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
- horizontal component of the wing lift force calculated with the analytical model
- horizontal component of the wing lift force obtained from numerical simulations
- Faz
- vertical component of the aerodynamic lift force produced by the wings
- vertical component of the wing lift force calculated with the analytical model
- 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
- 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