Stroke patterns and regulation of swim speed and energy cost in free-ranging Brünnich's guillemots
1 Department of Zoology, University of Wyoming, Laramie, WY 82071,
USA
2 Graduate School of Fisheries Sciences, Hokkaido University, Minato-cho
3-1-1, Hakodate 041-8611, Japan
3 National Institute of Polar Research, 9-10 Kaga 1-chome, Itabashi-ku,
Tokyo 173-8515, Japan
4 Department of Mechanical Engineering, University of British Columbia,
Vancouver, BC V6T 1Z4, Canada
* Author for correspondence (e-mail: lovvorn{at}uwyo.edu)
Accepted 4 October 2004
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Summary |
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Key words: bird swimming, buoyancy, costs of diving, diving birds, drag, guillemots, stroke patterns, swim speed
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Introduction |
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For example, because air volumes in the respiratory system and plumage
change with hydrostatic pressure, work against buoyancy varies dramatically
with depth (Lovvorn and Jones,
1991a; Wilson et al.,
1992
; Lovvorn et al.,
1999
; Skrovan et al.,
1999
). It has been suggested that penguins, cormorants and sea
turtles manipulate their air volumes or dive depths to optimize the effects of
buoyancy on dive costs (Hustler,
1992
; Minamikawa et al.,
2000
; Sato et al.,
2002
; Hays et al.,
2004
). However, as the thickness of the insulative layer of air in
bird plumage is compressed with increasing depth, heat loss increases
(Grémillet et al.,
1998b
), perhaps creating a conflict between decreased work against
buoyancy and increased costs of thermoregulation. Work against buoyancy
becomes minimal below the depth at which most compression of air spaces has
occurred (
20 m; Lovvorn and Jones,
1991a
; Lovvorn,
2001
), and much of the energy expended against buoyancy during
descent may be recovered during ascent
(Lovvorn et al., 1999
). Thus,
the influence of buoyancy manipulation on total cost of a dive will decrease
rapidly with increasing dive depth, and may be negligible for deeper dives by
many bird species.
Another potential determinant of swim speed is the fact that, for muscles
containing mostly similar fiber types such as alcid flight muscles
(Kovacs and Meyers, 2000),
muscle contraction is most efficient over a relatively narrow range of
contraction speeds and loads (Lovvorn et
al., 1999
, and references therein). Consequently, as buoyant
resistance changes with depth, swim speed may be altered to bring about
compensatory changes in work against drag, thereby conserving work
stroke1. Alternatively, gliding between strokes may be used
to prevent changes in speed as buoyant resistance changes, without altering
contraction speed or work stroke1
(Lovvorn et al., 1999
;
van Dam et al., 2002
;
Watanuki et al., 2003
).
Changes in work during the upstroke with varying forward speed have been
identified in aerial flight (Rayner et
al., 1986
; Hedrick et al.,
2002
; Spedding et al.,
2003
), but such patterns have not been investigated in diving
birds.
Especially at depths below which buoyancy becomes negligible, simulation
models suggest that the main determinant of the mechanical cost of swimming is
hydrodynamic drag (Lovvorn,
2001). Based on tow-tank measurements of the drag of a frozen
common guillemot (COGU, Uria aalge) mounted on a sting, Lovvorn et
al. (1999
) suggested that the
mean speed observed in free-ranging Brünnich's guillemots (BRGU, Uria
lomvia) was that which minimized the drag coefficient. These authors also
predicted that, for reasons of muscle contraction efficiency, mean speed was
regulated by altering glide duration while work stroke1
remained constant. However, the inference about choice of mean speed did not
account for effects of accelerational (oscillatory) stroking, in which
instantaneous speed varies widely throughout individual strokes.
In subsequent analyses of work against drag and inertia throughout strokes
during horizontal swimming (Lovvorn and
Liggins, 2002), models suggested that dividing thrust between
upstroke and downstroke as in wing-propelled divers, as opposed to having all
thrust on the downstroke as in most foot-propelled divers, had important
effects on swimming costs. At the same mean speed, higher instantaneous speeds
during stronger downstrokes incurred higher drag, owing to the rapid nonlinear
increase of drag with increasing speed. However, the strokeacceleration
curves used in those models were only reasonable approximations, having never
been directly measured. At that time, the only way to measure such patterns
was by high-speed filming (Lovvorn et al.,
1991
; Johansson and Aldrin,
2002
; Johansson,
2003
), either during horizontal swimming or during vertical dives
in shallow tanks where buoyancy is quite high and strongly influences
strokeacceleration patterns. Subsequent advances in instrumentation
have allowed measurement of acceleration throughout strokes in free-ranging
birds. Results indicate that strokeacceleration patterns of BRGU change
with dive depth and among descent, ascent and horizontal swimming
(Watanuki et al., 2003
). These
new instruments provide an opportunity to incorporate complete empirical data
into models that include effects of accelerational stroking on work against
drag.
When swimming in a horizontal tank 33.5 m long to reach food supplied at
the other end, COGU typically swam at speeds of 2.22.6 m
s1 (Swennen and Duiven,
1991; see also Bridge,
2004
). However, free-ranging BRGU in Canada and Norway regulated
their speed throughout descent and ascent within a narrow range of about
1.6±0.2 m s1, despite large changes in buoyancy with
depth (Lovvorn et al., 1999
;
Watanuki et al., 2003
). These
birds appeared to be feeding on or near the sea floor or in distinct
epipelagic layers (Lovvorn et al.,
1999
; Mehlum et al.,
2001
), showing sustained speeds during transit between the surface
and relatively stationary food resources.
To investigate the reasons for these speed patterns and ways they are
achieved, we used loggers on free-ranging BRGU to describe swim speeds, body
angles, stroke rates, stroke and glide durations, and relative thrust on
upstroke vs downstroke throughout dives
(Watanuki et al., 2003), and
used these data in a simulation model of dive costs. In particular, we tested
for effects of mean swim speeds and varying strokeacceleration patterns
on dive costs, given the rapid nonlinear increase of drag with increasing
speed. We also asked whether work stroke1 remained
relatively constant, while speed was regulated by varying the duration of
glide periods between strokes.
