Energy minimizing shapes of partially inflated large scientific balloons

Abstract

A large scientific balloon is constructed from long tapered sheets of polyethylene called gores that are sealed edge to edge with a load tape attached along each seal. Usually the film is assumed to be inextensible and fully deployed at float. In reality, the film is elastic and some straining is present in the film. Because the balloon film cannot support a compressive stress, a small internal contiguous fold of excess material can form along the center of each gore when excess material is present. The complete shape is cyclic and can be generated from a single half-gore. To model these configurations, we utilize a variational principle based on the gravitational potentials of the lifting gas and balloon film and strain energy. The balloon system includes external caps, load tapes, payload, and top fitting. The balloon is modeled as a faceted surface and a constant strain model is used to describe the state of strain within each facet. An isotropic plane-stress constitutive model is used to estimate the stress distribution. We will use the volume ν as a parameter and compute a family of strained balloon shapes for 0.91 ν d ≤ ν ≤ ν d .