A PORPOISE FOR POWER
West Chester University
ffish{at}wcupa.edu
Frank Fish writes about James Gray's 1936 publication on the power output of a swimming dolphin.
Sometimes the most innocent of scientific endeavors can have the most
far-reaching and profound ramifications. For James Gray, a simple calculation
to determine the power output of a swimming dolphin
(Gray, 1936) would launch a
contentious argument known as `Gray's Paradox'. Gray's classic study would
provide the impetus for studies of bio-hydrodynamics and would affect the
fields of material science, hydrodynamics, biorobotics, and diving
physiology.
The Gray's Paradox controversy resulted from the first attempt to evaluate
swimming energetics in animals (Webb,
1975). In his 1936 study, Gray used a rigid-body hydrodynamic
model to calculate drag power and applied it to a dolphin and a porpoise
swimming at high speeds (>7.6 m s-1). The results indicated that
the estimated drag power could not be reconciled with the available power
generated by the muscles. Gray
(1936
) stated: `If the
resistance of an actively swimming dolphin is equal to that of a rigid model
towed at the same speed, the muscles must be capable of generating energy at a
rate at least seven times greater than that of other types of mammalian
muscle.'
Gray's calculations assumed that turbulent flow conditions existed in the
boundary layer between the dolphin's skin and the water, because of the speed
and size of the animal. His resolution to the problem was that the drag on the
dolphin would have had to be lower than the turbulent conditions dictated, and
that this could be achieved by maintenance of a fully laminar boundary layer
against the dolphin's skin. In other words, the water against the dolphin skin
flowed in orderly, parallel streams over the entire body, although this ran
counter to accepted hydrodynamic theory. Gray proposed that the motion of the
dolphin's flukes, which are the broad, lateral extensions of the tail used for
propulsion, accelerated water flow over the posterior half of the body and
that this action could provide a mechanism to laminarize the boundary layer.
This mechanism was largely ignored in subsequent work, but the basic premise
that dolphins could somehow maintain a laminar boundary remained and became
the focus and justification of much of the work on dolphin hydrodynamics for
the next 60 years (Fish and Hui,
1991; Fish and Rohr,
1999
).
This basic premise of Gray's Paradox, however, was flawed, because of
potential errors in estimation of dolphin swimming speed and inconsistencies
between dolphin swimming performance and data on muscle power outputs. To
measure drag power, Gray used a shipboard observation of a dolphin swimming
along the side of the ship from stern to bow in 7 s. If the dolphin was
swimming close enough to utilize the flow pattern around the ship, its speed
may have been artificially enhanced and energetic effort reduced due to
freeriding behaviors (Lang,
1966; Williams et al.,
1992
; Weihs,
2004
). More important than the actual speed of the dolphin, the
duration of this high performance swimming was for a sprint and Gray used
measurements for muscle power output of sustained performance (3-5 min) by
human oarsmen (Henderson and Haggard,
1925
). Muscle fibers specialized for quick bursts of anaerobic
activity can produce maximum metabolic power output 2-17 times greater than
muscle fibers using a sustained aerobic metabolism
(Hochachka, 1991
;
Askew and Marsh, 1997
). The
higher muscle power outputs produced by anaerobic mechanisms offset the power
required to overcome the drag when the boundary layer is turbulent.
In effect, the dolphin has the capacity to swim at high speeds for short durations while maintaining a fully attached turbulent boundary layer between itself and the surrounding water. These turbulent boundary flow conditions would delay separation of the boundary layer from the dolphin's skin surface. When the boundary layer separates from the skin surface and interacts with outer flow, this results in a broader wake and increased drag, so delaying separation is beneficial to the dolphin. Separation is more likely to occur with a laminar boundary flow, producing a greater drag penalty compared to turbulent boundary conditions. Thus, the turbulent boundary layer remains attached longer, because it has more energy than the laminar boundary layer. The increased drag of a turbulent boundary layer is small compared to the increase in drag due to separation, which is more prone to occur with a laminar boundary layer.
The idea that laminar flow could be maintained over the entire body of the
dolphin was invigorated by Kramer
(1960a,b
).
Kramer claimed that the dolphin's smooth, compliant skin could achieve a
laminar boundary layer without separation. The skin was proposed to deform and
eliminate drag by the process of viscous dampening. In viscous dampening, the
compliance of the skin due to its viscoelastic properties would absorb energy
from pressure oscillations and dampen turbulence-forming perturbations to
maintain laminar flow. A torpedo with an artificial skin based on the skin of
a dolphin was reported to produce a 59% reduction in drag when compared to a
reference model with fully turbulent flow. These results exposed the
`dolphin's secret' and provided what Kramer
(1960b
) erroneously believed
was the resolution to Gray's Paradox.
The promise of faster submarines, ships and torpedoes was equally enticing
to the great navies of the world as the Cold War heightened
(Fish and Rohr, 1999). In what
has been characterized as `enthusiastic optimism'
(Vogel, 1994
), research on
compliant coatings and dolphin hydrodynamics was accelerated
(Lang and Daybell, 1963
;
Wood, 1973
;
Aleyev, 1977
;
Riley et al., 1988
). Attempts
to later verify Kramer's results on passive compliance subsequently failed
(Landahl, 1962
;
Riley et al., 1988
). Possible
mechanisms for drag reduction then focused on active skin compliance by
dolphins. Fast swimming dolphins were observed to have large mobile skin folds
that moved posteriorly along the body. To determine if mobile skin folds
observed in dolphins were actively controlled, naked women were towed through
water to emulate passive skin deformations
(Aleyev, 1977
). Although
amusing, the skin folds in the women were shown to increase drag. Recent
analyses of swimming kinematics, bioluminescence, physiology and diving
behaviors have demonstrated no special drag-reduction mechanisms for dolphins
(Fish, 1998
;
Rohr et al., 1998
;
Fish and Rohr, 1999
;
Williams et al., 2000
), while
the low drag performance of tuned compliant panels and robotic fish continue
to be bolstered by Gray's Paradox (Barrett
et al., 1999
; Carpenter et al.,
2000
).
