Page 224 - Aerodynamics for Engineering Students

Two-dimensional wing theory 207

-Accurate computation
Thin-aerofoil theory
a 64panels
0 Experimental data

- 1 . 0 0
-20 -15 -10 -5 0 5 10 15 20
Angle of attack,degrees
Fig. 4.26 Variation of lift and moment coefficients with angle of attack for NACA 4412 aerofoil

Exercises
1 A thin two-dimensional aerofoil of chord c is operating at its ideal lift coeffrcient
CL~. Assume that the loading (i.e. the pressure difference across the aerofoil) varies
linearly with its maximum value at the leading edge. Show that

where yc defines the camber line, a is the angle of incidence, and 5 = x/c.
[Hint: Do not attempt to make the transformation x = (c/2)(1 - cos e), instead
write the singular integral as follows:

Then, using this result, show that the angle of incidence and the camber-line shape
are given by

[Hint: Write -1 = C - 1 - C where 1 + C = 27ra/C~ and the constant C is deter-
mined by requiring that yc = 0 at 5 = 0 and 5 = 1.1