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Experimental verification of dynamic soaring in albatrosses

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Dynamic soaring is a small-scale flight manoeuvre which is the basis for the extreme flight performance of albatrosses and other large seabirds to travel huge distances in sustained non-flapping flight. As experimental data with sufficient resolution of th ese small-scale movements are not available, knowledge is lacking about dynamic soaring and the physical mechanism of the energy gain of the bird from the wind. With new in-house developments of GPS logging units for recording raw phase observations and of a dedicated mathematical method for postprocessing these measurements, it was possible to determine the small-scale flight manoeuvre with the required high precision. Experimental results from tracking 16 wandering albatrosses (Diomedea exulans) in the southern Indian Ocean show the characteristic pattern of dynamic soaring. This pattern consists of four flight phases comprising a windward climb, an upper curve, a leeward descent and a lower curve, which are continually repeated. It is shown that the primary energy gain from the shear wind is attained in the upper curve where the bird changes the flight direction from windward to leeward. As a result, the upper curve is the characteristic flight phase of dynamic soaring for achieving the energy gain necessary for sustained non-flapping flight.
Fig.12. Force and speed vector diagram. (A)View of the bird seen from behind in the direction of the airspeed vector V. The lift vector denoted by L is perpendicular to the wings of the bird. It can be decomposed into a component L V1 in the plane made up by the speed vectors V inert , V and V W (appearing as a line), and into a component L V2 perpendicular to that plane. The plane made up by the speed vectors V inert , V and V W has no fixed relationship to the horizontal, but is continually changing according to the motion of the bird in the course of the dynamic soaring flight manoeuvre. (B)View on the plane of the speed vectors: the inertial speed vector V inert , which describes the motion of the bird with respect to the Earth used as an inertial reference system; the airspeed vector V, which describes the motion with respect to the moving air in the shear wind; and the wind speed vector V W. Furthermore, the lift vector component L V1 , the drag vector D and the angle α W are presented. The angle α W describes the inclination of the airspeed vector V relative to the inertial speed vector V inert. There is an inclination (α W ≠0) if the wind speed vector V W is not parallel to but instead inclined relative to the inertial speed vector V inert. The angle α W can be determined using the relationship between the speed vectors V inert and V W , which are known from the GPS logger in-flight measurements and the QuikSCAT wind data (as described in Materials and methods, 'Wind determination'). The lift vector component L V1 is, by definition, orthogonal to the airspeed vector V. Because of the inclination of V relative to V inert by the angle α W , L V1 has a component L V1 sinα W parallel to the inertial speed vector V inert. This component is effective in terms of a propulsive force F propulsive =L V1 sinα W. As a result, the work done by F propulsive =L V1 sinα W yields an increase in the total energy. The drag vector D exerts a dissipative effect concerning the energy, producing a negative work due to its component Dcosα W acting in the negative direction of V inert. The component L V1 sinα W and, thus, its propulsive effect, is large when there is a wide angle α W between V inert and V. The angle α W is wide when V W is large and highly inclined with regard to V inert , as in B. In the upper curve, the wind speed V W takes on the largest values during the entire cycle and the angle α W is wide. This is evidence for the significance of the upper curve for dynamic soaring as that phase where the energy gain is achieved.
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4222
INTRODUCTION
Albatrosses excel in an extreme travelling performance by covering
huge distances in their foraging trips with sustained non-flapping
flight. Flight recordings show distances of thousands of kilometres
as well as flights around the world in 46days (Jouventin and
Weimerskirch, 1990; Bonadonna et al., 2005; Croxall et al., 2005).
Furthermore, albatrosses are able to fly persistently at high speed
by using favourable winds (Catry et al., 2004).
The reason for this unique performance capability is a flight mode
termed dynamic soaring. With dynamic soaring, the birds achieve
an energy gain from the shear wind above the ocean surface, enabling
sustained non-flapping flight. As a result, the birds can fly at virtually
no cost when compared with flapping flight (Weimerskirch et al.,
2000). By applying dynamic soaring (Sachs, 2005; Sachs et al.,
2012), the birds gain access to an unlimited external energy source
in terms of the shear wind above the sea surface. The unique
advantage of having an unlimited energy source is due to the fact
that there are permanently strong winds in the areas in which
albatrosses live (Suryan et al., 2008). These brief considerations
show that dynamic soaring is fundamental for the extreme travelling
performance of albatrosses, enabling their unique way of flying and
living.
