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Unstable, Cyclically Symmetric and Stable, Asymmetric Pumpkin-Balloon Configurations

2007; American Institute of Aeronautics and Astronautics; Volume: 44; Issue: 3 Linguagem: Inglês

10.2514/1.20874

1533-3868

Frank Baginski, Kenneth A. Brakke, Willi Schur,

Astro and Planetary Science

By design, a pumpkin balloon is intended to assume a cyclically symmetric pumpkin-like shape once it reaches float altitude and is fully inflated. Recent work by the authors showed that under certain circumstances, a strained, cyclically symmetric, pumpkin-balloon configuration can be unstable. This means that the balloon must assume an alternate, noncyclically symmetric, stable-equilibrium shape. Julian Nott's round-the-world balloon Endeavour was one of the first pumpkin-type balloons to encounter this instability. In this paper, we will explore the phenomena of unstable, cyclically symmetric and stable, asymmetric pumpkin-balloon configurations. Through numerical computations using our mathematical model for strained balloon shapes, we find asymmetric equilibria that bear a striking resemblance to those observed in the ground inflation tests of the Endeavour. One difficult aspect of modeling such configurations is dealing with the problem of self-contact. By including certain linear constraints in our variational formulation of the problem, we are able to represent balloon configurations with significant regions of self-contact in a way that mimics how a real balloon stores excess material. We apply our finite element model for strained balloon shapes to Endeavour-like pumpkin balloons and compute a number of asymmetric-equilibrium balloon configurations.