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.

中文翻译：

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通过胸腹结与具有建设性腹部振荡的蝴蝶质心之间的平移运动增强升力和推力

蝴蝶飞行时腹部相对于胸部摆动；腹部摆动会导致身体部位相对于蝴蝶的质心平移波动，这可能会对飞行产生重大影响。基于实验测量，我们创建了一个数值模型来研究自由飞翔的蝴蝶（Idea leuconee）。我们固定了扑翼和胸部俯仰的运动，并通过不同的振荡相位参数化了腹部振荡。为了将分析集中在平移动力学上，我们使用了胸腹结点的运动，即胸部和腹部围绕其旋转的关节，来表达身体部位相对于质心的平移运动。结果表明，腹部摆动通过胸腹结相对于质心的平移运动增强了升力和推力。用真实蝴蝶记录的腹部摆动相位，腹部摆动导致胸腹结在向下行程中相对于质心向下移动，在向上行程中相对于质心向上移动。这种建设性的运动放大了相对于质心的机翼拍动速度，从而增强了攻角以及机翼上前缘和后缘涡流的强度。与没有腹部摆动的情况相比，机翼由此产生的瞬时升力和推力值分别增加了 50.32% 和 32.57%。据说天然蝴蝶利用腹部振荡的特定相位偏移来飞行。通过比较不同的摆动相位，只有从天然蝴蝶记录的腹部摆动相位对胸腹结的平移运动产生最佳的建设性影响，最大限度地提高了翅膀产生的升力和推力。它阐明了蝴蝶使用这一特定范围的腹部摆动相位来调节胸腹结和质心之间的平移运动，以增强飞行。我们的工作揭示了腹部振荡的平移机制，这与胸部俯仰效应一样重要。这项工作的发现提供了对蝴蝶飞行和微型飞行器设计的深入了解。