Simultaneous optimisation of earwig hindwings for flight and folding

Abstract

Earwig wings are highly foldable structures that lack internal muscles. The behaviour and shape changes of the wings during flight are yet unknown. We assume that they meet a great structural challenge to control the occurring deformations and prevent the wing from collapsing. At the folding structures especially, the wing could easily yield to the pressure. Detailed microscopy studies reveal adaptions in the structure and material which are not relevant for folding purposes. The wing is parted into two structurally different areas with, for example, a different trend or stiffness of the wing veins. The storage of stiff or more flexible material shows critical areas which undergo great changes or stress during flight. We verified this with high-speed video recordings. These reveal the extent of the occurring deformations and their locations, and support our assumptions. The video recordings reveal a dynamical change of a concave flexion line. In the static unfolded state, this flexion line blocks a folding line, so that the wing stays unfolded. However, during flight it extends and blocks a second critical folding line and prevents the wing from collapsing. With these results, more insight in passive wing control, especially within high foldable structures, is gained.

Keywords: Dermaptera; Earwig hindwing; Insect flight; Passive wing control; Structural stabilisation; Wing folding.

Fig. 1.

Schematic wing of Labia minor. A, squama; B, mid-wing mechanism; C, central area; D, outer apical area; E, inner apical area; F, ulnar area; G, claval flexion line; H, radial vein; I, intercalary vein; K, patch (broadened area); L, ring cross vein; the numbers represent the vein number. Shaded in grey is the surface area of the folded state. Green dashed line highlights the folding line running through the central area, between ulnar area and fan and ends near the wing base at the end of the fan. Blue dashed line shows the shape of a single fan unit.

Fig. 2.

Unfolded dermapteran wings. (A) F. auricularia. (B) L. minor. The vertical dividing line (red) indicates the functional division of the wing. (C) In the distal part (left), the radial veins are joined, while in the proximal part they are separate and have a broadened base (green arrow). (D) Radial veins are either straight or curved (blue arrows). (E) Along the folding line, the crossing vein exhibits a reduced degree of sclerotisation (orange arrow). (F) The veins of L. minor show an overall distribution of resilin.

Fig. 3.

Mechanical features of the wing cross vein. (A) Stop of rip propagation (right) versus a hypothetical situation without the vein (left). (B) Ripping event resulting during folding. Lateral forces put high strain on the membrane while (C) at the presence of a ring cross vein, the tearing forces are transmitted through the vein.

Fig. 4.

Folding inhibition and wing deformation of L. minor; (A-C) folding-inhibition through the claval flexion line. (A) Resting position, the claval flexion line inhibits only the folding line within the ulnar area. The tip of the white arrow indicates the end of the resulting deformation. (B) Downstroke during take-off, squama is slightly tilted forward (green arrow indicates the flexion line behind the squama), pronation of the wing is initiated, the yellow arrow indicates the end of the claval flexion line, the white arrow the end of the deformation. (C) Deformation of the wing during upstroke within a curve flight, white arrow indicates end of the deformation caused by the inhibition through the claval flexion line. (D-F) Shape-changes of the leading edge (red line) during flight. (D) Downstroke, the leading edge of the wing shows a slight kink. (E) Deformation during upward movement, the leading edge is more pointed out, the deformation transition within the wing is nearly situated at the vertical dividing line (green dashed line). (F) Deformation during downstroke, the trailing edge is moving along with a short delay starting at the ring cross vein. All images are sharpened using Inkscape for a clearer texture. Scale bar: 2 mm. Images taken at 1000 fps, 201 μs shutterspeed.