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Materials and methods |
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Volume of air in the respiratory system (in l) was estimated by
Vresp=0.1608Mb0.91
(Lasiewski and Calder, 1971).
To assess effects on dive costs of active regulation of respiratory volume by
the birds, costs were modeled with respiratory volume at ±60% of the
value used in all other simulations (0.153 l); this percentage range
corresponds to that estimated for freely diving king penguins (Aptenodytes
patagonicus) by Sato et al.
(2002
). Volume of the plumage
air layer (Vplum, l) of our instrumented birds, estimated
by the equation of Lovvorn and Jones
(1991a
) based on dead diving
ducks Aythya spp.
(Vplum=0.2478+0.1232Mb), yielded a
mean of 0.365 l kg1 for the instrumented BRGU. Air volumes
calculated here are presumed to be those upon initial submersion at the start
of a dive. The buoyancy of air is 9.79 N l1
(Lovvorn et al., 1999
). The
buoyancy of body tissues, based on water, lipid, protein and ash content of
the body, was calculated to be 0.626 N or 0.659 N
kg1 for the mean body mass of the instrumented BRGU (0.95
kg; see Lovvorn et al.,
1999
).
Hydrodynamic drag D (in N) of single frozen specimens of COGU and
BRGU was measured at a range of speeds U (m s1) in
a tow tank. Propulsive limbs (wings only for guillemots) were removed from the
body fuselage (head and trunk). Drag of the same COGU was measured both when
mounted on a sting (a rod which enters the bird from the rear)
(Lovvorn et al., 1999) and
when towed by a harness and drogue system
(Lovvorn et al., 2001
). Drag
of the BRGU was measured only with the harness and drogue
(Lovvorn et al., 2001
). The
drag data were also expressed in terms of dimensionless drag coefficients
(CD=2D/
AswU2)
and Reynolds numbers (Re=ULb/
), where
is the density (1026.9 kg m3) and
is the kinematic
viscosity (1.3538x106 m2
s1) of salt water at 10°C; surface areas and body
lengths Lb are given in Lovvorn et al.
(2001
). Dimensionless
CD:Re curves are the same for the same shape
regardless of variation in size.
Studies of anguilliform and thunniform swimmers, which propel themselves by
flexing the body itself, have shown that actively swimming animals have higher
drag than gliding or frozen specimens
(Webb, 1971;
Williams and Kooyman, 1985
;
Fish, 1988
,
1993
). However, these swimming
modes are quite different from those of penguins and alcids, which maintain a
rather rigid fuselage while stroking with lateral propulsors. During swimming,
the wings of guillemots are shaped into a narrow proximal `strut' separating
the body from a distal and broader lift-generating surface (see illustrations
in Spring, 1971
); such shapes
can substantially reduce interference drag caused by interactions of flow
around oscillating propulsive limbs and the body fuselage
(Blake, 1981
). Although even
streamlined attachments to the body can cause interference drag (see
Tucker, 1990
), differences in
the fuselage drag of frozen vs swimming animals may be far less for
guillemots than for anguilliform swimmers. Such effects are still probably
appreciable, but no measurements have been made to allow their estimation for
wing-propelled swimmers, and we did not consider them. Drag coefficients
determined from the deceleration of gliding alcids were similar to those from
our measurements (Johansson,
2003
).
Stroke periods, stroke acceleration curves and inertial work
The periods (durations) of wing strokes, and acceleration of the body
fuselage throughout entire strokes (including both upstroke and downstroke),
were determined from accelerometer data. Based on acceleration parallel to the
body fuselage (surge) recorded at 0.03125 s intervals (32 Hz), plots of
acceleration throughout each stroke were used to distinguish the beginning and
end of each stroke. Plots of each stroke were superimposed to identify groups
of strokes with similar periods and acceleration patterns. Data from groups of
similar strokes were then fitted with stepwise multiple regression. The shapes
of the fuselage acceleration curves were complex, and we wished to fit them
closely to capture important aspects of these shapes. Consequently, we
selected models from combinations of up to 12 polynomial terms, and visually
examined plots to arrive at the simplest model that closely fit the data (see
Lovvorn et al., 2001).
For groups of strokes with similar acceleration curves, we then calculated changes in fuselage speed at 0.03125 s intervals throughout strokes, starting with the mean speed at that depth estimated from the TDR data, and the appropriate acceleration curve for that depth. We averaged these calculated speeds at the end of each interval, and determined the difference between this average and the estimated mean speed (from the TDR) at the end of the stroke. This difference was then added (or subtracted) to the speed at the end of each interval, so that the new average over all intervals resulted in no change in mean speed during the stroke. We then expressed the speed at the end of each interval as the fraction of mean stroke speed vs fraction of stroke period, so that curves fitted to these values could be applied to different mean speeds throughout a dive. These curves did not include much smaller values of net acceleration over the entire stroke needed to achieve observed small increments in overall mean speed. Resulting curves were fitted with stepwise multiple regression to yield polynomials used in the model.
Water displaced from in front of a swimming animal must be accelerated
around the animal to fill the space vacated behind it. Added mass is the mass
of that accelerated water, and the added mass coefficient is the ratio
of the added volume of water to body volume
(Daniel, 1984
;
Denny, 1988
). For ideal fluids
with no viscosity, plots have been developed that relate
to ratios of
the three axes of an ellipsoid that describe the object
(Kochin et al., 1964
). Based
on total body length minus length of the culmen, and maximum height and width
of the body, we used these plots to estimate
for BRGU as 0.075
(Lovvorn and Liggins, 2002
).
Added mass was calculated as
Ma=
Vb, where
is the
density of salt water at 10°C (1026.9 kg m3) and
Vb is total body volume (see above). The force G
(in N) required to accelerate the virtual mass
(Mb+Ma), known as the acceleration
reaction (Denny, 1988
), was
calculated as
G=(Mb+Ma)(dU/dt),
where dU/dt is the change in speed over intervals of 0.02
s.
