A Parallel Shooting Method for Determining the Natural Shape of a Large Scientific Balloon

Abstract

Large scientific balloons provide a dependable low cost platform for carrying out research in the upper atmosphere. Usually, the design of such a balloon is based on an axisymmetric natural shape defined by the solutions of a mathematical model derived by researchers at the University of Minnesota in the 1950s. For a natural-shape balloon, all the tension in the balloon fabric is carried in the meridional direction and the circumferential stress is assumed to be zero. In this paper, we will establish existence results for the model equations and present numerical solutions for a variety of parameters. For the case of a balloon at float altitude, the model equations can be solved by an ordinary shooting method. To model axisymmetric ascent shapes, one needs to make some crude assumptions on how excess film is handled. When the volume of the lifting gas is very small, the ordinary shooting method is ineffective for computing axisymmetric ascent shapes. In the past, ad hoc assumptions were employed to circumvent this difficulty. In the work presented here, a parallel shooting method is used to determine these shapes without the need of additional assumptions.