Non-Linear Time-Varying Modeling and Simulation Methods for Hydrodynamic–Aerodynamic Coupling Near-Surface Flight Scenarios

Due to irregular hydrodynamic–aerodynamic coupling, the modeling and simulation of near-surface flight are extremely complex. For the present study, a practical dynamic model and a complete motion simulation method for the solution of such problems were established for engineering applications. A discrete non-linear time-varying dynamics model was employed in order to ensure the universality of the method; thereafter, force models—including gravity, aerodynamic, hydrodynamic, control, and thrust models—were established. It should be noted that a non-linear approach was adopted for the hydrodynamic model, which reflects the influences of waves in real-world situations; in addition, a Proportional–Integral–Derivative (PID) control law was added to realize closed-loop simulation of the motion. Considering a take-off flight as a study case, longitudinal three Degrees of Freedom (DoF) motion was simulated. The velocity, angle of attack, height, and angular velocity were selected as the state vectors in the state–space equations. The results show that, with the equilibrium state as the initial setting for the motion, reasonable time–history curves of the whole take-off phase can be obtained using the proposed approach. Furthermore, it is universally applicable for aircraft operating under hydrodynamic–aerodynamic coupling scenarios, including amphibious aircraft, seaplanes, Wing-in-Ground-Effect (WIGE) aircraft, and Hybrid Aerial–Underwater Vehicles (HAUVs).