Enhanced: Unsteady Aerodynamics

Robert Dudley* [HN13]

Insects are a conspicuous and abundant feature of life on Earth. With approximately 7000 new insect species described annually, entomologists regularly celebrate the taxonomic and morphological diversity of their favorite winged arthropods [HN1]. Most of these taxa are fairly small by anthropomorphic standards (1, 2) (see the figure). Some of the smallest beetles, for example, are the appropriately named nanoselliine ptiliids [HN2] with body lengths on the order of 0.3 to 0.4 mm (3). Flight [HN3] with small wings at such low Reynolds numbers [HN4] (the ratio of inertial to viscous forces) is aerodynamically challenging--viscosity exerts a predominant influence on moving appendages, and wing flapping is often described as swimming in molasses. High wingbeat frequencies and novel wing morphologies are well known to be associated with flight under such viscous circumstances. But how exactly do small insects create the aerodynamic forces necessary to offset their body weight against gravity? By using a cleverly designed "robotic fly," Dickinson [HN5] and co-workers (4) have now added substantially to our understanding of the aerodynamic mechanisms underpinning the flight of small insects (see page 1954). Because miniaturization has historically been a key process in the generation of the richness of insect species, elucidation of the associated physical means of flight can yield insight into contemporary arthropod diversity.

Figure 1
To fly a fly. For large insects, lift forces derive from the presence of a leading-edge vortex that precludes stall and that transiently yields aerodynamic forces greater than those associated with steady-state flow. By contrast, flight of smaller insects is facilitated by rapid wing rotation at the ends of the down- and upstroke, and by taking advantage of vortices shed previously from the translating wing.

Traditional aerodynamic analysis of animal flight has followed conceptually the analogy of airplane wings moving at a constant speed and orientation (that is, angle of attack) relative to oncoming airflow. The spatial and temporal complexities of wing flapping are decomposed into consecutive instances of such steady-state airflow. As with the wings on airplanes, a single vortex circulating around the wing is presumed to generate aerodynamic lift. For many bats and birds, this steady-state analysis yields force balances consistent with those manifested by the animals themselves in free flight (see the figure). Lift production is progressively impeded at higher viscosities, however, and serious problems with the steady-state approach became evident when the estimated forces on flapping insect wings were shown to be insufficient to sustain hovering or even forward flight in some cases (5). Accelerations and changes in the wing's angle of attack during flapping badly violate the assumptions of steady-state flow, of course, and unsteady aerodynamic mechanisms must instead apply. Leading-edge vortices were recently shown to be generated on the flapping wings of hawkmoths [HN6] , fairly large insects about the size of hummingbirds (6) (see the figure). High-speed rotation of the leading-edge vortex creates a low-pressure zone above the wing, and transiently increases lift production above that feasible through steady-state translation alone [HN7]. For smaller insects, however, forces of viscosity progressively dissipate the energy of a leading-edge vortex, and additional mechanisms of force production must be sought.

Drosophila [HN8] has long served as a useful model in biology, and the new studies in this issue on insect flight aerodynamics (4) are no exception. Large-scale (25 cm) rigid models of Drosophila wings were attached to multiple motor drives that enabled flapping geometries similar to those of actual fruit flies. The apparatus was then immersed in a vat of viscous mineral oil to obtain Reynolds numbers equivalent to those experienced by small insects in air and thus nondimensional force coefficients on the model wings similar to those of hovering flies. A transducer at the base of one model wing enabled instantaneous forces to be measured throughout the flapping cycle. In most insects, reversal between the down- and upstroke motions of the wings is characterized by substantial rotation of each wing about its longitudinal axis. The flapping apparatus of Dickinson and co-workers faithfully replicated these rapid rotations for Drosophila, and revealed peaks of force production at the ends of each down- and upstroke. These forces were well in excess of those predicted by steady-state modeling, and substantially supplemented the forces of delayed stall produced during the translational period of each half-stroke. Thus, wing rotation and the associated circulation of air in an opposite rotational direction (see the figure) are a major force-producing mechanism in fruit flies and likely in many other small insects.

Intriguingly, the model Drosophila wings also produced substantial forces when transiently held stationary at the end of a half-stroke. This mechanism, termed wake capture, derives from airflow associated with the vortex shed from the wing during its previous stroke (see the figure). The lingering vortex wake is sufficiently strong and nearby so as to induce force-generating circulatory airflow around the wing.

Also important to force production is the relative timing (the phase relation) between wing rotation and translation. Along with the location of the rotational axis with respect to the leading edge of the wing, the relative phase of rotation was found to exert a strong influence on the magnitude of unsteady forces produced by rotational circulation and wake capture. The authors (4) point out that this sensitivity renders the timing of wing rotation an important parameter in the control of flight. Insects need change only by several percent the relative timing of wing rotation in order to alter substantially the magnitude and direction of forces on the wings, and thus to effect maneuvers. A general conclusion from this and other physical studies of flapping airfoils [HN9] (7, 8) is that unsteady aerodynamic forces are profoundly sensitive to the kinematic details of wing motion.

