Flight dynamics in forward flights of cabbage white butterfly

Abstract

We conducted measurements of a butterfly’s motion in forward flight and numerical simulations using a computational model reflecting its motion. We measured the motion of a cabbage white butterfly (Pieris rapae), and then we constructed a computational model composed of a thorax, an abdomen, and four wings (i.e., left and right wings with fore and hind parts). Furthermore, we calculated the flow field and aerodynamic force and torque generated by the butterfly model using the immersed boundary–lattice Boltzmann method. In this simulation, we considered two types of periodic motions corresponding to slightly-descending and ascending forward flights. As a result, we found that the wing-tip and leading-edge vortices are formed on the wings and then released backward and downward in both flights. The major difference between the two flights is the flapping amplitude, indicating that the butterfly changes the flapping amplitude for each period and increases it to ascend. In addition, we considered a chimera model whose motion is based on the slightly-descending flight but partly given by the ascending flight. As a result, we found that the pitching angle and the angle of attack determine the traveling direction, but simply changing these angles does not achieve the ascending flight due to insufficient lift force. Thus, the butterfly should adjust the flapping and lead–lag angles in response to the pitching angle and the angle of attack to change the flight mode.

Keywords

• flapping flight
• butterfly
• fluid-solid interaction
• wake vortex structure
• computational fluid dynamics