Power requirements of butterflies in hovering flight

Previous studies have shown that many insects frequently alternate between hovering and forward flight with comparable power expenditure. However, hovering is relatively rare in butterflies, raising the question of whether this behavior entails higher energy costs-a possibility that remains unexplored due to limited research on the power of butterfly hovering. To address this gap, this study employs an integrated experimental and computational approach to investigate the aerodynamic and inertial forces governing power consumption during butterfly hovering. High-speed videography is employed to capture detailed morphology and kinematic parameters of the body and wings. The flow field around the wings is simulated using the lattice Boltzmann method coupled with the immersed boundary method, enabling high-fidelity resolution of unsteady aerodynamic forces and moments. Theoretical analyses are further applied to interpret the contributions to aerodynamic and inertial power. Results demonstrate that, despite substantial wing inertia and pronounced body pitching motion, aerodynamic power constitutes the dominant portion of total power expenditure. Inertial power arises primarily from wing motion rather than body dynamics. The mass-specific power of hovering butterflies is approximately 28 W kg^-1, which aligns with the range observed in most insects (20-60 W kg^-1). Furthermore, even with the assumption of complete elastic energy storage, the maximum energy savings amount to only about 10% of the total power. These findings offer new insights into the energetics of butterfly flight and provide valuable guidance for the design of bio-inspired flapping-wing micro aerial vehicles.