DESIGN OF A MEMBRANE APERTURE DEPLOYABLE STRUCTURE * J. Enders 1 , S. Kas-Danouche 2 , W. Liao 3 , B. Rasmussen 4 , T. Anh Vo 5 , K. Yokley 6 L. Robertson 7 and R.C. Smith 6,8 Abstract Ultra-lightweight, membrane primary mirrors offer a promising future for space telescope technology. However, the advantages of the lightweight structure of the mirrors are restricted by an extremely high susceptibility to microyield. Hence, careful packag- ing of the membranes is required when transport- ing mirrors of this type into space. Four packag- ing models, a cylindrical roll, an umbrella model, a multi-cut model and a single cut model, are pre- sented and compared with each other. Factors such as curvature of the compressed membrane, stability after deployment, and the size of the launch vehicle are considered. All four packaging models appear to be feasible with certain materials and hence warrant physical testing. Introduction As described in [2], there have been dramatic im- provements in technologies and concepts for large telescopes for both ground and space applications. However, the act of launching objects into space poses specific constraints on the structure and de- ployment of the cargo transported. Due to the high launch cost, ultra-lightweight, membrane pri- mary mirrors have long been sought after by both NASA and the Department of Defense as a technol- ogy that could realize large aperture systems with low areal densities. Research on membrane struc- tures has culminated in the fabrication of meter- class lightweight structures with optical quality sur- faces. These membranes are 10-100 microns thick * This problem was investigated by the first six authors under the direction of the last two authors during the Indus- trial Mathematics Modeling Workshop for Graduate Students held at North Carolina State University on July 22-July 30, 2002. 1 Michigan State University 2 N.J. Inst. of Tech.; Univer. de Oriente, Venezuela 3 Mississippi State University 4 Georgia Institute of Technology 5 California State University Fullerton 6 North Carolina State University 7 US Air Force Research Lab, Kirtland AFB 8 Center for Research in Scientific Computation and have surface qualities usable in visible spec- trum applications. However, the available struc- tures that provide boundary support are so heavy that they eliminate the benefit derived from such lightweight apertures. Since these membranes must maintain an extremely high surface quality after re- lease into space, the membranes cannot be packaged in ways that deform their shape outside an extremely small acceptable range. Thus, many factors must be taken into consideration when developing strategies for folding the membranes. A sketch of a prototypical telescope is depicted in Figure 1. As diameter length of the primary mir- ror increases, so does its power of resolution. Cur- rently, the size of such telescopes has been bounded by the size of the launch vehicle. More recently, however, researchers have begun to consider ideas regarding packaging methods that would enable the compactification of much larger mirrors without cre- ating damage beyond desired accuracy. In order to attain the successful packaging of a large mirror, one must carefully consider the size of such an aperture, the size of the launch vehicle, the ease of deployment of the membrane into space, stability, the curvature of the folding method, as well as the allowable de- formation of the material after being compacted. primary mirror secondary mirror D Figure 1: Schematic representation of membrane mirror system. 1