THREE GRAY CLASSICS ON THE BIOMECHANICS OF ANIMAL MOVEMENT
1 Harvard University
2 Harvard University
glauder{at}oeb.harvard.edu tytell{at}fas.harvard.edu
|
It is a rare scientific paper that, 70 years later, is still being used as
a source of both figures for review papers and experimental data for current
research. And yet many still turn to the figures and plates published in 1933
by James Gray to understand how animals propel themselves through water.
Gray's three papers on aquatic animal locomotion published in volume ten of
the Journal of Experimental Biology in 1933 (Gray,
1933a,b,c
)
form the cornerstone of modern attempts to understand aquatic locomotion.
These papers, made easily available again with this issue of the journal,
ushered in the era of quantitative studies of animal movement that had its
heritage in the work of Borelli, Muybridge, Pettigrew and Marey, and continues
to the present day as the burgeoning field of animal locomotor mechanics
(Alexander, 2003
;
Bels et al., 2003
;
Biewener, 2003
).
Gray's remarkable physical insights into the complex physics of locomotion
in the water combined with the detailed analysis of his experimental data are
the touchstone for current research on locomotor kinematics, muscle dynamics,
and computational fluid dynamic analyses of animals moving through water.
Virtually every recent textbook in the field either reproduces one of Gray's
figures directly or includes illustrations that derive their inspiration from
his figures (e.g. Alexander,
2003; Biewener,
2003
).
In his 1933a paper, Gray aimed to provide the first quantitative analysis
of the body movements of a swimming fish, and link these motions to the forces
that propel the fish forward. He used frames from motion picture films taken
of fish swimming to visualize the deformation of the body, and relied on a
clever timing circuit that he had developed earlier for his studies of ciliary
motion (Gray, 1930) to ensure
that he had precise knowledge of the time between each film frame. Knowledge
of accurate inter-frame times was critical for calculating velocities of
points on the fish body. Other than the reference to this earlier paper, Gray
gave few details of the experimental arrangement, number of fishes, and
methods of analysis used for his study.
From his analysis of sequences of film frames, Gray was able to track the
crest of waves on the body of swimming fish, and he recognized that the body
wave traveled backward faster than the forward swimming speed of the fish. In
a further significant conceptual breakthrough, he divided the body of swimming
eels into a series of interconnected segments which he treated as flat plates
and considered the velocity of each segment. He realized that segments changed
their angle to oncoming flow in a cyclical manner, and that the velocity of
each segment was greatest as it passed near the midline. Because high velocity
is correlated with high force, he inferred that each segment would produce
maximal thrust as it crossed the midline. Additionally, the recognition that
each segment has an angle of attack to the flow, like a small wing,
immediately suggested the application of airfoil theory to eel segments,
inspiring an entire class of theoretical models (e.g.
Taylor, 1952). His
illustration (figure 14 of Gray, 1933a) of the angles of the tail segment and
the figure-eight pattern it makes is an oft-reproduced classic image. Gray's
kinematic analysis also served as the foundation for James Lighthill's
enormously important theoretical work on aquatic propulsion (e.g. Lighthill,
1960
,
1969
,
1970
,
1971
), and has inspired a
generation of modeling efforts (Weihs,
1972
; Wu et al.,
1975
, 1961).
The other two papers in this series explore results from the first paper in more detail. In his 1933b paper Gray uses patterns of body bending in the eel to infer how the muscles are acting to place body segments at an angle appropriate for thrust generation. The 1933c paper is noteworthy for its investigation of tail function by removing the tail of a whiting (a cod-like fish) to examine the effect of the tail on swimming performance. Gray concluded that whiting could still swim forward at a slow swimming speed even though they lacked a tail, but that the motion of the body changed significantly after tail removal. He analogized the fish tail to a propeller, and estimated that the tail generates 40% of total thrust in a non-anguilliform fish. Better estimates are still not available today.
It is the four plates from the 1933a paper (containing figures 211),
however, that provide the most enduring practical legacy of Gray's work. These
plates show how a variety of fishes bend their bodies as they swim. Gray used
a movie camera to capture a series of images of fishes swimming over a
background grid, then printed frames from these movies, and finally assembled
a composite figure aligning the images through time side-by-side using the
background grid and a known reference point. Each separate figure within the
plates thus illustrates motion of the fish body in both space and time,
clearly showing the wave-like pattern of body movement and forward progress of
the fish. By marking the locations of maximal body curvature with dots on the
pictures, the reader could easily see the wave of bending that passes down the
body, propelling the fish forward like a screw propeller, to use Gray's
analogy. Gray's plates not only illustrate forward locomotion, but also
backward movement (an issue only recently addressed again:
D'Août and Aerts, 1999)
and the ontogeny of locomotion, by showing body movements of glass eels which
have yet to complete their metamorphosis into the juvenile eel morphology.
These plates have influenced subsequent research in three other noteworthy ways. First, although the 1933a paper focused on locomotion of the eel, the locomotion of six other species is represented in the plates, forming the first broadly comparative analysis of aquatic locomotion in fishes. Gray demonstrated that the underlying physical principle he described in eels, in which a wave travels backward down the body faster than the eel moves forward, is a general one underlying aquatic undulatory propulsion.
Second, these plates have continued to be a source of kinematic data for
biomechanical analysis. Because obtaining kinematic data on moving animals is
difficult and time-consuming, it is perhaps not surprising that Gray's plates
have themselves been digitized to obtain data on the pattern of eel body
motion. One example of this is the elegant work of Carling et al.