In real fluids such as water that have viscosity, some of the momentum
imparted to the added mass may be dissipated in the fluid during the stroke.
Vortices shed from the entrained boundary layer may move away from the body,
thereby decreasing the added mass
(Sarpkaya and Isaacson, 1981).
In this way, part of the forward-directed, in-line work done by the animal to
accelerate the added mass during the power phase of the stroke can be lost in
the free stream, thereby decreasing the momentum remaining to propel the body
forward passively during deceleration in the recovery phase. Although loss of
momentum in a shed vortex imparts an opposite impulse on the bird's body, this
opposing impulse would typically not be in line with the direction of
swimming. This loss of momentum via shedding of added mass means that
the animal may do net positive inertial work over the entire stroke cycle,
when there is no net acceleration of the body in line with the direction of
motion over that stroke cycle.
Unfortunately, for real fluids there is no theory for estimating added mass
and its variations, which are affected in complex ways by the shape and
surface roughness of the object, and the pattern of acceleration. The only
measurements have been for simple motions and shapes such as oscillating
cylinders (Sarpkaya and Isaacson,
1981). Nevertheless, these measurements indicate that added mass
during the acceleration phase can be much higher than during deceleration, so
that the force exerted on the fluid by the cylinder during acceleration is
less than the in-line, forward force exerted on the cylinder by the fluid
during deceleration. This effect is presumed to result from vortex shedding of
added mass between acceleration and deceleration phases
(Sarpkaya and Isaacson,
1981
).
This mechanism may explain why calculations based on instantaneous
velocities measured from high-speed films have indicated positive inertial
work over entire stroke cycles in animals swimming by oscillatory strokes
without net acceleration along the direction of motion
(Gal and Blake, 1988;
Lovvorn et al., 1991
;
Lovvorn, 2001
). Thus, the
frequent assertion that the acceleration reaction must sum to zero over entire
stroke cycles when mean speed is constant (e.g.
Stephenson, 1994
), which may
be true for inviscid fluids (Batchelor,
1967
; Daniel,
1984
), is not necessarily true for real fluids. In fact, in
viscous fluids where some dissipation of momentum is unavoidable, analyses of
oscillatory stroking at constant mean speed that do not account for inertial
work may be incomplete.
If the added mass coefficient changes throughout strokes, and there are no
theories or measurements for estimating added mass in real fluids, what value
of should be used? We used the value for ideal fluids described above
as a constant for the entire stroke cycle. This convention probably causes
overestimates of negative inertial work during the recovery phase, so our
resulting values of net inertial work may be conservative. Some of the same
boundary-layer and vortex dynamics that alter the drag coefficient with
changes in speed also change the added mass coefficient, so drag and added
mass effects are probably not independent. However, we make the conventional
assumption that work against drag and inertia are additive
(Morison et al., 1950
). This
assumption has been the subject of much research, but no better operational
approach has yet been developed (Denny, 1998; review in
Sarpkaya and Isaacson,
1981
).
Calculation of work throughout strokes
Work throughout swimming strokes was modeled by calculating the linear
distance moved by the body fuselage (head and trunk without propulsive limbs)
during 0.02 sintervals, according to the equations relating fraction of mean
stroke speed to fraction of stroke period. Inertial (accelerational) work was
the work done to accelerate the body and the added mass of entrained water
over each 0.02 sinterval. Work against drag and buoyancy
(WD+B) was calculated by multiplying drag (D) and
buoyancy (B) at the given depth by displacement during the same time
interval (ds/dt):
WD+B=(D+B)(ds/dt). Body angle
was considered in calculating vertical work against buoyancy. We used a
quasi-steady modeling approach, in which drag of the body fuselage for a given
interval during the stroke is assumed to be the same as drag at that speed
under steady conditions. In quasi-steady fashion, work to overcome drag,
buoyancy and inertia during each 0.02 s interval was then integrated over the
entire stroke to yield total work parallel to the body fuselage during the
stroke (Lovvorn et al., 1991,
1999
). This calculation of
work for forward swimming does not include work perpendicular to the body
(heave), or of any pitching or yawing movements.
Our estimates of mechanical costs were for propelling the body fuselage,
and did not include models of the complex flows around oscillating propulsive
limbs (e.g. Spedding et al.,
2003). The reduced frequency parameter has been used to judge when
quasi-steady vs unsteady models for propulsive limbs are justified
(Spedding, 1992
;
Dickinson, 1996
). Alcid wings
exhibit time-variable shape and movement, being swept back and flexing at the
wrist and stationary where attached to the body
(Johansson and Aldrin, 2002
;
Johansson, 2003
). These
aspects make it difficult to determine the effective chord length (blade
width) needed to calculate the reduced frequency (but see
Johansson, 2003
), or at least
argue for separate consideration of different wing segments
(Hedrick et al., 2002
). Work
on unsteady (vs quasi-steady) flow around oscillating propulsors has
focused on rigid robotic limbs with constant planform (e.g.
Dickinson, 1996
;
Dickinson et al., 1999
), and
only recently has the more complex situation of flexing wings with varying
shape been explored (Combes and Daniel,
2001
; Hedrick et al.,
2002
). Consequently, when our models are used to estimate food
requirements (e.g. Lovvorn and Gillingham,
1996
), the efficiency of propulsive limbs is subsumed in an
aerobic efficiency (mechanical power output ÷ aerobic power input) by
which the limbs propel the body fuselage. For this paper, however, our intent
is to evaluate the mechanical cost of propelling the body fuselage at speeds
and accelerations measured with loggers throughout swimming strokes, and
values of mechanical work have not been adjusted by an aerobic efficiency.
Time-depth recordings and accelerometry
Electronic TDRs were attached to wild birds captured on their nests
(Watanuki et al., 2003).
