Enhanced: Unsteady Aerodynamics
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
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
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
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.
- R. M. May, Science
241, 1441 (1988).
- E. Siemann, D. Tilman, J. Haarstad, Nature
380, 704 (1996).
- M. Sörensson, Syst. Entomol.
22, 257 (1997).
- M. H. Dickinson, F.-O. Lehmann, S. Sane, Science
284, 1954 (1999).
- C. P. Ellington, Philos. Trans. R.
Soc. Lond. Ser. B 305, 145 (1984); R. Dudley and
C. P. Ellington, J. Exp. Biol. 148, 53
- C. P. Ellington et
al., Nature 384, 626 (1996).
- K. Ohmi et al., J. Fluid
Mech. 225, 607 (1991).
- J. Panda and K. B. M. Q. Zaman, ibid.
265, 65 (1994).
- R. J. Wootton, Annu. Rev. Entomol.
37, 113 (1992).
- 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: firstname.lastname@example.org
Related Resources on the World Wide
Nearctica Web site provides an annotated
list of recommended Web entomological resources.
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.
Department of Entomology, Colorado State University, provides a
links to entomology Web resources.
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
lecture notes for a course on
of Biomechanics This guide to biomechanics was suggested to me by
Ally Hazelton (June 2009) when she discovered by earlier link was not
American Society of Biomechanics was founded in 1977 to provide a
forum for the exchange of information and ideas among researchers in
- R. Dryden's
Flapping Wings Web site provides an introduction to animal
University of California Museum of Paleontology presents a Web
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
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
aerodynamics of animal flight. An
instructor's text edition is also provided.
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
Japan Science and Technology Corporation.
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.
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,
chapter on biodiversity that discusses
measuring species and the discovery of new species.
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.
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
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.
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.
M. Dickinson is in the
Department of Integrative Biology, University of California,
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
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.
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
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).
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).
Compendium of Hexapod Classes and Orders, presented by J. Meyer,
Department of Entomology, North Carolina State University, provides
Diptera, the order to which Drosophila belongs. The
Interactive Fly, a hypertext encyclopedia of fly genes and
developmental processes, provides images of the
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,
presentation on performance during free flight in Drosophila
Institute for Aerospace Studies, University of Toronto, presents
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.
- J. Meyer offers lecture notes on
insect wings for a course on general entomology.
article titled "It's a fly! It's a bug! It's a microplane!" by M.
Dwortzan appeared in the October 1997 issue of
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.
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,
symposium paper by J. Weygandt titled "Flow analysis of dragonfly
aerodynamic mechanisms using particle image velocimetry" is available
Exploratory Research for Advanced Technology (ERATO) Web site of
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.
R. Dudley is in the Section of Integrative Biology, University of