King Abduaziz University

Faculty of Engineering
Department of Aerospace Engineering
AE-311: Low Speed Aerodynamics

Aerodynamic Design
(Airfoil Design)

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Airfoil Design: Lift, Drag, and Moment Coefficients
Lift Curve Slope:
- It indicates how rapidly lift changes with angle of attack.
- It is usually linear at low angles of attack; however, it is nonlinear
outside this range and can have a negative slope.
- A nonlinear lift curve slope is indicative of flow separation prevailing
on the body.

Maximum and Minimum Lift Coefficients:

- dictates the stalling speed and therefore wing size and airplane
weight)
- The stall is defined as the flow conditions that follow the first lift curve
peak, which is where the Clmax occurs.

Zero Lift Angle:

- It is important when considering wing washout
- Lift coefficient at zero angle: It affects the wing’s angle-of-incidence.

Min Drag: should be as low as possible, but it must be low where it

counts, in the region of intended lift coefficient of climb and cruise.

Lift coefficient at Minimum Drag:

- It is the lift coefficient where at min drag.
- we prefer an airfoil whose lift coefficient in cruise is close to min drag
coefficient.

Pitching Moment Coefficient:

-It is usually measured about its quarter-chord or aerodynamic center.
-It is a function of the airfoil’s camber.
-Larger camber leads to greater moment.

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Airfoil Design: Pressure Distribution
→ Cp is plotted "upside-down" with negative values
(suction), higher on the plot.

→ The Cp curve starts from about 1.0 at the stagnation

point near the leading edge.

→ It rises rapidly (pressure decreases) on both the

upper and lower surfaces.

→ It recovers to a small positive value of Cp near the

trailing edge.

1. Upper Surface: the upper surface Cp is normally lower than the lower surface Cp but it doesn't have to be.
2. Lower Surface: the lower surface sometimes carries a positive pressure, but at many design conditions is pulling the wing downward.
3. Pressure Recovery region: in this region the pressure increases from its minimum value to the value at the trailing edge.
➢ This area is also known as the region of adverse pressure gradient and is associated with boundary layer transition and possibly
separation, if the gradient is high.
4. Trailing Edge Pressure: it is related to the airfoil thickness and shape near the trailing edge.
➢ For thick airfoils the pressure here is slightly positive (the velocity is a bit less than the freestream velocity). For infinitely thin sections Cp
= 0 at the trailing edge. Large positive values of Cp at the trailing edge imply more severe adverse pressure gradients.
5. CL and Cp: CL is the area between the two curves upper and lower Cp
6. Stagnation Point: the stagnation point occurs near the leading edge. It is the place at which the velocity is zero. Note that in incompressible flow
Cp = 1.0 at this point. In compressible flow it may be somewhat larger

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Airfoil Design: Pressure Distribution

Conventional Pressure Distribution “Rooftop” or Stratford Pressure Distribution

Aft-loaded Pressure Distribution Low-moment Pressure Distribution

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Airfoil Design: Geometrical Parameters

❖ Chord line: The chord line is a line drawn from

the leading edge to the trailing edge.

❖ Mean camber line: The mean camber line is a

line created by the locus of points midway
between the upper and lower surfaces of the
airfoil measured perpendicular to the camber
line.

❖ Maximum camber: The maximum camber is the

maximum rise of the camber line from the
chord line.
❖ Center of Pressure: The point where the magnitude of the
❖ Thickness ratio: The thickness is the height of moment equals zero.
airfoil profile measured perpendicular to the
chord line. ❖ Aerodynamic Center: The point on a body about which the
aerodynamic moment is independent of the angle of attack
❖ Leading edge radius: The leading-edge radius is
the radius of a circle that is tangent to the
upper and lower surfaces with its center
located on a line drawn tangent to the mean
line at the leading edge.

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Airfoil Design: Geometrical Parameters

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Airfoil Design: Effect Camber

1. Increasing camber increases zero lift angle and decreases stall angle.
2. Camber distribution affect the lift coefficient and stall behavior:
a) Higher camber is located near the leading edge, the stall is very abrupt
b) Higher camber at the trailing edge is more effective

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Airfoil Design: Effect of Thickness
1. Increasing Max. Thickness > increases the maximum
local velocity. Therefore
❖ CLmax increases.
❖ Adverse pressure gradient increases.
❖ CDmin increases.
❖ In transonic range, CL decreases and CD increases
❖ Thick sections have boundary layers just on the
verge of separation throughout the recovery
region due to high adverse pressure gradient.

2. Thickness Distribution affects pressure distribution and

thus boundary layer behavior (separation, transition).
❖ If the airfoil is thick, the separation tends to begin
at the trailing edge and move forward as the AOA
increases.
❖ On the other hand, if the airfoil is thin, the
separation tends to begin at the leading edge in
the form of a separation bubble.

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Airfoil Design: Effect of Leading-Edge Radius
Leading Edge Radius: has a significant effect on boundary layer separation and stall:
1. Small leading edge radius has abrupt stall.
2. Large leading edge radius has more gradual stalling behavior.
3. The larger the radius the more lift will be generated at high angles of attack.
4. Large radius can also increase the airfoil’s drag.

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Airfoil Design: effect of Angle of attack

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Airfoil Design: effect of Reynolds Number

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Airfoil Design: effect of Reynolds Number
Low Re number

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Airfoil Design: effect of Mach Number

As the Mach number increases:

1. The slope of the lift curve increases

2. The stall angle decreases

3. The drag coefficient remains relatively

constant until the airfoil approaches the critical
Mach number range.

