The oscillating rectangular airfoil at supersonic speeds

The pressure distribution on a quarter infinite, zero thickness airfoil having a prescribed distribution of downwash (on the wing only), which exhibits a harmonic time dependence, is determined by a Fourier transform solution of the linearized, potential equation for supersonic flow. The solution is effected with the aid of the Wiener-Hopf technique and leads to a Green’s function, which may be expressed either as a finite, definite integral or as an expansion in powers of a dimensionless frequency parameter. It is shown that the results are applicable to the calculation of the forces and moments on rectangular airfoils of effective aspect ratio ($A\cot \theta$, where $\theta$ is the Mach angle) greater than unity. It appears that the force and moment coefficients of practical interest may be expressed in terms of known functions, including certain integrals which have been calculated for the two-dimensional, oscillating airfoil. The extension of the two-dimensional results to rectangular wings for which the prescribed downwash is constant along the span is particularly simple. The extension of the results for harmonic time dependence to the step function (Heaviside) case is indicated.