We can look with hindsight at Gray's work on dolphin hydrodynamics and see
some of the mistakes that created the paradox. In 1936, there were very
limited data on muscle physiology, hydrodynamics, and swimming performance.
However, the error seems to have had the fortunate effect of stimulating more
research than probably would have occurred had all the answers been known. The
real paradox was that, despite its inaccuracies, Gray's paper was the impetus
for novel innovations that have furthered the areas of dolphin biology,
hydrodynamics and biomimetics. There is still more to be discovered; perhaps
the dolphin has not given up all its secrets. It may be as written by
Scholander (1959): `When
playing around in the ocean, dolphins are pleasing to the eye no end, but let
it only add to your thrill that these rascals are a graveyard to our wits. For
is not finding out infinitely more exciting than knowing the answer?'
Footnotes
A PDF file of the original paper can be accessed online: http://jeb.biologists.org/cgi/content/full/208/6/977/DC1
References
Aleyev, Y. G. (1977). Nekton. The Hague: Junk.
Askew, G. N. and Marsh, R. L. (1997). The
effects of length trajectory on the mechanical power output of mouse skeletal
muscles. J. Exp. Biol.
200,3119
-3131.
Barrett, D. S., Triantafyllou, M. S., Yue, D. K. P., Grosenbaugh, M. A. and Wolfgang, M. J. (1999). Drag reduction in fish-like locomotion. J. Fluid Mech. 392,183 -212.[CrossRef]
Carpenter, P. W., Davies, C. and Lucey, A. D. (2000). Hydrodynamics and compliant walls: Does the dolphin have a secret? Curr. Sci. 79,758 -765.
Fish, F. E. (1998). Comparative kinematics and hydrodynamics of odontocete cetaceans: Morphological and ecological correlates with swimming performance. J. Exp. Biol. 201,2867 -2877.
Fish, F. E. and Hui, C. A. (1991). Dolphin swimming - a review. Mamm. Rev. 21,181 -195.
Fish, F. E. and Rohr, J. (1999). Review of dolphin hydrodynamics and swimming performance. SPAWARS Tech. Rep. 1801.
Gray, J. (1936). Studies in animal locomotion VI. The propulsive powers of the dolphin. J. Exp. Biol. 13,192 -199.
Henderson, Y. and Haggard, H. W. (1925). The maximum of human power and its fuel. Amer. J. Physiol. 72,264 -282.
Hochachka, P. W. (1991). Design of energy metabolism. In Environmental and Metabolic Animal Physiology (ed. C. L. Prosser), pp.325 -351. New York: Wiley-Liss.
Kramer, M. O. (1960a). Boundary layer stabilization by distributed damping. J. Amer. Soc. Nav. Eng. 72,25 -33.
Kramer, M. O. (1960b). The dolphins' secret. New Sci. 7,1118 -1120.
Landahl, M. T. (1962). On stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech. 13,609 -632.
Lang, T. G. (1966). Hydrodynamic analysis of cetacean performance. In Whales, Dolphins and Porpoises (ed. K. S. Norris), pp.410 -432. Berkley, CA: University of California Press.
Lang, T. G. and Daybell, D. A. (1963). Porpoise performance tests in a seawater tank. Nav. Ord. Test Sta. Tech. Rep. 3063.
Riley, J. J., Gad-el-Hak, M. and Metcalfe, R. W. (1988). Compliant coatings. Ann. Rev. Fluid Mech. 20,393 -420.
Rohr, J., Latz, M. I., Fallon, S., Nauen, J. C. and Hendricks,
E. (1998). Experimental approaches towards interpreting
dolphin-stimulated bioluminescence. J. Exp. Biol.
201,1447
-1460.
Scholander, P. F. (1959). Wave-riding dolphins. Science 130,1658 .[Medline]
Vogel, S. (1994). Life in Moving Fluids. Princeton: Princeton University Press.
Webb, P. W. (1975). Hydrodynamics and energetics of fish propulsion. Bull. Fish. Res. Bd. Can. 190,1 -159.
Weihs, D. (2004). The hydrodynamics of dolphin drafting. J. Biol. 3,8 .1-8.16.[CrossRef][Medline]
Williams, T. M., Friedl, W. A., Fong, M. L., Yamada, R. M., Sedivy, P. and Haun, J. E. (1992). Travel at low energetic cost by swimming and wave-riding bottlenose dolphins. Nature 355,821 -823.[CrossRef][Medline]
Williams, T. M., Davis, R. W., Fuiman, L. A., Francis, J.,
LeBoeuf, B. J., Horning, M., Calambokidis, J. and Croll, D. A.
(2000). Sink or swim: strategies for cost-efficient diving by
marine mammals. Science
288,133
-136.
Wood, F. G. (1973). Marine Mammals and Man: The Navy's Porpoises and Sea Lions. Washington: Robert B. Luce.