4. At the critical Mach number range there is an

abrupt reduction in lift and a sharp rise in drag

5. The pitch stability and stick force will rise

rapidly as the Mach number approached unity
and might render the aircraft uncontrollable.

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Airfoil Design: effect of Mach Number

⚫ As air expands around top surface near leading edge, velocity and M will increase
⚫ Local M > M∞

Flow over airfoil may have

Sonic/Supersonic regions even though
freestream Mach number M∞ < 1

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Airfoil Design: effect of Mach Number

⚫ Pressure Distribution for transonic freestream conditions

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Airfoil Design: effect of Roughness

1. Roughness causes a boundary layer to

become turbulent almost immediately
after it is formed thereby
• substantially increasing the values of
drag
• causing more rapid increase in drag
with angle of attack.
2. Smooth surfaces are important even for
non-NLF airfoils.
• surfaces do not have to be superbly
polished.
• surface particles are more detrimental
than surface scratches when comes to
the transition of laminar to turbulent
boundary layer.

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Airfoil Design: High Lift Devices

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Airfoil Design: High Lift Devices ( TRAILING-EDGE DEVICES )

Split Flap

Junker Flap

Zap Flap

Double-Slotted
Flap

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Airfoil Design: High Lift Devices ( TRAILING-EDGE DEVICES )

• The purpose of the trailing edge

high-lift device is to increase the
maximum lift coefficient.

• Deploying a flap will affect not

only CLmax and stall but also the
pitching moment.

• The pitching moment increases

substantially.

• Deploying flaps has a major effect

on the stall characteristics of the
aircraft.

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Airfoil Design: High Lift Devices ( LEADING-EDGE DEVICES )

• The purpose of the leading edge high-lift device

is to increase stall angle and maximum lift
coefficient

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Airfoil Design: Design Specifications
❑ Airfoil design specifications may vary from one application to another. Here are some
examples.
▪ Target CL given, max L/D is required.
▪ Target pressure distribution, known to have good boundary layer characteristics, is given.
▪ Higher lift stall angle is required or specified.
▪ Trailing edge (or leading edge) separation is to be eliminated.
▪ Laminar flow is required.

❑ The airfoil section may be required to achieve this performance with constraints on thickness,
pitching moment, off-design performance, or any other parameter.
▪ May be geometric:
• Airfoil too thin or too thick.
• Leading edge radius is too small, which may lead to leading edge stall.
▪ May be performance related:
• Good transonic performance as well as supersonic cruise performance desired.
• Good cruise performance as well as high enough CLmax for take-off / landing performance.

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Airfoil Design:
Single Point vs. Multi-Point Design

❑ In some design problems, it is enough to meet a single operation point. This is called a
single point design.
➢ Example: design an airfoil that has the maximum L/D at Cl=0.5, at a cruise Mach
number of 0.75.
❑ In other cases, the design must meet satisfactory performance at two or more conditions.
This is called a multi-point design.
➢ Example: satisfactory subsonic cruise performance (maximum L/D at M=0.75 at Cl=0.5),
and a supersonic performance ( L/D ~ 4 at M=2.0)

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Airfoil Design:
Multiple Design Point Airfoils

⚫ One of the difficulties in designing a good airfoil is the

requirement for acceptable off-design performance.
➢ While a very low drag section is not too hard to design, it
may separate at angles of attack slightly away from its
design point.
➢ Airfoils with high lift capability may perform very poorly at
lower angles of attack.

⚫ One can approach the design of airfoil sections with

multiple design points in a well-defined way.
➢ Often it is clear that the upper surface will be critical at
one of the points and we can design the upper surface at
this condition.
➢ The lower surface can then be designed to make the
section behave properly at the second point.
➢ Similarly, constraints such as Cm0 are most effected by
airfoil trailing edge geometry.

⚫ When such a compromise is not possible, variable

geometry can be employed (at some expense) as in the
case of high lift systems.

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Airfoil Design: Design Methodologies
I - Manual Iterative Process:
1. Specify design criteria.
2. Start with a known airfoil shape, as close to
the target as you can.
3. Use analysis tools in an iterative process to
gradually improve the starting
geometry/shape.

• the design changes are driven by engineering

intuition to interpret simulation and change design
• Designers must be aware of analysis tools’ limitations
• The final design must be validated to make sure that
the new airfoil does indeed perform better

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Airfoil Design: Design Methodologies
II - Optimization:
1. Specify performance metrics based on design
criteria to guide the optimization process.
2. Start with a known airfoil shape, as close to
the target as you can.
3. Use an optimization tool coupled with
analysis tools to optimize the starting
geometry/shape.
• Engineering intuition is also required here because
automatic optimization tends to produce unrealistic
shapes.
• Designers must be aware of analysis tools’
limitations
• The final design must be validated to make sure that
the new airfoil does indeed perform better

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Airfoil Design: Airfoil Selection Guidelines

1. Select airfoils with drag bucket over

those without.

2. Select airfoils with wider drag bucket

over those with narrower drag bucket.

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Airfoil Design: Airfoil Selection Guidelines

3. Select the airfoil with the largest CL/CD

possible at design CL.

4. However, avoid airfoils with sharp drop

in CL immediately after stall

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Airfoil Design: Airfoil Selection Guidelines

5. Select airfoils with the lowest quarte-chord

moment Cmc/4 possible at design CL.

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Airfoil Design: Airfoil Selection Guidelines
⚫ Table Used to Down-select Candidate Airfoils

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