Unsteady Transonic Flow Analysis for Low Aspect Ratio, Pointed Wings

Abstract

Oswatitsch and Keune's parabolic method for steady transonic flow is applied and extended to thin slender wings oscillating in the sonic flowfield. The parabolic constant for the wing was determined from the equivalent body of revolution. Laplace transform methods were used to derive the asymptotic equations for pressure coefficient, and the Adams-Sears iterative procedure was employed to solve the equations. A computer program was developed to find the pressure distributions, generalized force coefficients, and stability derivatives for delta, convex, and concave wing planforms. Input for the program includes planform shape, acceleration constant, pitch axis location, and frequency of oscillation. Sample calculations were performed for the delta, convex, and concave wings including a possible space shuttle configuration. The results were compared with those obtained by the slender body theory and by Landahl's theory. The present method obtained more negative dam ping-in-pitch than that predicted by Landahl's theory. In particular, the present method provides the stability derivatives in the low-frequency range where Landahl's theory breaks down.