Recorders measured depth (pressure) with accuracy of 1 m and resolution of 0.1
m. Near Ny-Ålesund, Svalbard, Norway in July 1998 (7681°N,
2025°E; see Mehlum and
Gabrielsen, 1993
; Mehlum et
al., 2001
), nine BRGU (including numbers 82 and 87) were fitted
with TDRs (15 mm wide x 48 mm long, 14 g, Little Leonardo Ltd., Tokyo)
that recorded depth every 1 s (Watanuki et
al., 2001
). Also near Ny-Ålesund in July 2001, three BRGU
(including number 13) were fitted with loggers that recorded depth at 1 Hz and
acceleration at 32 Hz (2-axis capacitive sensor, ADXL202E, Analog Devices,
Norwood, MA, USA). The latter packages could measure both dynamic acceleration
(as by propulsion) and static acceleration (such as gravity), allowing
calculation of body angle based on the low-frequency component of surge
acceleration (Sato et al.,
2002
; Watanuki et al.,
2003
). The angle between the logger and the axis of the bird's
body was determined by assuming that the bird's body axis was horizontal when
the bird was floating on the water surface; there may have been a small
difference between this body axis and that during underwater swimming. Body
angle during dives was corrected for the attachment angle of the logger
relative to the body axis of the floating bird. Knowing body angle then
allowed calculation of actual swim speed from vertical speed. These loggers
were 15 mm x 60 mm, and weighed 16 g (<2% of the birds' mass). The
accelerometers measured both tail-to-head (surge) and dorsal-to-ventral
(heave) accelerations; for analyses in this paper, only surge data were used.
All loggers were attached to feathers on the lower backs of the birds with
quick-set glue and cable ties, and were retrieved after one or more foraging
trips.
We later selected the deepest dives for calculating dive profiles and
vertical speeds. We considered deep dives more likely to reflect sustained
descent and ascent without other activities in the water column, so that
swimming speeds would correspond either to direct transit to a known prey
concentration at a given depth, or searching for prey without immediate
pursuit (see Wilson et al.,
1996,
2002
;
Ropert-Coudert et al., 2000
).
Dives analyzed for BRGU were to depths of 102135 m; adults collected at
sea in this area had eaten mostly epipelagic squids, amphipods, euphausiids
and copepods, but chicks were fed demersal polar cod Boreogadus saida
(Mehlum and Gabrielsen, 1993
).
The latter pattern resembled that for BRGU in the eastern Canadian arctic,
where adults appeared to make many shallower dives to feed themselves on
epipelagic prey before making a series of much deeper dives to capture
demersal fish for chicks (see Lovvorn et
al., 1999
).
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Results |
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A `U-shaped' dive to a maximum depth of 113 m by a third individual guillemot with a logger that was 25% longer showed similar rates of depth change during descent and ascent (cf. Figs 2 and 3). During descent, vertical speeds and actual swim speeds were almost identical over a range of mostly 1.51.8 m s1, reflecting the nearly vertical body angle of 80° to 90°. Swim speed increased very rapidly in the first few meters, and increased gradually thereafter from 1.3 to 1.8 m s1. Body angle and speed varied little above a depth of 90 m. However, in the last 5 m of descent, body angle decreased sharply, thereby reducing vertical speed by about 0.3 m s1 while swim speed was reduced by only 0.1 m s1.
During ascent, body angle was very constant to about 63 m, being less vertical (70° from horizontal) than during descent but still steep enough so that vertical speed was only 0.1 m s1 lower than actual swim speed. Shallower than 63 m, body angle varied over a range of about 17°, resulting in up to 0.8 m s1 difference between vertical speed and actual swim speed. As during descent, speed increased very rapidly within the first few meters of ascent, ranging thereafter from about 1.3 to 1.6 m s1. Both vertical and actual swim speeds increased by about 0.7 m s1 in the last 1520 m of ascent, when buoyancy rapidly increased.
Given the large changes in buoyant resistance during dives
(Fig. 3A), and that very
similar COGU can readily swim at speeds of 2.22.6 m
s1 (Swennen and Duiven,
1991), the narrow range of speeds during steady descent (mostly
1.61.9 m s1) and the majority of ascent (mostly
1.41.7 m s1) is striking. Variations of only about
±0.2 m s1 during descent, and during ascent up to
depths of
20 m above which buoyancy rapidly increases, suggest consistent
regulation of swim speed. In BRGUs 82 and 87
(Fig. 2), vertical swim speed
was about 0.2 m s1 lower during ascent than descent, perhaps
due mostly to differences in body angles
(Fig. 3). However, in BRGU 13,
actual swim speed during ascent was about 0.3 m s1 lower
than during descent. Stroke rate of the wings varied little and decreased only
slightly with depth during descent. During ascent, stroke rate was far more
variable, decreasing up to near the depth of neutral buoyancy (
71 m) but
with no obvious trend from there to the surface
(Fig. 3).
Acceleration and speed during strokes
Patterns of surge acceleration during swimming strokes changed appreciably
with depth during descent and ascent, and between descent, ascent and
horizontal swimming (Figs 4,
5). During descent, the first
two strokes to a depth of 2 m were quite different from all subsequent
strokes, lasting far longer and exhibiting much lower (first stroke) or much
higher (second stroke) variation in acceleration during the stroke
(Fig. 4A). These two curves
include acceleration from a standing start at the water surface against very
high buoyancy at the start of the dive. They also encompass a rapid change in
body angle from horizontal to vertical, perhaps confounding estimates of work
based on measurements of surge acceleration only. For this reason, the first
two strokes were not included in calculations of dive cost.
