Abstract :
A feature characterizing partially inflated scientific balloons is a lobe structure surrounding the gas bubble. In addition, when the gas bubble is of insufficient volume, the balloon envelope will collapse and form folds of excess material. We present a mathematical model for a balloon shape with such features. We formulate a variational principal for the balloon system, and seek to determine a shape that minimizes energy subject to a volume constraint. The energy includes film and load tape strain, film and load tape weight, and hydrostatic pressure. Numerical solutions are presented.
