Numerical simulation of the dynamic launching process for high-altitude balloons

In this paper, we establish a mathematical model to simulate the dynamic behavior of the high-altitude zero-pressure balloon system during the ground dynamic launching process. The dynamic launching mathematical model includes the solution of the bubble shape and the dynamics model derived by taking the bubble, the membrane bundle, the cable, and the gondola as a whole. The bubble shape is considered as a combination of zero circumferential stress shape at the bottom and fully expanded shape at the top. Under the hypothesis, we use the multiple shooting method and the sequential quadratic programming method together to solve the partially expanded shape in the lower bubble region. Based on bubble shapes, the bubble is modeled as a “spring damping system” and we can establish its dynamic model. The “membrane bundle-cable system” is equivalent to a variable mass rope structure and we solve its dynamic behavior by using the mass particle model. We calculate the swing angle of the gondola by its geometry constraint and force analyses. The Hertz contact model and the Coulomb friction law are used to analyzing the contact between the “membrane bundle-cable system” and the ground or the main boom of the launching vehicle. Based on these dynamic models, we calculate the dynamic launching simulation under three operating conditions of the launching vehicle, which corresponds to three ambient wind speeds. The three operational modes of the launching vehicle are the static operation (2 m/s wind speed), the forward operation to chase the bubble (4 m/s), and the backward operation to increase the gondola releasing angle (0 m/s). We analyze the influence of the wind speed and the launching vehicle action on the force and geometric time history of the dynamic launching system. Furthermore, we discuss the three times typical overload in the dynamic launching system and its influencing factors, which are the opening of the roller, the straightening of the “membrane bundle-cable system” and the releasing of the gondola. The purpose of this paper is to present a set of methods and models for the dynamic launching simulation. It not only calculates the shapes of the bubble and simulates the motion of the quasi rope structure system individually, but also the bubble, the “membrane bundle-cable system” and the gondola are combined to establish a complete set of dynamic models to reflect the main characteristics of the dynamic launching process.