Extremely large sweep amplitude enables high wing loading in giant hovering insects

Beetle Allomyrina dichotoma is one of the largest insects that performs many remarkable modes of locomotion, particularly hovering flight capability. In order to stay airborne, its flexible hindwings are flapped so as to work as a thrust generator. However, the wing loading of the beetle is relatively large (38.94  ±  3.73 N m^-2) compared to those of other insects and hummingbirds, indicating that it is challenging for it to achieve flight. Here, we measured the hindwing morphology and kinematics of the beetle in order to discover its flight performance. Unlike many other insects, the beetle flaps its hindwings with an extremely large sweep amplitude of about 191.33  ±  6.12 deg at high flapping frequencies ranging from 36 to 41 Hz (mean wing tip speed  ≈  13.45  ±  0.58 m s^-1). These capabilities enable the beetle to produce enough lift force to stay airborne with its bulky body (4-10 g). In order to investigate how the sweep amplitude affects the beetle's flight efficiency, we utilized the unsteady blade element model to estimate the power requirements of the same vertical force production for various sweep amplitudes. The results indicate that the sweep amplitude as high as 190 deg is more beneficial for power requirements than the smaller amplitudes, which require higher frequencies resulting in higher inertial powers to produce the same vertical force. Thus, for this large beetle, high sweep amplitude may be a biological strategy for staying airborne. In addition, we thoroughly discussed the effects of input constraints on the outcome by investigating power loadings for variable sweep amplitudes at a constant vertical force, mean wing tip speed, and flapping frequency. Effect of wing surface area was also investigated and discussed to provide useful information for the development of an insect-inspired flapping-wing robot.