Wings [HN10] of many insects are highly flexible about deformational axes largely determined by an often cross-connected network of hollow veins (9). Many tiny insects also express fringing hairs about the perimeter of the wing that likely enhance torsional and bending abilities. Use of flexible wing models in the robotic fly apparatus, however, only marginally altered forces during symmetrical wing flapping (4). Instead, the aerodynamic effects of wing flexibility may be most evident during maneuvers when these bilaterally paired locomotor appendages are activated asymmetrically. Much aeronautical attention has recently been focused on the construction of miniature flying machines, also known as microair vehicles [HN11]. Can humans emulate technologically the elegance of a hovering hummingbird or the miniaturized maneuverability of a fruit fly? Wing flexibility, opposite wing interference, and the use of four rather than two wings (as characterizes the highly maneuverable dragonflies) [HN12] (10) all potentially influence the magnitude of such unsteady force-producing mechanisms as rotational circulation and wake capture. Given this informative demonstration of the "robotic fly" for low-Reynolds number aerodynamics, the skies are now clear for functional evaluation of the wonderfully numerous evolutionary variants in insect design.


  1. R. M. May, Science 241, 1441 (1988).
  2. E. Siemann, D. Tilman, J. Haarstad, Nature 380, 704 (1996).
  3. M. Sörensson, Syst. Entomol. 22, 257 (1997).
  4. M. H. Dickinson, F.-O. Lehmann, S. Sane, Science 284, 1954 (1999).
  5. C. P. Ellington, Philos. Trans. R. Soc. Lond. Ser. B 305, 145 (1984); R. Dudley and C. P. Ellington, J. Exp. Biol. 148, 53 (1990).
  6. C. P. Ellington et al., Nature 384, 626 (1996).
  7. K. Ohmi et al., J. Fluid Mech. 225, 607 (1991).
  8. J. Panda and K. B. M. Q. Zaman, ibid. 265, 65 (1994).
  9. R. J. Wootton, Annu. Rev. Entomol. 37, 113 (1992).
  10. G. Rüppell, J. Exp. Biol. 144 , 13 (1989).

The author is in the Section of Integrative Biology, University of Texas at Austin, Austin, TX 78712, USA. E-mail:

Related Resources on the World Wide Web

General Hypernotes

The Nearctica Web site provides an annotated list of recommended Web entomological resources.

The Entomology Index of Internet Resources, maintained by J. VanDyk, Department of Entomology, Iowa State University, is a directory and search engine of insect-related resources on the Internet.

The Department of Entomology, Colorado State University, provides a collection of links to entomology Web resources.

The Entomology Department of the New York State Agricultural Experiment Station offers a primer on insect biology and ecology.

J. Meyer, Department of Entomology, North Carolina State University, provides lecture notes for a course on general entomology.

Best of Biomechanics This guide to biomechanics was suggested to me by Ally Hazelton (June 2009) when she discovered by earlier link was not longer available.

The American Society of Biomechanics was founded in 1977 to provide a forum for the exchange of information and ideas among researchers in biomechanics.

R. Dryden's Flapping Wings Web site provides an introduction to animal flight.

The University of California Museum of Paleontology presents a Web exhibit on vertebrate flight. A discussion of the biomechanics of flight is included.

G. Spedding, Department of Aerospace Engineering, University of Southern California, offers an essay titled "Hydro- and aerodynamics of animal swimming and flight."

The K-8 Aeronautics Internet Textbook, a cooperative educational effort by NASA's Learning Technologies Project, Cislunar Aerospace, and the University of California, Davis, includes an introduction to the aerodynamics of animal flight. An instructor's text edition is also provided.

The Millibioflight Project, directed by K. Kawachi, Research Center for Advanced Science and Technology, University of Tokyo, studied flight characteristics of small organisms. A research report by A. Willmott titled "Numerical modelling as a tool for investigating the aerodynamics of insect flight" is available. The project was sponsored by the Exploratory Research for Advanced Technology (ERATO) program of the Japan Science and Technology Corporation.

The Journal of Experimental Biology, published by the Company of Biologists Limited, often publishes articles on the biomechanics of flight. The contents of back issues 1992 to the present may be browsed and searched; the full text of articles is available in Adobe Acrobat format.

Numbered Hypernotes

  1. The Wonderful World of Insects is provided by G. Ramel as part of his Entomological Home Page. R. Redak, Department of Entomology, University of California, Riverside, presents lecture notes on insect diversity for a course in the natural history of insects. Biodiversity and Conservation, a Web hypertextbook by P. Bryant, includes a chapter on biodiversity that discusses measuring species and the discovery of new species.

  2. The Tree of Life, maintained by D. Maddison of the University of Arizona, offers a section on Coleoptera (beetles) that includes an entry for Ptiliidae: Featherwing beetles.

