Enhanced thrust and speed revealed in the forward flight of a butterfly with transient body translation

A butterfly with broad wings, flapping at a small frequency, flies an erratic trajectory at an inconstant speed. A large variation of speed within a cycle is observed in the forward flight of a butterfly. A self-propulsion model to simulate a butterfly is thus created to investigate the transient translation of the body; the results, which are in accordance with experimental data, show that the shape of the variation of the flight speed is similar to a sinusoidal wave with a maximum (J=0.89) at the beginning of the downstroke, and a decrease to a minimum (J=0.17) during a transition from downstroke to upstroke; the difference between the extrema of the flight speed is enormous in a flapping cycle. At a high speed, a clapping motion of the butterfly wings decreases the generation of drag. At a small speed, a butterfly is able to capture the induced wakes generated in a downstroke, and effectively generates a thrust at the beginning of an upstroke. The wing motion of a butterfly skillfully interacts with its speed so as to enable an increased speed with the same motion. Considering a butterfly to fly in a constant inflow leads to either an underestimate of its speed or an overestimate of its generated lift, which yields an inaccurate interpretation of the insect's flight. Our results reveal the effect of transient translation on a butterfly in forward flight, which is especially important for an insect with a small flapping frequency.