The long distance flight of albatrosses, constituting a large-scale
movement of the order of hundreds to thousands of kilometres, has
been experimentally investigated at great length and is well
documented (Jouventin and Weimerskirch, 1990; Weimerskirch et
al., 2000; Weimerskirch et al., 2002; Catry et al., 2004; Bonadonna
et al., 2005; Croxall et al., 2005). By contrast, the dynamic soaring
flight mode of albatrosses and other large seabirds has not been
experimentally investigated. This is because dynamic soaring is a
small-scale movement of the order of tens to hundreds of metres
(Sachs, 2005).
A primary goal of this paper is to advance the knowledge in the
field of dynamic soaring in albatrosses and their unique flight method
of gaining energy from the wind for flying without flapping. The
current state of knowledge manifests in a variety of theories and
explanations for the small-scale dynamic soaring flight of albatrosses.
There is a theory termed wind-gradient soaring (Lighthill, 1975;
Norberg, 1990; Spedding, 1992; Tickell, 2000; Dhawan, 2002;
Lindhe Norberg, 2004; Azuma, 2006; Denny, 2009); according to
this theory, soaring is continually possible using the wind gradient in
the shear layer above the sea surface. Another theory termed gust
soaring relates to discontinuities in the wind flow (Pennycuick, 2002;
Pennycuick, 2008; Suryan et al., 2008; Langelaan, 2008; Langelaan
and Bramesfeld, 2008); according to this theory, energy pulses are
obtained from flight through the separated air flow region behind wave
crests. Furthermore, wave soaring and wave lift are regarded as a
technique to obtain energy for flying (Berger and Göhde, 1965;
Wilson, 1975; Pennycuick, 1982; Sheng et al., 2005; Richardson,
2011); here, updrafts at waves are supposed to be usable for soaring.
Another point relates to the aerodynamic ground effect (Blake, 1983;
Hainsworth, 1988; Norberg, 1990; Rayner, 1991); this effect yields
a decrease of the drag when flying close to the water surface so that
an energetic advantage is possible at low levels.
To sum up, current theories and explanations are differing and
show various findings and conclusions. As a result, there is a lack
of both knowledge of dynamic soaring and clarity about this flight
mode, particularly with regard to the magnitude of the achievable
energy gain and the physical transfer mechanism of energy from
the wind to the bird. This is due to the fact that there are so far no
SUMMARY
Dynamic soaring is a small-scale flight manoeuvre which is the basis for the extreme flight performance of albatrosses and other
large seabirds to travel huge distances in sustained non-flapping flight. As experimental data with sufficient resolution of these
small-scale movements are not available, knowledge is lacking about dynamic soaring and the physical mechanism of the energy
gain of the bird from the wind. With new in-house developments of GPS logging units for recording raw phase observations and
of a dedicated mathematical method for postprocessing these measurements, it was possible to determine the small-scale flight
manoeuvre with the required high precision. Experimental results from tracking 16 wandering albatrosses (Diomedea exulans) in
the southern Indian Ocean show the characteristic pattern of dynamic soaring. This pattern consists of four flight phases
comprising a windward climb, an upper curve, a leeward descent and a lower curve, which are continually repeated. It is shown
that the primary energy gain from the shear wind is attained in the upper curve where the bird changes the flight direction from
windward to leeward. As a result, the upper curve is the characteristic flight phase of dynamic soaring for achieving the energy
gain necessary for sustained non-flapping flight.
Key words: non-flapping flight, energy gain from wind, GPS logger, shear wind.
Received 14 January 2013; Accepted 5 August 2013
The Journal of Experimental Biology 216, 4222-4232
© 2013. Published by The Company of Biologists Ltd
doi:10.1242/jeb.085209
RESEARCH ARTICLE
Experimental verification of dynamic soaring in albatrosses
G. Sachs1,*, J. Traugott1, A. P. Nesterova2and F. Bonadonna2
1Institute of Flight System Dynamics, Technische Universität München, Boltzmannstrasse 15, 85748 Garching, Germany and
2Behavioural Ecology Group, Centre d’Ecologie Fonctionnelle et Evolutive, U.M.R., 5175 CNRS Montpellier, France
*Author for correspondence (sachs@tum.de)
THE JOURNAL OF EXPERIMENTAL BIOLOGY
4223Dynamic soaring in albatrosses
experimental data of the small-scale movements of albatrosses so
that a full understanding of dynamic soaring could not be achieved.
