Three-dimensional wing structure attenuates aerodynamic efficiency in flapping fly wings

The aerial performance of flying insects ultimately depends on how flapping wings interact with the surrounding air. It has previously been suggested that the wing's three-dimensional camber and corrugation help to stiffen the wing against aerodynamic and inertial loading during flapping motion. Their contribution to aerodynamic force production, however, is under debate. Here, we investigated the potential benefit of three-dimensional wing shape in three different-sized species of flies using models of micro-computed tomography-scanned natural wings and models in which we removed either the wing's camber, corrugation, or both properties. Forces and aerodynamic power requirements during root flapping were derived from three-dimensional computational fluid dynamics modelling. Our data show that three-dimensional camber has no benefit for lift production and attenuates Rankine-Froude flight efficiency by up to approximately 12% compared to a flat wing. Moreover, we did not find evidence for lift-enhancing trapped vortices in corrugation valleys at Reynolds numbers between 137 and 1623. We found, however, that in all tested insect species, aerodynamic pressure distribution during flapping is closely aligned to the wing's venation pattern. Altogether, our study strongly supports the assumption that the wing's three-dimensional structure provides mechanical support against external forces rather than improving lift or saving energetic costs associated with active wing flapping.