Aerodynamic forces on rectangular wings oscillating in a supersonic air stream

Abstract

The aerodynamic forces on rectangular wings of various aspect ratios describing simple harmonic oscillations of small amplitude in a supersonic air stream are determined. Linearized theory is used and numerical solutions are derived by the method of 'Relaxation'. The problem is formulated in section 4 and in section 6 it is reduced to one of finding a series of conical flow solutions. Only a few terms of this series need be determined since the process converges quickly for the range of values of the frequency parameter considered. This range is believed to cover most of the practical supersonic flutter values. Moment coefficients for a range of Mach numbers and various frequency parameter values were calculated and they are tabulated and plotted at the end of the report. The coefficients are referred to tile leading-edge axis position but can be referred to any other axis by the usual formulae. For a range of Mach numbers in two-dimensional flow, the aerodynamic damping for pitching oscillation can be negative for certain positions of the axis of pitch oscillation and this implies instability (R. & M. 2140 and 2194). The results of this report show that aspect ratio has a stabilizing effect for axes less. than about 0.7 of the chord downstream of the leading edge, but has the opposite effect for axes nearer than this to the trailing edge.