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Unofficial Draft Version (psl) 06-12-2008
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Does drag reduction by air release promote fast ascent in jumping
Emperor Penguins? A novel hypothesis
John Davenport
a*
, Roger Hughes
b
, Marc Shorten
a
, Poul S. Larsen
c
a
Department of Zoology, Ecology and Plant Science, University College Cork, Distillery Fields, North Mall, Cork, Ireland
b
School of Biological Sciences, University of Wales, Bangor, UK
c
Department of Mechanical Engineering, Fluid Mechanics Section, Technical University of Denmark, Building 403, 2800 Kgs.
Lyngby, Denmark
* Corresponding author
E-mail address j.davenport@ucc.ie (J. Davenport)
Abstract
To jump out of water onto sea ice, emperor penguins must achieve sufficient underwater speed to overcome the influence of gravity
when they leave the water. The relevant combination of density and kinematic viscosity of air is much lower than for water. Injection
of air into boundary layers (‘air lubrication’) has been used by engineers to speed movement of vehicles (ships, torpedoes) through
sea water. Analysis of published and unpublished underwater film leads us to present a hypothesis that free-ranging emperor pen-
guins employ air lubrication in achieving high, probably maximal, underwater speeds (mean 5.3 m s
-1
, SD 1.01 m s
-1
), prior to jumps.
Here we show evidence that penguins dive to 15-20 m with air in their plumage and that this compressed air is released as the birds
subsequently ascend whilst maintaining depressed feathers. Fine bubbles emerge continuously from the entire plumage, forming a
smooth layer over the body and generating bubbly wakes behind the penguins. In several hours of film of hundreds of penguins, none
were seen to swim rapidly upwards without bubbly wakes. Penguins descend and swim horizontally at about 2 m s
-1
; from simple
physical models and calculations presented, we hypothesise that a significant proportion of the enhanced ascent speed is due to air
lubrication reducing frictional and form drag, and that buoyancy forces alone cannot explain the observed speeds.
Keywords: Emperor penguins; Air lubrication; Bubbly wakes; Jumping
1. Introduction
Emperor penguins Aptenodytes forsteri Gray are the
largest living penguins, standing around 1.2 m high and
weighing 25-40 kg (depending upon gender plus repro-
ductive and nutritional states). They breed and rest on sea
ice around Antarctica. As they have short hindlimbs and
limited climbing ability, they have to jump from the sea
onto sea ice that can vary a great deal in thickness. Their
predators include leopard seals (Hydrurga leptonyx) and
killer whales (Orca orcinus) and it is usually assumed that
their ability to jump swiftly and without falling back into
the sea is also an effective antipredator adaptation. Most
Antarctic penguin colonies have semi-resident leopard
seals that exploit the local abundance of prey.
Emperor penguins exhibit stereotypical responses
when entering and leaving the water that are assumed to
reflect adaptations to sustained predator presence. When
entering the water they usually enter en masse, but reluc-
tantly, with birds often pushing other penguins into the
water first. Leaving the water by jumping is also usually
accomplished gregariously and at high speed. To jump, an
emperor penguin must achieve sufficient underwater
speed to overcome the influence of gravity while the ki-
netic energy of entrained mass is assumed to stay with the
water and contribute to splash and surface waves.
Sato et al. (2005) studied emperor penguins, instru-
mented to provide detailed time records of speed, flipper
action and depth, during dives and ascents to jump onto
the ice surface through small, 1.2 m dia. holes in 2.3 to
2.5 m thick ice far from the open sea. The above-water
heights that they achieved were small (0.2 to 0.46 m), but
recorded exit speeds rose above the normal 2 m s
-1
to 2.5
to 3 m s
-1
just prior to exit; this correlated well with the
velocities required to overcome the effects of gravity for
the given heights. Flipper action stopped some distance
below the free surface, which was interpreted as implying
that buoyancy played a significant role in attaining the
higher exit speed (effectively reached in glide mode), a
behaviour observed and modelled earlier for king and
Adélie penguins (Sato et al. 2002).
The present study is based on close inspection and
analysis of a widely-published film of swimming and
jumping emperor penguins (BBC 2001), plus unpublished
associated film provided by the BBC, which leads us to
hypothesize that free-ranging emperor penguins employ
drag reduction by air bubble release (‘air lubrication’) in
achieving high speeds prior to jumping from sea water
onto ice shelves. We present a model and analysis of the
means by which this previously unreported phenomenon
is achieved.
The air release from the plumage during ascent (as
also evidenced at first glance by the pronounced wakes of
air bubbles trailing ascending penguins) is believed to be
similar to the process of air lubrication studied for engi-
neering purposes. Thus early flat plate studies for turbu-
lent flow showed that frictional drag could be reduced by
up to 80% immediately downstream of microbubble in-
jection (McCormick and Bhattacharryya, 1973) and ‘near-
100%’ if plates were covered by a thin film of air. In-
creasing air flow reduces the skin friction. For example,
to achieve a 60% reduction in local skin friction by injec-
tion of microbubbles in a turbulent boundary layer at a
free stream velocity of 4.6 m s
–1
, Madavan et al. (1985,
Fig. 13 therein) needed a volume flow of air that was 54%
of the volume flow of water in the boundary layer in the
absence of bubbles. This measurement was taken at a
distance of about 0.14 m downstream of the short porous
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section of wall where injection occurred, but drag reduc-
tion appeared to persist for as much as 60-70 boundary-
layer thicknesses downstream (about 0.52–0.61 m).
Measured turbulence spectra also indicated a reduction of
high-frequency shear-stress fluctuations, hence a reduc-
tion of the near-wall turbulence, as one cause of drag re-
duction. It was found that microbubbles had to be present
in the boundary layer close to the test surface, having no
drag-reducing effect if they were outside the boundary
layer (see also Guin et al. 1996 for discussion). A de-
tailed recent plate study at high flow rates (6-18 m s
-1
;
Sanders et al., 2006) showed that a large void fraction
(i.e. high ratio of bubble volume to bubble+water volume)
close to the test plate yielded the greatest reductions in
drag, while bubble size was rather less important. How-
ever, although reduction in fluid density from water to air-
water mixture is believed to be a major factor, this does
not explain the whole of the drag reduction achieved
(Sanders et al., 2006).
