B(i,j) = sin((2*j-1) * theta(i)) * (1 + (mu(i) * (2*j-1)) /

sin(theta(i)));
end
end
A=B\transpose(LHS);
for i = 1:N
sum1(i) = 0;
sum2(i) = 0;
for j = 1 : N
sum1(i) = sum1(i) + (2*j-1) * A(j)*sin((2*j-1)*theta(i));
sum2(i) = sum2(i) + A(j)*sin((2*j-1)*theta(i));
end
end
CL = 4*b*sum2 ./ c;
CL1=[0 CL(1) CL(2) CL(3) CL(4) CL(5) CL(6) CL(7) CL(8) CL(9)];
y_s=[b/2 z(1) z(2) z(3) z(4) z(5) z(6) z(7) z(8) z(9)];
plot(y_s,CL1,'-o')
grid
title('Lift distribution’)
xlabel(‘Semi-span location (m)’)
ylabel (‘Lift coefficient’)
CL_wing = pi * AR * A(1)

Figure 5.59 shows the lift distribution of the example wing as an output of the m-file.
Lift Distribution
0.35

0.3

0.25

0.2
Lift coefficient

0.15

0.1

0.05

0
0 1 2 3 4 5 6 7 8
semi-span Location (m)

Figure 5.59. The lift distribution of the wing in example 5.5

Wing Design 88
As noted, the distribution in this wing is not elliptical, so it is not ideal. The wing needs some
modification (such as increasing wing twist) to produce an acceptable output. The total lift
coefficient of the wing is CL = 0.268. The lift generated by this wing is as follows:

V 2 SC L   0.736  180  0.5144 2  25  0.268  21,169.2 N

1 1
L (5.1)
2 2

To check the accuracy of lifting line theory, several aircraft are selected (from Ref. 4) to compare
their real cruise lift coefficients with calculated lift coefficients based on this theory. The
characteristics of these aircraft are given in table 5.17. For instance, the cruising lift coefficient
for the Bellance aircraft based on the lift equation (Equation 5.10) is 0.2193, while the theoretical
lift coefficient based on the lifting line theory would be 0.229. The difference between these two
lift coefficients is only 4.5 percent. Thus, it can be concluded that the lifting line theory is fairly
accurate for the low speed aircraft and can be utilized in the initial wing design process.

Aircraft S  AR t NACA o Cdmin Clmin iw mass Vc

(m2) (deg) (deg) (deg) (kg) (knot)
Cessna 17.1 0.7 7.2 5.9 23018- - - - 2o 3‟ 2717 233 @
304A 23015 24500 ft
@ %75
power
Brandli 8.5 0.77 5.7 - 747A415 -2 0.0043 0.5 3 550 -
Aerocare 10.4 1 7 - 4415 -4 0.0065 0.3 0 703 130
IMP
Cojetkovic 11.75 1 6 0 4415 -4 0.0065 0.3 0 430 104
CA61-61R
Scottish 12.52 0.59 8.4 0 632-615 -4 0.005 0.4 1.15 1066 120
Aviation @ 1200 m
@ %75
SA-3-120 power
Bellanca 16.92 0.7 6.7 0 632-215 -1 0.0047 0.2 2 1860 262
19-25 @ 7300 m
@ %75
power
Table 5.17. Characteristics of several aircraft to check the accuracy of lifting line theory

5.15. Accessories
Depending upon the aircraft type and flight conditions, the wing may have a few accessories to
improve the flow over the wing. The accessories such as wingtip, fence, vortex generator, stall
stripes, and strake are employed to increase the wing efficiency. In this section, few practical
considerations will be introduced.
5.15.1. Strake
A strake (also known as a leading edge extension) is an aerodynamic surface generally mounted
on the fuselage of an aircraft to fine-tune the airflow and to control the vortex over the wing. In
order to increase lift and improve directional stability and maneuverability at high angles of

Wing Design 89
attack, highly swept strakes along fuselage forebody may be employed to join the wing sections.
Aircraft designers choose the location, angle and shape of the strake to produce the desired
interaction. Fighter aircraft F-16 and F-18 have employed strakes to improve the wing efficiency
at high angles of attack. The design of the strake needs a high fidelity CFD software and is
beyond the scope of this book.
5.15.2. Fence
Stall fences are used in swept wings to prevent the boundary layer drifting outboard toward the
wing tips. Boundary layers on swept wings tend to drift because of the spanwise pressure
gradient of a swept wing. Swept wing often have a leading edge fence of some sort, usually at
about 35 percent of the span from fuselage centerline as shown in figure 5.60. The cross-flow
creates a side lift on the fence that produces a strong trailing vortex. This vortex is carried over
the top surface of the wing, mixing fresh air into the boundary layer and sweeping the boundary
layer off the wing and into the outside flow. The result is a reduction in the amount of boundary
layer air flowing outboard at the rear of the wing. This improves the outer panel maximum lift
coefficient.

