Abstract: We study the link between wing deformation and aerodynamic force production of an insect-inspired two-vein flexible flapping wing. The three-dimensional deformation of the wing is monitored during experiments, while the instantaneous aerodynamic forces are simultaneously recorded using a force balance. We demonstrate that the optimal wing stiffness distribution, controlled by the angle between the two veins, results from a subtle passive control of the phase lag between the leading and trailing edges. Specifically, we identify an optimal inter-vein angle β in the range of 15–20 degrees, which maximizes the thrust coefficient ?CT ? by enabling a phase lag of approximately π/2 between leading and trailing edge kinematics. This optimal deformation timing enhances wing curvature during peak flapping velocity, thereby improving aerodynamic efficiency. A complementary modal analysis provides a structural interpretation of the observed deformation dynamics and clarifies the role of stiffness anisotropy. Our findings indicate that insects may exploit passive structural properties to optimize flight performance without active control, highlighting the importance of venation patterns in governing aerodynamic effectiveness.

Key words: Flapping wings')">Flapping wings, Phase lag, Aerodynamic force, Wing flexibility