NEWTONIAN AND HYPERSONIC FLOWS OVER OSCILLATING BODIES OF REVOLUTION .1. CIRCULAR CONES

This paper presents unsteady Newtonian and hypersonic perturbation theories for the flow past slender pointed-nose bodies of revolution performing small-amplitude pitching oscillations about any pivot position at zero incidence. By extending and perturbing recently developed steady flow theories for such bodies of revolution, systems of approximate equations for unsteady hypersonic and Newtonian flows are obtained. However, solutions are given only for Newtonian flow past circular cones. Thus, simple closed-form formulas for the unsteady pressure and the aerodynamic derivatives are found. It is shown that pitching oscillations of circular cones are always dynamically stable.