Enhanced lift and thrust via the translational motion between the thorax-abdomen node and the center of mass of a butterfly with a constructive abdominal oscillation.

Butterflies fly with an abdomen oscillating relative to the thorax; the abdominal oscillation causes body parts to undulate translationally relative to the center of mass of a butterfly, which could generate a significant effect on flight. Based on experimental measurements, we created a numerical model to investigate this effect in a free-flying butterfly (Idea leuconoe). We fixed the motions of wing-flapping and thorax-pitching, and parametrized the abdominal oscillation by varied oscillating phase. To concentrate the analysis on translational dynamics, we used a motion of a thorax-abdomen node, a joint that the thorax and the abdomen rotate about, to express the translational motion of body parts relative to the center of mass. The results show that the abdominal oscillation enhances lift and thrust via the translational motion of the thorax-abdomen node relative to the center of mass. With the abdominal oscillating phase recorded from real butterflies, the abdominal oscillation causes the thorax-abdomen node to move downward relative to the center of mass in downstroke and move upward relative to the center of mass in upstroke. This constructive movement amplifies the wing-flapping speed relative to the center of mass, which enhances the angle of attack and the strength of leading- and trailing-edge vortices on the wings. The wings thereby generate increased values of instantaneous lift and thrust by 50.32% and 32.57% compared to the case of no abdominal oscillation. Natural butterflies are stated to utilize a particular phase offset of abdominal oscillation to fly. With comparing varied oscillating phases, only the abdominal oscillating phase recorded from natural butterflies produces the best constructive effect on the translational motion of thorax-abdomen node, which maximizes the lift and thrust generated on the wings. It clarifies that butterflies use this specific range of abdominal oscillating phase to regulate the translational motion between the thorax-abdomen node and the center of mass to enhance flight. Our work reveals the translational mechanism of the abdominal oscillation, which is as important as the thorax-pitching effect. The findings in this work provide insight into the flight of butterflies and the design of micro aerial vehicles.