It should also be stressed that most plate studies have
focused on the injection of bubbles into the water flow at
the upstream end of the plate and been concerned with the
degree to which bubbles are effective in downstream drag
reduction. This follows from the principal motivation for
such studies – the achievement of reduced fuel consump-
tion in large commercial vessels such as oil tankers, in
which frictional drag can make up as much as 80% of
total drag (Fukoda et al., 2000), but where air injection
over the whole wetted surface is impracticable. Drag
reductions of 15-40% and speed increases of 27% have
been achieved in far more modest-sized experimental
vessels (though by use of macroscopic air spaces not by
injection of bubbles). A major obstacle to progress has
been that propulsors (e.g. ship screws, water jets) must be
protected from air bubbles (Matveev 2003).
In another approach relevant to the present study,
Fukoda et al. (2000) applied air injection to plates and
large ship models that had been painted with a hydropho-
bic paint. In this case, bubbles coalesced to form thin air
films over the painted surfaces; frictional resistance was
reduced by 80% in a flow of 4 m s
-1
and 55% at 8 m s
-1
,
which was significantly more than without paint. The
reason for a significant drag reduction is readily illus-
trated qualitatively by considering the frictional drag F
d
for the simple cases of a laminar and a turbulent boundary
layer over a flat plate of length L and width B (Schlicht-
ing, 1968, pp. 128 and 599 therein),
F
d,lam
= ½ρV
2
L B × 0.664 Re
–1/2
∝ V
3/2
ρ ν
1/2
(1)
F
d,tur
= ½ρV
2
L B × 0.074 Re
–1/5
∝ V
9/5
ρ ν
1/5
(2)
where Re = VL/ν denotes the Reynolds number, ν ≡ µ/ρ
the kinematic viscosity, µ the dynamic viscosity and ρ the
density. For a given free stream velocity V, the ratio of
frictional drag for flow of pure water and pure air at at-
mospheric pressure and 0ºC (where the ratio of densities
is 1000:1.3 and of kinematic viscosities 1.75:13.5) is
about 277 for laminar flow and 511 for turbulent flow.
These ratios explain qualitatively why the formation of a
continuous air film along a flat plate due to coalescence of
injected bubbles may give rise to ‘near-100%’ reduction
of the skin friction, even though such a double boundary
layer of air film driven water flow does not satisfy Eqs.
(1) and (2).
2. Methods
The published film sequences of emperor penguins
(BBC 2001) were collected at Cape Washington, Ross
Sea, Antarctica under calm conditions with a flat sea sur-
face. They total 56.04 s, consisting of 1401 fields, 0.04 s
apart, and show penguins ascending rapidly and jumping
out of the sea onto the ice shelf. The BBC also supplied
unedited, unpublished film collected as part of the film-
making. This latter film, which showed that at least one
leopard seal was present in the area of penguin activity,
totalled about 2 hours, but most footage was unusable in
analytical terms. However, there were sufficient usable
sequences to evaluate downwards and horizontal swim-
ming near the sea surface. Selected sequences from both
published and unpublished material were copied to a PC
and loaded onto Motion Analysis Tools, a software ana-
lytical program that allows frame-by-frame study, plus
linear and angular measurements. Much of the material
could only be considered qualitatively as the camera was
either in constant motion (panning), or was directed sub-
stantially upwards or downwards, so that birds moved
away from or towards the camera. No sequences permit-
ted reliable analysis of flipper action (e.g. beat frequency,
angle of incidence). However, there were several se-
quences that satisfied the following criteria: 1) the back-
ground (usually ice shelf) was stationary, indicating a
non-moving camera; 2) the camera was close to horizon-
tal; 3) the birds were constantly in focus; 4) if viewed
from the dorsal aspect, ascending penguins were at the
near-vertical phase of their ascents (so were not moving
away from the camera); 5) descending birds, or horizon-
tally-swimming birds were viewed from a completely
lateral aspect (i.e. not moving away from or towards the
camera); 6) distance between birds and camera was suffi-
cient to minimize parallax problems. In these circum-
stances, quantitative data were extracted. Distances and
speeds for any continuous sequence of fields were cali-
brated by assuming a standard bird length (bill tip to
hindmost visible limit of feet) of 1.25 m (emperor pen-
guins stand some 1.10 - 1.20 m high on ice with the beak
at right angles to the body axis, but swim with the beak
parallel to the body axis). There will inevitably be a linear
error of about ± 0.05 m (±4%), simply because of the
variability of penguin size. The beak tip (readily dis-
cernible) was the marker position used in all such se-
quences.
Several near-surface sequences were available where
the quantitative criteria were met, where the birds were in
side view, and where the sea surface was visible. In these
circumstances, it was possible to establish the angle be-
tween the body axis of the ascending/descending penguin
and the horizontal sea surface.
3. Results
Observations. The most crucial observation of our
study is that emperor penguins swimming upwards to
jump out of the water trail long visible wakes of air bub-
bles (Fig.1). In underwater portions of the published film,
46 different penguins were seen to swim near-vertically
Unofficial Draft Version (psl) 06-12-2008
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Fig. 1. Ascending emperor penguin approaching sea wa-
ter surface close to edge of Antarctic ice shelf. Note
highly visible trail of air bubbles. From BBC (2001), with
permission.
Fig. 2. Images of near-vertically ascending emperor pen-
guins. Note that these drawings (drawn from sequential
close-up fields (from BBC 2001) of two different penguins)
demonstrate that the bubble clouds envelop most of the body
and obscure the tail and hind limbs. Note also that the identi-
fied anterior edges of the bubble clouds correspond to areas
where bright bubbles can be seen against the penguin sur-
face. It is likely (given the close-up image shown in Fig. 3)
that less visible bubbles emerge more anteriorly.
