Performance of a Butterfly in Take-Off Flight

Abstract

The flight of a butterfly, Pieris melete, was observed in the take-off phase and was analyzed theoretically from aerodynamic and kinetic viewpoints. A vortex method, which was recently developed by the present authors, was used in this analysis. During the downstroke, the butterfly generates mainly a vertical force. The acceleration of the butterfly's body during the first half of the downstroke is especially large, and this acceleration is mainly caused by a large unsteady pressure drag acting on the wings. This large unsteady pressure drag is generated by the vortices shed into the flow from the outer edges of each wing of a pair; it is increased by the interference effect between a pair of wings when the opening angle is small. This force can be estimated by the previous quasi-steady analysis when the force coefficient is changed to 4. In addition to the unsteady pressure drag, an aerodynamic force due to added mass is generated and this is also increased by the interference effect between a pair of wings. During the upstroke the butterfly generates mainly a horizontal force. The change of direction of the forces during the down- and upstrokes is controlled by variation in the inclination of the stroke plane. The moment, which is created by the aerodynamic force acting on the wings and by abdominal motion, changes the thoracic angle, that is the inclination of the stroke plane.

Beneficial wake-capture effect for forward propulsion with a restrained wing-pitch motion of a butterfly

“…For small α A , the speed of forward flight increases, but begins to decrease for α A > 45°. According to the literature, a butterfly flies with a small amplitude of wing-pitch angle [6,13,22,23]; our analysis provides an essential aerodynamic feature for a butterfly to adopt a small amplitude of the wing-pitch motion to enhance the wake-capture effect so as to increase forward propulsion. The wing-pitch motion is conventionally considered to benefit the lift force [12,24,45], but a large amplitude of the motion decreases the speed of forward flight, which might be useful for the design of wing kinematics for a micro-aerial vehicle.…”

“…A wing-pitch motion is commonly observed in insects [15,17], and is also described for butterflies [6,13,22,23]. The amplitude of the wing-pitch motion (α A ) of a butterfly, which is about 50° [13], is much smaller than that of other insects, such as a cicada, 100° [14], a dragonfly, 135° [15], a hawkmoth, 95° [16], a mosquito, 145° [17], or a fruit fly, 135° [18].…”

“…Most forward propulsion of a butterfly arises during the upstroke (figure 6b) [5,6], as then the wings flap backward and move in a direction opposite to that of the body when a butterfly is flying forward, which might greatly weaken the relative flow to the wings and decrease the aerodynamic force. Unsteady mechanisms occur at the downstroke reversal stage (t à = 0.60) that increases the propulsion of the butterfly.…”

“…This frequency of a butterfly is only about 10 Hz, much less than most insects such as a bumblebee, 152 Hz [1], or a hawk moth, 26.1 Hz [2], or a cicada, 46.5 Hz [3]. Besides gliding flight [4], a butterfly has a notable oscillatory motion of the body [5,6] that is unique among insects. The fore and hind wings of a butterfly partially overlap, so resemble flapping with one pair of broad wings [7].…”

“…Dudley [19] assumed that the wing-pitch motion of a butterfly is not obvious; Fei & Yang [5] likewise maintained that the wing-pitch angle is small; Tanaka & Shimoyama [20] neglected the wing-pitch motion in its butterfly-like flapping mechanism; Senda et al [21] declared that a butterfly can be considered to implement an almost one degree-of-freedom flapping mechanism. The above literature shows that many researchers neglected the wing-pitch motion of a butterfly, but there are still articles that take this motion into account [6,13,22,23]. Bode-Oke & Dong [13] stated that the upstroke of a butterfly is characterized by not only body oscillation but also wing-pitch motion to aid the wings.…”