Viscous contribution to the high Mach number damping in pitch of blunt slender cones at small angles of attack

Abstract

Summary The dynamic stability derivatives of blunt cones for small variations in angles of attack have been previously derived by the current author. However, no account of the unsteady nature of the boundary layer was made in that work. In this paper closed form expressions for the increment in dynamic stability due to the presence of the boundary layer are derived by considering the pressure distribution perturbations as the boundary layer continuously adjusts to the enclosed oscillating body. The theory provides a first hand estimate of the complete pitch derivative damping without having to resort to more rigorous and expensive computational methods. Calculations performed at Mach numbers of 7 to 10 with axis positions ranging from 0·5 to 0·7 of the chord length for cones of semi-angle 10° and 20°, indicate that the effect of boundary layer is to slightly reduce the magnitude of the inviscid damping derivative. For blunt cones at angles of attack less than 5°, this was in good agreement with the limited experimental data available.