On some problems of unsteady supersonic aerofoil theory

Unsteady supersonic flow round an aerofoil of infinite span is considered in the first part of the paper.It is shown that the pressure at any given point of an aerofoil under forward acceleration can be analysed into three components, one of which is the steady (Ackeret)pressure due to the instantaneous velocity, while of the other two, one depends directly on the acceleration, and one on the square of the velocity, during a limited time interval preceding the instant under consideration. However, the difference between the total pressure and the "steady pressure component" is such that it can be neglected in all the definitely supersonic conditions which are likely to occur in practice.

The oscillatory supersonic flow round a Delta wing inside the Mach cone emanating from its apex is considered in the second part of the paper. Particular "normal" solutions are obtained by means of a special system of curvilinear coordinates. It is shown that the velocity potentials corresponding to vertical and pitching oscillations of the wing can be represented by series of such normal solutions. The assumptions of linearised theory arc adopted throughout.