# Application of a Coupled Eulerian-Lagrangian Approach to the Shape and Force of Scientific Balloons
## 4 Dynamic Fluid-Structure Coupling Shape and Force Analysis
### Aerodynamic Shape and Force Analysis of Wind-Driven Balloons  
During the launching and ascent of a zero-pressure balloon, the balloon envelope remains in a partially unfolded state, and the interior is not fully filled with helium. Crosswinds can cause significant deformation. As a flexible material, the polyethylene  
Figure 16: Top and bottom stress curves of the zero-pressure balloon. Figure 15: Bottom tensile force curve of the zero-pressure balloon. envelope can only withstand tensile forces and cannot endure shear or compressive forces. When the windward side of the balloon envelope is impacted by airflow, it caves inward, compressing the helium mass inside the balloon and transmitting pressure to the leeward side of the envelope. This increases the stress on the leeward side, causing significant deformation. At this point, the balloon's shape is no longer symmetric or consistent with the physical equations of a rotational body, necessitating the recalculation of the stress distribution on the envelope. Figure 17 illustrates the drag-induced shape observed during the launching of a scientific balloon. In dynamic launchings, the balloon bubble is constrained by a roller on the ground, and a soft collar is used below the bubble to maintain its shape and prevent drag-induced deformation. However, in the launching shown in Figure 17, the premature detachment of the soft collar resulted in large-scale drag deformation, making it difficult to control the launching angle and causing launching challenges. In summary, crosswinds significantly impact the stress distribution on the zero-pressure balloon envelope, as well as the motion and stability of the overall system. These factors must be carefully considered in launching design and control. Additionally, crosswinds can disrupt the dynamic equilibrium of the payload during ascent. Crosswinds exert lateral forces on the balloon and payload, causing the system to sway laterally. Simultaneously, the deformation of the balloon alters its buoyancy and center of buoyancy, affecting the distribution of longitudinal forces and moments, which further influences the stability of the system's motion. Under strong wind conditions, these effects can interfere with the successful execution of launching tasks or even lead to mission failure. Therefore, the detailed calculation and simulation of the drag-induced deformation process are of great significance for engineering practice. In [28], for the dynamic launching and rising process, a mathematical model of the \"membrane bundle system\" under a quasi-static assumption was established. The geometric trajectory of the \"membrane bundle system\", the force at the bottom of the bubble, and the change in the contact length with the ground were simulated. However, the changes in the bubble shape and the characteristics of the membrane bundle as a variable mass system were not considered. Currently, there is no effective method for the approximation of this behavior in engineering calculations. A commonly used reference formula is found in the scientific Ballooning Handbook [29], edited by [PERSON], which approximates the drag-induced shape as a \"hemispherical teacup\". The \"teacup\" shape refers to the wind-facing depression formed inside the balloon. This drag effect compresses the helium gas upward inside the balloon, causing the helium mass to move laterally upward, forming a shape resembling a \"handle\". Figure 17: The wind-scooping shape of a scientific balloon during ground launching. In this section, we apply a CEL simulation framework to calculate the drag-induced shape and corresponding forces on the balloon. We import the zero-pressure balloon model calculated from the static shape solution and expand the Eulerian domain to simulate the wind-induced \"cupping\" shape. The external flow field around the zero-pressure balloon is set as a uniform, rightward horizontal flow to simulate the wind forces acting on the balloon membrane.