Fig. 3. Image of ascending emperor penguin about to
break through water surface. Note fine bubbles emerging
from throat plumage and waves in bubble cloud over
nape. Note also the bubble cloud visible at the base of
right flipper. Large bubbles are visible issuing from
breast/belly plumage. Note that no air is issuing from
beak or nares. From BBC (2001), with permission.
upwards at high speed before adopting a rather shallower
angle to the horizontal as they jumped through the water
surface close to the ice shelf. No birds fell back and all
created wakes of air bubbles throughout the ascent. The
density of bubble wakes varied amongst individual pen-
guins, but the wakes remained constant for an individual
throughout the upwards swim – there were no signs of the
birds exhausting the air supply, and – as expected – wake
flows followed the birds as they moved through the water
surface. Also, most birds continued to use their flippers
throughout the swim to the surface (i.e. there was no glide
phase prior to emergence).
A priori there could be two possible sources of air
that could generate the wakes, the respiratory system or
the plumage. Antarctic fur seals exhale on ascents to
avoid shallow water blackout (Hooker et al. 2005), so
close-up sequences were inspected to see whether air is-
sued from the beak/nares area; none did. It was clear that
air issued from the plumage over most of the body, form-
ing a tight-fitting cloud of bubbles (Fig. 2). Close inspec-
tion of the bubble clouds showed that bubbles were ex-
tremely fine (visible as light blue clouds in which indi-
vidual bubbles could not be discerned) at the anterior of
the penguins’ bodies, but became thicker and whiter to-
wards the tail. In most close-up views the cloud was
smoothly applied to the penguin body, forming a tube
around the tail and hind limbs; coherent structures were
visible in the early part of the wake behind the animal, but
faded away as the wake bubbles dispersed and rose. Only
in one image of a penguin very close to the water surface
(Fig. 3) was the bubble cloud disturbed; large bubbles
were also visible issuing from the breast/belly region of
the individual. Bubble clouds appeared stronger on the
dorsal surface of penguins ascending at angles from the
vertical, presumably reflecting the tendency of air to rise
in the water column (c.f. Madavan et al., 1985).
In all underwater sequences the bulk of the flippers
were outside the bubble clouds, so acting against an in-
compressible medium. Localized signs of dorsal bubble
cloud disturbance (posterior to the flippers) as the flippers
beat were occasionally visible, while bubble clouds af-
fected the base of the visible right flipper in a penguin
filmed close to the sea surface (Fig. 3).
Six fast-ascending penguins trailing bubble wakes
were seen to abort ascents, their paths curving in abrupt
near-vertical turns before the penguins descended again.
The penguins appeared to be responding to the close
proximity of other penguins or the camera operative; ef-
fectively their ascents were baulked. It was seen that air
bubble wakes continued to issue from the penguins’
plumage until after they had completed the turns, but died
away completely as the penguins descended. Clearly the
bubble wakes are related to ascents in the water column,
not descents. Only one of the aborted ascents could be
analyzed quantitatively; before slowing during the abort,
the penguin concerned was travelling at 5.8 m s
-1
. This
value is within the range of swimming speeds of success-
fully-ascending penguins (see below). This reinforces our
impression that ascents are not aborted because of inade-
quate speed, but because of interference.
Although we inspected several hours of film in total,
which recorded the movements of several hundred pen-
guins, in no case did we see free-ranging penguins that
Unofficial Draft Version (psl) 06-12-2008
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rapidly ascended without bubble trails or without active
use of their flippers. This strongly suggests that rapid up-
ward swimming without bubbly wakes is very rare (if it
ever occurs at all). Some penguins swam upwards (with-
out bubbly wakes) but, although these sequences were not
analyzable (camera moving slightly, or birds too close to
the camera), they were obviously very slow – the animals
were often not even flapping the flippers, simply drifting
upwards (presumably because of slight positive buoy-
ancy) through the last couple of metres of the water col-
umn to the surface. Air bubble trails were seen in the case
of descending penguins. In almost all cases this occurred
as animals left the water surface; they died away within 2-
3 flipper strokes. There were two exceptions, both being
penguins that had clearly dived through the water surface
from the ice shelf (of an unknown height) and trailed
bubbles for several metres. One entered at a steep angle
and briefly achieved 6.2 m s
-1
, but had slowed to 1.9 m s
-1
by the time the bubble trail ceased. The other penguin’s
track could not be analyzed, but the bird concerned en-
tered the water at a shallower angle, soon converted to a
very rapid horizontal movement that ended in a glide.
The only example of long bubbly wakes other than
during an ascent was seen in a single example of a par-
tially ‘porpoising’ penguin swimming horizontally. This
was seen in the additional footage supplied by the BBC,
but the cameraman panned the camera, so we could not
analyze the footage (i.e. we could not estimate the speed,
though it was clearly quite rapid). However, the penguin
(which was not jumping entirely out of water, but follow-
ing an undulating path during parts of which the dorsal
section of the body was emersed), trailed bubbles
throughout the sinusoidal swimming path, presumably
because the plumage was loading with air each time the
dorsum emerged from water. In dolphins and penguins,
porpoising has been modeled as a method of intermittent
locomotion whereby animals reduce their energetic
expenditure at high speeds by capitalizing on short
periods of unpowered movement through the air (Au and
Weihs, 1980). Weihs has recently (2002) revisited the
topic of porpoising, but all of the emphasis has been upon
reconciling the high energy cost of jumping out of water
with the much reduced drag when in air. No-one has pre-
viously reported bubbly wakes during the underwater
phases of porpoising in penguins.
Film analysis. Quantitative analysis of approp-riate
parts of the film, assuming a standard bird length (tip of
beak to hindmost foot) of 1.25 m, showed swimming
speeds during bubble trail ascents (n=10 different pen-
guins; all recorded when camera was still) as follows:
range 3.8-6.1 m s
-1
, mean 5.3 m s
-1
(SD 1.01 m s
-1
). The
mean ascending speed corresponds to 4.3 body lengths s
-1
.
