Modeling the shapes of constrained partially inflated high-altitude balloons

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

“…Since infinitesimal circumferential tension cannot support compressive load of balloon, the film will wrinkle and form internal folds of excess material. [7][8][9] However, film tension in circumferential direction is not necessarily zero, since it is essential for a circumferential tension to balance against the pressure of lifting gas. Thus the influence of circumferential tension on the geometrical shape of natural-shape balloon is taken into account in this article.…”

“…From equations ( 3), ( 5) to (8), it is clear that meridional and circumferential tensions of N 1 and N 2 are dominated by pressure differential Áp across the balloon film and equivalent rotary radius r 2 . If the parameters of Áp and r 2 are determined, then N 1 and N 2 can be analytically obtained.…”

“…According to membrane theory, analytical models were developed to obtain film tension applied to a small segment on the balloon surface, based on the assumptions of deformation constraint of constant meridional length and infinitesimal excess along circumference, by solving the equilibrium between pressure and film tension. Presently, based on the assumptions of constant strain and isotropic plane-stress constitutive relationship, a significant amount of research has been conducted to analyze balloon deformation and detailed stress field, by using variational principles of strain energy [7][8][9] or finite element analysis (FEA). 10,11 In order to produce finite element (FE) models, straight inclined segments or continuous mathematical functions have been used to depict in more detail the idealized gore and other structures.…”

“…In addition, it is difficult for FE models to address partially inflated balloon shapes with internal folds of excess material resulted from the thin film without the capability to support a compressive load. [7][8][9] For a natural shape high-altitude balloon vented to the atmosphere, it can be observed that the shape and volume of balloon varied with increasing of ascent altitude. Partially inflated shape and fine folds and wrinkling in balloon fabric first appeared during launch.…”