A mathematical model for the strained shape of a large scientific balloon at float altitude

A large scientific balloon is constructed from long flat tapered sheets of thin polyethylene film called gores which are sealed edge to edge to form a complete shape. The balloon is designed to carry a fixed payload to a pred etermined altitude. Its design shape is based on an axisymmetric model that assumes that the balloon film is inextensible and that the circumferential stresses are zero. While suitable for design purposes, these assumptions a re not valid for a real balloon. In this paper, we present a variational ap proach for computing strained balloon shapes at float altitude. Our model i s used to estimate the stresses in the balloon film under various loads and for different sets of material constants. Numerical solutions are computed .