To address the aims of this paper, in-flight measurements of the
small-scale movements in free-flying birds were performed so that
experimental verification of dynamic soaring in albatrosses could
be accomplished. The experimental verification was achieved with
new in-house developments of appropriate GPS logger hardware
and of a novel mathematical method for computing the albatrosses’
flight path and speed with the high precision required for this small-
scale flight mode.
MATERIALS AND METHODS
New in-house developments were accomplished in order to achieve
the required high precision in determining the small-scale
movements of dynamic soaring in albatrosses (Traugott et al.,
2008a). One pertains to the hardware, yielding a miniaturized GPS
logging unit for recording raw L1 phase measurements at high
sampling rate. The other in-house development is a new
mathematical method for determining the flight path and speed with
high precision. The new in-house developments were tested for
correct functioning prior to being used for the albatross flight
measurements. These trials included test runs with a car as well as
flight tests with several aeroplanes (Traugott et al., 2008a; Traugott
et al., 2008b).
New logger hardware
Three different types of GPS data loggers were developed for the
albatross flight measurements. The core of each device was a passive
25×25mm patch antenna plugged to the single frequency GPS
module LEA-4T (size 17×22.4mm, mass 2.1g; u-blox, Thalwil,
Switzerland). This module is capable of calculating position and
velocity online with a sampling rate of 4Hz. When logging the data
to the on-chip 8MB flash memory or to an external memory this
yields a data stream of 0.8MBh–1. As an additional feature, the
LEA-4T module makes the GPS raw data available with a sampling
rate of up to 10Hz (~9.6MBh–1). These data are the basis for online
positioning but can also be re-processed back for precision and
sampling rate augmentation. Because of known issues when forcing
the module to output both the online solution and the raw data at
maximum rates, the online solution rate was limited to 1Hz during
the measurement campaign (210kBh–1). The average power
consumption of the loggers was given by 40–60mA and 2.9–3.7V.
Energy was provided by two or three 3.6V primary lithium–thionyl
chloride cells (Saft LS 14500 and LS 14500 C).
Two types of loggers featured an external 2GB memory card.
Equipped with three batteries, these devices were capable of logging
the raw GPS data throughout a period of up to 6days. Their form
factor was 89×55×22mm and 108×55×19mm at a total mass of 103
and 93g.
The third type of logger additionally featured a 3-axes MEMS
accelerometer. No external memory was provided but all data were
logged to the on-chip 8MB flash which yielded possible recording
intervals to about 40min. For bridging the delay between mounting
a logger on a bird at the nesting site and the bird finally cruising over
open waters, these loggers implemented a reliable sleep/wake-up logic
triggering high rate recording only when the bird had left a predefined
area and was exceeding a given speed threshold.
In Fig.1A, a miniaturized GPS data logger is shown. The
complete logging unit includes the logger, the batteries, the wiring
and the casing. The GPS logging unit was flight tested prior to being
used for the albatross flight measurements. One of the aircraft used
in the flight test programme is shown in Fig.1B. This test vehicle
is a research aircraft of the Institute of Flight System Mechanics of
the Technische Universität München. The goal of the trials was to
test the GPS data logger hardware as well as the new mathematical
method for precise position determination. As no experience was
on hand with regard to the required high position precision and high
sampling rate, the development of the system involved significant
test efforts. An issue of proper functioning for the planned albatross
flight measurements was GPS signal shadowing at large bank angles,
like the values occurring in dynamic-soaring-type flight manoeuvres
of albatrosses. Therefore, the flight tests comprised, among others,
dynamic manoeuvres with high bank angles to simulate those of
dynamic soaring in albatrosses.
New mathematical method
A new mathematical method was developed to achieve relative
position precision in the low decimetre range depending on
environmental conditions. The high precision is obtained by forming
single differences between raw L1 phase measurements taken by
the moving receiver at two moments in time. Neither a second,
nearby base receiver nor any (static) initialization procedures as
commonly used in geodetic applications exploiting the same type
of precise measurements are required by this differential GPS (D-
GPS) approach. Details of the method are given elsewhere (Traugott
et al., 2008a; Traugott et al., 2008b).