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During descent from 2 to 20 m where buoyancy was appreciable (Fig. 3A), relative acceleration during upstroke and downstroke were similar (Fig. 4B). However, deeper than 20 m, where buoyancy was low and changed little with depth, relative acceleration during the upstroke decreased dramatically, and continued a gradual decline to the final stroke of steady descent at 109 m (Fig. 4C; cf. Fig. 3). Relative surge acceleration during the upstroke was even lower during horizontal swimming in the bottom phase of the dive (Fig. 4D). Thus, relative upstroke thrust declined as resistance from buoyancy decreased from shallow descent to deeper descent to horizontal swimming. Stroke frequency declined very slowly with increasing depth during descent (Fig. 3E). Short glide periods, during which speed decreased steadily and very gradually, were difficult to identify from accelerometer data at 0.03125 s intervals (32 Hz). However, it appeared that, during descent, a glide period of about 0.03 s was added to most strokes starting at about 45 m, and that glides were extended to 0.06 s at about 85 m. Because these glides were only 713% of stroke period, were variable in occurrence, and were difficult to distinguish, gliding did not appear to be an important component of locomotion during descent in BRGU and was not considered in calculations.
Despite regular trends of change in acceleration patterns during descent and at the bottom, trends during ascent were less consistent. Throughout ascent, surge acceleration was mainly during the downstroke (Fig. 5), consistent with the idea that relative upstroke thrust is low when buoyant resistance is low or negative. However, in BRGU 13, a few strokes from 71 to 61 m lasted longer and had lower peaks, resembling a single stroke that occurred at 42 m. Body angle was very constant below 60 m, becoming more variable at shallower depths (Fig. 3F). Above 50 m depth, strokes lasted much longer than below that depth, but within the shallower range, trends with depth were not apparent. Above 20 m where buoyancy increased dramatically (Fig. 3A), strokes were long and with little acceleration. Throughout ascent, smaller fluctuations in acceleration (peaks <1 m s2), which were not clearly recognizable as strokes, suggested that the bird made minor adjustments to speed and body angle by partial wing movements without executing regular strokes.
Based on speed changes from acceleration curves, we identified nine basic
curves standardized as fraction of mean stroke speed vs fraction of
stroke period (Figs 6 and
7,
Table 1). For descent, where
there was little or no gliding between strokes, mean speed was calculated from
a regression of swim speed U vs depth Z
(U=1.193+0.0169Z0.000159Z2+4.877x107Z3,
r2=0.97, P<0.001). For ascent, where almost
all strokes were followed by gliding, mean speed was calculated separately for
individual strokes or groups of strokes excluding glide periods. At the
bottom, we calculated the fraction of stroke speed using a mean of 1.76 m
s1, which was the descent speed at neutral buoyancy (71 m),
and 2.18 m s1, which was the mean speed of COGU swimming
horizontally in a tank 33.5 m long to reach food at the other end
(Swennen and Duiven, 1991; see
also Bridge, 2004
). Resulting
curves were about the same, so we pooled them to yield the curve for bottom
swimming in Fig. 6. Although we
did not include the first two strokes (Curves 1 and 2,
Fig. 6) in calculations of dive
cost, it is notable that speed was substantially greater on the upstroke than
downstroke as the bird initially submerged and worked to overcome very high
buoyancy at the start of the dive.
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Patterns of work per stroke throughout dives
Based on estimated changes in buoyancy with depth
(Fig. 3A), changes in speed
throughout strokes for different stroke types
(Fig. 6), and drag at those
speeds (Fig. 1), a quasi-steady
model was used to estimate mechanical work per stroke against drag, buoyancy,
surge acceleration and all three combined throughout descent
(Fig. 8). Costs of the first
two strokes (Fig. 6) were not
included. The importance of differences between strokeacceleration
patterns was evaluated by estimating costs if all strokes followed Curve 3
(actually occurring at depths of 220 m,
Fig. 6), and if all strokes
followed Curve 4 (actually occurring at depths >20 m). The importance of
accounting for variations in speed throughout individual strokes was assessed
by a third set of work curves that assumed steady speed, i.e. work against
drag and buoyancy at the same mean speed without acceleration from oscillatory
stroking. For drag, Curve 3 with similar thrust on upstroke and downstroke
yielded almost the same work as the steady curve; Curve 4 with most thrust on
the downstroke yielded slightly lower work against drag, but this effect was
so small as to be negligible (Fig.
8). Differences among curves in work against buoyancy were also
negligible. Inertial work to accelerate the body throughout single strokes
(which did not include longer-term changes in mean speed among strokes) was
slightly higher when thrust was more evenly distributed between upstroke and
downstroke (Curve 3). Based on these differences among work components, the
total cumulative work of descent was 6% higher for Curve 3 than Curve 4. Total
cumulative work was 10% higher for Curve 3 and 4% higher for Curve 4 than when
the costs of oscillatory stroking were not accounted for (steady curve,
Fig. 8). Given that most of
descent to 105 m (depths >20 m) would follow Curve 4
(Fig. 6), not considering
strokeacceleration patterns would cause underestimates of about
56% of total mechanical cost.
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During ascent, work stroke1 was consistent as the bird swam upward against negative buoyancy with a steady stroke pattern (Fig. 9). However, when near and above the depth of neutral buoyancy at about 71 m, increasingly variable strokeacceleration patterns and stroke frequency resulted in highly variable work stroke1 (note that work stroke1 in Fig. 9 does not include intervening glide periods). Inertial work to accelerate the body fuselage based on Curve 7 (Fig. 7) atdepths of 7161 m and at 42 m was anomalously low (Fig. 9); apparently, the form of Curve 7 as derived from accelerometer data by our methods was incorrect or incomplete, perhaps due to changes in body angle. Glide periods separated each stroke during ascent, and these glides were fairly consistent in duration up to 80 m (Fig. 10). Above that depth, it was difficult to distinguish the ends of strokes from subsequent glide periods in the accelerometer data, because there was no discrete return of speed to that at the beginning of strokes (Fig. 7). Moreover, an increasing fraction of work against drag during ascent above 71 m was done passively by buoyancy (Fig. 3). Consequently, mechanical work stroke1 in Fig. 9 at depths shallower than 71 m is an unreliable measure of work done by the bird's muscles, and cannot be compared directly with work stroke1 during descent, horizontal swimming, or powered ascent from 105 to 80 m.
