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
AerodynamicsRobert 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.eduHyperNotes
Related Resources on the World Wide WebGeneral 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.