Multi-objective optimization of the wing shape and kinematics of a hovering flapping wing.

We investigate optimal wing shapes and kinematics of a hovering flapping flight using multi-objective optimization considering vertical force generation and flight power consumption. Given wing aspect ratio of 5 and Reynolds number of 100 (based on the wing mean chord length and wing tip velocity), a Pareto front of the optimal wing shapes and kinematics is obtained using a quasi-steady aerodynamic model (Oh et al. JFM, 2020) together with a non-dominated sorting genetic algorithm (NSGA-II). The results indicate that optimal wing shapes and kinematics can be classified into three different categories based on the purposes of flight (minimization of mechanical power coefficient, maximization of vertical force coefficient, and maximization of flight efficiency). Furthermore, these classifications are qualitatively valid even for different Reynolds numbers and aspect ratios. Lastly, the optimization results are compared to real insect flapping flights.