A trapezoidal wing equivalent to a Janatella leucodesma's wing in terms of aerodynamic performance in the flapping flight of a butterfly model.

Wing planform is one of the most important factors for lift and thrust generation and enhancement in flapping flight. In a previous study based on a simple numerical model of a butterfly, we found that the wing planform of an actual butterfly (Janatella leucodesma) is more efficient than any rectangular or trapezoidal wing planform. In the present study, we make a hypothesis that the efficient aerodynamic performance of a butterfly's wings can be reproduced by the following four geometrical parameters of wing planform: aspect ratio, taper ratio, position of the rotational axis for the geometric angle of attack, and sweepback angle. In order to test this hypothesis, we explore a trapezoidal wing planform equivalent to an actual butterfly's wing planform in terms of aerodynamic performance in a parameter space consisting of these four parameters. We use a simple butterfly model composed of two rigid thin wings and a rod-shaped body and calculate the aerodynamic performance of the model by an immersed boundary-lattice Boltzmann method to find such a trapezoidal wing planform. As a result, we find a trapezoidal wing planform which gives almost the same lift, thrust, pitching moment, power, and power-loading coefficients as an actual butterfly's wing planform. Furthermore, in the free flight of the butterfly model with pitching motion control, the flight behavior of the model with the resulting trapezoidal wing planform is almost the same as that with an actual butterfly's wing planform.