Allometry of wing twist and camber in a flower chafer during free flight: How do wing deformations scale with body size?

Intraspecific variation in adult body mass can be particularly high in some insect species, mandating adjustment of the wing's structural properties to support the weight of the larger body mass in air. Insect wings elastically deform during flapping, dynamically changing the twist and camber of the relatively thin and flat aerofoil. We examined how wing deformations during free flight scale with body mass within a species of rose chafers (Coleoptera: Protaetia cuprea) in which individuals varied more than threefold in body mass (0.38–1.29 g). Beetles taking off voluntarily were filmed using three high-speed cameras and the instantaneous deformation of their wings during the flapping cycle was analysed. Flapping frequency decreased in larger beetles but, otherwise, flapping kinematics remained similar in both small and large beetles. Deflection of the wing chord-wise varied along the span, with average deflections at the proximal trailing edge higher by 0.2 and 0.197 wing lengths compared to the distal trailing edge in the downstroke and the upstroke, respectively. These deflections scaled with wing chord to the power of 1.0, implying a constant twist and camber despite the variations in wing and body size. This suggests that the allometric growth in wing size includes adjustment of the flexural stiffness of the wing structure to preserve wing twist and camber during flapping.

[1]  P Wu,et al.  Structural dynamics and aerodynamics measurements of biologically inspired flexible flapping wings , 2011, Bioinspiration & biomimetics.

[2]  R. Dudley The Biomechanics of Insect Flight , 2018 .

[3]  Steven Vogel,et al.  Comparative Biomechanics: Life's Physical World , 2003 .

[4]  M. Dickinson,et al.  The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight. , 2002, The Journal of experimental biology.

[5]  M. Dickinson,et al.  Wing rotation and the aerodynamic basis of insect flight. , 1999, Science.

[6]  A. R. Ennos THE IMPORTANCE OF TORSION IN THE DESIGN OF INSECT WINGS , 1988 .

[7]  Erick Greene,et al.  Allometry of Alarm Calls: Black-Capped Chickadees Encode Information About Predator Size , 2005, Science.

[8]  David N. Byrne,et al.  Relationship Between Wing Loading, Wingbeat Frequency and Body Mass in Homopterous Insects , 1988 .

[9]  Eyal Dafni,et al.  Kinematic compensation for wing loss in flying damselflies. , 2016, Journal of insect physiology.

[10]  R. McNeill Alexander,et al.  Principles of Animal Locomotion , 2002 .

[11]  Jon Cohen The Asian Epidemic Model's Provocative Curves , 2004, Science.

[12]  S. Sane,et al.  Aerodynamic effects of flexibility in flapping wings , 2010, Journal of The Royal Society Interface.

[13]  W. Vargas,et al.  Visible light reflection spectra from cuticle layered materials , 2011 .

[14]  J. Marden From damselflies to pterosaurs: how burst and sustainable flight performance scale with size. , 1994, The American journal of physiology.

[15]  Andrew M. Mountcastle,et al.  Aerodynamic and functional consequences of wing compliance , 2009 .

[16]  G. Ribak,et al.  Flying with eight wings: inter-sex differences in wingbeat kinematics and aerodynamics during the copulatory flight of damselflies (Ischnura elegans) , 2016, The Science of Nature.

[17]  T. Hedrick,et al.  Wingbeat Time and the Scaling of Passive Rotational Damping in Flapping Flight , 2009, Science.

[18]  C. H. Greenewalt Dimensional relationships for flying animals , 1962 .

[19]  R. Wootton,et al.  The hind wing of the desert locust (Schistocerca gregaria Forskål). III. A finite element analysis of a deployable structure. , 2000, The Journal of experimental biology.

[20]  A. R. Ennos The Inertial Cause of Wing Rotation in Diptera , 1988 .

[21]  Toshiyuki Nakata,et al.  Aerodynamic performance of a hovering hawkmoth with flexible wings: a computational approach , 2012, Proceedings of the Royal Society B: Biological Sciences.

[22]  R. Wootton,et al.  The hind wing of the desert locust (Schistocerca gregaria Forskål). I. Functional morphology and mode of operation. , 2000, The Journal of experimental biology.

[23]  R. Wootton Support and deformability in insect wings , 2009 .

