1ö ù
ë è ø û
(12.22)
or
ë 2
2 æ l -1ö 3 ù
Cld A
=
2CLaw tCr é y 2
ê
Sb
+ ç ÷ y ú
3 è b ø û 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
lnç P 2 +
è
öù
3 ÷÷ú
é
F1 = ê
êë
I xx
ryD3 (Sw + Sht + Svt )CDR
æ
ç
Pss
V 2 SCl b
(Sw + Sht + Svt )CDR yD øúû 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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