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Joukowski Airfoil: Geometry

​
The circle centered at
iδ
me
passes through critical point at ζ = 1.
m
0.30
δ
0.70
π
The Joukowski transformation
z(ζ)=ζ+
1
ζ
is an analytic function of a complex variable that maps a circle in the
ζ
plane to an airfoil shape in the
z
plane. The mapping is conformal except at critical points of the transformation where
z'(ζ)=0
. This occurs at
ζ=±1
with image points at
z=±2
. The sharp trailing edge of the airfoil is obtained by forcing the circle to go through the critical point at
ζ=1
. The trailing edge of the airfoil is located at
z=2
, and the leading edge is defined as the point where the airfoil contour crosses the
x
axis. This point varies with airfoil shape and is computed numerically. The distance from the leading edge to the trailing edge of the airfoil is the chord, which the aerodynamics community uses as the characteristic length for dimensionless measures of lift and pitching moment per unit span. The shape of the airfoil is controlled by a reference triangle in the
ζ
plane defined by the origin, the center of the circle at
ζ=m
iδ
e
and the point
ζ=1
.

Details

Details of potential flow over a Joukowski airfoil and the background material needed to understand this problem are discussed in a collection of documents (CDF files) available at[1].
Snapshot 1: circular arc reference airfoil
Snapshot 2: highly cambered airfoil
Snapshot 3: thick airfoil with moderate camber

References

[1] R. L. Fearn. "Two-Dimensional Potential-Flow Aerodynamics." (Mar 8, 2017) plaza.ufl.edu/rlf/Richard L. Fearn.

External Links

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