  3. T. Miller, Department of Entomology, University of California, Riverside, provides lecture notes on insect muscles and flight for a course on insect physiology. The Hooper Virtual Palaeontological Museum offers a presentation on the development of insect flight. S. Childress and J. Wang, Department of Mathematics, New York University, present a page about the simulation of insect flight, which includes an animation.

  4. Reynolds number is defined in the Dictionary of Mining, Mineral, and Related Terms. The Process Associates of America provides a definition of Reynolds number on its Process Tools page. C. Heintz of the Zenith Aircraft Company discusses Reynolds numbers in an article on airfoils. A discussion of the Reynolds number is provided in the biography of Osbourne Reynolds by J. D. Jackson, Manchester School of Engineering, University of Manchester, UK.

  5. M. Dickinson is in the Department of Integrative Biology, University of California, Berkeley. The Journal of Experimental Biology had an article (vol. 192, pp. 207-224, 1994) by M. Dickinson titled "The effects of wing rotation on unsteady aerodynamic performance at low Reynolds numbers" and an article (vol. 174, pp. 45-64, 1993) by M. Dickinson and K. Götz titled "Unsteady aerodynamic performance of model wings at low Reynolds numbers."

  6. The Entomology Department of the Natural History Museum, London, provides an introduction to the evolutionary biology of the hawk moths. The Royal British Columbia Museum offers a presentation on Sphingidae (sphinx or hawk moths). The U.S.G.S. Northern Prairie Wildlife Research Center provides a collection of photos and descriptions of North American Sphingidae (hawk moths); an entry about the Carolina sphinx (Manduca sexta) hawkmoth is included.

  7. C. van den Berg, Faculty of Human Movement Sciences, Vrije Universiteit, Amsterdam, presents information about research on the flight of hawkmoths. A feature titled "The secret behind impossible flight" about C. Ellington's research on hawkmoth flight is available on the InScight Web site. The 11 October 1997 issue of New Scientist had an article by M. Brookes titled "On a wing and a vortex" about research on insect flight by C. Ellington and others. The March 1997 issue of Mechanical Engineering had an article by S. Ashley titled "Against all odds: How bugs take wing" that discusses hawkmoth flight research. Two articles by A. Willmott and C. Ellington on the mechanics of flight in the hawkmoth Manduca sexta (part I and part II) appeared in Journal of Experimental Biology (vol. 200, no. 21, 1997). An article by Hao Liu et al. titled "A computational fluid dynamic study of hawkmoth hovering" appeared in the Journal of Experimental Biology (vol. 201, pp. 461-477, 1998).

  8. The Compendium of Hexapod Classes and Orders, presented by J. Meyer, Department of Entomology, North Carolina State University, provides information about Diptera, the order to which Drosophila belongs. The Interactive Fly, a hypertext encyclopedia of fly genes and developmental processes, provides images of the male and female Drosophila. The Drosophila Virtual Library, a collection of links to Web resources maintained by G. Manning, provides an introduction to Drosophila melanogaster. J. Marden, Biology Department, Pennsylvania State University, offers a presentation on performance during free flight in Drosophila melanogaster.

  9. The Institute for Aerospace Studies, University of Toronto, presents information on flapping wing research; a video of an ornithopter in flight is presented. K. Jones, Department of Aeronautics and Astronautics, Naval Postgraduate School, offers a presentation about his flapping-wing propulsion research.

  10. J. Meyer offers lecture notes on insect wings for a course on general entomology.

  11. An article titled "It's a fly! It's a bug! It's a microplane!" by M. Dwortzan appeared in the October 1997 issue of Technology Review; links to related Web resources are included. Discovery Channel Online offers a feature by D. Pescovitz on micro air vehicles, which includes a discussion of how they fly. The January-March 1998 issue of High Technology Careers Magazine featured an article by D. Page titled "Micro air vehicles: Learning from the birds and bees" The Micro Air Vehicle Web site at the U.S. Defense Advanced Research Projects Agency makes available an article by J. McMichael and J. Francis titled "Micro air vehicles - Toward a new dimension in flight." The Robotics and Intelligent Machines Laboratory, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, provides a Web page about its Micromechanical Flying Insect (MFI) Project.

  12. R. Beckemeyer maintains a Web site about Odonata (dragonflies and damselflies). The Tree of Life provides information about Odonata: Dragonflies and damselflies. An introduction to the flight mechanics of dragonflies and damselflies is presented by F. SaintOurs, Department of Biology, University of Massachusetts, Boston. A symposium paper by J. Weygandt titled "Flow analysis of dragonfly aerodynamic mechanisms using particle image velocimetry" is available from the Exploratory Research for Advanced Technology (ERATO) Web site of the Japan Science and Technology Corporation. Digital Dragonflies, a project of the Entomology Program at the Texas A&M University Research and Extension Center at Stephenville, offers an intensive collection of images of dragonflies.

  13. R. Dudley is in the Section of Integrative Biology, University of Texas, Austin.