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Research Article
Force balance in the take-off of a pierid butterfly: relative importance and timing of leg impulsion and aerodynamic forces
Gaëlle Bimbard, Dmitry Kolomenskiy, Olivier Bouteleux, Jérôme Casas, Ramiro Godoy-Diana
Journal of Experimental Biology 2013 216: 3551-3563; doi: 10.1242/jeb.084699
Gaëlle Bimbard
1Institut de Recherche sur la Biologie de l'Insecte (IRBI), CNRS UMR 7261, UFR Sciences et Techniques, Université François Rabelais, 37200 Tours, France
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  • For correspondence: gaelle.bimbard@etu.univ-tours.fr
Dmitry Kolomenskiy
2Centre de Recherches Mathématiques (CRM), Department of Mathematics and Statistics, McGill University, 805 Sherbrooke W., Montréal, QC, Canada, H3A 2K6
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Olivier Bouteleux
1Institut de Recherche sur la Biologie de l'Insecte (IRBI), CNRS UMR 7261, UFR Sciences et Techniques, Université François Rabelais, 37200 Tours, France
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Jérôme Casas
1Institut de Recherche sur la Biologie de l'Insecte (IRBI), CNRS UMR 7261, UFR Sciences et Techniques, Université François Rabelais, 37200 Tours, France
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Ramiro Godoy-Diana
3Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS UMR 7636, ESPCI ParisTech, UPMC (Paris 6), Univ. Paris Diderot (Paris 7), 10 rue Vauquelin, 75231 Paris, Cedex 5, France
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SUMMARY

Up to now, the take-off stage has remained an elusive phase of insect flight that was relatively poorly explored compared with other maneuvers. An overall assessment of the different mechanisms involved in force production during take-off has never been explored. Focusing on the first downstroke, we have addressed this problem from a force balance perspective in butterflies taking off from the ground. In order to determine whether the sole aerodynamic wing force could explain the observed motion of the insect, we have firstly compared a simple analytical model of the wing force with the acceleration of the insect's center of mass estimated from video tracking of the wing and body motions. Secondly, wing kinematics were also used for numerical simulations of the aerodynamic flow field. Similar wing aerodynamic forces were obtained by the two methods. However, neither are sufficient, nor is the inclusion of the ground effect, to predict faithfully the body acceleration. We have to resort to the leg forces to obtain a model that best fits the data. We show that the median and hind legs display an active extension responsible for the initiation of the upward motion of the insect's body, occurring before the onset of the wing downstroke. We estimate that legs generate, at various times, an upward force that can be much larger than all other forces applied to the insect's body. The relative timing of leg and wing forces explains the large variability of trajectories observed during the maneuvers.

FOOTNOTES

  • AUTHOR CONTRIBUTIONS

    G.B. collected and analysed all data, and produced the first draft of the paper. D.K. carried out the numerical simulations and designed the leg force model (Eqn 7). O.B. participated in the leg kinematics experiment design, and collection and analysis of the data. J.C. participated in the design of the study and the writing of the manuscript. R.G.-D. designed the analytical force balance, participated in the design of the overall study and in the writing-up phase.

  • Supplementary material available online at http://jeb.biologists.org/cgi/content/full/216/18/3551/DC1

  • COMPETING INTERESTS

    No competing interests declared.

  • FUNDING

    This work was financially supported by the French National Research Agency [ANR-08-BLAN-0099].

  • LIST OF SYMBOLS AND ABBREVIATIONS

    c
    wing chord
    dA
    area of an element of the wing
    dF
    vertical component of the wing element force
    Fax
    horizontal component of the aerodynamic lift force produced by the wings
    Embedded Image
    horizontal component of the wing lift force calculated with the analytical model
    Embedded Image
    horizontal component of the wing lift force obtained from numerical simulations
    Faz
    vertical component of the aerodynamic lift force produced by the wings
    Embedded Image
    vertical component of the wing lift force calculated with the analytical model
    Embedded Image
    vertical component of the wing lift force obtained from numerical simulations
    Flx
    horizontal component of the leg force
    Flz
    vertical component of the leg force
    Fz(t)
    lift force
    g
    acceleration due to gravity
    Kl
    spring compression rate of the legs
    L
    wing length
    Ll
    leg extension length
    m
    mass of the insect
    Oxyz
    global coordinate system
    O′x′y′z′
    wingbase-referenced coordinate system
    t
    time
    T
    downstroke period
    tl
    spring releasing time
    Embedded Image
    instantaneous velocity of an element of the wing
    xb
    x coordinates of the insect's base point
    xcg
    x coordinates of the insect's center of gravity
    zb
    z coordinates of the insect's base point
    zcg
    z coordinates of the insect's center of gravity
    zw
    initial vertical distance between the insect's base point and the ground
    γ
    incidence angle
    θ
    positional angle of the wing
    ν
    air kinematic viscosity
    ρ
    fluid density
    ϕl
    angle formed by the leg of the insect and the horizontal
    • © 2013. Published by The Company of Biologists Ltd
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    Keywords

    • butterflies
    • Take-off
    • Variability
    • aerodynamic force
    • leg force
    • Insect flight
    • Flapping flight

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    Research Article
    Force balance in the take-off of a pierid butterfly: relative importance and timing of leg impulsion and aerodynamic forces
    Gaëlle Bimbard, Dmitry Kolomenskiy, Olivier Bouteleux, Jérôme Casas, Ramiro Godoy-Diana
    Journal of Experimental Biology 2013 216: 3551-3563; doi: 10.1242/jeb.084699
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    Research Article
    Force balance in the take-off of a pierid butterfly: relative importance and timing of leg impulsion and aerodynamic forces
    Gaëlle Bimbard, Dmitry Kolomenskiy, Olivier Bouteleux, Jérôme Casas, Ramiro Godoy-Diana
    Journal of Experimental Biology 2013 216: 3551-3563; doi: 10.1242/jeb.084699

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      • SUMMARY
      • INTRODUCTION
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      • RESULTS
      • DISCUSSION
      • ACKNOWLEDGEMENTS
      • FOOTNOTES
      • LIST OF SYMBOLS AND ABBREVIATIONS
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