Modeling of Higher-Order Rotor Flap Angle Dynamics for Flybarless Uncrewed Helicopters in High-Speed Flight

Stable autonomous flight at high speeds is essential to expand the operational capabilities of flybarless uncrewed helicopters. This study develops a high-fidelity flapping dynamics model to accurately describe rotor behavior at high speeds. We derive a dynamics model that incorporates higher-order terms of the advance ratio. By expanding the flapping angle into a Fourier series, we obtain an n -th-order constant-coefficient differential equation model that accounts for inter-harmonic coupling. Numerical simulations were conducted at low (μ x =0.04) and high (μ x =0.25) speeds. Power spectral density analysis revealed that higher-order harmonics (2 /rev and 3 /rev) become significant at high speeds, rendering the conventional first-order approximation inadequate. Furthermore, the impact on the aerodynamic forces and moments of the rotor was quantified. In high-speed flight, the first-order model produces substantial errors in lateral force, drag, and moments owing to lift asymmetry between blades. Second-order or higher models significantly improve accuracy. Considering the balance between computational load and precision, a second-order model is the most practical choice for high-speed aerodynamic evaluation. These findings provide fundamental insights for the advanced control system design of high-speed flybarless uncrewed helicopters.