Designing the shape of a large scientific balloon

摘要

Large scientific balloons are used to carry out research in the upper atmosphere. By Archimedes' principle, a balloon in equilibrium at a fixed altitude must displace an amount of air equal to its weight. The system that we model here includes the balloon film, reinforcing caps, load tapes and payload. 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 condition gives rise to a cubic equation whose solution gives the unique shape for a given set of design parameters.