Volume 284, Number 5422, Issue of 18 Jun 1999, pp. 1937-1939.   Science
Copyright © 1999 by The American Association for the Advancement of Science.
 

 BIOMECHANICS:
 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.
 
 

 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.

 References

    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: r_dudley@utxvms.cc.utexas.edu

 HyperNotes
 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.
      Biomechanics World Wide, maintained by J. Baudin, University of Alberta, Canada, is a
      guide to Internet biomechanics resources.
      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.