The aerodynamic benefit of wing–wing interaction depends on stroke trajectory in flapping insect wings

Abstract

SUMMARY Flying insects may enhance their flight force production by contralateral wing interaction during dorsal stroke reversal (`clap-and-fling'). In this study, we explored the forces and moments due to clap-and-fling at various wing tip trajectories, employing a dynamically scaled electromechanical flapping device. The 17 tested bio-inspired kinematic patterns were identical in stroke amplitude, stroke frequency and angle of attack with respect to the horizontal stroke plane but varied in heaving motion. Clap-and-fling induced vertical force augmentation significantly decreased with increasing vertical force production averaged over the entire stroke cycle, whereas total force augmentation was independent from changes in force produced by a single wing. Vertical force augmentation was also largely independent of forces produced due to wing rotation at the stroke reversals, the sum of rotational circulation and wake capture force. We obtained maximum (17.4%) and minimum(1.4%) vertical force augmentation in two types of figure-eight stroke kinematics whereby rate and direction of heaving motion during fling may explain 58% of the variance in vertical force augmentation. This finding suggests that vertical wing motion distinctly alters the flow regime at the beginning of the downstroke. Using an analytical model, we determined pitching moments acting on an imaginary body of the flapping device from the measured time course of forces, the changes in length of the force vector's moment arm,the position of the centre of mass and body angle. The data show that pitching moments are largely independent from mean vertical force; however,clap-and-fling reinforces mean pitching moments by approximately 21%, compared to the moments produced by a single flapping wing. Pitching moments due to clap-and-fling significantly increase with increasing vertical force augmentation and produce nose-down moments in most of the tested patterns. The analytical model, however, shows that algebraic sign and magnitude of these moments may vary distinctly depending on both body angle and the distance between the wing hinge and the animal's centre of mass. Altogether, the data suggest that the benefit of clap-and-fling wing beat for vertical force enhancement and pitch balance may change with changing heaving motion and thus wing tip trajectory during manoeuvring flight. We hypothesize that these dependencies may have shaped the evolution of wing kinematics in insects that are limited by aerodynamic lift rather than by mechanical power of their flight musculature.

Elastic deformation and energy loss of flapping fly wings

“…It has further been shown that a delay in timing of wing rotation during the dorsal and ventral stroke reversal may attenuate force generation (Dickinson et al, 1999;Sane and Dickinson, 2002) and most insects such as beetles (Coccinella), dipterans (Calliphora, Tipula and Eristalis) and hymenopterans (Apis and Bombus) exhibit rather symmetrical wing rotation, in which 50% of the change in angle of attack occurs before and after each stroke reversal, respectively (Ellington, 1984b;Nachtigall, 1966). We modelled wing kinematics in this study close to the patterns mentioned above and similar to the patterns used in other experimental and numerical studies on dipteran flight: 150Hz stroke frequency, 135deg flapping amplitude in a flat horizontal stroke plane, symmetrical wing rotation (equal rotational time during upstroke and downstroke), and an angle of attack at mid stroke of 40 and 20deg during downstroke and upstroke, respectively (Dickinson et al, 1999;Lehmann and Pick, 2007) (Fig.2). Using a rotational axis for wing rotation at 28.6% mean wing chord length (see Rotational wing axis), our kinematic pattern produces a mean vertical force opposite to gravity of 596N (two wings), supporting the fly's body weight within 2.8% accuracy (body mass, 59.1±10.2mg, mean ±s.d., N10 C. vicina).…”

“…According to Ellington (Ellington, 1984b) and Lehmann and Pick (Lehmann and Pick, 2007), inertial forces due to translational acceleration of the wing in the horizontal (F* i,h ) are given by:…”

Bristles reduce the force required to ‘fling’ wings apart in the smallest insects

“…Previous research has also shown that this stroke results in a large attached leading edge vortex on each wing, which leads to larger lift forces (Lighthill, 1973;Maxworthy, 1979;Spedding and Maxworthy, 1986;Lehmann et al, 2005;Peskin, 2005, 2009;Lehmann and Pick, 2007). However, it is possible that clap and fling may naturally result from an increase in wing stroke amplitude to make up for a decrease in wing area as the size of the insect decreases.…”

Design, Aerodynamics, and Vision-Based Control of the DelFly

“…Thanks to the upward motion during clap, the foil is pulled tight during the rotation. The downward leading edge motion during peel might reinforce the leading edge vortex generation by increasing the velocity of the fluid moving into the opening gap 33 .…”