Wing inertia influences the phase and amplitude relationships between thorax deformation and flapping angle in bumblebees

Flying insects have a robust flight system that allows them to fly even when their forewings are damaged. The insect must adjust wingbeat kinematics to aerodynamically compensate for the loss of wing area. However, the mechanisms that allow insects with asynchronous flight muscle to adapt to wing damage are not well understood. Here, we investigated the phase and amplitude relationships between thorax deformation and flapping angle in tethered flying bumblebees subject to wing clipping and weighting. We used synchronized laser vibrometry and high-speed videography to measure thorax deformation and flapping angle, respectively. We found that changes in wing inertia did not affect thorax deformation amplitude but did influence wingbeat frequency. Increasing wing inertia increased flapping amplitude and caused a phase lag between thorax deformation and flapping angle, whereas decreasing wing inertia did not affect flapping amplitude and caused the flapping angle to lead thorax deformation. Based on our findings, we proposed a qualitative model of the insect flight system. This model suggests insects leverage a wing hinge-dominated vibration mode to fly, and highlights the possibility of a disproportionate damping between the wing hinge and thorax when the insect's wings are clipped. The results of our study provide insights into the robust design of insect-inspired flapping wing micro air vehicles.