Exact Involute Bodies of Revolution

Involute construction is an approach used in contemporary rocket nozzle technology for the fabrication of exit cones and other bodies of revolution and consists of laminating identical composite sheets of uniform thickness along curved surfaces, called involute surfaces. In this work, the exact solution is derived for these surfaces, which guarantees that the volume of the body being generated is precisely filled, with no gaps or overlaps. The equations of the developed surface, or ply pattern, a formulation of the kinematics of the fabrication debulking process, and an experimental validation of the theoretical work are also presented.