Kinetics of Elastic Recoil in the Wings of the cicada, Dundubia rufivena

In this paper, we quantitatively characterise the kinetics of elastic recoil in the wings attached to the cicada Dundubia rufivena. We use high-speed videography to deduce the velocities of recoil motion in both bending (B) and torsion (T), in downstroke and upstroke modes of flapping. Elastic recoil is faster in downstroke (DS) than it is in upstroke (US), reaching average velocities, ̄ í µí±£ , 244 • ⋅ s − 1 in DS-B versus 6434 • ⋅ s − 1 in US-B, and 5887 • ⋅ s − 1 in DS-T versus 4545 • ⋅ s − 1 in US-T. Our results also therefore evidence that bending velocities during elastic recoil are higher than the velocities in torsion, and conclude that this is a result of the necessary geometrical distances that need to be covered over a stroke. The wings do not act alone as biological springs, but rather, we find that the stiffnesses of the wings (1.7-3.6 GPa) are higher when attached to the cicada body than they are when detached. This evidences thoracical involvement as part of the biological spring enabling elastic recoil, indicating that elastic recoil of flapping wings should be approached from a systems perspective, rather than solely through a localised understanding of wing mechanics. 1 Introduction Energy is required for flight [ 1 ], and while insect muscles are efficient, they are not a sole source of input energy [ 2 ]. The energy requirements of flight in Drosophila hydei , for example, are minimised through thoracical elastic elements, which recover excess energy during deceleration in the first half stroke of a flapping cycle [ 3 ]. Similar mechanisms of energy saving in flight are evident in wider bodied insects like cicadas [ 4 ], which are the world's loudest insects [ 5 ], producing sound through striated viscoelastic tymbals [ 6 ] that vibrate at extremely high (> 3 kHz) frequencies [ 7 ]. Cicadas carry relatively heavy bodies using wings that exhibit simpler designs [ 8 ] than those of other higher order insects [ 9 ]. The estimation of a cicada's aerodynamic, inertial and mechanical power in a free forward flight indicates that the total mechanical power in a downstroke is negative. As such, by extension, this power could potentially be stored and restored in a subsequent stroke [ 4 ]. In nature, elastic springs contribute to insect flight efficiency. Weis-Fogh [ 10 ], for example, evidenced the presence of passive elastic forces as drivers for acceleration in the wings of dead locusts by lifting wings into stroke positions and releasing them. They noted that kinematic responses were present, even after all flight muscles were removed from the animal, indicating that residual elastic energy was provided by the extant materials of the wing, some of which is derived from resilin protein in the wing base cuticle [ 11 ]. Resilin is a rubber-like material with high-energy absorption capabilities [ 12, 13 ] and respectable tolerances to fracture damage [ 14 ]. Passive wing deformation plays a role in aerodynamic force production and is a characteristic influenced by its flexural stiffness. The leading edge This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.