The natural shape balloon and related models

Abstract

Typically, the design shape of a large scientific balloon is taken to be an axisymmetric inextensible shape in which only the lifting gas and weight of the balloon system are taken into consideration. The most common model equations were originally developed in the 1950s at the University of Minnesota, and in the special case when the circumferential stress is zero, have come to be known as the natural shape equations . Over the years, variants of these equations have been rediscovered and their relation to the general framework sometimes obscured. We will present a brief exposition of the natural shape equations, and show how a number of balloon models follow from it.