|
|
During descent (Fig. 8), total work stroke1 was highest in the first few meters, decreased to a low at 1520 m, and then increased slightly to stabilize at 2.7 to 2.8 J stroke1 (Curve 4 for descent at >20 m). Work against drag and buoyancy were about the same initially, with buoyancy work decreasing rapidly with depth to become unimportant below 20 m, and drag increasing to become the main cost of descent (Fig. 8). Gradual increases in speed below 20 m (Fig. 3D) resulted in gradual increases in drag that roughly offset the gradual decline in buoyancy, so that total work stroke1 stayed about the same (Fig. 8). Additional simulations in which the volume of air in the respiratory system was varied over a likely maximum range (±60%) indicated that the resulting changes in buoyancy would result in variation of only ±4.7% in total mechanical cost of descent (Fig. 11).
|
Oscillatory stroking yielded small values of inertial work (Figs 8, 9), but affected drag by determining instantaneous speeds at which drag was exerted. During horizontal swimming at 109 m (`bottom', Fig. 9), work against buoyancy and inertia (acceleration) were negligible, with total work being attributed almost solely to drag. Total work per stroke at the bottom (2.4 J),based on an estimated mean speed of 1.76 m s1, was about 11% lower than during most of descent (2.7 J). During ascent, work per stroke was initially about the same as at the bottom (2.3 J), increasing to 3.3 J during the last strokes before reaching neutral buoyancy (Fig. 9). Thus, when strokes were discrete and recognizable, mechanical work per stroke varied between only 2.3 and 2.8 J throughout most of descent, bottom swimming, and initial (powered) ascent. Work against drag constituted almost all mechanical work during most of these strokes, and drag is a strong function of speed (Fig. 1). Thus, it appears that regulating speed serves to maintain work stroke1 within a relatively narrow range by regulating drag. Given this observation, can observed speed be predicted by identifying speeds that optimize drag?
Observed speeds of guillemots relative to drag
If work stroke1 by BRGU is calculated for a range of
speeds at different depths during descent
(Fig. 12), total work
(essentially all against drag) rises slowly and almost linearly to a speed of
about 2 m s1, rises at a slightly higher rate from 2 to 2.6
m s1, and then increases rapidly and nonlinearly at higher
speeds. Note that effects of mean speed on drag are very similar for
accelerational vs steady models
(Fig. 8), so that effects of
mean speed on total drag apply directly to costs of oscillatory stroking. In
an earlier analysis based on the drag of a COGU mounted on a sting, it was
concluded that observed speeds corresponded to a minimum in the curve of
CD vs Re (Fig.
1; see Lovvorn et al.,
1999). CD:Re plots derived from a
different measurement system, however, did not indicate this minimum
(Fig. 1B). Free-ranging BRGU
swam at speeds in the mostly linear part of the curve (less than about 2 m
s1), before major increases in drag occur
(Fig. 12). At speeds above the
maximum of 2.6 m s1 observed in COGU swimming horizontally
in a tank (Swennen and Duiven,
1991
), rapid nonlinear increases in drag may impose a limit on
achievable speeds.
|
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Discussion |
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---|
Curves of drag vs speed and CD vs Re
Curves of drag vs speed looked similar for tow-tank measurements
on the same frozen specimen when either mounted on a sting or pulled with a
harness and drogue system. However, small variations between the drag:speed
curves resulted in appreciable differences between corresponding plots of
CD vs Re, with sting measurements indicating a
much lower Re at which CD was minimized
(Fig. 1). This difference might
have resulted from greater stability of the sting-mounted specimen at low
speeds, but inability of the sting to adjust automatically to the angle of
minimum drag at high speeds, as was possible with the harness and drogue
(Lovvorn et al., 2001).
Moreover, slight overestimates of drag at low speeds if the drag:speed data
were fitted with quadratic or other low-order equations resulted in
substantial overestimates of CD at low Re, and
thus an erroneous drop in CD at higher Re.
Consequently, to derive correct inference from the shape of
CD:Re plots, the drag:speed curves from which
they are calculated should be fit very closely (including multiple
higher-order terms if needed) over the entire range of speeds.
Effects of buoyancy regulation
For sea turtles, marine mammals and penguins, it has been suggested that
respiratory air volumes are manipulated to optimize buoyancy during dives to
different depths, or else that dive depth or gliding behavior are adjusted to
air volume and resulting buoyancy
(Hustler, 1992;
Skrovan et al., 1999
;
Minamikawa et al., 2000
;
Williams et al., 2000
;
Nowacek et al., 2001
;
Sato et al., 2002
;
Hays et al., 2004
). However,
for dives to >20 m by BRGU, substantial changes in air volume (±60%)
had little effect on mechanical costs of descent (<5%,
Fig. 11), and work against
buoyancy was always negligible during horizontal swimming at the bottom at
these depths (Fig. 9). As
variations in respiratory volume may alter the depth at which penguins stop
stroking during ascent (Sato et al.,
2002
), either the number of strokes or work
stroke1 of guillemots might still vary with respiratory
adjustments during ascent.
Below about 40 m, however, changes in buoyancy with depth were quite small
(Fig. 3A), as were buoyancy
effects on the work of descent (Figs
8,
11). During the dive to 113 m
by BRGU 13 (Fig. 3), only 6 of
25 strokes during ascent were above 40 m
(Fig. 5). In comparison, there
were 157 strokes during all of descent
(Fig. 4), and at the bottom
about 37 regular strokes and 23 times that many erratic strokes during
pursuit of prey. Thus, the six strokes appreciably influenced by buoyancy
during ascent would probably constitute at most 3% (for a bounce dive) and
typically less than 2% (for a foraging dive) of all strokes. Varying work
during this 23% of strokes during ascent by a maximum ±60%
through respiratory manipulation is unlikely to have an important influence on
total dive costs. Consequently, although respiratory volume may secondarily
affect the depth during ascent at which stroking ceases, effects on the
energetics of diving via changes in buoyancy are probably minimal for
deeper-diving species like BRGU. For diving depths typical of BRGU
(Croll et al., 1992;
Mehlum et al., 2001
), effects
of dive duration and intensity of prey pursuit on metabolic oxygen demand are
probably the main considerations in any manipulation of respiratory air volume
(Wilson, 2003
).