(1998), who used the kinematic
data from Gray's (1933a) eel plates to define a computational fluid dynamic
model. This model calculated the forces exerted on the water by the bending
eel, and, in turn, the forces exerted back on the eel by the water. Carling et
al. (1998
) were able to
calculate the movement of their virtual eel resulting from the interplay of
these forces, show that the eel swims forward reaching a constant average
speed, and predict the pattern of fluid flow around the swimming eel.
One downside to using the Gray (1933a) images for quantitative data is that
Gray did not specify the precise conditions under which he obtained his data.
Given the relatively brief time represented in each sequence of images, it is
hard to tell if the fish are accelerating, turning slightly, or if they are
moving up or down in the water column. Modern research uses flow tanks to
minimize these confounding effects, often with two simultaneous camera views
to select sequences with minimal unsteady or out-of-plane motion. In fact,
recent kinematic data obtained under controlled conditions indicates that
Gray's eels may have been accelerating as they moved across the field of view.
One indication of this acceleration is the relatively large lateral head
movement. Recent data show convincingly that head motion is minimal during
constant speed swimming at speeds less than two body lengths per second
(Gillis, 1996,
1998a
,b
).
However, during linear acceleration or during searching behavior, lateral head
movement increases dramatically. Nonetheless, the large sideways head
excursion Gray observed during eel locomotion endures in the literature, and
eel outlines derived from his figures are reproduced in countless reviews
(e.g. Lindsey, 1978
) with
lateral head excursions substantially greater than observed during carefully
controlled constant speed swimming. These new results suggest strongly that
Gray's eels were accelerating and that kinematic data derived from his plates
need to be treated with caution.
Even so, Gray's (1933a) plates can still illuminate interesting features of
fish locomotion. For example, his Plate II of a mackerel swimming shows a
complex pattern of movement in the tail itself, strongly indicative of
intrinsic tail bending and three-dimensional deformation. The
three-dimensional nature of fish tail function has only recently been explored
in detail. In particular, image two in figure 5 of Plate II shows the mackerel
tail as a forked surface, inclined significantly to the bottom plane of the
tank, while image seven shows the tail as a thin plate at a small angle of
inclination. There must be bending and tilting of the tail even during
relatively steady forward propulsion, and Gray's images provide the first
convincing evidence of the complexity of tail motion. It was, in part, study
of these figures in the mid-1990s that led one of us to undertake a more
comprehensive three-dimensional analysis of tail function in fishes
(Lauder, 2000). All of us who
study animal propulsion owe a tremendous debt to Sir James Gray, whose elegant
papers continue to inspire new experiments.
Footnotes
George Lauder and Eric Tytell write about James Gray's 1933 ground breaking publications on fish locomotion. Pdf files of Gray's papers can be accessed as supplemental data at jeb.biologists.org
References
Alexander, R. M. (2003). Principles of Animal Locomotion. Princeton: Princeton University Press.
Bels, V., Gasc, J.-P. and Casinos, A. (2003). Vertebrate Biomechanics and Evolution. Oxford: BIOS Scientific Publishers.
Biewener, A. (2003). Animal Locomotion. Oxford: Oxford University Press.
Carling, J. C., Williams, T. L. and Bowtell, G.
(1998). Self-propelled anguilliform swimming: simultaneous
solution of the two-dimensional NavierStokes equations and Newton's
laws of motion. J. Exp. Biol.
201,3143
-3166.
D'Août, K. and Aerts, P. (1999).
Kinematic comparison of forward and backward swimming in the eel, Anguilla
anguilla. J. Exp. Biol.
202,1511
-1521.
Gillis, G. B. (1996). Undulatory locomotion in elongate aquatic vertebrates: anguilliform swimming since Sir James Gray. Amer. Zool. 36,656 -665.
Gillis, G. B. (1998a). Environmental effects on
undulatory locomotion in the American eel Anguilla rostrata:
kinematics in water and on land. J. Exp. Biol.
201,949
-961.
Gillis, G. B. (1998b). Neuromuscular control of
anguilliform locomotion: patterns of red and white muscle activity during
swimming in the American eel Anguilla rostrata. J. Exp.
Biol. 201,3245
-3256.
Gray, J. (1930). The mechanism of ciliary movement. VI. Photographic and stroboscopic analysis of ciliary movement. Proc. R. Soc. Lond. B 107,313 -332.
Gray, J. (1933b). Studies in animal locomotion. I. The movement of fish with special reference to the eel. J. Exp. Biol. 10,88 -104.
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.
Lauder, G. V. (2000). Function of the caudal fin during locomotion in fishes: kinematics, flow visualization, and evolutionary patterns. Amer. Zool. 40,101 -122.
Lighthill, J. (1960). Note on the swimming of slender fish. J. Fluid Mech. 9, 305-317.
Lighthill, J. (1970). Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44,265 -301.
Lighthill, J. (1971). Large-amplitude elongated body theory of fish locomotion. Proc. R. Soc. Lond. B 179,125 -138.
Lighthill, M. J. (1969). Hydromechanics of aquatic animal propulsion: a survey. Ann. Rev. Fluid Mech. 1,413 -446.[CrossRef]
Lindsey, C. C. (1978). Form, function, and locomotory habits in fish. In Fish Physiology. Vol.VII . Locomotion (ed. W. S. Hoar and D. J. Randall), pp. 1-100. New York: Academic Press.
Taylor, G. (1952). Analysis of the swimming of long and narrow animals. Proc. R. Soc. Lond. A 214,158 -183.
Weihs, D. (1972). A hydrodynamic analysis of fish turning manoeuvres. Proc. Roy. Soc. Lond. B 182, 59-72.
Wu, T. Brokaw, C. J. and Brennen, C. (1975). Swimming and Flying in Nature. New York: Plenum.
Wu, T. Y. (1961). Swimming of a waving plate. J. Fluid Mech. 10,321 -344.