Performance and stability of hypervelocity aircraft flying on a minor circle

Abstract

The equations of motion pertinent to the study of steady and perturbed motions of a rigid vehicle flying on a minor circle at constant altitude above a spherical non-rotating earth are presented. Solutions to the steady-state equations (performance) and perturbation equations (stability) are presented in the form of altitude-speed regions where flight is possible, and root loci, respectively. The linearized equations and performance boundaries are discussed. The principal conclusions are that steady flight is limited mainly by available thrust, and that characteristic oscillations about the steady-flight condition are poorly damped. Minor instabilities were found in all cases examined. New characteristic modes, not present in conventional flight, are discussed—they involve the movement of the vehicle mass-centre relative to the equilibrium flight trajectory. A representative vehicle was chosen for which numerical values were obtained.