Practical analytical model to predict high-altitude balloon shape and film tension

This article seeks to outline novel simplified model and analytical solution for predicting geometrical shape and film tension of high-altitude balloon. Sphero-conical and ellipsoid-conical models were proposed to depict geometrical configuration of high-altitude balloon subjected to a payload. By considering the effect of atmospheric factors and lifting gas temperature on geometrical shape of balloon, geometrical parameters of equilibrium shape were solved, based on minimum potential energy principle satisfying material constraint. New analytical solution was derived to allow balloon film tensions in meridional and circumferential directions. Finally, new model and its solution were used for predicting geometrical shape and film tension of natural-shape balloon on the ground and on float in stratosphere respectively, demonstrating the practical and effective use of the proposed model.