Importance of body rotation during the flight of a butterfly

In nature the body motion of a butterfly is clearly observed to involve periodic rotation and varied flight modes. The maneuvers of a butterfly in flight are unique. Based on the flight motion of butterflies (Kallima inachus) recorded in free flight, a numerical model of a butterfly is created to study how its flight relates to body pose; the body motion in a simulation is prescribed and tested with varied initial body angle and rotational amplitude. A butterfly rotates its body to control the direction of the vortex rings generated during flapping flight; the flight modes are found to be closely related to the body motion of a butterfly. When the initial body angle increases, the forward displacement decreases, but the upward displacement increases within a stroke. With increased rotational amplitudes, the jet flows generated by a butterfly eject more downward and further enhance the generation of upward force, according to which a butterfly executes a vertical jump at the end of the downstroke. During this jumping stage, the air relative to the butterfly is moving downward; the butterfly pitches up its body to be parallel to the flow and to decrease the projected area so as to avoid further downward force generated. Our results indicate the importance of the body motion of a butterfly in flight. The inspiration of flight controlled with body motion from the flight of a butterfly might yield an alternative way to control future flight vehicles.

Figure 1

Coordinate systems to describe the motion of a butterfly in flight. The butterfly body rotates along axis $Y$ and the wing flaps along axis $X_w$.

Figure 2

Wing and body kinematics of butterflies recorded in free flight.

Figure 3

Physical model of a butterfly in flight; $S$ in the figure denotes the wing span of a butterfly.

Figure 4

Flight kinematics, flapping angle α($t$), and body angle β($t$) of a butterfly in the simulation.

Figure 5

Definitions of initial body angle and rotational amplitude; the motions in (a–c) refer to the posture at the instant labeled in Fig. 4.

Figure 6

(a) Upward and forward speeds of a butterfly in forward flight tested in a free-flight simulation. The butterfly can perform forward flight with the body motion, $\beta ={70}^{\circ }\pm {27}^{\circ }$. (The circles and squares are the mean forward speed and upward speed within a cycle.) (b) Comparison of flight speeds of a butterfly in forward flight between simulation and real flight.

Figure 7

Vorticity magnitude for the butterfly in forward flight from (a) top view and (b) side view. In the figures, DV and DV′ refer to downstroke vortex rings; UV and UV′ refer to upstroke vortex rings.

Figure 8

Flight trajectories within a cycle with varied rotational amplitude and initial body angle (a) ${\beta }_0={70}^{\circ }$, (b) ${\beta }_0={80}^{\circ }$, and (c) ${\beta }_0={90}^{\circ }$ [23]. The squares, triangles, diamonds, and circles on the lines represent the body positions at $t/T=0.25$, 0.5, 0.75, and 1.00, respectively.

Figure 9

Vorticity magnitude and vectors of the flow field at $t/T=0.50$ for a butterfly with rotational amplitudes (a,c) $\mathrm{\Delta }\beta ={27}^{\circ }$, and (b,d) $\mathrm{\Delta }\beta ={40}^{\circ }$ when the initial body angle is 70°.

Figure 10

The upper figure is a simplified diagram of the body motion and an irregular flight trajectory of a butterfly within a cycle. Lower figures (a,b) illustrate the flow, relative to a butterfly, and the flight postures at the moment labeled in the upper figure.