Abstract
Abstract : A second-order theory was developed for 2 dimensional pitching airfoils at supersonic speeds. The development is based on considering airfoils with arbitrary symmetrical cross sections, but the analysis can be extended to airfoils with unsymmetrical cross sections. An expression for the lifting pressure caused by steady pitching is obtained which permits the stability derivatives to be calculated. The equation considered is similar to the equation of steady supersonic flow. The assumptions were that the second-order solution could be obtained by iteration and that the characteristics of the first- and second-order solutions are the same. The partial differential equation for airfoils with a steady pitching velocity was expressed in a time-independent form by conversion to a set of axes fixed to the airfoil. The first-order solution of this form of the equation was taken as the first approximation to the second-order equation. The second approximation was obtained by substituting this first-order solution into the second-order equation and solving the resulting non-homogeneous equation.
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