An improved quasi-steady model capable of calculating flexible deformation for bird-sized flapping wings

Flapping wing air vehicles (FWAVs) are a type of bio-inspired aerial robot, whose application potential is currently receiving significant attention. However, the dynamic modeling techniques for flapping motion remain underdeveloped, particularly for bird-sized 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. Some improved reduced-order models also struggle to describe the effects caused by irregular flexible deformations of the wing surface. 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: the dynamic solver that calculates the corresponding aerodynamic loads based on the deformation state of the wing surface, and the structural solver that determines the new deformation state based on the load distribution on the wing surface. In each iteration cycle, these solvers exchange their output data until they converge to a stable wing surface displacement distribution and output the predicted aerodynamic data. Wind tunnel experiments, utilizing high-speed cameras and six-dimensional force sensors, validated the reliability of both the structural solver and the dynamic solver. This aerodynamic model, balancing efficiency and accuracy, shows strong potential for applications in FWAVs’ structural and controller design, including but not limited to airfoil optimization and flight attitude stabilization.