Final angle of ascent to the horizontal before jumping
through the water surface was measured in 6 birds (mean
60°, SD 8°). Swimming speeds of descending penguins
(n=10) were as follows: range 1.3-2.8 m s
-1
, mean 1.9 m s
-
1
(SD 0.49 m s
-1
). The mean descending speed corre-
sponds to 1.5 body lengths s
-1
. Mean angle of descent
(n=10) to the horizontal was 41°, SD 9°. Horizontal
swimming speeds (n=5) were: range 1.2-2.7 m s
-1
, mean
1.7 m s
-1
(SD 0.57 m s
-1
). The mean horizontal speed cor-
responds to 1.4 body lengths s
-1
. The variability of these
data is similar to that observed by Kooyman et al. (1992),
who used electro-mechanical data loggers to measure
swimming speed. One-way ANOVA showed that there
were highly significant differences amongst the ascend-
ing, descending and horizontal swimming speeds
(p<0.0005). Post hoc Tukey analysis showed that the de-
scending and horizontal speeds were not significantly
different from each other (p>0.05), but that the penguins
ascending with bubble trails traveled far more quickly,
reaching a mean of 2.8 times the descending speed.
It was difficult to determine the depth at which bub-
ble trail ascents started. No fixed camera sequences were
available, nor was there a complete panned sequence from
appearance of the wake to jumping through the sea sur-
face. However, in one panned sequence, white wakes
could be followed until the sequence ended about 3.2 m
below the water surface. This sequence lasted 2.48 s, im-
plying that the wakes started at a depth of about 16 m on
the assumption that penguins moved vertically at 5.3 m s
-
1
.
In four jumping sequences, filmed above water at the
ice edge on a different occasion and at a different loca-
tion, it was possible to estimate the maximum height (of
the approximate penguin centre of gravity) above the wa-
ter surface achieved during jumps out of water (1.12-1.78
m). All heights substantially exceed those recorded by
Sato et al. (2005) in emperor penguins jumping through
ice holes. Given the mean emergence angle (α) of 60º and
mean emergence velocity (V
0
) of 5.3 m s
-1
recorded in this
study, the maximal height (h
max
) of the jumping trajec-
tory, ignoring drag, is calculated from the equation of
motion, giving h
max
= h
0
+
V
0
2
sin
2
α / (2g) = 1.07 m
(where h
0
is assumed to be zero), which agrees with ob-
servations of around 1 m for most jumping penguins.
Jumps as high as 1.7-1.8 m agree well with a few ob-
served high velocities, up to 8.2 m s
-1
, just before com-
pletely leaving the water (it is likely that some accelera-
tion occurs as the forepart of the body is in air, while the
propulsive flippers are still acting against incompressible
water (c.f. flying fish; Davenport, 1994).
Air release during ascent. Before jumping out of the
water onto ice, the penguins swim at the surface and then
dive on inspiration (Kooyman et al. 1971) - we believe
with plenty of air in the plumage (i.e. with erected feath-
ers making room for an air layer about 25 mm thick (fol-
lowing Du et al., 2007)). Kooyman et al. (1971) described
the grooming behaviour by which surface swimming em-
peror penguins load their plumage with air and we con-
firmed this by observation of parts of the unpublished
BBC film. They subsequently dive to around 15-20 me-
tres (by which depth the air volume will have decreased
by a substantial amount, see below). During the dive, or
when achieving that depth, they depress the feathers (to
fix the plumage volume at the new, decreased level).
When the birds swim quickly upwards, the decompressing
air will flow out by virtue of the available fixed plumage
volume being substantially less than the initial surface
volume. Plumage consists of a fine, multi-layered mesh
over the whole of the body surface comparable to a po-
rous medium with an estimated pore-size of less than 20
µm (Du et al., 2007), so the expanding air will automati-
cally issue as small bubbles. This arrangement resembles
the flat-plate experiments of Sanders et al., (2006) who
used a 40 µm pore-size sintered stainless steel strip for
Unofficial Draft Version (psl) 06-12-2008
5
Initial depth = 10 m
12
15
20
-0.2
0.0
0.2
0.4
0.6
0 5 10 15 20
Depth, d (m)
Air layer, S/So
Fig. 4. Calculated air layer thickness versus depth during
ascent with constant velocity and constant air release. k = 1,
effect of increasing initial depth, V = 5.3 m s
–1
.
microbubble air injection. The 'active' part of the process
consists solely of maintenance of depressed feathers dur-
ing the near-vertical phase of the ascent in order to regu-
late expulsion of air driven by decompression. As bubbles
continue to enter the boundary layer along the plumage,
they are swept downstream and move outwards, thus in-
creasing the void fraction in the boundary layer down-
stream to finally leave in the wake behind the bird – or
they coalesce with other bubbles to form rather large bub-
bles at the outer edge of the boundary layer (see Fig. 3). It
is likely that a large number of small bubbles may still
remain within the boundary layer as seen by calculating a
typical liquid, turbulent boundary layer thickness δ a dis-
tance, say x = 0.5 m downstream from the leading edge of
a flat plate, estimated from Schlichting (1968, p. 599) δ =
0.37 x (xV/ν)
-0.2
= 0.37×0.5×(0.5×5.3/10
-6
)
-0.2
= 0.010 m =
10 mm, increasing to 17 mm at x = 1.0 m. Although the
growth of the boundary layer on a body like a penguin is
different from that of a flat plat, the order of magnitude of
thickness is similar.
As an aid to understanding the strategy used by pen-
guins during ascent, two alternative simple physical mod-
els have been examined for estimating the rate of air re-
lease during ascents. To this end, assume the entrapped
air can be represented by a layer of initial thickness s
0
of
pure air at atmospheric pressure (i.e. an absolute pressure
of ≈10 m water column). As long as there is no release,
the thickness of air layer varies with depth d below the
free surface as:
s = s
0
(1 + d /10)
–1
(3)
so that at d
1
= 15 m, for example, we have 40% of the
initial thickness, s
1
= 0.4 s
0
. Here we have used the ideal
gas law, assuming isothermal conditions, so the product
of absolute pressure and volume (or thickness s over a
fixed area) remains constant. Also, we can safely ignore
the varying dynamic pressure associated with the change
of free stream velocity along the surface of the penguin.
At the front stagnation point, the pressure is higher than
the local hydrostatic pressure (by 1.4 m water column at
an onset flow of 5.3 ms
–1
) while it is lower (by an esti-
mated 0.98 m water column) near the head and (by no
more than 0.15 m water column) over the rest of the body.
