Designing the shape of a large scientific balloon

Large scientific balloons are used to carry out research in the upper atmos phere. By Archimedes' principle, a balloon in equilibrium at a fixed attitu de must displace an amount of air equal to its weight. The system that we m odel here includes the balloon film, reinforcing caps, load tapes and paylo ad. We consider two mathematical models for the design shape of a balloon. One is a design in the shape of an ellipsoid-on-cone. The equilibrium condi tion gives rise to a cubic equation whose solution gives the unique shape f or a given set of design parameters, A second model is the natural-shape de sign, a system of nonlinear ordinary differential equations that is commonl y used for modeling the shape of large scientific balloons, In both models, caps are included as an added thickness, thus the resulting film weight de nsity is discontinuous. The discontinuities in the natural-shape model are handled with a parallel shooting method. We present numerical solutions for various design parameters and consider issues related to the efficient des ign of a balloon. (C) 2001 Elsevier Science Inc. All rights reserved.