Relative thrust on upstroke and downstroke
Before development of accelerometers that allowed direct measurements in
free-ranging birds, strokeacceleration patterns could be measured only
by high-speed filming. Such filming is done during horizontal swimming or
vertical dives in shallow tanks, where buoyancy is quite high and can strongly
influence strokeacceleration patterns
(Hui, 1988;
Lovvorn et al., 1991
;
Johansson and Aldrin, 2002
;
Johansson, 2003
). Logger data
from free-ranging guillemots showed that deceleration between upstroke and
downstroke is much greater than in the hypothetical curves used previously in
models for guillemots (Lovvorn et al.,
1999
). Moreover, the actual curves changed with depth (buoyancy)
in ways undetectable in shallow tanks; in particular, much greater relative
thrust on the upstroke was evident at depths <20 m during descent
(Fig. 4).
Although large differences in relative upstroke thrust can theoretically
have important effects on work stroke1 to propel the body
fuselage (Lovvorn, 2001;
Lovvorn and Liggins, 2002
),
variations directly measured on guillemots in this study had relatively small
effects on simulated costs (<6%). This difference resulted from the fact
that the observed maximum fraction of mean stroke speed achieved during
individual strokes (
1.14 during descent,
Fig. 6) was far less than for
hypothetical curves used in previous models (
1.6;
Lovvorn et al., 1999
;
Lovvorn, 2001
;
Lovvorn and Liggins, 2002
).
Thus, even when the guillemots increased relative downstroke thrust,
instantaneous speeds were still low enough to avoid rapid nonlinear increases
in drag incurred by the hypothetical curves.
For birds and bats just after takeoff and during slow flight in air,
downstroke lift and thrust predominate with little or no lift on the upstroke
(Rayner et al., 1986;
Hedrick et al., 2002
;
Spedding et al., 2003
). Under
such conditions, when lift is derived from generation of separate vortex rings
shed at the end of each downstroke, lift must be imparted upward and not
downward to support the bird's weight. Only after forward speed increases and
lift is generated via a continuous-vortex wake does upstroke lift
become important (Hedrick et al.,
2002
; Spedding et al.,
2003
). In contrast, penguins swimming horizontally underwater at
shallow depths appeared to use downward lift during the upstroke to oppose
buoyancy (Hui, 1988
). The
upstroke also imparted mainly a downward force on the body in Atlantic puffins
Fratercula arctica swimming horizontally near the surface
(Johansson, 2003
).
During vertical descent, buoyancy directly opposes forward motion rather
than being perpendicular to it, as is gravity during aerial flight or buoyancy
during horizontal swimming. Consequently, in contrast to slow aerial flight
when only the downstroke is suitable for overcoming gravity, both the upstroke
and downstroke can generate useful lift and thrust for diving birds descending
directly against high buoyancy. During the first two strokes of the dive
(<2 m depth), thrust on the upstroke was substantially greater than on the
downstroke (Fig. 6); e.g. in
their first stroke, guillemots extend their wings under the water and sweep
them upward as they pitch forward (J. R. Lovvorn, personal observation;
Sanford and Harris, 1967). In
the subsequent 220 m of the dive when the birds were increasing speed
against appreciable buoyancy, they had similar thrust on upstroke and
downstroke. Below that depth, where buoyancy was relatively unimportant and
cruising speed had been achieved, thrust on the upstroke was much reduced. The
latter pattern predominated throughout descent below 20 m, during sustained
horizontal swimming at depths where buoyancy was negligible
(Fig. 3), and during powered
ascent to neutral buoyancy.
Therefore, it appears that the general pattern in air, in which takeoff and
slow flight are dominated by the downstroke and the upstroke becomes important
mainly in fast flight, is quite different from underwater flight during
descent and during horizontal swimming at low buoyancy. For diving alcids,
upstroke thrust appears to be important mainly when the opposing force is
high, and perhaps during rapid acceleration while pursuing prey or escaping
predators. Note that when the upstroke in Atlantic puffins was found to be
appreciable (Johansson and Aldrin,
2002; Johansson,
2003
), the birds were swimming horizontally near the surface, were
stimulated to dive by approaching humans, and were filmed only 23 m
from a standing start; thus, these birds were probably accelerating rather
than swimming steadily, analogous to our guillemots swimming against high
resistance in the first 20 m of descent. When swimming horizontally at lower
buoyancy and more constant speeds, upstroke thrust was less apparent in our
free-ranging birds. Hedrick et al.
(2002
) reported that birds in
air increased downstroke thrust at very high speeds or when
accelerating to high speeds, i.e. when flying directly against increasing drag
forces. In contrast, guillemots swimming underwater appear to increase
upstroke thrust when accelerating or swimming directly against high
buoyancy.
Given that our BRGU did little or no gliding between strokes during
descent, why was the upstroke thrust much reduced below 20 m? Dividing thrust
equally between upstroke and downstroke resulted in about 6% higher work
stroke1 in propelling the body fuselage
(Fig. 8). It is likely that if
drag of the wings were included in the model, their greater drag during a more
active upstroke would have increased total work even more. For our
free-ranging birds, we had no data on wing kinematics to calculate this
effect. However, it appears that just as takeoff and slow flight without
upstroke lift is more costly for aerial fliers than fast flight with upstroke
lift (Marden, 1987;
Ward et al., 2001
),
wing-propelled divers may face a similar hurdle of less efficient but more
powerful flight with strong upstroke to overcome initial high buoyancy and
accelerate to cruising speed. After that, more efficient downstroke-based
flight, perhaps with lower drag of the wings, is probably more viable (cf.
Dial et al., 1997
;
Ward et al., 2001
). Note that
the relatively small effect of strokeacceleration pattern on work to
propel the body fuselage (Fig.