In Fig.2, the basic concept of the approach for coping with the
position determination task is graphically presented: in this exemplary
scenario, a starting point is specified for an arbitrary time tb1 at the
beginning of a flight manoeuvre of interest. The corresponding
Fig.1. GPS logger and research aircraft used in flight testing. (A)A
miniaturized GPS data logger with an attached 25×25mm patch antenna
used in the albatross flight measurements is depicted. (B)The GPS logging
unit, which includes the logger, the batteries, the wiring and the casing,
was flight tested using several aircraft. The vehicle shown is a research
aircraft of the Institute of Flight System Mechanics of the Technische
Universität München.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
4224 The Journal of Experimental Biology 216 (22)
position of the vehicle is not known exactly but is estimated by
techniques such as code-based single point positioning, a technique
yielding robust, absolute position information limited to metre-level
accuracy. Therefore, the start position is biased from the true location
by Δ. The subsequent trajectory is now determined by time-differential
processing relative to this starting point. In other terms, the base vectors
pointing from the starting epoch to the current position are determined
exactly. Hence, all fixes are afflicted by the same bias Δ. Phase
measurements are sensible to signal shadowing – a short upside-down
interlude can cause signal obstruction and prevent further processing.
A new base at tb2 can be imported from the single point solution right
after the manoeuvre (no re-initialization) and processing can be
continued relative to the new base. Such an event causes a gap in the
resulting trajectory. In the case shown in Fig.2, the solution fails again
between the base epoch tb2 and the current time tj. However, this time
there are enough healthy satellites observed at tj–1 and tjto calculate
the baseline between these two points. A base hand-over preventing
a gap in the solution can be realized and processing is hereupon
continued to tb3. A detailed description is given elsewhere (Traugott
et al., 2008a; Traugott et al., 2008b).
The new mathematical method yields a position precision in the
low decimetre region (Traugott et al., 2008a) so that an improvement
in precision by a factor of 10 when compared with the state of the
art is achieved. This holds for position precision in the longitudinal
and lateral directions as well as in the vertical direction. In addition
to this precision improvement, the position data are recorded at a
sampling rate of 10Hz, which is also significantly higher than the
state of the art as regards comparable miniaturized devices.
Wind determination
Wind information was obtained using SeaWinds on QuikSCAT
Level 3 Daily, Gridded Ocean Wind Vectors (JPL SeaWinds
Project; winds.jpl.nasa.gov). The data are sampled on an
~0.25°×0.25° global grid twice a day (equal to 28km in north–south
direction and 18km in east–west direction at 49° south). The data
provide local wind velocity vectors at a reference altitude of 10m
with an accuracy of 2ms–1 (or 10% for velocities above 20ms–1)
and the wind direction within ±20°. Additional information is
provided elsewhere (Perry, 2001).
For calculating the wind at the respective trajectory point, an in-
house computational procedure was developed using one-
dimensional linear interpolation in the time domain and bivariate
Akima interpolation in the position domain (Müller, 2009).
Field work
The field work took place during a research stay of 3months close
to the Albatross colony at Cap Ratmanoff, Kerguelen Archipelago,
southern Indian Ocean, on wandering albatrosses (Diomedea exulans
Linnaeus 1758).
The miniaturized GPS logging units were taped to the back
feathers of the birds using TESA tape according to the procedure
suggested by Wilson et al. (Wilson et al., 1997). The mass of the
miniaturized GPS logging units, which was 107g in the heaviest
version, represented about 1.0–1.3% of the mass of the birds, thus
being less than 3% of the birds’ mass as recommended by Phillips
et al. (Phillips et al., 2003). The GPS units were recovered at the
end of a foraging trip. Twenty GPS units were deployed, of which
16 provided high-quality flight data of the bird’s trajectories. Two
GPS units were damaged by saltwater, two others provided data
from sitting birds that delayed their departure.
RESULTS AND DISCUSSION
Large-scale and small-scale movements
Reference is first made to the large-scale movement in terms of a
foraging trip of an albatross to show a complete data recording of
high-precision tracking at 10Hz. In Fig.3, the ground track of the
flight that begins and ends at the Kerguelen Archipelago is presented.
The overall duration of the trip was 3.2days and its length was
1120km.
