Clearing Maximum Height With Constrained Kinetic Energy

Abstract

This paper addresses the question: In order to clear a given height, defined as that which is passed over by all points in the moving body, what is the minimum initial kinetic energy required and what are the other conditions that specify the solution completely? An expression is derived for the height cleared above an original supporting ground plane. This transcendental expression is maximized numerically subject to certain equality and inequality constraints using nonlinear constrained optimization techniques. The optimal solution includes the height cleared and the required control variables. The parameter space of body descriptors in which the optimal solution is presented decomposes into two regions in which the solutions differ qualitatively.