Cleft formation in pumpkin balloons

NASA’s development of a large payload, high altitude, long duration balloon, the Ultra Long Duration Balloon, centers on a pumpkin shape super-pressure design. Under certain circumstances, it has been observed that a pumpkin balloon may be unable to pressurize into the desired cyclically symmetric equilibrium configuration, settling into a distorted, undesired state instead. Success of the pumpkin balloon for NASA requires a thorough understanding of the phenomenon of multiple stable equilibria and developing of means for the quantitative assessment of design measures that prevent the occurrence of undesired equilibrium. In this paper, we will use the concept of stability to classify cyclically symmetric equilibrium states at full inflation and pressurization. Our mathematical model for a strained equilibrium balloon, when applied to a shape that mimics the Phase IV-A balloon of Flight 517, predicts instability at float. Launched in Spring 2003, this pumpkin balloon failed to deploy properly. Observations on pumpkin shape type super-pressure balloons that date back to the 1980s suggest that within a narrowly defined design class of pumpkin shape super-pressure balloons where individual designs are fully described by the number of gores n_g and by a single measure of the bulging gore shape, the designs tend to become more vulnerable with the growing number of gores and with the diminishing size of the bulge radius r_B Weight efficiency considerations favor a small bulge radius, while robust deployment into the desired cyclically symmetrical configuration becomes more likely with an increased bulge radius. In an effort to quantify this dependency, we will explore the stability of a family of balloon shapes parametrized by (n_g, r_B) which includes a design that is very similar, but not identical, to the balloon of Flight 517. In addition, we carry out a number of simulations that demonstrate other aspects related to multiple equilibria of pumpkin balloons.