A closer examination of the large-scale movement reveals that
there are individual cycles constituting the bird’s small-scale
movements which are continually repeated. While the large-scale
movement appears as a steady-state cruise-type motion horizontal
to the Earth’s surface (Fig.3), the small-scale movements are of a
pronounced three-dimensional and highly dynamic nature, yielding
repetitive cycles (Fig.4). They show distinct motions in the
longitudinal, lateral and vertical directions. There are four flight
phases, which are the characteristic elements of each cycle, denoted
by numbers 1–4 at the first cycle: (1) windward climb; (2) upper
curve from windward to leeward flight direction; (3) leeward
descent; and (4) lower curve from leeward to windward flight
direction. A flight cycle is the basic constituent of dynamic soaring.
Characteristics of dynamic soaring
Altitude, speed and total energy
A more detailed examination of dynamic soaring cycles yields the
behaviour and magnitude of quantities relevant for this flight mode.
With knowledge of these features, further characterization of
dynamic soaring is possible. For this purpose, two cases were
selected from the experimental data obtained in the in-flight
measurements. These cases refer to the altitude interval that the bird
traverses during dynamic soaring cycles, yielding cycles with a large
or a small altitude interval (Figs5 and 6, where Fig.5 is the case
already shown in Fig.4). Selection of the altitude interval instead
of another quantity is based on its importance for energy gain.
This is because the greatest wind speed that the bird encounters in
a dynamic soaring cycle is determinative for the achievable energy
gain. The greatest wind speed is at the top of the altitude interval
because the wind speed increases with altitude (Stull, 2003), i.e.
with distance from the sea surface, where it is practically zero. With
the altitude intervals selected for Figs5 and 6, a wide range is
covered, yielding representative results for dynamic soaring in
albatrosses.
The altitude region extends from zero to about 15m in the larger
altitude interval case, and to less than 9m in the small altitude
interval one. Altitude and inertial speed (i.e. the speed related to
tj=tb3
tb1
tb2
Δ
Fig.2. Principle of time difference approach. tb1–3, time base; tj, current
time; Δ, bias.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
4225Dynamic soaring in albatrosses
the Earth as an inertial reference system) show a cyclic behaviour
such that they are continually repeated, with the speed lagging behind
the altitude. The speed range run through during a cycle is greater
in the larger altitude interval case, while the highest speed level,
which is close to 30ms–1, is the same in the two cases. The duration
of a cycle is of the order of 10s, with somewhat greater values in
the large altitude interval case and smaller values in the other.
Furthermore, the results of an energy analysis are presented in
Figs5 and 6, showing the total energy referenced to the weight:
where Eis the total energy, mis the mass of the bird, gis the
acceleration due to gravity, his the altitude and Vinert is the inertial
speed. The total energy made up of the sum of the potential and
kinetic energy shows also a cyclic behaviour. Its higher levels are
E
mg hV
g2,(1)
inert
2
=+
about E/(mg)=40m for all cycles in both altitude interval cases while
the lower levels differ.
There are characteristic properties concerning the energy gain in
terms of the energy extraction from the shear wind and its transfer
to the bird. The main point is the section of the dynamic soaring
cycle where the energy gain is achieved. This is graphically
illustrated in Figs5 and 6 (indicated by the grey shading). The total
energy begins to increase during the climb. At the top of the
trajectory, the energy increase, being in full progress, continues. It
comes to a stop in the course of the descent, after the altitude has
already decreased. At this point, the total energy of the bird is at
its maximum. There are large energy gains in all cycles, reaching
as high as 300% of the value at beginning of a cycle (Fig.5, first
and third cycle). The way in which the energy gain is achieved holds
for all cycles shown in Figs5 and 6. Thus, it applies to the large
altitude interval case as well as to the small interval case.
The energy diagrams in Figs5 and 6 also show the kinetic and
the potential energy. A comparison of the individual energy curves
reveals that the increase in the total energy during the energy gain
phase consists primarily of an increase in the kinetic energy, whereas
the potential energy increase is significantly smaller. Thus, the total
energy gain from the shear wind is mainly a kinetic energy gain.
This means that, with regard to the motion of the bird, there is an
increase in favour of speed when compared with altitude.