Fuselage Center Line

a. Fence over the wing

b. Fence over the canard of Beech Starship

Figure 5.60. Example of a stall fence

Wing Design 90
Similar results can be achieved with a leading edge snag. Such snags tend to create a vortex
which acts like a boundary layer fence. The ideal device is the under-wing fence, referred to as
vertilon. Pylons supporting the engines under the wing, in practice, serve the purpose of the
leading edge fences. Several high subsonic transport aircraft such as DC-9 and Beech Starship
have utilized fence on their swept lifting surfaces. The design of the fence needs a high fidelity
CFD software and is beyond the scope of this book.
5.15.3. Vortex generator
Vortex generators are very small, low aspect ratio wings placed vertically at some local angle of
attack on the wing, fuselage or tail surfaces of aircraft. The span of the vortex generator is
typically selected such that they are just outside the local edge of the boundary layer. Since they
are some types of lifting surfaces, they will produce lift and therefore tip vortices near the edge
of the boundary layer. Then these vortices will mix with the high energy air to raise the kinetic
energy level of the flow inside the boundary layer. Hence, this process allows the boundary layer
to advance further into an adverse pressure gradient before separating. Vortex generators are
employed in many different sizes and shapes.
Most of today‟s high subsonic jet transport aircraft have large number of vortex generators on
wings, tails and even nacelles. Even though vortex generators are beneficial in delaying local
wing stall, but they can generate considerable increase in aircraft drag. The precise number and
orientation of vortex generators are often determined in a series of sequential flight tests. For this
reason, they are sometimes referred to as “aerodynamic afterthoughts”. Vortex generators are
usually added to an aircraft after test has indicated certain flow separations. In Northrop
Grumman B-2A strategic penetration bomber utilizes small, drop-down spoiler panels ahead of
weapon bay doors to generate vortexes to ensure clean weapon release. Figure 5.61 illustrates the
Hawker Beechcraft Beech King 1900D twin turboprop regional airliner that equipped with small
horizontal vortex generator on fuselage ahead of wing roots.

Figure 5. 61. The Hawker Beechcraft Beech King 1900D (note on winglets)
(Photo courtesy of Prestwick 99)

5.15.4. Winglet
Since there is a considerable pressure difference between lower and upper surfaces of a wing, tip
vortices are produced at the wingtips. These tip vortices will then roll up and get around the local
edges of a wing. This phenomenon will reduce the lift at the wingtip station, so they can be
represented as a reduction in effective wing span. Experiments have shown that wings with

Wing Design 91
square or sharp edges have the widest effective span. To compensate this loss, three solutions are
tip-tank; extra wing span; and winglet. Winglets are small, nearly vertical lifting surfaces,
mounted rearward and/or downward relative to the wing tips.
The aerodynamic analysis of a winglet (e.g. lift, drag, local flow circulation) may be
performed by classical aerodynamic techniques. The necessity of wingtips depends on the
mission and the configuration of an aircraft, since they will add to the aircraft weight. Several
small and large transport aircraft such as Pilatus PC-12, Boeing 747-400, McDonnell Douglas C-
17A Globemaster III, and Airbus 340-300 have winglets. Figure 5.61 illustrates the Hawker
Beechcraft Beech King 1900D twin turboprop regional airliner that equipped with winglets in
order to improve hot and high performance.

5.16. Wing Design Steps

At this stage, we are in a position to summarize the chapter. In this section, the practical steps in
a wing design process are introduced (see figure 5.1) as follows:
Primary function: Generation of the lift
1. Select number of wings (e.g. monoplane, bi-plane). See section 5.2.
2. Select wing vertical location (e.g. high, mid, low). See section 5.3.
3. Select wing configuration (e.g. straight, swept, tapered, delta).
4. Calculate average aircraft weight at cruise:

Wave 
1
Wi  W f  (5.44)
2

where Wi is the aircraft at the beginning of cruise and Wf is the aircraft at the end of
cruising flight.
5. Calculate required aircraft cruise lift coefficient (with average weight):

2Wave
C Lc  (5.45)
Vc2 S

6. Calculate the required aircraft take-off lift coefficient:

2WTO
C LTO  0.85 (5.46)
VTO2 S

The coefficient 0.85 originates from the fact that during a take-off, the aircraft has the take-
off angle (say about 10 degrees). Thus about 15 percent of the lift is maintained by the
vertical component (sin (10)) of the engine thrust.

