Skip to main content
    • Aa
    • Aa

Energy-minimizing kinematics in hovering insect flight

  • GORDON J. BERMAN (a1) and Z. JANE WANG (a2)

We investigate aspects of hovering insect flight by finding the optimal wing kinematics which minimize power consumption while still providing enough lift to maintain a time-averaged constant altitude over one flapping period. In particular, we study the flight of three insects whose masses vary by approximately three orders of magnitude: fruitfly (Drosophila melanogaster), bumblebee (Bombus terrestris), and hawkmoth (Manduca sexta). Here, we model an insect wing as a rigid body with three rotational degrees of freedom. The aerodynamic forces are modelled via a quasi-steady model of a thin plate interacting with the surrounding fluid. The advantage of this model, as opposed to the more computationally costly method of direct numerical simulation via computational fluid dynamics, is that it allows us to perform optimization procedures and detailed sensitivity analyses which require many cost function evaluations. The optimal solutions are found via a hybrid optimization algorithm combining aspects of a genetic algorithm and a gradient-based optimizer. We find that the results of this optimization yield kinematics which are qualitatively and quantitatively similar to previously observed data. We also perform sensitivity analyses on parameters of the optimal kinematics to gain insight into the values of the observed optima. Additionally, we find that all of the optimal kinematics found here maintain the same leading edge throughout the stroke, as is the case for nearly all insect wing motions. We show that this type of stroke takes advantage of a passive wing rotation in which aerodynamic forces help to reverse the wing pitch, similar to the turning of a free-falling leaf.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

R. McN. Alexander 2001 Design by numbers. Nature 412, 591.

A. Andersen , U. Pesavento & Z. J. Wang 2005 aUnsteady aerodynamics of fluttering and tumbling plates. J. Fluid Mech. 541, 6590.

A. Andersen , U. Pesavento & Z. J. Wang 2005 bAnalysis of transitions between fluttering, tumbling and steady descent of falling cards. J. Fluid Mech. 541, 91104.

M. H. Dickinson , F.-O. Lehmann & S. P. Sane 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284, 19541960.

C. P. Ellington 1984 The aerodynamics of hovering insect flight. Phil. Trans. R. Soc. Lond. B 305, 1181.

S. N. Fry , R. Sayaman & M. H. Dickinson 2005 The aerodynamics of hovering flight in Drosophila. J. Expl Biol. 208, 23032318.

J. F. Harrison & S. P. Roberts 2000 Flight respiration and energetics. Annu. Rev. Physiol. 62, 179205.

A. E. Kammer & B. Heinrich 1978 Insect flight metabolism. Adv. Insect Physiol. 13, 133228.

M. Milano & P. Koumoutsakos 2002 A clustering genetic algorithm for cylinder drag optimization. J. Comput. Phys. 175, 79107.

R. A. Norberg 1972 The pterostigma of insect wings an inertial regulator of wing pitch. J. Comput. Physiol. A 81, 922.

G. A. Parker & J. M. Smith 1990 Optimality theory in evolutionary biology. Nature 348, 2733.

U. Pesavento & Z. J. Wang 2004 Falling paper: Navier-stokes solutions, model of fluid forces, and center of mass elevation. Phys. Rev. Lett. 93, 144501144504.

M. Srinivasan & A. Ruina 2006 Computer optimization of a minimal biped model discovers walking and running. Nature 439, 7275.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 125 *
Loading metrics...

Abstract views

Total abstract views: 331 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th September 2017. This data will be updated every 24 hours.