First published online April 23, 2004
Journal of Experimental Biology 207, 1953-1967 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.00993
Swimming gaits, passive drag and buoyancy of diving sperm whales Physeter macrocephalus
Patrick J. O. Miller1,2,*,
Mark P. Johnson3,
Peter L. Tyack2 and
Eugene A. Terray3
1 Sea Mammal Research Unit, University of St Andrews, Fife, KY16 8LB,
Scotland
2 Biology Department, Woods Hole Oceanographic Institution, Woods Hole, MA
02543, USA
3 Department of Applied Ocean Physics and Engineering, Woods Hole
Oceanographic Institution, Woods Hole, MA 02543, USA
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Fig. 3. Pitch and vertical velocity of sperm whales during descent (left side of
each panel), and ascent (right side of each panel). Periods of gliding are
marked in light red on the pitch and velocity traces. (A) The most commonly
observed pattern, with steady fluking during descent and stroke-and-glide
swimming during the ascent. Note that the ascent in A is considered a `steep'
ascent as pitch is >60° throughout and there are no pauses during the
ascent. This same ascent is shown in more detail in
Fig. 1. (B) Another example of
predominantly active fluking during descent with stroke and glide during
ascent. This ascent is considered `non-steep' as pitch is often less than
60°. The dive in (C) reveals steady fluking during the descent, but
prolonged gliding of almost 600 m during the ascent. In (D), the whale use a
stroke-and-glide swimming gait during descent and primarily steady fluking
during ascent.
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Fig. 1. Examples of measurements of data from Dtag during the descent and ascent of
the fourth dive recorded from animal sw275b. In all panels, gliding periods
are colored light red and thrusting periods black. Each blue cross marks the
position at which depth, pitch, speed and acceleration values were measured
from descent (Ai–Di) and ascent (Aii–Dii) glides. The beginning of
a descent was the time the whale left the surface, while the end was the time
when whale pitch first exceeded 0° (i.e. when was no longer oriented
downward). Conversely, an ascent was defined to start at the last point in
time when an animal's pitch was downward (<0°) and ended when the whale
reached the surface. (A) Depth versus time; (B) pitch of the whale
(note the oscillations in pitch caused by fluking by the whale); (C) fluking
energy (FE; see text for further details); (D) speed through the water,
calculated as vertical velocity (broken line) divided by sin(pitch). Note the
oscillations in speed corresponding to the acceleration of the whale during
glide and thrusting intervals.
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Fig. 4. Acceleration during glides as a function of glide depth and speed
(gray-scaling). Note the strong change in acceleration from negative to
positive values at depths less than 200 m, due to increased buoyancy from
expanding air within the sperm whale. The effect of speed as predicted by the
drag equation is apparent, since accelerations within any depth range were
lower when the glide speeds were higher.
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Fig. 5. Observed versus predicted acceleration during seven descent
glides. Predicted descent glide accelerations are calculated using
coefficients estimated from ascent glides for each whale. The number close to
each data point is the mean depth of the descent glide. Predicted and observed
values are positively correlated with a slope of 0.95 (P<0.01).
The average offset of predictions from observed values is calculated by
fitting a line with slope of 1.0 (dotted line) to the data yielding a
y-intercept of–0.0052 m s-2. This offset could be
explained by an average tissue-density decrease of 0.064% between ascents and
descents due to tissue warming while the whale is at the surface.
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Fig. 6. Estimate of drag coefficient Cd versus
Reynold's number for the sub-glides analyzed from five sperm whales.
Individual sub-glides are shown as small symbols, and the mean for each animal
is the large symbol. The black line is the theoretically derived drag
coefficient for a completely turbulent spindle of fineness ratio 5.50 (see
Stelle et al., 2000 ). Note
that the mean drag coefficient for each animal is quite close to the
theoretical level for a turbulent spindle, and that there is little variation
across animals in the drag estimate.
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Fig. 7. Predicted drag and buoyancy forces acting on a 12.5 m spermwhale, with a
mass of 25x103 kg, assumed to be ascending/descending at a
speed of 1.5 m s-1. Drag and buoyancy coefficients are based upon
the model coefficients for sw275b and the temperature profile in the
Mediterranean Sea. A sharp thermocline between 50 and 100 m causes a rapid
decrease in negative buoyancy due to tissue density relative to seawater.
After descent, the whale is at near-neutral buoyancy at 1000 m depth, which
changes to  250 m prior to ascent due to body density increases
via cooling at depth. Positive buoyancy forces from expanding air
exceed drag forces at 80 m during ascent. Thus, from this depth upward, even a
whale gliding at 1.5 m s-1 should positively accelerate toward the
surface. Note that buoyancy forces never exceed ±170 N (or half of the
drag force) once the whale exceeds roughly 220 m depth.
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© The Company of Biologists Ltd 2004
of 75°. VV, or
vertical velocity, of the whale can be accurately measured as the change of
depth. Speed through the water is then equal to the absolute value of
VV/sin