7. Select the high lift device (HLD) type and its location on the wing. See section 5.12.
8. Determine high lift device geometry (span, chord, and maximum deflection). See section
5.12.

Wing Design 92
 9. Select/Design airfoil (you can select different airfoil for tip and root). The procedure was
introduced in Section 5.4.
10. Determine wing incidence or setting angle (iw). It is corresponding to airfoil ideal lift
coefficient; Cli (where airfoil drag coefficient is at minimum). See section 5.5.
11. Select sweep angle (0.5C) and dihedral angles (). See sections 5.9 and 5.11.
12. Select other wing parameter such as aspect ratio (AR), taper ratio (and wing twist
angle (twist). See sections 5.6, 5.7, and 5.10.
13. Calculate lift distribution at cruise (without flap, or flap up). Use tools such as lifting line
theory (See section 5.14), and Computational Fluid Dynamics).
14. Check the lift distribution at cruise that must be elliptic. Otherwise, return to step 13 and
change few parameters.
15. Calculate wing lift at cruise (CLw). Do not employ HLD at cruise.
16. The wing lift coefficient at cruise (CLw) must be equal to the required cruise lift
coefficient (step 5). If not, return to step 10 and change wing setting angle.
17. Calculate wing lift coefficient at take-off (CL_w_TO). Employ flap at take-off with the
deflection of f and wing angle of attack of: w = sTO – 1. Note that s at take-off is
usually smaller than s at cruise. Please note that the minus one (-1) is for safety.
18. The wing lift coefficient at take-off (CL_w_TO) must be equal to take-off lift coefficient
(step 6). If not, first, play with flap deflection (f), and geometry (Cf, bf); otherwise,
return to step 7 and select another HLD. You can have more than one for more safety.
19. Calculate wing drag (Dw).
20. Play with wing parameters to minimize the wing drag.
21. Calculate wing pitching moment (Mow). This moment will be used in the tail design
process.
22. Optimize the wing to minimize wing drag and wing pitching moment

A fully solved example will demonstrate the application of these steps in the next section.

5.17. Wing Design Example

In this section, a major wing design example with the full solution is presented. To avoid
lengthening the section, few details are not described and left to the reader to discover. These
details are very much similar to the solutions that are explained in other examples of this section.

Example 5.6
Design a wing for a normal category General Aviation aircraft with the following features:
S = 18.1 m2, m = 1,800 kg, VC = 130 knot (@ sea level), VS = 60 knot
Assume the aircraft has a monoplane high wing and employs the split flap.

Wing Design 93
Solution:
The number of wings and wing vertical position are stated by the problem statement, so we do
not need to investigate these two parameters.
1. Dihedral angle

Since the aircraft is a high wing, low subsonic, mono-wing aircraft, based on table 5.8, a “-5”
degrees of anhedral is selected. This value will be revised and optimized when other aircraft
components are designed during lateral stability analysis.

2. Sweep angle
The aircraft is a low subsonic prop-driven normal category aircraft. To keep the cost low in the
manufacturing process, we select no sweep angle at 50 percent of wing chord. However, we may
need to taper the wing; hence the leading edge and trailing edge may have sweep angles.

3. Airfoil
To be fast in the wing design, we select an airfoil from NACA selections. The design of an
airfoil is out of the scope of this text book. The selection process of an airfoil for the wing
requires some calculations as follows:
- Section‟s ideal lift coefficient:

2Wave 2  1800  9.81

C LC    0.356 (5.10)
Vc S 1.225  130  0.514 2  18.1
2

C LC 0.356
C LCw    0.375 (5.11)
0.95 0.95

C LC w 0.375
C li    0.416 (5.12)
0.9 0.9
- Section‟s maximum lift coefficient:

2WTO 2  1800  9.81

C Lmax    1.672 (5.13)
 oVs S 1.225  60  0.514 2  18.1
2

C Lmax 1.672
C Lmaxw    1.76 (5.14)
0.95 0.95
C Lmaxw 1.76
Clmaxgross    1.95 (5.15)
0.9 0.9

The aircraft has a split flap, and the split flap generates an CL of 0.55 when deflected 30
degrees. Thus:

Wing Design 94
C lmax  C lmaxgross  C lmaxHLD  1.95  0.45  1.5 (5.16)

Thus, we need to look for NACA airfoil sections that yield an ideal lift coefficient of 0.4 and a
net maximum lift coefficient of 1.5.