In terms of hydrostatic pressure change with depth, the
variations mentioned are comparable with the variation
over length of a vertically oriented penguin. One may
now consider two strategies: (i) the thickness of air layer
in the plumage remains constant at the value s
1
during
ascent while air is released due to decompression accord-
ing to the isothermal volume increase of air with decreas-
ing depth; or (ii) the thickness s of the air layer decreases
during ascent in a controlled way (by decompression and
depression of feathers) so as to maintain a constant rate of
air outflow per unit area (a velocity denoted u) at any
depth. Model (i) would imply that most of the mass of
entrapped air is expended at great depths, leaving little as
the surface is approached, so that the bubbly wake should
diminish with decreasing depth. Since observations show
all bubbly wakes to be of unchanged strength during ob-
servable ascents we favour model (ii).
In this case, the air-outflow velocity u is maintained
constant by the combined action of decompression and
depression of feathers such that the thickness of the gen-
erated bubble layer (and ensuing drag reduction) should
be unchanged during the ascent. Here the depression of
feathers may help overcome the pressure drop associated
with the flow of air through the fine mesh of feathers. The
resulting drag reduction is assumed to depend only on the
volume of air bubbles formed, not the air pressure, which
varies with depth. We now calculate how the air-layer
thickness s of entrapped air varies during vertical ascent
with constant velocity V, starting at time t = 0 with the
value s
1
at depth d
1
as before. Without air release, s varies
as given by Eq. (3), where d = d
1
– Vt, but with constant
air release u it becomes:
s = s
0
[1+ (d
1
–Vt) /10]
–1
– ut . (4)
Introducing the time of ascent t
a
= d
1
/V and t
a
u = ks
0
,
where k = 1 would correspond to the case when all of the
initially entrapped air has just been used up when arriving
at the sea surface, Eq.(4) becomes,
s/s
0
= [1+ (d
1
/10)(1–t/t
a
)]
–1
– k t/t
a
. (5)
Fig. 4 shows how the air layer thickness decreases with
depth during ascent from initial depths of d
1
= 10, 12, 15
and 20 m according to eq. (5) for k = 1. Only positive
values of s/s
0
have physical meaning, so the maximal fea-
sible initial depth is about 10 m if air release were to con-
tinue until the free surface has been reached. Starting at a
depth of 15 m, however, air release would terminate at a
depth of about 5 m. It is clearly costly to start releasing air
at great depths because, for a given layer thickness, rela-
tively more mass of air is expended due to its compres-
sion. However, starting from greater depths than 10 m
would be possible by the use of alternative strategies,
such as intermittent release spatially along body and/or in
time, or by reducing u through values of k < 1. Fig. 5
shows, for d
1
= 15 m, how decreasing the value of k en-
sures that s remains positive during full ascent, but then
not all of the available air becomes useful. Considering a
reference case (k = 0.9, L = 1 m, s
0
= 25 mm and d
1
= 15
m), the air-outflow velocity becomes u = ks
0
V/d
1
= 0.008
m s
–1
and 90% of the available air becomes useful (com-
pared with only 60% as can be shown for model (i)).
Thickness of bubble boundary layer. Next, with a
few more assumptions, it is possible to estimate the thick-
ness δ of the released air layer (evidently the air appears
Unofficial Draft Version (psl) 06-12-2008
6
k = 0.8
0.9
1.0
-0.1
0.0
0.1
0.2
0.3
0.4
0 5 10 15
Depth, d (m)
Air layer, S/So
Fig. 5. Calculated air layer thickness versus depth during
ascent from d
1
= 15 m with constant velocity and constant
air release. Effect of decreasing k, V = 5.3 m s
–1
.
as bubbles, but for conservation of mass it is simpler to
think in terms of a layer of pure air, which later may be
interpreted as a bubble layer of some void fraction). When
air is released at the rate u along a section of length L of
the body, δ would increase with distance x from the up-
stream point (x = 0) as given by the equation of continu-
ity, d(V
BL
δ)/dx = u, subject to the boundary condition δ(0)
= 0, where V
BL
denotes a representative velocity of the air
in the boundary layer. Taking V
BL
to be one-half of the
constant swimming velocity, V
BL
= ½ V, the linear in-
crease of δ would give a mean value over length L of δ
mean
= ½Lu/(½V) = Lu/V.
For our model (ii), δ
mean
would be constant during
ascent and (using t
a
u = ks
0
and t
a
= d
1
/V,) given by δ
mean
=
kLs
0
/d
1
. For the reference case (k = 0.9, L = 1 m, s
0
= 25
mm and d
1
= 15 m) this gives δ
mean
= 1.5 mm and a mean
bubble layer (at 10% void) of 15 mm, increasing to 30
mm at the tail end, during the whole period of ascent. Due
to the body shape of a penguin, the free stream velocity
will be somewhat higher than the swimming velocity, but
aside from the head region (where local high velocities
are incurred) not by more that 5 -6%, which would imply
a slightly thinner bubble layer. On the other hand, bubbles
probably move at velocities less than the assumed ½V and
thus tend to lead to a thicker bubble layer.
Measurements made with Motion Analysis Tools
from a close-up frame of a penguin near to the sea surface
suggest fine bubble layers of thickness of approximately
20 mm, at locations 0.28 m and 0.68 m from the tip of
beak in the dorsal region (observations could not be col-
lected from the ventral region). However, because the bird
was travelling at around 60º to the horizontal at this time,
it is likely that the tendency of bubbles to rise will have
led to greater thicknesses of bubbles being evident in the
dorsal than the ventral areas, so it is probable that 20 mm
is an overestimate. This (distinctly limited) observation
nevertheless shows an order of magnitude agreement with
the model results.
