A method for calculating the lifting forces on wings (unsteady subsonic and supersonic lifting-surface theory)

Abstract

A numerical method is given for calculating the lifting forces on oscillating wings of any plan-form. The principles and techniques of Multhopp's subsonic theory have been applied to the supersonic problem resulting in a single basic theory which embraces both subsonic and supersonic cases. One of the most important features of the method is the careful choice of the points at which the lift and downwash distributions are measured. The position of these points in the chordwise direction depend upon whether the local leading and trailing edges are subsonic or supersonic. Extensive use has been made of various interpolation functions which simplify the evaluation of the integrals required for both the downwash and the generalised forces. In the latter case it is shown that the continuous lift distribution can be replaced without loss of accuracy by a set of concentrated lift forces at the lift points. The lift distribution is expressed in terms of these discrete forces since for most purposes they are more convenient to use. It is shown that control surfaces can be dear with by using equivalent continuous deflections and downwash angles to replace the true discontinuous values. Simple expressions are given for these equivalent values, and these expressions are applicable to both subsonic and supersonic cases.