[24]  V. Soroker,et al.  Effect of larval growth conditions on adult body mass and long-distance flight endurance in a wood-boring beetle: Do smaller beetles fly better? , 2017, Journal of insect physiology.

[25]  K. Schneider,et al.  Aerodynamic Ground Effect in Fruitfly Sized Insect Takeoff , 2015, PloS one.

[26]  Sanjay P Sane,et al.  The aerodynamics of insect flight , 2003, Journal of Experimental Biology.

[27]  C. Ellington The novel aerodynamics of insect flight: applications to micro-air vehicles. , 1999, The Journal of experimental biology.

[28]  T. Daniel,et al.  The Journal of Experimental Biology 206, 2989-2997 © 2003 The Company of Biologists Ltd , 2003 .

[29]  John Young,et al.  Details of Insect Wing Design and Deformation Enhance Aerodynamic Function and Flight Efficiency , 2009, Science.

[30]  G. Wilkinson,et al.  Wing shape, wing size, and sexual dimorphism in eye-span in stalk-eyed flies (Diopsidae) , 2009 .

[31]  Olavi Sotavalta,et al.  The flight-tone (wing-stroke frequency) of insects (Contributions to the problem of insect flight 1.) , 1947 .

[32]  A. R. Ennos INERTIAL AND AERODYNAMIC TORQUES ON THE WINGS OF DIPTERA IN FLIGHT , 1989 .

[33]  R. M. Alexander Models and the scaling of energy costs for locomotion , 2005, Journal of Experimental Biology.

[34]  Wei Shyy,et al.  Scaling law and enhancement of lift generation of an insect-size hovering flexible wing , 2013, Journal of The Royal Society Interface.

[35]  R. Mittal,et al.  Time-Varying Wing-Twist Improves Aerodynamic Efficiency of Forward Flight in Butterflies , 2013, PloS one.

[36]  K. Gaston,et al.  Body size variation in insects: a macroecological perspective , 2010, Biological reviews of the Cambridge Philosophical Society.

[37]  Haecheon Choi,et al.  A scaling law for the lift of hovering insects , 2015, Journal of Fluid Mechanics.

[38]  R. Wootton,et al.  An Approach to the Mechanics of Pleating in Dragonfly Wings , 1986 .

[39]  E. Holmes On being the right size , 2005, Nature Genetics.

[40]  G. Wilkinson,et al.  Compensation for exaggerated eye stalks in stalk-eyed flies (Diopsidae) , 2011 .

[41]  S. Timoshenko,et al.  Elements Of Strength Of Materials , 1935 .

[42]  Diana D Chin,et al.  Flapping wing aerodynamics: from insects to vertebrates , 2016, Journal of Experimental Biology.

[43]  T. Daniel,et al.  Into thin air: contributions of aerodynamic and inertial-elastic forces to wing bending in the hawkmoth Manduca sexta , 2003, Journal of Experimental Biology.

[44]  Bo Zheng,et al.  Agent-Based Model with Asymmetric Trading and Herding for Complex Financial Systems , 2013, PloS one.

[45]  F. Haas,et al.  Wing folding and the functional morphology of the wing base in Coleoptera. , 2001, Zoology.

[46]  R. Wootton,et al.  The hind wing of the desert locust (Schistocerca gregaria Forskål). II. Mechanical properties and functioning of the membrane. , 2000, The Journal of experimental biology.

[47]  T. Daniel,et al.  The Journal of Experimental Biology 206, 2979-2987 © 2003 The Company of Biologists Ltd , 2022 .

[48]  P. Suñé,et al.  Positive Outcomes Influence the Rate and Time to Publication, but Not the Impact Factor of Publications of Clinical Trial Results , 2013, PloS one.

[49]  C. Ellington The Aerodynamics of Hovering Insect Flight. III. Kinematics , 1984 .

[50]  James Lighthill,et al.  Aerodynamic Aspects of Animal Flight , 1975 .

[51]  J. P. Whitney,et al.  Effect of flexural and torsional wing flexibility on lift generation in hoverfly flight. , 2011, Integrative and comparative biology.

[52]  Adrian L. R. Thomas,et al.  Operation of the alula as an indicator of gear change in hoverflies , 2012, Journal of The Royal Society Interface.

[53]  Xinyan Deng,et al.  Flight mechanics and control of escape manoeuvres in hummingbirds. I. Flight kinematics , 2016, Journal of Experimental Biology.

