Studies also examined the effect of the distance between the hinges of two wings on enhancing lift and torque generations

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Experimental and computational studies have extensively investigated the effect of the clap and fling on the aerodynamic lift generation in insect flight [12,24,33–37]. Miller & Peskin used the immersed boundary method for a low Reynolds number of 10 to investigate the effect of wing flexibility on aerodynamic performance during a clap-and-fling process. The study indicated that the clap-and-fling mechanism in the flexible wing reduced the drag by approximately 50%, while relatively improving the lift when compared with those in a rigid wing. Bennett conducted two-dimensional experiments at a Reynolds number of 83 000 by using a robotic rectangular wing with a vertical wall as a symmetric plane to observe the benefits of the clap-and-fling effect. The measurement indicated that the wing in the presence of vertical plane contributed to an increase of 15% in the total lift when compared with that in the absence of vertical plane. An experimental study on various insects, small birds and bats conducted by Marden reported that flapping wings with the clap-and-fling effect led to an increased lift per unit flight muscle mass of approximately 25% when compared with that of conventional flapping wings without the clap-and-fling motion. Furthermore, a numerical study by Sun & Yu performed a two-dimensional simulation at a Reynolds number of 17 and revealed that the clap-and-fling effect augmented the lift generation when compared with that of a single wing. An increase in the distance from 0.1c to 0.2c (c = wing chord) resulted in a slight decrease in lift but greatly attenuated detrimental torque . The lift and torque enhancements were diminished when the distance approached 1c . Lehmann et al. performed experiments based on the small three-dimensional wing of a Drosophila fruit fly at Reynolds numbers of 100–200, and found that the near-clap-and-fling effect could lead to a lift enhancement of 17% based on wing kinematics.

Figure 1. Snapshot of the kinematics of a rhinoceros beetle’s hind wing at the ends of the upstroke and downstroke during (a) take-off and (b) hovering.

The time histories of the flapping angle and the rotation angles were then obtained from the coordinates of the dots during the flapping motion. The first eight terms of sine and cosine functions were added, and the summation was used as a fitting function to fit the measured time histories of the flapping angle and wing rotation angles, based on the least-square method as expressed below:

Figure 6posite images of two flapping-wing models used for the force measurement. (a) The flapping-wing system with the clap-and-fling effect placed at each stroke reversal and (b) the flapping-wing system with an extended distance between the flapping axes to minimize the effect of the clap and fling.

Figure 8. Distribution of (a) the vertical force or thrust (F_z), (b) horizontal force (F_y) and (c) force in the ?-direction or horizontal drag (F_?) produced by the two flapping-wing systems in a flapping cycle.

Figure 9. Force enhancement due to the clap-and-fling effect in (a) the vertical force or thrust (F_z) and (b) force in the ?-direction or horizontal drag (F_?) in the flapping-wing system.

Figure 11. Plots of swirling strength combined with velocity vector at the wingspan of 0.25R created by the flapping-wing system with the clap-and-fling effect (case A) and without the clap-and-fling effect (case B). LEV, leading edge vortex; TEV, trailing edge vortex; DW, downwash.