Cli  0.416  0.4

Clmax  1.95 (Flap down)

Clmax  1.5 (Flap up)

By referring to Reference 2 and figure 5.23, we find the following seven airfoil sections whose
characteristics match with or is close to our design requirements (all have Cli = 0.4, Clmax  1.5):

631-412, 632-415, 641-412, 642-415, 662-415

Now we need to compare these airfoil sections to see which one is the best. The Table 5.18
compares the characteristics of the seven candidates. The best airfoil is the airfoil whose Cmo is the
lowest, the Cdmin is the lowest, the s is the highest, the (Cl/Cd)max is the highest, and the stall quality is
docile. By comparing the numbers in the above table, we can conclude the followings:

1- The NACA airfoil section 662-415 yields the highest maximum speed, since it has the
lowest Cdmin (i.e. 0.0044).
2- The NACA airfoil section 642-415 yields the lowest stall speed, since it has the highest
maximum lift coefficient (i.e. 2.1).
3- The NACA airfoil section 662-415 yields the highest endurance, since it has the highest
(Cl/Cd)max (i.e. 150).
4- The NACA 632-415 and 642-415 yield the safest flight, due to its docile stall quality.
5- The NACA airfoil section 642-415 delivers the lowest longitudinal control effort in flight,
due to the lowest Cmo (i.e. -0.056).

No NACA Cdmin Cmo s (deg) o (deg) (Cl/Cd)max Cl Clmax Stall

Flap up f = 60o f = 30o quality
1 631-412 0.0049 -0.075 11 -13.8 120 0.4 2 Moderate
2 632-415 0.0049 -0.063 12 -13.8 120 0.4 1.8 Docile
3 641-412 0.005 -0.074 12 -14 111 0.4 1.8 Sharp
4 642-415 0.005 -0.056 12 -13.9 120 0.4 2.1 Docile
5 662-415 0.0044 -0.068 17.6 -9 150 0.4 1.9 Moderate
6 4412 0.006 -0.1 14 -15 133 0.4 2 Moderate
7 4418 0.007 -0.085 14 -16 100 0.4 2 Moderate

Table 5.18. A comparison between seven airfoil candidates for the wing in example 5.6
Since the aircraft is a non-maneuverable GA aircraft, the stall quality cannot be sharp; hence
NACA 641-412 is not acceptable. If the safety is the highest requirement, the best airfoil is

Wing Design 95
 NACA 642-415 due to its high Clmax. When the maximum endurance is the highest priority,
NACA airfoil section 662-415 is the best, due to its high (Cl/Cd)max. On the other hand, if the low
cost is the most important requirement, NACA 662-415 with the lowest Cdmin is the best.
However, if the aircraft stall speed, stall quality and lowest longitudinal control power are of
greatest important design requirement, the NACA airfoil section 642-415 is the best. This may be
performed by using a comparison table incorporating the weighted design requirements.
Due to the fact that NACA airfoil section 642-415 is the best in terms of three criteria, we
select it as the most suitable airfoil section for this wing. Figure 5.62 illustrates the characteristics
graphs of this airfoil.

Ideal lift
coefficient

Wing setting angle Ideal lift coefficient

Figure 5.62. Airfoil section NACA 662-415

4. Wing setting angle

Wing setting angle is initially determined to be the corresponding angle to the airfoil ideal lift
coefficient. Since the airfoil ideal lift coefficient is 0.416, figure 5.62 (left figure) reads the
corresponding angle to be 2 degrees. The value (iw = 2 deg) may need to be revised based on the
calculation to satisfy the design requirements later.
5. Aspect ratio, Taper ratio, and Twist angle

Wing Design 96
Three parameters of aspect ratio, taper ratio, and twist angle are determined concurrently, since
they are all influential for the lift distribution. Several combinations of these three parameters
might yield the desirable lift distribution which is elliptical. Based on the table 5.6, the aspect
ratio is selected to be 7 (AR = 7). No twist is assumed (t = 0) at this time to keep the
manufacturing cost low and easier to build. The taper ratio is tentatively considered 0.3 ( = 3).
Now we need to find out 1. if the lift distribution is elliptical; 2. if the lift created by this wing at
cruise is equal to the aircraft weight. The lifting line theory is employed to determine lift
distribution and wing lift coefficient.
Lift distribution
0.7