Upper curve: trajectory section of energy gain
For verification of dynamic soaring, the trajectory section in which
the energy gain is achieved is determinative. This is made
recognisable in Figs7 and 8, with colour coding used to show the
relationship between total energy and trajectory. The central issue
is the trajectory section associated with the energy gain. The energy
gain is achieved in the curve where the flight direction changes from
windward to leeward, as indicated by the colour change from blue
to red. Reference to Figs5 and 6 reveals that this flight direction
change occurs in the upper altitude region of each cycle, around the
top of the trajectory. Thus, the curve in question where the change
of flight direction from windward to leeward takes place is in the
upper altitude region, yielding the upper curve of the dynamic
Fig.3. Foraging trip of a wandering albatross:
large-scale movement. The flight path of a
long-distance foraging trip of a wandering
albatross is shown (flight tracking duration:
3.2days, data sampling rate: 10Hz throughout
the whole flight). The foraging trip begins (t=0)
and ends (t=3.2days) at the Kerguelen
Archipelago. Its length is 1120km. The flight
path shows the movement of the bird on a
large-scale basis, which is of a cruise-type
steady-state nature. On this basis, the small-
scale movements that comprise the large-scale
movement are not visible. The small-scale
movements, which are of a highly dynamic
nature, are made up of dynamic soaring
cycles. Map data: Google, SIO, NOAA, US
Navy, NGA, GEBCO.
2
34
Wind
Altitude (m)
x (m)
y (m)
–500
–400
–300
–200
–100
400
300
200
100
1
10
0
0
0
Fig.4. Dynamic soaring cycles. A perspective view on dynamic soaring
cycles is presented. The small-scale movements, which show distinct
motions in the longitudinal, lateral and vertical directions, are made up of
dynamic soaring cycles. As shown for the first cycle (indicated by nos.
1–4), a dynamic soaring cycle consists of (1) a windward climb, (2) a curve
from windward to leeward at the upper altitude, (3) a leeward descent and
(4) a curve from leeward to windward at low altitude close to the sea
surface. This holds for all dynamic soaring cycles.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
4226 The Journal of Experimental Biology 216 (22)
soaring cycle. The trajectory position at which the maximum total
energy is reached is at the end of the upper curve. This holds for
all cycles, in the large as well as in the small altitude interval cases.
As a result, the upper curve can be qualified as the characteristic
flight phase of dynamic soaring for achieving an energy gain.
The lower curve is the trajectory section where a total energy
loss occurs (with red to blue change, Figs7 and 8). This also holds
for all cycles, in both the large as well as small altitude interval
cases. As the wind speed is low here (Stull, 2003), the energy loss
is not as large as it would be at a higher altitude. This is the reason
why the curve where the flight direction changes from leeward to
windward is in the lower altitude region, close to the sea surface.
Dynamic soaring cycles on a large-scale representation
In Figs4–8, the decisive motion quantities and the energy balance
essential for dynamic soaring as well as their relationship to the
flight trajectory are presented so that the physical mechanism of
the energy gain from the wind can be shown and identified as a
unique characteristic of this flight mode. Supplementary to the
small-scale movement representation, trajectory sections of greater
length are depicted in Fig.9 to illustrate how dynamic soaring
manifests on a larger scale. Three wind cases are selected because
of the essential significance of the wind for dynamic soaring, i.e.
downwind flights at low and at high wind speed as well as upwind
flight. Basically, all three trajectory sections show the typical
pattern of dynamic soaring, which consists entirely of winding
and curving segments.
The downwind flight cases at low and high wind speed are
similar with regard to the extension of the curved segments in
the longitudinal and lateral directions. Furthermore, the overall
flight directions in both cases appear as a straight movement on
a large-scale basis. Compared with this, the upwind case shows
significant differences. Here, the extension of the curved segments
in the longitudinal and lateral directions is much more
pronounced. The overall flight direction is not so straight,
being more of a meandering type. The individual segments are
rather irregular, particularly in comparison with the downwind
cases.
h (m)
Vinert
(m s–1)
Energy gain section
0102030
Time (s)
50
10
20
30
40
30
20
10
0
0
10
20
0
15
5
E/(mg) (m)
Potential
energy
Kinetic
energy
50
10
20
30
40
30
20
10
0
0
10
20
0
15
5
Energy gain section
Potential
energy
Kinetic
energy
Time (s)
10 20 300
h (m)
Vinert
(m s–1)E/(mg) (m)
Fig.5. Altitude, inertial speed and energy of dynamic soaring cycles with a
large altitude interval. (These cycles are the dynamic soaring cycles
presented in Fig.4.) The altitude hshows a cyclic behaviour (between
minimum at sea surface and maximum at the top of the trajectory). The
inertial speed Vinert, which is also cyclic, has a time lag relative to the altitude
with regard to its oscillatory behaviour. But it is increased already during the
climb, despite the altitude increase. This indicates that there is a
simultaneous increase of potential and kinetic energy to yield an increase of
the total energy. The total energy, E/(mg)=h+Vinert2/(2g), begins to increase
during the climb and reaches its maximum after the top of the trajectory has
been passed. Thus, the energy gain is achieved around the top of the
trajectory. The total energy curve is smooth and continuous. Hence, the
extraction of energy from the shear wind is also smooth and continuous.
