An Improved Quasi-Steady Model Capable of Calculating Flexible Deformation for Bird-Like Flapping Wings

Abstract Flapping wing air vehicles (FWAVs) are bio-inspired aerial robots that boast high flight efficiency, excellent maneuverability, and stealth capabilities. However, the dynamic modeling techniques for flapping motion remain underdeveloped, particularly for bird-like FWAVs. Traditional quasi-steady (QS) models' accuracy heavily relies on empirical coefficients, leading to unacceptable errors when analyzing flapping motion at different scales and wing flexibilities. This paper presents an improved QS model that incorporates the interaction mechanism between wing flexible deformation and relative flow state, enabling quantitative analysis of wing deformation's aerodynamic influence and significantly reducing reliance on empirical coefficients. The model comprises two solvers: an aerodynamic solver that outputs wing surface force distribution at each discrete time point, and a structural deformation solver that provides corresponding relative flow state distribution. In each iteration cycle, these solvers exchange their output data until they converge to a stable wing surface displacement distribution and output the predicted time-varying aerodynamic data. Wind tunnel experiments, utilizing high-speed cameras and six-dimensional force sensors, validated the reliability of both the structural deformation solver and the aerodynamic solver. This aerodynamic model, balancing speed and accuracy, shows strong potential for applications in FWAVs' structural and controller design, including but not limited to airfoil optimization and flight attitude stabilization.