Propulsive force and power At a steady, horizontal
swimming velocity V, the propulsive force F
P
equals the
drag force,
F
d
= C
d
A ½ρV
2
, (6)
and the expended power is,
P = F
P
V= C
d
A ½ρV
3
. (7)
To attain a swimming velocity of about 5.3 m s
-1
, a factor
of 5.3/2 = 2.65 times the normal cruising speed of 2 m s
-1
,
would imply increases in propulsive force and power by
factors 2.65
2
= 7.02 and 2.65
3
= 18.6, respectively, assum-
ing an unchanged C
d
. Such increases are unlikely, even
for the short duration (ca. 3 s) of ascent. However, if bub-
ble release from the plumage causes a reduction of the
product C
d
ρ by a factor of 18.6 (i.e. to about 5.4% of the
single-phase liquid flow drag), the expended power would
be unchanged from that at the normal cruising speed of 2
m s
-1
, and the required propulsive force would be corre-
spondingly reduced. However, it is likely that, during
ascents, penguins expend more power and are aided by
buoyancy, so that less drag reduction would be required to
achieve the observed high speeds.
The total drag on a streamlined body such as a pen-
guin is the sum of frictional drag in the boundary layer
along the surface and form drag associated with the pres-
sure distribution around the body. Form drag may consti-
tute as much as 20% or more of the total drag (Schlicht-
ing, 1968, Figs. 25.4 and 25.5 for a streamlined body of
length to diameter ratio of 4), so even if skin friction were
reduced to a negligible amount due to bubbles in the
boundary layer and/or coalescence of bubbles to form
patches of air film along the plumage surface, there would
still remain a sizable contribution from form drag, unless
this was also affected by air release. Considering the clas-
sical analysis used in calculating total drag on a body
from experimental data of wake measurements (e.g.
Schlichting 1968, p. 166 therein) it is readily shown quali-
tatively that drag must be reduced when the density of the
wake flow is reduced due to the presence of bubbles. An
evaluation of the amount of reduction, however, requires
either a reliable numerical method for turbulent bubbly
flow or an experiment.
To examine this problem we consider the classical
analysis used in calculating total drag on a body from
experimental data of wake measurements (e.g. Schlichting
1968, p. 166 therein). Figure 6 shows a control volume
(dashed contour) surrounding the body subject to an in-
coming flow of uniform velocity V
1
and liquid density ρ
over area A
1
, leaving the body partly along the cylindrical
side og area A
3
(to satisfy continuity) and partly down-
stream over area A
2
with reduced velocity and density in
the wake due to the air release Q
a
= uA
p
of density ρ
a
.
Assuming the control volume surface to be far enough
from the body that pressure is uniform, the conservation
of mass and balance of momentum become,
∫
∫
−+=
222113
dAVdAVQQ
aa
ρρρρ
,
132
2
221
2
1
VQdAVdAVF
d
ρρρ
−−=
∫
∫
or, after elimination of Q
3
,
122122
)()1( VQdAVVVF
aad
ραρ
−−−=
∫
, (8)
where the mixture density has been approximated by ρ
2
=
ρ
a
α
2
+ ρ(1–α
2
) ≈ ρ(1–α
2
), and where void fraction α
2
var-
ies across the area A
2
.
Unofficial Draft Version (psl) 06-12-2008
7
Fig. 6. Control volume (CV) around body to express drag
force F
d
in terms of momentum change of flow past body
with air release Q
a
Although total drag can only be evaluated from
(8) if detailed data from wake measurements are avail-
able, this equation suggests that both skin friction and
form drag are affected by air release. The difference be-
tween the cases of air release with bubble flow wake and
no air release with pure liquid flow (α
2
= 0 and Q
a
= 0) is
to be found in the distribution over A
2
of velocity V
2
and
void fraction α
2
since the last term in (8) is negligible.
Increasing air release will increase α
2
and increase V
2
as
bubbles in the wake are being accelerated by the liquid
flow, both contributions that will reduce F
d
as compared
to the case of no air release hence increase the drag reduc-
tion.
Required drag reduction To determine the required
drag reduction to achieve the observed high ascent speeds
we estimate the magnitude of the buoyancy force, the
propulsive force and propulsive power. During normal
cruising manoeuvres near the surface, penguins appear to
be only slightly positively buoyant, judging by the slow
rise of penguins not flapping their flippers. They are evi-
dently quite close to neutral buoyancy.
However, prior to dive and subsequent ascent to jump
we assume the penguin fills its plumage with air at the sea
surface and inspires to fill its respiratory system with air
(Sato et al. (2002) state that king and Adélie penguins
always dive on inspiration; there is no reason to believe
that emperor penguins differ in this respect). As in the
previous analysis, the air-layer thickness is taken to be s
0
= 25 mm over surface area A = 0.6 m
2
, i.e. an air volume
of 15 l, and the air volume of the respiratory system is
taken to be at most 25×0.1 = 2.5 l for a 25 kg emperor
penguin at an estimated 100-200 ml kg
-1
according to
Sato et al. (2002, table 2 therein for king and Adélie pen-
guins). Denoting by g the acceleration of gravity, the as-
sociated buoyancy force at the sea surface is,
F
b
= (ρ–ρ
a
) ×Vol
air
×g ≈ 1000×(0.015+0.0025)×9.81
= 172 N . (9)
This significant force corresponds to about 70% of the
weight. As the penguin dives to depth d the air is com-
pressed and the buoyancy force F
b
decreases as s accord-
ing to eq.(3),
s = s
0
(1 + d /10)
–1
(3)
The air density increases inversely with respect to s ac-
cording to the ideal gas law for isothermal conditions, but
the approximation ρ >> ρ
a
is still reasonable for the
depths in question. At depth d
1
= 15 m, for example, we
have 40% of the initial thickness, s
1
= 0.4 s
0
and a buoy-
ancy force of about F
b,1
= 69 N if no air has been released.
First, assuming no air release during ascent (the hy-
pothetical case of a fast ascending penguin not showing
bubbly trails) the effect of buoyancy on attainable speed
can be evaluated as follows. For steady, horizontal
swimming the propulsive force F
P
and propulsive power
P
P
may be evaluated at normal cruising speed by using
the established typical values of drag coefficient of C
d
=
0.02 to 0.04 (Hirata & Kawai, 2001) based on surface
(wetted) area for streamlined bodies of revolution. The
lowest drag occurs at a length to diameter ratio of about
4.5, which is close to that of the emperor penguin (about
3.4). Hence at V
0
= 2 m s
-1
,
F
P,o
= F
d,o
= 0.02 × 0.6× ½ × 1000 × 2
2
= 24 N , (10)
P
P,o
= F
P,o
V
0
= 48 W . (11)
Due to observed flipper action we assume the propulsive
power to be at least the same during ascent as during
cruising, except that there will now be an additional
buoyancy-driven propulsive power, P
b
= F
b
V, where F
b
is
the buoyancy force (assuming a vertical ascent). For a
trajectory forming the angle θ with the vertical it will be
smaller by the factor cos θ.
