This paper proposes a dynamic simulation method for solving balloon shapes. The mass-spring-damping model is used to discretize two-dimensional generatrixes and three-dimensional membrane surfaces, respectively. We solve two-dimensional/three-dimensional ascent shapes at different zero-pressure heights and numerically simulate mushroom cloud shapes that occur during the balloon ground launch. The typical rapid transition feature of the mushroom cloud shape at the waist is depicted. In addition, a preliminary numerical simulation study was conducted for the pumpkin superpressure balloon deployment instability problem. The Calladine instability critical curve for constant angle design lobes is compared and validated for different gore numbers and lobe angles. Further, simulations were carried out on fully inflated shapes of two derived superpressure balloon designs developed by the Japan Aerospace Exploration Agency/Institute of Space and Astronautical Science, namely, the Tawara intermediate cylindrical segment balloon and the diamond-shaped tendon balloon. We verify the ISAS conclusion that the diamond-shaped tendon balloon has a cylindrical shape when fully inflated. Finally, a preliminary simulation study was carried out on the deployment shape of four ballonet architectures in the superpressure balloon. The proposed method for solving various types of balloon shapes based on the mass particle method is simple and efficient, and it has been well applied in our actual balloon engineering.

本文提出了一种求解气球形状的动态模拟方法。质量-弹簧-阻尼模型分别用于离散二维母线和三维膜表面。我们求解不同零压高度下的二维/三维上升形状，并对气球地面发射过程中出现的蘑菇云形状进行数值模拟。描绘了腰部蘑菇云形状的典型快速过渡特征。此外，针对南瓜超压气球展开不稳定问题进行了初步的数值模拟研究。针对不同的戈尔数和波瓣角度，对恒定角度设计波瓣的 Calladine 不稳定性临界曲线进行了比较和验证。此外，还对日本宇宙航空研究开发机构/宇宙航空科学研究所开发的两种衍生超压气球设计的完全膨胀形状进行了模拟，即田原中间圆柱段气球和菱形腱气球。我们验证了ISAS结论，即菱形肌腱球囊在完全膨胀时呈圆柱形。最后对超压气球中四种气球结构的展开形态进行了初步的模拟研究。所提出的基于质量粒子法求解各类气球形状的方法简单高效，在我国实际气球工程中得到了很好的应用。