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Abstract Flapping-wing micro-air vehicles (FWMAVs) are an emerging technology inspired by flying insects that show promise in applications favoring maneuverability and vehicle compactness. However, current designs are limited by inefficient energetics, and current dynamical models of the flight system employ limiting assumptions when considering power demands. Here, we derive a system-level model of the insect flight system including the thorax, wing, and wing hinge that can inform insect-inspired FWMAV design. We applied the model to study the flight system of a hawkmoth, and used a genetic algorithm optimization to tune uncertain model parameters to minimize the power required to hover. Results show that performance is improved by utilizing multimodal excitation to produce favorable flapping kinematics. This is achieved by locating the flapping frequency of the moth between the nonlinear resonant frequencies, resulting in magnified flapping response and aerodynamically advantageous phase. The optimal flapping frequency can be predicted from the system’s underlying linear natural frequencies and is roughly 54% of the system’s mean natural frequency. Furthermore, effective solutions are configured so that the timing of the applied load and thorax responses are matched such that little effort is spent reversing the wing stroke. The optimized model parameters and corresponding kinematics show moderate agreement with those reported for the hawkmoth. To maintain hovering flight, the successful moths in the population expend approximately 58.5 W/kg. The system-level model and the governing principles identified here can inform the design of energy efficient FWMAVs moving forward. 

Flapping, flexible insect wings deform under inertial and fluid loading. Deformation influences aerodynamic force generation and sensorimotor control, and is thus important to insect flight mechanics. Conventional flapping wing fluid–structure interaction models provide detailed information about wing deformation and the surrounding flow structure, but are impractical in parameter studies due to their considerable computational demands. Here, we develop two quasi three-dimensional reduced-order models (ROMs) capable of describing the propulsive forces/moments and deformation profiles of flexible wings. The first is based on deformable blade element theory (DBET) and the second is based on the unsteady vortex lattice method (UVLM). Both rely on a modal-truncation based structural solver. We apply each model to estimate the aeromechanics of a thin, flapping flat plate with a rigid leading edge, and compare ROM findings to those produced by a coupled fluid dynamics/finite element computational solver. The ROMs predict wing deformation with good accuracy even for relatively large deformations of 25% of the chord length. Aerodynamic loading normal to the wing's rotation plane is well captured by the ROMs, though model errors are larger for in-plane loading. We then perform a parameter sweep to understand how wing flexibility and mass affect peak deflection, mean lift and average power. All models indicate that flexible wings produce less lift but require lower average power to flap. Importantly, these studies highlight the computational efficiency of the ROMs—compared to the convention modeling approach, the UVLM and DBET ROMs solve 4 and 6 orders of magnitude faster, respectively.