Page 216 - Aerodynamics for Engineering Students

Two-dimensional wing theory 199

The theory in the form given above is of limited usefulness for practical aerofoil
sections because most of these have rounded leading edges. At a rounded leading
edge dyt/dxl becomes infinite thereby violating the assumptions made to develop the
thin-aerofoil theory. In fact from Example 4.3 given below it will be seen that the
theory even breaks down when dyt/dxl is finite at the leading and trailing edges.
There are various refinements of the theory that partially overcome this problem*
and others that permit its extension to moderately thick aerofoikT

.=+ (321
Example 4.3 Find the pressure distribution on the bi-convex aerofoil
2c
c

(with origin at mid-chord) set at zero incidence in an otherwise undisturbed stream. For the
given aerofoil

and

From above:

or

-8 t
- - - [xln(x - XI) + x1
-
,iT c2
Thus

At the mid-chord point:

-8t
x=o Cp==
At the leading and trailing edges, x = fc, C, + -m. The latter result shows that the approx-
imations involved in the linearization do not permit the method to be applied for local effects
in the region of stagnation points, even when the slope of the thickness shape is finite.

* Lighthill, M.J. (1951) ‘A new approach to thin aerofoil theory’, Aero. Quart., 3, 193.
J. Weber (1953) Aeronautical Research Council, Reports & Memoranda No. 2918.