8) did not account for any differences in muscle efficiency or
propulsive efficiency of the oscillating limbs. At any rate, it is clear that
the relative function of upstroke and downstroke can vary greatly throughout
dives, and that strokeacceleration patterns measured with loggers on
free-ranging birds provide critical insights to complement work in shallow
tanks.
Why and how is speed regulated?
During sustained swimming, BRGU in this and similar studies
(Lovvorn et al., 1999)
maintained their speed at about 1.6±0.2 m s1,
although COGU swimming horizontally in a tank could readily swim at
2.22.6 m s1
(Swennen and Duiven, 1991
).
Our free-ranging BRGU swam at speeds at the upper end of the mostly linear
part of the drag curve, before major increases in drag occur
(Fig. 12). However, there were
no obvious thresholds of drag over this part of the curve to explain the
observed range of cruising speeds. Above the maximum of 2.6 m
s1 observed for COGU, rapid nonlinear increases in drag may
impose a limit on speeds achievable with available muscle power.
Swim speed might be limited by aerobic capacity of the muscles, whereby
high speeds and associated high power output require unsustainable anaerobic
metabolism (Dial et al., 1997;
Pennycuick, 1997
). In Atlantic
puffins, fibers in muscles used for both upstroke and downstroke were mainly
fast-twitch, highly oxidative, and only moderately glycolytic. However, the
percentage of fast-twitch, moderately oxidative, highly glycolytic fibers in
the main upstroke muscle (supracoracoideus) was higher (28%) than in
the main downstroke muscle (pectoralis, 13%)
(Kovacs and Meyers, 2000
).
This difference suggests that swimming with strong upstroke thrust as during
early descent can involve greater anaerobic metabolism, perhaps discouraging
use of the upstroke to achieve speeds beyond the usual range.
Several studies have suggested that marine mammals and birds regulate their
swim speed by varying the duration of gliding between strokes
(Skrovan et al., 1999;
Williams et al., 2000
;
Watanuki et al., 2003
). Before
data on stroke frequency throughout dives were available, Lovvorn et al.
(1999
) suggested that
guillemots maintain relatively constant work stroke1 to
maximize muscle efficiency, while varying glide duration to modulate speed as
buoyant resistance changes. Data from accelerometers in this study indicate
that guillemots do indeed maintain relatively constant work
stroke1, but make little use of gliding during descent.
Because speed stays so similar despite large changes in buoyant resistance,
guillemots may have regulated swim speed during descent by altering stroke
amplitude or attack angle (see Zamparo et
al., 2002
), or by small decreases in stroke frequency
(Fig. 3E), rather than gliding
between strokes. Variation in stroke amplitude as a means of modulating speed,
alone or in addition to changes in stroke frequency, has recently been found
in sea turtles, sea lions and penguins
(Wilson and Liebsch,
2003
).
For a range of penguin species during horizontal swimming, the duration of
gliding generally increased with increasing body mass (130 kg;
Clark and Bemis, 1979).
Momentum to perpetuate a glide increases with body mass, and drag opposing the
glide depends on surface area, which declines relative to body volume as mass
increases. Respiratory air volume (and thus buoyant resistance to gliding
during descent) also decreases allometrically with increasing body mass (see
Materials and methods). Consequently, although they often glide during
horizontal swimming, relatively small-bodied guillemots may be unable to glide
as effectively during descent as do larger penguins and marine mammals.
Ascent with positive buoyancy
Stroke patterns during ascent from the bottom of the dive to the depth of
neutral buoyancy (71 m) were similar to those during descent and
horizontal swimming; however, strokeacceleration patterns and work
stroke1 were different and quite variable during ascent with
positive buoyancy. Despite maintaining relatively constant mean speed, the
guillemot did not simply use the same stroke form with progressively longer
glide periods as buoyancy increased during ascent (Figs
5,
7,
10). This unpredictable
variation may have reflected searching the water column for prey that are more
visible from below; however, the steady mean speed suggested no appreciable
diversions to attack prey (cf.
Ropert-Coudert et al., 2000
;
Wilson et al., 2002
).
Strokeacceleration patterns might also have been confounded by
irregular changes in body angle. Regardless of these variations and reasons
for them, there were only 11 strokes from 71 m to the water surface during
ascent, compared to 108 strokes during descent to 71 m. Thus, the error in
estimating costs of strokes during ascent will have relatively small effects
on estimates of the costs of travel to and from a prey patch.
Stroke patterns, cost and predicted speeds for diving birds
For deep-diving guillemots, variations in relative thrust on the upstroke
vs downstroke had rather small effects on total dive costs (<6%).
This pattern suggests that effects of drag on the body fuselage can be modeled
reasonably well relative to mean speed without considering
strokeacceleration patterns. In smaller-bodied alcids, shearwaters and
diving-petrels, which dive to shallower depths
(Bocher et al., 2000), higher
buoyancy, lower inertia and higher drag relative to body volume may increase
effects of instantaneous speed during strokes. Such insights await further
miniaturization of accelerometers. Strokeacceleration patterns might
also be more important for foot-propelled divers with little positive
thrust or even negative thrust during the recovery phase, swimming at the same
mean speed requires higher instantaneous speeds during the power phase,
perhaps incurring higher drag on the body fuselage
(Lovvorn, 2001
).
For guillemots, the maximum observed speed of about 2.6 m
s1 (Swennen and Duiven,
1991) appears to correspond to the speed at which rapid nonlinear
increase in drag begins (Fig.
12). The range of observed cruising speeds, with a mean about 1 m
s1 below maximum speed, might correspond to optimal work
against drag. However, there are no obvious breakpoints in the drag curve,
making it difficult to predict optimum speeds based on that curve alone. Other
factors such as the power output or efficiency of muscles for different speeds
or stroking modes (e.g. Dial and Biewener,
1993
; Dial et al.,
1997
) may determine optimal work against drag.
List of symbols and abbreviations
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Acknowledgments |
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Footnotes |
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