[54]  C. Ellington Limitations on Animal Flight Performance , 1991 .

[55]  Charles P. Ellington,et al.  THE AERODYNAMICS OF HOVERING INSECT FLIGHT. , 2016 .

[56]  N. Pirie "On being the right size". , 1973, Annual review of microbiology.

[57]  Adrian L. R. Thomas,et al.  Deformable wing kinematics in free-flying hoverflies , 2010, Journal of The Royal Society Interface.

[58]  B. Balachandran,et al.  Influence of flexibility on the aerodynamic performance of a hovering wing , 2009, Journal of Experimental Biology.

[59]  Andrew M. Mountcastle,et al.  Wing flexibility enhances load-lifting capacity in bumblebees , 2013, Proceedings of the Royal Society B: Biological Sciences.

[60]  K. Kawano Horn and Wing Allometry and Male Dimorphism in Giant Rhinoceros Beetles (Coleoptera: Scarabaeidae) of Tropical Asia and America , 1995 .

[61]  F. Lehmann,et al.  Elastic deformation and energy loss of flapping fly wings , 2011, Journal of Experimental Biology.

[62]  Xinyan Deng,et al.  Flight mechanics and control of escape manoeuvres in hummingbirds. II. Aerodynamic force production, flight control and performance limitations , 2016, Journal of Experimental Biology.

[63]  Ainhoa Berciano-Alcaraz,et al.  A computational approach of , 2010 .

[64]  Tyson L Hedrick,et al.  Software techniques for two- and three-dimensional kinematic measurements of biological and biomimetic systems , 2008, Bioinspiration & biomimetics.

[65]  Hoon Cheol Park,et al.  Aerodynamic forces and flow structures of the leading edge vortex on a flapping wing considering ground effect , 2013, Bioinspiration & biomimetics.

[66]  M. Dickinson,et al.  The aerodynamic effects of wing–wing interaction in flapping insect wings , 2005, Journal of Experimental Biology.

[67]  Peter Aerts,et al.  Comparative Biomechanics: Life’s Physical World, 2nd edn. Steven Vogel, editor. , 2013 .

[68]  Ramiro Godoy-Diana,et al.  Behind the performance of flapping flyers , 2010 .

[69]  R. Oppermann Strength of materials, part 2, advanced theory and problems , 1941 .

[70]  Mao Sun,et al.  Effects of wing deformation on aerodynamic forces in hovering hoverflies , 2010, Journal of Experimental Biology.

[71]  Sridhar Ravi,et al.  Bumblebee flight performance in cluttered environments: effects of obstacle orientation, body size and acceleration , 2015, The Journal of Experimental Biology.

[72]  Qiang Zhu,et al.  Performance of a wing with nonuniform flexibility in hovering flight , 2013 .

[73]  Thomas L Daniel,et al.  Flexible Wings and Fins: Bending by Inertial or Fluid-Dynamic Forces?1 , 2002, Integrative and comparative biology.

[74]  J. Brackenbury,et al.  Kinematics of take‐off and climbing flight in butterflies , 1991 .

[75]  Ramiro Godoy-Diana,et al.  How wing compliance drives the efficiency of self-propelled flapping flyers. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[76]  Hoon Cheol Park,et al.  Biomechanical Properties of Insect Wings: The Stress Stiffening Effects on the Asymmetric Bending of the Allomyrina dichotoma Beetle's Hind Wing , 2013, PloS one.

[77]  J. Marden Maximum Lift Production During Takeoff in Flying Animals , 1987 .

[78]  G. Wilkinson,et al.  Sexual dimorphism in wing beat frequency in relation to eye span in stalk-eyed flies (Diopsidae) , 2011 .

[79]  C. Boggs,et al.  Larval food limitation in butterflies: effects on adult resource allocation and fitness , 2005, Oecologia.

[80]  A. K. Davis,et al.  Measuring Intraspecific Variation in Flight-Related Morphology of Monarch Butterflies (Danaus plexippus): Which Sex Has the Best Flying Gear? , 2015 .

[81]  Olaf Ellers,et al.  Scaling in biology , 2001, Complex..

[82]  K. Weber Selection on wing allometry in Drosophila melanogaster. , 1990, Genetics.