A High-Speed 4-Tensor Computational Framework for the Solar Energy Prediction of Curved HAPS Photovoltaic Modules

In the long-duration stratospheric operation of High-Altitude Platform Stations (HAPSs), strict management of the limited solar energy balance is a decisive factor determining mission success. However, existing planar approximation models ignore self-shading and incidence angle losses associated with curved surfaces. In this study, we propose a novel framework that catalogs the airframe geometry as a 4-tensor, achieving both physical rigor and computational speed. This method is a thousand times faster than ray tracing methods, and successfully reproduces the minute output fluctuations observed in actual flight data. Notably, in the winter solstice analysis, when the energy balance is most severe, the planar model overestimates power generation by approximately 25% during level flight and by approximately 12% even during turning maneuvers. Quantifying this discrepancy in environments with minimal energy margins is essential for mitigating the risk of airframe loss and formulating feasible operational plans.