A novel 9-DOF coupling dynamic model for parafoil-assisted ship system

• A novel 9-degree-of-freedom coupling dynamic model is established, and the entire stage's dynamic characteristics are obtained. • The rigid-flexible coupling model of the ship, traction rope, and parafoil is established. • Three stages of the process of the parafoil-assisted ship system are proposed. • The dynamic characteristics of the parafoil ascent stage, ship acceleration stage, and wind-assisted stage are analyzed in depth, and the safe ascent zone is defined. The parafoil-assisted ship system can convert strong, stable, high-altitude wind energy into propulsion power. This paper clarifies the dynamic coupling strength relationships among the internal factors of the combined parafoil-ship system. Considering the pulling force of traction rope, the 6-DOF motion of the parafoil, and the 3-DOF motion of the ship, a 9-DOF dynamic model of the system is established based on the Newton-Euler laws. The fourth-order Runge-Kutta method is adopted to carry out simulation calculations for the full-phase process. According to the motion characteristics of the system, with the process divided into four stages for factor analysis. Results indicate that a faster extension velocity makes a smoother trajectory, quicker ascent, and increased pulling force and peak angle of attack, but prevents stable ascent if exceeding 3.5m/s. The parafoil’s height or the pulling force are unaffected by wind deflection angle during the ascent stage. In the ship acceleration stage, the parafoil’s height and pulling force decrease as the ship accelerates, reducing the assist force. In the wind-assisted stage, the parafoil stalls when the wind deflection angle exceeds 30°; smaller angles yield lower pulling force but better assistance. In the parafoil recovery stage, a faster retrieval speed of the traction rope results in a quicker descent of the parafoil, but it increases the angle of attack and airspeed, thereby requiring greater pulling force for parafoil recovery. The angle of attack stabilizes at 6.29° in the stable state of the parafoil. The findings inform the design of the parafoil-assisted ship system.