Equating total propulsive power P to drag at the new
velocity V
1
at depth d
1
gives,
P = P
b
+ P
P,o
= F
b,1
V
1
+ P
P,o
= C
d
A ½ρV
1
3
. (12)
Using F
b,1
= 69 N and P
P,o
from eq.(9) in (12) gives V
1
=
3.70 m s
-1
at depth d
1
= 15 m. Similarly, using F
b,o
= 172
gives V
o,o
= 5.49 m s
-1
at depth d
0
= 0 m.
Within the assumptions made, we conclude that
buoyancy could theoretically help to increase the velocity
during ascent from about 3.8 m s
-1
at depth 15 m to about
5.5 m s
-1
when the free surface is reached, but only if all
air remained within the plumage throughout the ascent
(which it clearly does not). However, this is still less than
the highest observed emergence speeds (8 m s
-1
). We may
therefore again conclude that drag reduction due to the
release of air bubbles must be involved in the real situa-
tion.
Second, for the actual case of air release from the
plumage during ascent with an estimated constant air-
outflow velocity u = 0.008 m s
-1
, optimally the air layer
thickness would then decrease from 40% of the initial
thickness at depth d
1
= 15 m to about 10% as the free sur-
face is reached (Fig. 5, case of k = 0.9). It follows that the
buoyancy force would decrease from 69 N to about 39.2
N during the ascent (still assuming 2.5 l air in the respira-
tory system). For unchanged propulsive power, again us-
ing (12), the maximal attainable velocity would decrease
rather than increase during ascent, from 3.70 to 3.03 m s
-1
.
To reach the observed average velocity of 5.3 m s
-1
would
require an increase in propulsive power from 48 W to 685
W, a factor of more 14 times the power for the normal
swimming velocity of 2 m s
-1
. Although buoyancy plays a
non-negligible role, its effects are insufficient to explain
the observed velocities, and therefore there must be a sub-
stantial contribution from drag reduction due to air release
Unofficial Draft Version (psl) 06-12-2008
8
during ascent to achieve the observed velocities of the
order of 5.3 m s
-1
or more.
The required drag reduction to attain the observed
velocities of ascent can be evaluated as follows. For the
actual case of 2.5 l air in the respiratory system and air
release, leaving air layers of 40% and 10% of the initial
thickness s
0
, corresponding to depth d
1
= 15 m and near
the surface, we set V
1
= 5.3 m s
-1
in (12) and calculate the
required reduced value of drag coefficient C
d,r
to obtain
the value of required reduced drag ratio as C
d,r
/C
d
. Results
for the estimated normal propulsive power of 48 W and
twice this value are shown in Table 1.
Table 1. Drag reduction required to achieve the observed mean
velocity of 5.3 m s
-1
at depth 15 m (s/s
0
= 0.40) and near the
surface (s/s
0
= 0.10) at normal power and twice normal power.
The results in Table 1 show that not much is gained
by doubling the propulsion power and that more than 70%
drag reduction is needed for the considered average veloc-
ity of 5.3 m s
-1
, and considerably more for the higher ve-
locities observed. Some approximate (unpublished) calcu-
lations of a bubble boundary layer on a flat plate (vali-
dated against experimental data of Madavan et al., 1985)
have shown that a uniform air release of u = 0.008 m s
-1
can provide only an about 14% reduction of the frictional
drag, which suggests that coalescence of bubbles to form
patches of air film and/or a reduction of form drag are
likely to account for the remaining reduction.
4. Discussion
Our recorded descent and horizontal speeds (and their
variability) for emperor penguins closely agree with pre-
viously published data, giving confidence in our measured
ascent speeds. Cruising speed has been estimated at about
2 m s
-1
(Culik et al.1994; Wilson 1995), which is similar
to our observed descending and horizontal speeds (1.9 m
s
-1
and 1.7 m s
-1
respectively). Kooyman et al. (1992)
recorded 2.8 m s
-1
from penguins swimming beneath solid
ice between air holes – which constrained situation may
have stimulated slightly elevated swimming speeds; Sato
et al. (2005) have more recently recorded 1.7 m s
-1
. Given
the fact that none of the filmed material inspected in our
study, collected from hundreds of penguins, showed ani-
mals moving upwards at high speed without bubble trails,
we strongly suspect that our measured upward speeds
(mean 5.3 m s
-1
) represent the maximum speeds of which
emperor penguins are capable. Our estimated speeds are
certainly the highest recorded in scientific studies.
Compared with a penguin cruising speed of 2 m s
-1
,
drag would be increased about 5.8-fold at the observed
mean ascent speed of 5.3 m s
-1
, given no mechanism to
reduce it [Eq. (2)]. Clearly, drag reduction will be advan-
tageous provided that the energetic cost of doing so is not
prohibitive.
Our observations and analysis unequivocally demon-
strate that emperor penguins ascending rapidly in the wa-
ter column to jump onto ice shelves emit bubble clouds
into the turbulent boundary layer over most of the body
surface throughout their ascent. Emission does not dimin-
ish as a penguin approaches the surface, but increases.
Because the bubbles are produced over most of the body
surface, their drag-reducing function should exceed the
performance of marine engineering plate/models where
retaining an adequate bubble concentration in the turbu-
lent boundary layer is a major problem. Moreover, pen-
guin plumage is water-repellent (due to application of
preen oil), so it is feasible that thin air films may form
over the feather surfaces, as shown for water-repellent
paints by Fukuda et al. (2000), promoting drag-reduction
still further.
