By Holt Ashley
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Extra info for Aerodynamics of Wings and Bodies
As described in the references, Theodorsen's so-called E-method has many uses in the theory of low-speed airfoils. For instance, one can generate families of profiles from assumed forms of the function E(I/». Approximate means have been developed, starting from an airfoil of known shape and pressure distribution, for adjusting this pressure distribution in a desired fashion. 4 - J 2-11] I 1 1 1 J THE KUTl'A CONDITION AND LIFT I 1 57 which played such an important role in the early 1940's. Their shapes sustain a carefully adjusted, favorable pressure distribution to assure the longest possible laminar run prior to transition in the boundary layer.
J(x) and 1i(x) 81 '< I I 82 I J J 1 1 THIN-WING THEORY \l 5 z x ------~. define the distribution of thickness and camber, respectively, along the chord. If will be assumed that 71 and Ti are both smooth and that U' and Ti' are of order of unity everywhere along the chord. A blunt leading edge is thus excluded. In the limit of E -+ 0 the airfoil collapses to a segment along the x-axis assumed to be located between x = 0 and x = c. We will seek the leading terms in a series expansion in E of cI> to be used as an approximation for thin airfoils with small camber and angle of attack.
I J I I I J I 4 and no longer a constant. Only for a very restricted class of pressure distributions is it possible to find self-similar solutions and hence reduce the partial differential equation (4-58) to an ordinary one. When this is not possible one has to resort to some approximate method of solution. A discussion of some proposed methods may be found in Schlichting (1960). Having evaluated the first-order inner solution one may proceed to calculate the first-order effect on pressure. As was seen, this could be obtained in an equivalent manner by considering the original body to be thickened by an amount equal to the displacement thickness of the boundary layer.
Aerodynamics of Wings and Bodies by Holt Ashley