insects Article The Geometry and Mechanics of Insect Wing Deformations in Flight: A Modelling Approach Robin Wootton Department of Biosciences, University of Exeter, Address for correspondence 61 Thornton Hill, Exeter EX4 4NR, UK; [email protected] Received: 16 June 2020; Accepted: 13 July 2020; Published: 17 July 2020 Abstract: The nature, occurrence, morphological basis and functions of insect wing deformation in flight are reviewed. The importance of relief in supporting the wing is stressed, and three types are recognized, namely corrugation, an M-shaped section and camber, all of which need to be overcome if wings are to bend usefully in the morphological upstroke. How this is achieved, and how bending, torsion and change in profile are mechanically interrelated, are explored by means of simple physical models which reflect situations that are visible in high speed photographs and films. The shapes of lines of transverse flexion are shown to reflect the timing and roles of bending, and their orientation is shown to determine the extent of the torsional component of the deformation process. Some configurations prove to allow two stable conditions, others to be monostable. The possibility of active remote control of wing rigidity by the thoracic musculature is considered, but the extent of this remains uncertain. Keywords: insects; wings; deformation; flight; bending; torsion; camber; control; physical models 1. Introduction This paper has a dual function: to review the occurrence of flight-related deformations in the morphological upstroke of insect wings and to investigate the geometric principles underlying the interaction of bending, torsion and camber change, by means of simple physical models. Orthodox, flight-adapted insect wings are smart structures: they are flexible aerofoils whose three-dimensional shape from instant to instant in flight is largely determined by their elastic response to the aerodynamic and inertial forces they are receiving. While the profile of the wing base can normally be altered and controlled by the direct flight muscles of the thorax, the absence of muscles within the wing requires that three-dimensional shape control beyond the base is to a great extent automatic — encoded in the wing’s detailed structure. Four decades ago, I discussed the nature and function of the deformations they undergo, and identified a range of morphological adaptations to facilitate and to limit them [1]. The extensive research carried out since then has expanded and broadly confirmed these early conclusions and predictions [2–26] (in particular, see [19,21] for summaries of the extensive Russian literature), and major advances in insect aerodynamics have greatly helped to interpret their significance, e.g., [27–35]. Our knowledge of wing kinematics and deformations has come from high speed still and cine photography and video-recording. These sources show, unsurprisingly, that in the insects studied, the wings’ cyclic deformations are not rigidly determined: they vary in extent, even within a given flight sequence. To take just one example, high speed photographs of Panorpa communis (Mecoptera) in the upstroke published by Brackenbury [16] show virtually no bending in the wings, and Brodsky and Ivanov [4], filming tethered individuals, found little wing flexion, but a short high speed movie sequence of Panorpa germanica shortly after take-off shows extensive upstroke bending of the forewings and particularly the hindwings increasing from stroke to stroke [14] (Figure1). These are di fferent Insects 2020, 11, 446; doi:10.3390/insects11070446 www.mdpi.com/journal/insects Insects 2020, 11, 446 2 of 19 Insects 2020, 11, x FOR PEER REVIEW 2 of 20 differentspecies, species, but their but wings their are wings structurally are structurally identical, identical, and one and would one expectwould similarexpect similar behaviour behaviour in both. inThese both. variations These variations between between strokes may strokes be passive: may be wing passive: shape wing must shape certainly must be certainly influenced be by influenced variations byin variations angular velocity in angular in the velocity translation in the part translation of the stroke part andof the in stroke angular and acceleration in angular around acceleration stroke aroundreversal. stroke However, reversal. there However, is a possibility there is a that, possibility in some that, insects in some at least, insects a degree at least, of a control degree of of bending,control ofpassive bending, torsion passive and torsion section and may section be exerted may remotelybe exerted by remotely muscles atby the muscles wing base,at the and wing it isbase, interesting and it isto interesting explore how to suchexplore control how might such becontrol achieved. might Furthermore, be achieved. wings, Furthermore, as resonant wings, structures, as resonant need to structures,deform appropriately need to deform at their appropriately actual flapping at frequencies,their actual andflapping it is entirely frequencies, possible and that it theyis entirely may be possibletunable that by active they may control be tunable of wing by rigidity. active control of wing rigidity. FigureFigure 1. 1. (a()a Tracings) Tracings of of three three frames frames from from the the same same upstroke upstroke of of PanorpaPanorpa germanica germanica fromfrom a ahigh-speed high-speed filmfilm by by A.R. A.R. Ennos. Ennos. Note Note the the very didifferentfferent bendingbendingmodes modes of of forewings forewings and and hindwings, hindwings, reflecting reflecting the thedi ffdifferenterent lengths lengths of theof the subcosta, subcos SCP,ta, SCP, and and that that flexion flexion and torsionand tors persistion persist throughout throughout the half-stroke. the half- stroke.(b) Fore (b) and Fore hind and wings hind wings of Panorpa of Panorpa germanica. germanica.Here, andHere, in and subsequent in subsequent wing illustrations, wing illustrations, the median the medianflexion flexion line is shownline is shown in blue, in transverse blue, transverse flexion flexion lines in lines red in and red the an clavald the claval flexion flexion line in line green. in green. 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