0.6

0.5

0.4
Lift coefficient

0.3

0.2

0.1

0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
y/s

Figure 5.63. The lift distribution of the wing (AR = 7,  = 0.3, t =0, iw =2 deg)
A MATLAB m-file is developed similar to what is shown in example 5.5. The application of the
lifting-line theory is formulated through this m-file. Figure 5.63 shows the lift distribution of the
wing as an output of the m-file. The m-file also yields the lift coefficient to be:
CL = 0.4557
Two observations can be made from the results: 1. The lift coefficient is slightly higher than
what is needed (0.4557 > 0.356); 2. The lift distribution is not elliptical. Therefore, some wing
features must be changed to correct both outcomes.
After several trial and errors, the following wing specifications are found to satisfy the design
requirements:

Wing Design 97
 AR = 7,  = 0.8, t = -1.5 deg, iw = 1.86 deg
By using the same m-file and these new parameters, the following results are obtained:
- CL = 0.359
- Elliptical lift distribution as shown in figure 5.64.
Lift distribution
0.45

0.4

0.35

0.3
Lift coefficient

0.25

0.2

0.15

0.1

0.05

0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
y/s

Figure 5.64. The lift distribution of the wing (AR = 7, = 0.8, t =-1.5, iw =1.86 deg)
Hence, this wing with the above parameters satisfies the aircraft cruise requirements. Now, we
need to proceed to design the flap and to determine the flap parameters to satisfy the take-off
requirements.

6. Flap parameters
Flap is usually employed during take-off and landing operations. We design the flap based on the
take-off requirements and shall adjust it for the landing requirements. The take-off speed for a
GA aircraft is about 20 percent faster than stall speed:

m
VTO  1.2  VS  1.2  60  72 knot  37 (5.38)
sec

Hence, the wing; while flap is deflected; must generate the following lift coefficient during take-
off:

Wing Design 98
 2WTO 2  1800  9.81
C LTO    1.161 (5.46)
 oVTO S 1.225  37 2  18.1
2

As the problem statement indicates, the wing employs a split flap. We need to determine the flap
chord, flap span and flap deflection during take-off and landing. The flap chord is tentatively set
to be 20 percent of wing chord. The flap span is tentatively set to be 60 percent of wing span.
This is to leave about 30 percent of the wing span for aileron in future design applications. The
flap deflection for take-off operation is tentatively set to be 20 degrees. The reasons for these
three selections are found in the section 5.12. The wing angle of attack during take-off operation
also needs to be decided. This angle is assumed to be as high as possible. Based on the figure
5.57, the airfoil stall angle is about 12 degrees when the flap is deflected 20 degrees (using an
interpolation). For the sake of safety, we use only 10 degrees of angle of attack for wing during
take-off operation, which is two degrees less than stall angle of attack. Thus, the initial flap
parameters are as follows:

bf/b = 0.6; Cf/C = 0.2, TO_wing = 10 degrees, f = 20 degrees

The lifting line theory is utilized again to determine the wing lift coefficient at take-off by the
above high lift device specifications. A similar m-file is prepared as we did in previous section.
The major change is to apply a new zero-lift angle of attack for the inboard (flap) section. The
change in the zero-lift angle of attack for the inboard (flap) section is:

 o  10  CL (5.39)

Based on the figure 5.62, the split flap increases the section‟s lift coefficient by 0.3 when
deflected 20 degrees. Thus:

 o  10  (0.3)  3 deg (5.39)

This number will be entered in the lifting line program as input. This means that the inboard
section (60 percent of the wing span) will have zero lift angle of attack of -6 (i.e. (-3) + (-3) = -
6) due to flap deflection. The following is the matlab m-file to calculate the wing lift coefficient
while the flap is deflected down during the take-off operation:

clc
clear
N = 9; % (number of segments-1)
S = 18.1; % m^2
AR = 7; % Aspect ratio
lambda = 0.8; % Taper ratio
alpha_twist = -1.5; % Twist angle (deg)
i_w = 10; % wing setting angle (deg)
a_2d = 6.3; % lift curve slope (1/rad)
a_0 = -3; % flap up zero-lift angle of attack (deg)
a_0_fd = -6; % flap down zero-lift angle of attack (deg)
b = sqrt(AR*S); % wing span
bf_b=0.6; flap-to-wing span ratio

