Unlike other insects, a butterfly uses a small amplitude of the wing-pitch motion for flight. From an analysis of the dynamics of real flying butterflies, we show that the restrained amplitude of the wing-pitch motion enhances the wake-capture effect so as to enhance forward propulsion. A numerical simulation refined with experimental data shows that, for a small amplitude of the wing-pitch motion, the shed vortex generated in the downstroke induces air in the wake region to flow towards the wings, which enables a butterfly to capture this induced flow and to acquire an additional forward propulsion. When the amplitude of the wing-pitch motion exceeds 45^o, the flow induced by the shed vortex drifts away from the wings; it attenuates the wake-capture effect and causes the butterfly to lose a part of its forward propulsion. Our results provide a physical elucidation for a butterfly adopting a small amplitude of the wing-pitch motion to enhance the wake-capture effect and forward propulsion. This work clarifies the variation of the flow field correlated with the wing-pitch motion, which is useful in the design of a micro-aerial vehicle.

The readme file contains an explanation of each of the variables in the dataset. The supporting data files include the experiment data of the kinematics and the flight speed of the butterfly and the simulation data of the aerodynamic forces.