A PARALLEL SHOOTING METHOD FOR DETERMINING THE NATURAL SHAPE OF A LARGE SCIENTIFIC BALLOON

Large scientific balloons provide a dependable low cost platform for c arrying out research in the upper atmosphere. Usually, the design of s uch a balloon is based on an axisymmetric natural shape defined by the solutions of a mathematical model derived by researchers at the Unive rsity of Minnesota in the 1950s. For a natural-shape balloon, all the tension in the balloon fabric is carried in the meridional direction a nd 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 bal loon at float altitude, the model equations can be solved by an ordina ry shooting method. To model axisymmetric ascent shapes, one needs to make some crude assumptions on how excess film is handled. When the vo lume 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 w ork presented here, a parallel shooting method is used to determine th ese shapes without the need of additional assumptions.