Wing Design 99
MAC = S/b; % Mean Aerodynamic Chord
Croot = (1.5*(1+lambda)*MAC)/(1+lambda+lambda^2); % root chord
theta = pi/(2*N):pi/(2*N):pi/2;
alpha=i_w+alpha_twist:-alpha_twist/(N-1):i_w; % segment's angle of attack
for i=1:N
if (i/N)>(1-bf_b)
alpha_0(i)=a_0_fd; %flap down zero lift AOA
else
alpha_0(i)=a_0; %flap up zero lift AOA
end
end
z = (b/2)*cos(theta);
c = Croot * (1 - (1-lambda)*cos(theta)); % MAC at each segment
mu = c * a_2d / (4 * b);
LHS = mu .* (alpha-alpha_0)/57.3; % Left Hand Side
% Solving N equations to find coefficients A(i):
for i=1:N
for j=1:N
B(i,j) = sin((2*j-1) * theta(i)) * (1 + (mu(i) * (2*j-1)) /
sin(theta(i)));
end
end
A=B\transpose(LHS);
for i = 1:N
sum1(i) = 0;
sum2(i) = 0;
for j = 1 : N
sum1(i) = sum1(i) + (2*j-1) * A(j)*sin((2*j-1)*theta(i));
sum2(i) = sum2(i) + A(j)*sin((2*j-1)*theta(i));
end
end
CL_TO = pi * AR * A(1)

In take-off, the lift distribution is not a concern, since the flap increases the wing inboard lift
coefficient. The m-file yields the following results:

C LTO  1.254

Since the wing generated take-off lift coefficient is slightly higher than the required take-off lift
coefficient, one or more of the wing or flap parameters must be changed. The easiest change is to
reduce the wing angle of attack during take-off. Other options are to reduce the size of flap and
to reduce the flap deflection. By a trial and error, it is determined that by reducing the wing angle
of attack to 8.88 degrees, the wing will generate the required lift coefficient of 1.16.

C LTO  1.16

Since the wing has a setting angle of 1.86 degrees, the fuselage wil1 be pitched up 7 degrees
during take-off, since 8.88 - 1.86 = 7.02. Thus:

iw = 1.86 deg,  TO_wing = 8.88 deg,  TO_fus = 7.02 deg, f_TO = 20 deg

Wing Design 100

At this moment, it is noted that the wing satisfies the design requirements both at cruise and at
take-off.

7. Other Wing Parameters

To determine other wing parameters (i.e. wing span (b), root chord (Cr), tip chord (Ct), and
Mean Aerodynamic Chord (MAC), we have to solve the following four equations
simultaneously:

S  bC (5.17)

b2
AR  (5.18)
S

Ct
 (5.24)
Cr

2  1    2 
C Cr   (5.26)
3  1   

Solution of these equations simultaneously yields the following results:

b  11.256 m; MAC  1.608 m; C r  1.78 m; C t  1.42 m

Consequently, other flap parameters are determined as follows:

bf
 0.6  b f  0.6  11.256  6.75 m
b
Cf
 0.2  C f  0.2  1.608  0.32 m
C
Figure 5.65 illustrates the right half wing with the wing and flap parameters of example 5.6.
The next step in the wing design process is to optimize the wing parameters such that the wing
drag and pitching moment are minimized. This step is not shown in this example to reduce the
length of the chapter.

Wing Design 101

Cr = 1.78 m
MAC = 1.608 m Ct = 1.42 m

Cf = 0.32 m

bf/2 = 3.375 m

b/2 = 5.63 m

a . Top view of the right half wing

iw = 1.86 deg

Horizontal Fuselage Center Line (fus =0)

b. Side view of the aircraft in cruising flight

iw = 1.86 deg

w = 8.88 deg

fus =7.02 deg Horizontal

Fuselage Center Line (fus =7 deg)

c. Side view of the aircraft in take-off

Figure 5.65. Wing parameters of Example 5.6

Wing Design 102

Problems

5.1. Identify Cli, Cdmin, Cm, (Cl/Cd)max, o (deg), s (deg), Clmax, ao (1/rad), (t/c)max of the
NACA 2412 airfoil section (flap-up). You need to indicate the locations of all parameters
on the airfoil graphs as shown in figure 5.66.

Cm

Figure 5.66. Airfoil section NACA 2415

5.2. Identify Cli, Cdmin, Cm, (Cl/Cd)max, o (deg), s (deg), Clmax, ao (1/rad), (t/c)max of the
NACA 632-615 airfoil section (flap-up). You need to indicate the locations of all
parameters on the airfoil graphs as shown in figure 5.21.
5.3. A NACA airfoil has thickness-to-chord ratio of 18 percent. Estimate the lift curve slope
for this airfoil in 1/rad.

