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First published online May 1, 2006
Journal of Experimental Biology 209, 1789-1790 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02232
JEB Classics |
BAINBRIDGE SETS THE STAGE ON SCALING IN FISH SWIMMING
University of Michigan
pwebb{at}umich.edu
This classic by Richard Bainbridge is the first of three data papers
(Bainbridge, 1958
;
Bainbridge, 1960;
Bainbridge, 1962) on the
scaling of swimming motions and performance in fishes. When published, a
quarter century had passed since the earlier key 1933 papers by James Gray
(Gray, 1933a;
Gray, 1933b;
Gray, 1933c), recently
reviewed (Lauder and Tytell,
2004), showing the body deformations necessary for propulsion. The
intervening period saw a number of sallies probing the complexities of
swimming, as described in Sir James Gray's summary of the state of the art in
his 1968 book Animal Locomotion. Gray summarizes elegant studies on
shark stability by John Harris, various resistive- and reactive-based models
for fish propulsion, the ongoing fascination with maximum speed, and the
uncertainties of the power balance between availability and apparent
requirements. From Gray's review it was clear that further advances in the
understanding of fish swimming would require methods for the systematic and
accurate measurement of fish swimming motions in which key factors such as
speed and size could be controlled. Bainbridge was among the first, starting
in the late 1950s and early 1960s, to fill this vacuum.
In this 1958 paper, Bainbridge used natural variability in swimming speed
(plus a little bit of stimulation) to record tail-beat frequencies and
amplitudes of three species of fishes swimming at various speeds in annular
channels, dubbed `fish wheels' (Fig.
1). Bainbridge improved on earlier designs of annular channels
using ingenious gates to minimize slip and other uncontrolled water movements.
He studied swimming using fishes from 4 to 30 cm in total length, close to an
order of magnitude of fish length. As such, Bainbridge could extrapolate his
results to larger-sized fishes. However, his fish did have to swim in circles,
having to work harder than those swimming in straight lines
(Weihs, 1981), so Bainbridge
used two fish wheels with different diameters to reduce size effects of
swimming in circles.
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However, the Bainbridge Equation relating tail-beat frequency and speed did
not pass through the origin, as the tail-beat frequency was modulated at lower
speeds. Bainbridge found that tail-beat amplitude was also modulated at low
swimming speeds. He thought that the product of amplitude and frequency would
pass through the origin. This does not appear to be the case, but it is hard
to induce fish to swim in any regular fashion at very low speed. Consequently,
exactly what happens at low speeds is still not clear. Low-speed swimming
appears to pose challenges for fishes, perhaps associated with stability
(Webb, 2005).
Bainbridge's fish wheels followed a tradition dating at least as far back
as the late 18th century of using annular channels to study fish swimming
(Videler, 1993). Bainbridge
used his fish wheels to examine `steady swimming', speeds maintained for
multiple similar tail beats. At the time Bainbridge was doing his work, new
designs for straight water tunnels were being developed. These had advantages
in that fish speed could be rigidly controlled for long enough to ensure that
fish swam using many consecutive and similar tail beats and to estimate energy
costs of swimming from rates of oxygen consumption
(Blazka et al., 1960;
Brett, 1963;
Beamish, 1978). These flumes
steered studies of steady swimming towards low, sustainable speeds, a trend
that persists today. As a result, Bainbridge's results are especially notable,
and still unique, because they show relationships between tail-beat frequency
and amplitude in sprint swimming, the highest steady speeds maintained at best
for a few tail beats.
Unfortunately, the conditions under which fish swam in the fish wheel could
not be fully controlled. Consequently, maximum sprint speeds were probably not
accurate and it is not clear to what degree fish might have been accelerating
or decelerating at their highest observed speeds. However, the principles
established by Bainbridge provide for indirect approaches to the question of
limits to steady swimming performance. For example, given that tail-beat
frequency is the major modulator of speed and that stride length is constant
at higher speeds, it has been suggested that maximum speed is ultimately
limited by the twitch times of fish fast glycolytic (white) muscle. This can
be measured, maximum tail-beat frequency inferred, and hence maximum speed
estimated from the product of tail-beat frequency and stride length
(Wardle, 1975).
This application of principles established by Bainbridge on maximum speed
is just one example of the indirect consequences of his study. For me, a major
impact came from the use of Bainbridge's results with models of fish swimming.
James Lighthill's review of aquatic animal propulsion
(Lighthill, 1969), which he
developed with input from James Gray and Bainbridge
(Crocker, 1999), included a
simplified version of an elongated slender body model. This and subsequent
models have been especially important for calculating mechanical power
consumption from variables that Bainbridge demonstrated were readily
measurable. Power estimates using data on tail-beat frequencies and
amplitudes, improved knowledge of muscle power output and efficiency
(Hill, 1950;
Bainbridge, 1961), and measured
rates of oxygen consumption all combined to give a picture of fish swimming
energetics that has endured to today. Essentially, a convergence of results
from different approaches show that swimming is expensive compared to
transport costs of similar human engineering vehicles (Schmidt-Neilsen, 1972;
Tucker, 1975). This has been
attributed to high viscous-related energy losses along the body
(boundary-layer thinning).