Penguin plumage can contain considerable quantities
of air (Yoda and Ropert-Coudert 2004), recent calcula-
tions suggesting that as much as 96% of plumage volume
is occupied by air (Du et al., 2007), and during a dive the
volume of trapped air will decrease according to Eq.(3),
whence shrinkage decelerates with increasing depth. At a
depth of 15 m air in the plumage will be compressed to
40% of its initial volume (to 33% at 20 m). We believe
that emperor penguins essentially ‘lock’ the reduced
plumage air volume at a depth of 15-20 m. When they
swim rapidly towards the surface, from about 60% to 90%
(depending on strategy (i) or (ii)) of the initial volume is
available to diffuse out through the fine plumage mesh-
work in the form of small bubbles that progressively coa-
lesce along the body surface as the penguins ascend. At
present we favour strategy (ii) because of the observed
persistence of bubble wake formation right to the surface.
Because of the characteristics of the depth:volume rela-
tionship, the expansion rate of the trapped air will be
greater as the penguin approaches the sea surface (Fig. 4),
thus maintaining release of air, even though the mass of
trapped air is decreasing. Our model of compressed air
storage is supported by observations of penguins that
abort their ascent; on aborting, a penguin redives and
bubbles soon stop issuing from the plumage, so the pen-
guin and its 'track' become separated as the air in the
plumage is repressurised. We do not know whether pen-
guins that have aborted dives need to return to the surface
to recharge the plumage with air, or still retain enough
plumage air to try jumping again. Loading the plumage
with air will increase penguin buoyancy, thus imposing an
additional energetic cost as the birds swim downwards
from the surface. The buoyancy force decreases approxi-
mately by a factor 2.5 when diving from the free surface
to a depth of 15 m, so opposing buoyancy becomes easier
as the penguins dive. On the other hand, our calculations
indicate that buoyancy force, though non-negligible, can
play only a small part in enhancing ascent speed.
For the proposed mechanism of air lubrication to
work, emperor penguins need to have considerable con-
trol over their plumage. There is good evidence that this
control exists. Penguin plumage is unlike that of other
birds. First, feathers are present over the entire body sur-
face rather than being present in tracts as in most other
bird species (Stettenheim 2000). Secondly, each feather
has two parts, an anterior flattened pennaceous part that
provides the smooth, water proof (and water-repellent)
outer coating of the penguin body surface, and a posterior
down-like after-feather that provides insulation (Dawson
et al. 1999). Erection and depression of the pennaceous
part are both under muscular control (Kooyman et al.
Propulsive power 48 W 96 W
Air-layer s/s
0
40% 10% 40% 10%
C
d,r
/C
d
0.463 0.286 0.517 0.340
% reduction 54% 71% 48% 66%
Unofficial Draft Version (psl) 06-12-2008
9
1976; Dawson et al. 1999). On long foraging dives it is
believed that emperor penguins compress their plumage
to expel air, thereby reducing drag (Kooyman et al. 1976)
and the positive buoyancy that is undesirable in diving
birds (Wilson et al. 1992). Hence ‘locking’ of a fixed
volume of air by muscle action is entirely feasible. Fast
water flow will also help to flatten the pennaceous part,
squashing the after feather beneath, in turn helping to
keep air volume steady during ascents. Positive control by
feather depression may play a part in forcing out air dur-
ing the ascent, as suggested by strategy (ii).
How much does air lubrication enhance speed in fast
ascents? This question cannot be answered with precision
from our observations, since all penguins produced bub-
ble clouds when ascending (i.e. none was without the air
lubrication, so there were no ‘controls’). Though the val-
ues for ascent speeds recorded in our study considerably
exceed the accepted cruising speed (ca 2 m s
-1
) for all
penguin species (Culik et al.1994; Wilson 1995), some of
the extra swimming speed will undoubtedly be due to
enhanced flipper action (by some combination of in-
creased flipper beat frequency or increased angle of inci-
dence of flipper to water flow direction) underpinned by
anaerobic ‘sprint’ muscle action. Interestingly, our ascent
speed values (mean 5.3 m s
-1
, but occasionally as high as
8.2 m s
–1
) are much higher (by about 90%) than those
recorded (2.8 m s
-1
) in a recent study of emperor penguins
jumping to modest heights (<0.45 m) through ice holes
1.2 m in diameter (Sato et al. 2005). Sato et al. (op. cit.)
do not mention the occurrence of bubbly wakes, and 2.8
m s
-1
is identical with the horizontal under-ice speeds re-
ported earlier by Kooyman et al. (1992). Given the vari-
ability of the observed ascent and emergence speeds, it is
clear that emperor penguins can modulate speed and
emergence angle considerably, as do Adélie penguins
(Pygoscelis adeliae) (Yoda and Ropert-Coudert 2004).
The lack of ‘controls’ for the observed bubble wake
ascents means that our air lubrication hypothesis for at-
tainment of maximal emperor penguin speeds can only be
considered as highly viable at this stage. The only method
of confirming the hypothesis fully would seem to involve
the construction and testing of a penguin replica that
could be towed whilst emitting bubbles. This would be a
technically difficult task as the complexity of penguin
plumage would be difficult to replicate in a man-made
porous membrane or mesh. However, this approach
would appear to be more fruitful than any attempt (proba-
bly unethical) to constrain emperor penguins to ascend
rapidly without air emission.
Our study only considers the emperor penguin. Since
the plumage structure and control are similar in all pen-
guin species (Dawson et al. 1999), the air lubrication as-
cent adaptation may be more general amongst the Family
Spheniscidae. Adélie penguins in particular may repay
investigation as they leap to heights of 2-3 m above sea
level (Yoda and Ropert-Coudert 2004), yet cruise at 2 m
s
-1
(Sato et al., 2002).
Throughout our study we have assumed that the
adaptive value of air lubrication lies in enhanced swim-
ming speed and hence more effective jumps out of water.
There may be additional benefits; it has recently been
reported that air lubrication reduces the acoustic signal of
ships (Matveev 2005). If this also applies to ascending
emperor penguins, it may make them less detectable by
predators that hunt by echolocation (e.g. Orca).
Acknowledgements
The authors thank the BBC Natural History Unit for per-
mission to use the Blue Planet video grabs and sequences
presented, plus the supply of unpublished film. We thank
the research scientists led by Prof G. Kooyman who fa-
cilitated making of the relevant section of the Blue Planet
film. We particularly thank the photographer Doug Allen.
We also thank Nick Crane for discussion..
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