5.4. Select a NACA airfoil section for the wing for a prop-driven normal category GA
aircraft with the following characteristics:

mTO = 3,500 kg, S = 26 m2, Vc = 220 knot (at 4,000 m), Vs = 68 knot (@sea level)

The high lift device (plain flap) will provide CL = 0.4 when deflected.
5.5. Select a NACA airfoil section for the wing for a prop-driven transport aircraft with the
following characteristics:

mTO = 23,000 kg, S = 56 m2, Vc = 370 knot (at 25,000 ft), Vs = 85 knot (@sea level)

Wing Design 103

 The high lift device (single slotted flap) will provide CL = 0.9 when deflected.
5.6. Select a NACA airfoil section for the wing for a business jet aircraft with the following
characteristics:

mTO = 4,800 kg, S = 22.3 m2, Vc = 380 knot (at 33,000 ft), Vs = 81 knot (@sea level)

The high lift device (double slotted flap) will provide CL = 1.1 when deflected.
5.7. Select a NACA airfoil section for the wing for a jet transport aircraft with the following
characteristics:

mTO = 136,000 kg, S = 428 m2, Vc = 295 m/sec (at 42,000 ft), Vs = 118 knot (@sea level)

The high lift device (triple slotted flap) will provide CL = 1.3 when deflected.
5.8. Select a NACA airfoil section for the wing for a fighter jet aircraft with the following
characteristics:

mTO = 30,000 kg, S = 47 m2, Vc = 1,200 knot (at 40,000 ft), Vs = 95 knot (@sea level)

The high lift device (plain flap) will provide CL = 0.8 when deflected.
5.9. A designer has selected a NACA 2412 (figure 5.65) for an aircraft wing during a design
process. Determine the wing setting angle.
5.10. The airfoil section of a wing with aspect ratio of 9 is NACA 2412 (figure 5.65).
Determine the wing lift curve slope in terms of 1/rad.
5.11. Determine the Oswald span efficiency for a wing with aspect ratio of 12 and
sweep angle of 15 degrees.
5.12. Determine the Oswald span efficiency for a wing with aspect ratio of 4.6 and
sweep angle of 40 degrees.
5.13. A straight rectangular wing has a span of 25 m and MAC of 2.5 m. If the wing
swept back by 30 degrees, determine the effective span of the wing.
5.14. A trainer aircraft has a wing area of S = 32 m2, aspect ratio AR = 9.3, and taper
ratio of  = 0.48. It is required that the 50 percent chord line sweep angle be zero.
Determine tip chord, root chord, mean aerodynamic chord, and span, as well as leading
edge sweep, trailing edge sweep and quarter chord sweep angles.
5.15. A cargo aircraft has a wing area of S = 256 m2, aspect ratio AR = 12.4, and taper
ratio of  = 0.63. It is required that the 50 percent chord line sweep angle be zero.
Determine tip chord, root chord, mean aerodynamic chord, and span, as well as leading
edge sweep, trailing edge sweep and quarter chord sweep angles.
5.16. A jet fighter aircraft has a wing area of S = 47 m2, aspect ratio AR = 7, and taper
ratio of  = 0.8. It is required that the 50 percent chord line sweep angle be 42 degrees.
Determine tip chord, root chord, mean aerodynamic chord, span, and effective span, as
well as leading edge sweep, trailing edge sweep and quarter chord sweep angles.
5.17. A business jet aircraft has a wing area of S = 120 m2, aspect ratio AR = 11.5, and
taper ratio of  = 0.55. It is required that the 50 percent chord line sweep angle be 37
degrees. Determine the tip chord, root chord, mean aerodynamic chord, span, and

Wing Design 104

 effective span, as well as leading edge sweep, trailing edge sweep and quarter chord
sweep angles.
5.18. Sketch the wing for problem 5.16.
5.19. Sketch the wing for problem 5.17.
5.20. A fighter aircraft has a straight wing with a planform area of 50 m2, aspect ratio of
4.2 and taper ratio of 0.6. Determine wing span, root chord, tip chord, and Mean
Aerodynamic Chord. Then sketch the wing.
5.21. A hang glider has a swept wing with a planform area of 12 m2, aspect ratio of 7
and taper ratio of 0.3. Determine wing span, root chord, tip chord, and Mean
Aerodynamic Chord. Then sketch the wing, if the sweep angle is 35 degrees.
5.22. The planform area for a cargo aircraft is 182 m2. The wing has an anhedral of -8
degrees; determine the effective wing planform area of the aircraft.
5.23. A jet transport aircraft has the following characteristics:

mTO = 140,000 kg, S = 410 m2, Vs = 118 knot (@sea level), AR = 12,  = 0.7, iw = 3.4
deg, t = -2 deg, airfoil section: NACA 632-615 (figure 5.21), bA_in/b = 0.7
Design the high lift device (determine type, bf, Cf, f) for this aircraft to be able to take-
off with a speed of 102 knot while the fuselage is pitched up 10 degrees.
5.24. A twin engine GA aircraft has the following characteristics:

mTO = 4,500 kg, S = 24 m2, AR = 8.3,  = 0.5, iw = 2.8 deg, t = -1 deg, bA_in/b = 0.6
airfoil section: NACA 632-615 (figure 5.21)
Design the high lift device (determine type, bf, Cf, f) for this aircraft to be able to take-
off with a speed of 85 knot while the fuselage is pitched up 10 degrees.
5.25. Determine and plot the lift distribution for a business aircraft with a wing with the
following characteristics. Divide the half wing into 12 sections.