There are no discontinuities or energy pulses. Furthermore, the kinetic
energy and the potential energy are also shown in the total energy diagram.
Fig.6. Altitude, inertial speed and total energy of dynamic soaring cycles
with a small altitude interval. The altitude intervals in this case are
significantly smaller than those in Fig. 5. The upper speed level is of
comparable magnitude, whereas the speed intervals between the
maximum and minimum values are considerably smaller. Corresponding
with the smaller altitude interval, the duration of a dynamic soaring cycle is
shorter. An important result concerns the total energy behaviour when
comparing the small and large altitude interval cases. It turns out that the
level of the total energy is of equal magnitude in the two cases. The range
between the maximum and minimum values differs. In the small altitude
interval case, the potential energy level is reduced.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
4227Dynamic soaring in albatrosses
Comparison with current theories and explanations for
dynamic soaring
Theory of wind-gradient soaring
The theory of wind-gradient soaring is based on the wind gradient
in the shear layer above the sea surface (Lighthill, 1975; Norberg,
1990; Spedding, 1992; Tickell, 2000; Dhawan, 2002; Lindhe
Norberg, 2004; Azuma, 2006; Denny, 2009). According to this
theory, energy can be obtained by climbing against the wind because
the wind speed increases as a result of the wind gradient.
Analogously, an energy gain is considered to be possible when
descending in a leeward direction. For a climb without loss in
airspeed, the minimally required wind gradient is given by the
following expression (e.g. Pennycuick, 2002):
yielding, for an airspeed of V=15ms–1:
In Figs5 and 6, it is shown that the increase of the total energy
takes place in the upper altitude region. In that region, the wind
Vh gV(d / d ) / , (2A)
W required =
Vh(d / d ) 0.7 s . (2B)
W required –1
=
speed shows only minor changes with altitude so that the wind
gradient is very small. This was confirmed by an analysis of the
wind speed and the wind gradient using wind measurement data
(Perry, 2001; Müller, 2009) and a logarithmic wind model (Stull,
2003). The analysis yields an average effective wind gradient of:
for the altitude region in mind. A comparison of (dVW/dh)av=0.1s–1
with (dVW/dh)required=0.7s–1 shows that the existing wind gradient
is far too small when compared with the required value. This means
with regard to the theory of wind-gradient soaring that the wind
gradient itself is insignificant for the energy gain. Rather, the energy
gain is due to the change in the flight direction from windward to
leeward in the upper curve.
Theory of gust soaring
The theory of gust soaring is concerned with discontinuities in the
wind flow (Pennycuick, 2002; Pennycuick, 2008; Suryan et al.,
2008; Langelaan, 2008; Langelaan and Bramesfeld, 2008).
According to this theory, there is an alternative flight mode by which
Vh(d / d ) 0.1 s , (3)
Wav –1
=
40 m20
North (m)
Wind speed:
11.2 m s–1
Wind
direction
East (m)
Flight
direction
–100 –50 0 50 100
E/(mg)
600
500
400
300
200
100
0
North (m)
40 m25 3530
Wind speed:
8.6 m s–1
Wind
direction
Flight
direction
East (m)
0 200 600400
0
–80
–60
–40
–20
20
–100
E/(mg)
Fig.7. Relationship between total energy and flight trajectory of dynamic
soaring cycles with a large altitude interval (dynamic soaring cycles
presented in Fig.5). The total energy, E/(mg)=h+Vinert2/(2g), is indicated
along the trajectory using colour coding. Quantification is possible with
reference to the bar (at the top), which establishes a relationship between
colour and total energy where the change from blue through green and
yellow to red indicates the total energy increase from the lowest to the
highest level. The colour changes from blue to red and, thus, the total
energy increases in all curves where the flight direction is changed from
windward to leeward. The total energy in each cycle is at its maximum after
the upper curves have been completed. Thereafter, the colour changes
from red to blue and, thus, the total energy decreases in all curves where
the flight direction is changed from leeward to windward. These curves are
at low altitude. The direction and the speed of the wind are also indicated
in Fig.7. The wind speed holds for 10m altitude. The method for
determining wind direction and speed is given in Materials and methods
(‘Wind determination’).
