Optimal wing geometry and kinematics of a hovering rhinoceros beetle for minimum power consumption*

We investigate the optimal wing geometry and kinematics of a rhinoceros beetle in hovering motion for minimum power consumption. The original wing kinematics of a hovering beetle is measured using high speed cameras. Based on the measured wing kinematics, numerical simulations are conducted using an immersed boundary method. Numerical results indicate that the enhancement of vertical force and reduction of aerodynamic power requirement due to twist of hindwings are less than 3% as compared to their rigid counterparts, and the effect of elytra on the force generation is negligible. Therefore, we consider rigid and flat hindwings for optimization. We develop a predictive aerodynamic model which accurately predicts the force generation and power requirement of the flapping wing. Optimal wing kinematics and geometry are obtained applying this model together with a hybrid of a clustering genetic algorithm and a gradient-based optimizer. We find optimal solutions for the minimizations of aerodynamic and mechanical power consumption, respectively. Optimization results showed that optimal wing kinematics and geometry for mechanical power consumption are closer to those of a rhinoceros beetle than those for aerodynamic power consumption.