Shape of Deployable Membrane Reflectors

Abstract

The shape and stress distribution in the new Collapsible Rib-Tensioned Surface reflector are investigated both analytically and experimentally. A methodology is established for the preliminary design of symmetric reflectors of given aperture, focal length, and target root-mean-square (RMS) error, by extending form-finding methods originally developed for membrane roof covers. The concepts of a reference surface and of an equilibrium surface are introduced, and algorithms are developed to compute these surfaces and their associated RMS error. Then, the cutting pattern for making the membrane is computed and the RMS error of the actual surface is predicted. Estimates are made of the RMS error of reflectors with apertures of 1, 3, 5, and 10 m, with 6, 12, and 24 ribs. Measurements of prestress and shape in a one-sixth sector of a 1 m diameter reflector with 6 ribs are compared with predictions obtained from the computational study. In the central part of the gore, about half of the total surface, the average error on prestress is 22% whereas the shape has an RMS error of 0.7 mm, better than predicted.