S = 28 m2, AR = 9.2,  = 0.4, iw = 3.5 deg, t = -2 deg, airfoil section: NACA 63-209
If the aircraft is flying at the altitude of 10,000 ft with a speed of 180 knot, how much lift
is produced?
5.26. Determine and plot the lift distribution for a cargo aircraft with a wing with the
following characteristics. Divide the half wing into 12 sections.

S = 104 m2, AR = 11.6,  = 0.72, iw = 4.7 deg, t = -1.4 deg, NACA 4412, aTO-wing = 10 deg
If the aircraft is flying at the altitude of 25,000 ft with a speed of 250 knot, how much lift
is produced?
5.27. Consider the aircraft in problem 5.25. Determine the lift coefficient at take-off
when the following high lift device is employed.

Single slotted flap, bf/b = 0.65, Cf/C = 0.22, f = 15 deg, aTO-wing = 9 deg
5.28. Consider the aircraft in problem 5.26. Determine the lift coefficient at take-off
when the following high lift device is employed.

Wing Design 105

 triple slotted flap, bf/b = 0.72, Cf/C = 0.24, f = 25 degrees, aTO-wing = 12 deg
5.29. Consider the aircraft in problem 5.28. How much flap need to be deflected in
landing, if the fuselage is allowed to pitch up only 7 degrees with a speed of 95 knot.
5.30. Design a wing for an utility category General Aviation aircraft with the following
features:
S = 22 m2, m = 2,100 kg, VC = 152 knot (@ 20,000 ft), VS = 67 knot (@ sea level)
The aircraft has a monoplane low wing and employs the plain flap. Determine airfoil
section, aspect ratio, taper ratio, tip chord, root, chord, MAC, span, twist angle, sweep
angle, dihedral angle, incidence, high lifting device type, flap span, flap chord, flap
deflection and wing angle of attack at take-off. Plot lift distribution at cruise and sketch
the wing including dimensions.
5.31. Design a wing for a jet cargo aircraft with the following features:
S = 415 m2, m = 150,000 kg, VC = 520 knot (@ 30,000 ft), VS = 125 knot (@ sea level)
The aircraft has a monoplane high wing and employs a triple slotted flap. Determine
airfoil section, aspect ratio, taper ratio, tip chord, root, chord, MAC, span, twist angle,
sweep angle, dihedral angle, incidence, high lifting device type, flap span, flap chord,
flap deflection and wing angle of attack at take-off. Plot lift distribution at cruise and
sketch the wing including dimensions.
5.32. Design a wing for a supersonic fighter aircraft with the following features:
S = 62 m2, m = 33,000 kg, VC = 1,350 knot (@ 45,000 ft), VS = 105 knot (@ sea level)
The controllability and high performance are two high priorities in this aircraft.
Determine wing vertical position, airfoil section, aspect ratio, taper ratio, tip chord, root,
chord, MAC, span, twist angle, sweep angle, dihedral angle, incidence, high lifting
device type, HLD span, HLD chord, HLD deflection and wing angle of attack at take-off.
Plot lift distribution at cruise and sketch the wing including dimensions.
5.33. Determine and plot the lift distribution for the aircraft Cessna 304A at cruising
flight. The characteristics of this aircraft are given in table 5.17. Then determine the lift
coefficient at cruise.
5.34. Determine and plot the lift distribution for the aircraft Scottish Aviation SA-3-120
at cruising flight. The characteristics of this aircraft are given in table 5.17. Then
determine the lift coefficient at cruise.
5.35. Determine and plot the lift distribution for the aircraft Aerocare IMP at cruising
flight. The characteristics of this aircraft are given in table 5.17. Then determine the lift
coefficient at cruise.

Wing Design 106

References

1. Eppler, Richard, Airfoil Design and Data, Springer-Verlag, Berlin, 1990

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Third edition, 2006
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Wiley, 2003
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1996
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edition, Elsevier, 2003

Wing Design 107