Modeling ascent configurations of strained high-altitude balloons

We consider the problem of estimating stresses in the ascent shape of an elastic high-altitude scientific balloon. The balloon envelope consists of a number of long, hat, tapered sheets of polyethylene called gores that are seated edge-to-edge to form a complete shape. Because the film is so thin, it has zero bending stiffness and cannot support compressions. In particular, the balloon film forms internal folds of excess material when the volume is not sufficiently large. Because of these factors, a standard finite element approach will have difficulty computing partially inflated balloon shapes. In our approach, we develop a variational principle for computing strained balloon shapes that incorporates regions of folded material as a part of the geometric model. We can apply our model to fully inflated or partially inflated configurations. The equilibrium shape is the solution of minimum energy satisfying a given volume constraint, We apply our model to a design shape representative of those used in scientific ballooning and compute a family of ascent configurations with regions of external contact for a volume as low as 22% of its float value.