Experimental and computational studies of the aerodynamic performance of a flapping and passively rotating insect wing

Flapping wings are important in many biological and bioinspired systems. Here, we investigate the fluid mechanics of flapping wings that possess a single flexible hinge allowing passive wing pitch rotation under load. We perform experiments on an insect-scale ( ${\approx}1$ cm wing span) robotic flapper and compare the results with a quasi-steady dynamical model and a coupled fluid–structure computational fluid dynamics model. In experiments we measure the time varying kinematics, lift force and two-dimensional velocity fields of the induced flow from particle image velocimetry. We find that increasing hinge stiffness leads to advanced wing pitching, which is beneficial towards lift force production. The classical quasi-steady model gives an accurate prediction of passive wing pitching if the relative phase difference between the wing stroke and the pitch kinematics, ${\it\delta}$ , is small. However, the quasi-steady model cannot account for the effect of ${\it\delta}$ on leading edge vortex (LEV) growth and lift generation. We further explore the relationships between LEV, lift force, drag force and wing kinematics through experiments and numerical simulations. We show that the wing kinematics and flapping efficiency depend on the stiffness of a passive compliant hinge. Our dual approach of running at-scale experiments and numerical simulations gives useful guidelines for choosing wing hinge stiffnesses that lead to efficient flapping.