On the Design and Analysis of Inflated Membranes: Natural and Pumpkin Shaped Balloons

Abstract

Large scientific balloons are used by NASA and the space agencies of many countries to carry out research in the upper stratosphere. Such a balloon typically consists of a thin plastic shell with several external caps. Load tendons run the length of the balloon from top fitting to bottom fitting, dividing the balloon into identical regions called gores. The gores are made from flat panels of 20--30 $\mu$m polyethylene film that are sealed edge-to-edge to form the complete shape. A typical fully inflated shape can be over 120 meters in diameter and over 1 million cubic meters in volume. To date, the workhorse of NASA's balloon program has been the zero-pressure natural shape balloon, an axisymmetric onion-like design that dates back to the 1950s. The equilibrium equations at float for a natural shape balloon lead to a nonlinear boundary value problem that can be solved to determine the design shape. In recent years, demand for long duration midlatitude balloon flights has led to a design concept known as the pumpkin balloon. A number of ad hoc approaches based on crude approximations of equilibrium have been put forth that lead to pumpkin-like balloon shapes. In this paper, we derive equilibrium equations for a pumpkin balloon. We also present a brief review of balloon models that follow from the axisymmetric membrane theory. Numerical solutions are included.