Aerodynamic principles and modeling of high-altitude wind harvesting parachute systems

High-altitude wind energy exhibits significant advantages, such as high power density and stable wind direction and speed, thereby demonstrating great potential for large-scale development and utilization. A ground-based airborne wind energy system utilizing a parachute-ladder configuration offers a feasible solution, with its core component being the energy-harvesting parachute system composed of a series of working parachutes. The system captures wind energy primarily through drag-based "wind-catching" by the parachutes, which pull a ground-based generator via a tether to convert energy into electricity. First, considering the inclined reciprocating motion of the ladder and the aerodynamic similarity between working parachutes and deceleration parachutes, the aerodynamics of the energy-harvesting parachute system are clarified. Then, incorporating environmental parameters, a mechanical model of the system is developed that accounts for both design and operational parameters. Furthermore, through extremum analysis, the optimal power matching condition is derived, indicating that the tether speed should be one-third of the wind speed to achieve maximum power output (<1.7% error). Finally, based on the mechanical model and the optimal tether-speed matching condition, the maximum power output of the system is calculated, operational safety is evaluated, and a rapid design approach for the parachute system is achieved under constraints such as specific target power, stability, and engineering feasibility. Overall, the mechanical model provides a practical design tool for parachute systems under expected operating conditions.