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 mCT-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 ~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 to active wing flapping.

The supplementary data contain:

• STL files of all 12 wings used in the present study (four models for each of the three species).
• INI files required to run the simulations. The main parameters are species-dependent and can be found in PARAMS_corrugation_singlewing_*.ini when running the code, this file goes in the command-line call: $mpi ./flusi PARAMS_corrugation_singlewing_calliphora.ini. The kinematics are encoded as Fourier coefficients in corrugation_kinematics_JEB2011.ini. For each wing model, a separate ini file is used, e.g., Calliphora_C01leftuCTiso5k_profilo170512c_color_original.ini is the natural wing of the Calliphora model. This file needs to be set in the main ini file ( PARAMS_corrugation_singlewing_*.ini) in the line WingShape=*;.
• DATA files of the shown figures.