The roles of body and wing pitching angles in hovering butterflies

Abstract

Butterflies achieve their flight through a coupling of wing motion and remarkable body pitching and they seldom hover in nature compared to other flying insects. This study elucidates the aerodynamic mechanisms of the hovering butterfly using numerical simulation and vortex dynamics analysis, utilizing the detailed wing and body kinematics measured by highspeed filming. The results reveal that during each stroke, the leading-edge vortex (LEV) on the forewings and the trailing-edge vortex (TEV) on the hindwings initially attach to the wing surfaces and grow rapidly. The TEV, then, sheds, while the LEV maintains its strength and attachment. Thus, the high lift is mainly generated through the rapid acceleration and delayed stall mechanisms. During hovering, the mean body pitch angle approaches 90°, balancing the forward forces generated in each stroke. The substantial amplitude of body pitching enables the butterfly to project sufficient vertical force to support its weight. Notably, butterflies generate approximately 50% of the total aerodynamic force vertically, indicating lower efficiency. The wing motions during the upstroke and downstroke are approximately symmetrical, resulting in almost equal contributions to vertical force. The vertical force on the hindwings contributes only about 10% of weight supporting, attributed to earlier TEV shedding and the absence of low-pressure regions. However, the aerodynamic centers of the hindwings are far from the center of mass, ensuring the balance of pitching moments. This work provides deeper insights into hovering butterfly aerodynamics and offers theoretical guidance for the development of bio-inspired flying robots.