With the passing of almost 50 years since Bainbridge's study, efforts have
been made by many to verify and understand the basis and consequences of such
high locomotor costs, and another technological shift now appears to be taking
place. Recent abilities to visualize flow using Particle Image Velocity (PIV)
not only challenge postulated boundary-layer thinning
(Anderson et al., 2001), but
further suggest high costs relate more to kinetic energy lost in the wake
(Schultz and Webb, 2002). In
spite of such shifts, the generalizations showed by Bainbridge continue to
contribute to thinking, and his results remain important in evaluating scaling
aspects of such new ideas.
Footnotes
Paul Webb writes about Richard Bainbridge's 1958 Classic paper `The Speed of Swimming of Fish as Related to Size and to the Frequency and Amplitude of the Tail Beat'.
A PDF file of the original paper can be accessed online: http://jeb.biologists.org/cgi/content/full/209/10/1789/DC1
References
Anderson, E. J., McGillis, W. R. and Grosenbaugh, M. A. (2001). The boundary layer of swimming fish. J. Exp. Biol. 204,81 -102.[Abstract]
Bainbridge, R. (1958). The speed of swimming of
fish as related to size and to the frequency and the amplitude of the tail
beat. J. Exp. Biol. 35,109
-133.
Bainbridge, R. (1960). Speed and stamina in three fish. J. Exp. Biol. 37,129 -153.[Abstract]
Bainbridge, R. (1961). Problems of fish locomotion. Symp. Zool. Soc. Lond. 40, 23-56.
Bainbridge, R. (1962). Training, speed and stamina in trout. J. Exp. Biol. 39,537 -555.[Abstract]
Beamish, F. W. H. (1978). Swimming capacity. InFish Physiology, Vol 7, Locomotion (ed. W. S. Hoar and D. J. Randall), pp. 101-187. New York, NY: Academic Press.
Blazka, P., Volf, M. and Cepala, M. (1960). A new type of respirometer for the determination of the metabolism of fish in an active state. Physiologia Bohemoslovenica 9, 553-558.
Brett, J. R. (1963). The energy required for swimming by young sockeye salmon with a comparison of the drag force on a dead fish. Trans. R. Soc. Can. Ser. IV 1, 441-457.
Crocker, M. J. (1999). Sir James Lighthill and his contributions to science. Keynote Lecture, Sixth International Congress on Sound and Vibration, Technical University of Denmark, Lyngby, Denmark. http://www.iiav.org/sirjameslighthill.pdf.
Gray, J. (1933a). Studies in animal locomotion. I. The movement of fish with special reference to the eel. J. Exp. Biol. 10,88 -104.[Abstract]
Gray, J. (1933b). Studies in animal locomotion. II. The relationship between waves of muscular contraction and the propulsive mechanism of the eel. J. Exp. Biol. 10,386 -390.
Gray, J. (1933c). Studies in animal locomotion. III. The propulsive mechanism of the whiting (Gadus merlangus). J. Exp. Biol. 10,391 -400.
Gray, J. (1968). Animal Locomotion. London, England: Weidenfeld and Nicolson.
Hill, A. V. (1950). The dimensions of animals and their muscular dynamics. Science Progr. 38,209 -230.
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Gray classics on the biomechanics of animal movement. J. Exp.
Biol. 207,1597
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Lighthill, M. J. (1969). Hydromechanics of aquatic animal propulsion. Ann. Rev. Fluid Mech. 1, 413-446.[CrossRef]
Schmidt-Nielsen, K. (1972). Locomotion: energy
cost of swimming, flying, and running. Science
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Schultz, W. W. and Webb, P. W. (2002). Power requirements of swimming: Do new methods resolve old questions? Integ. Comp. Biol. 42,1018 -1025.
Tucker, V. A. (1975). The energetic cost of moving about. Am. Sci. 63,413 -419.[Medline]
Videler, J. J. (1993). Fish Swimming. New York: Chapman and Hall.
Wardle, C. S. (1975). Limit of fish swimming speed. Nature (Lond.) 255,725 -727.[CrossRef][Medline]
Webb, P. W. (2005). Stability and maneuverability. In Fish Physiology (ed. R. E. Shadwick and G. V. Lauder). San Diego: Elsevier Press. In press.
Weihs, D. (1981). Effect of swimming path curvature on the energetics of fish. Fish. Bull. US 79,171 -176.
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