VARIATIONAL-PRINCIPLES FOR ASCENT SHAPES OF LARGE SCIENTIFIC BALLOONS

Current mathematical models of large scientific balloons assume an axisymmetric ascent shape, sharply contrasting what is observed in real balloons. We propose an approach to computing nonaxisymmetric shapes of balloons which is based on the inextensibility of certain balloon fibers and a set of rules that model how excess material must fold away. The energy of a balloon configuration is modeled as the sum of the gravitational potentials of the lifting gas and balloon fabric. We evolve an initial guess to a shape that minimizes this energy while satisfying certain material constraints. We refer to a shape determined in this fashion as an energy-minimizing (EM) shape. Using our approach to compute axisymmetric EM shapes, we find our results agree with those obtained by solving the standard Sigma-shape model. For nonaxisymmetric shapes, we are able to compute shapes that possess features observed in actual balloons, including internally folded material, nat wing sections, and periodic lobe-like structures surrounding the gas bubble.