Modeling the shapes of constrained partially inflated high-altitude balloons

During a balloon mission, the maximum film stresses most likely occur while the balloon is constrained by the launch spool. The focus is on shapes of very small gas volume that are representative of spool shapes and partially inflated ascent shapes where a launch collar is still attached. The balloo n is constructed from long, flat, tapered sheets of 20.32-mum polyethylene that are sealed edge-to-edge to form a complete shape. Two caps are assumed to be located on top of the balloon. Load tapes are attached along the edg es of the gores. The potential energy of the balloon system includes contri butions due to hydrostatic pressure, film weight, load tape weight, film st rain, and load tape strain. Solutions are determined that minimize the tota l energy subject to a volume constraint plus appropriate constraints to mod el nonfully deployed configurations. To model fine wrinkling in the balloon 's membrane surface and to avoid compressive states, energy relaxation is e mployed. A number of numerical solutions are presented to illustrate the ap proach and provide estimates of the film stresses for these types of config urations.