Modeling nonaxisymmetric off-design shapes of large scientific balloons

The design of a large scientific balloon is usually based on an axisymmetric model, describing its shape at float altitude. However, the shapes observed during ascent are clearly nonaxisymmetric and are characterized by a number of distinctive features, including a periodic lobe pattern surrounding the gas bubble, internally folded balloon fabric, and flat winglike structures in the lower portion of the balloon below the gas bubble. In this paper, we present a mathematical model that captures the complex geometries of these off-design shapes. Real balloons are made from long tapered sheets of polyethylene that are sealed edge to edge. We base our geometric model on this construction, enabling us to define a reference configuration and to estimate the distortion in our computed balloon shapes. We compute one-parameter families of ascent shapes with triangular, square-shaped, and pentagonal symmetries. Our computed solutions possess many nonaxisymmetric features that are observed in real balloons.