Fig.8. Relationship between total energy and flight trajectory of dynamic
soaring cycles with a small altitude interval (dynamic soaring cycles
presented in Fig.6). The relationship between total energy, dynamic
soaring trajectory and wind direction is basically the same as in the large
altitude case presented in Fig.7. This particularly holds for the upper curve
where the energy gain is achieved. In each cycle, the total energy is at its
maximum after completion of the upper curves. Furthermore, the total
energy decreases in all lower curves, where the flight direction is changed
from leeward to windward. The direction and speed of the wind are also
indicated in Fig.8 (again for 10m altitude).
THE JOURNAL OF EXPERIMENTAL BIOLOGY
4228 The Journal of Experimental Biology 216 (22)
pulses of energy are obtained from a flight through the separated
air flow region behind wave crests. It implies that this happens at
low level.
Investigation of the energy behaviour (Figs5 and 6) shows that
all total energy curves are continuous and smooth. This means with
regard to the theory of gust soaring that there are no discontinuities
and no energy pulses, but there is a continuous extraction of energy
from the shear wind to the bird. Furthermore, the energy gain is not
attained at low level. Rather, it is achieved in the upper altitude
region, around the top of the trajectory.
This conclusion is further confirmed by data from the flight of an
albatross over flat land. In Fig.10, the trajectory obtained from in-
flight measurement of an albatross flying over land is presented. The
flight over land consists completely of dynamic soaring cycles, without
any straight trajectory portion in between. All cycles show the
characteristic pattern of dynamic soaring. The elevation of the terrain
in the area of the dynamic soaring trajectory over land is presented
in Fig.11, revealing how flat this area is. Because of the flatness of
the land, separated air flow is not possible. As a result, there cannot
be an effect such as energy pulses obtained from flight through a
separated air flow region. Rather, the energy gain is achieved in a
continuous and smooth manner in the upper curve of dynamic soaring.
Wave soaring and wave lift
Wave soaring and wave lift are considered to be a possible source
of energy gain (Berger and Göhde, 1965; Wilson, 1975; Pennycuick,
1982; Sheng et al., 2005; Richardson, 2011). By flying along the
flanks of waves, the birds can make use of rising air currents directly
related to the waves. This would imply flight at low altitude, close
to the waves.
The dynamic soaring cycles over flat land, as shown in Figs10
and 11, provide evidence for another energy transfer mechanism.
As the ground is flat there are no geometric forms similar to waves.
Thus, no rising air currents exist that may be used for achieving an
energy gain. Instead, there is only horizontal wind. This means that
the energy is extracted from horizontally moving air rather than
from rising air currents.
Furthermore, wave soaring and wave lift would show flight
segments close to the water surface where altitude and speed are
constant or slowly changing. However, this is not the case, as may
be seen in Figs4–7. Rather, the energy gain is achieved in the upper
altitude region where the effect of waves on air currents can be
assumed to be negligible, if not zero. As a result, this effect plays
no role in energy gain.
Aerodynamic ground effect
The aerodynamic ground effect yields a decrease of the drag when
a bird is close to the water surface (Blake, 1983; Hainsworth, 1988;
Norberg, 1990; Rayner, 1991). It rapidly reduces with the distance
from the ground. The aerodynamic ground effect has an influence
only during flight at low level. It yields a decrease of the induced
drag factor by about 10% at a distance of a wing semispan from the
ground, with less of a decrease for larger distances (Rayner, 1991).
Flight involving a high bank angle, as is the case in the lower curve
of dynamic soaring of albatrosses, suggests that the effectiveness of
the aerodynamic ground effect would be reduced.
A main point in this context is that the aerodynamic ground effect
cannot increase the total energy because it merely reduces the
aerodynamic drag so that there is still a dissipative effect of the
drag. As a result, the aerodynamic ground effect plays no role in
the energy gain.
Energy gain mechanism in dynamic soaring: propulsive force
due to the wind
A deeper insight into the physical mechanism underlying the energy
gain in dynamic soaring is possible with an analysis of the force
effecting this gain. There is a propulsive force that acts at the bird
and yields an increase of the total energy. The generation of this
force is shown in Fig.12.
Fig.12A shows the lift vector, as seen from behind in direction
of the airspeed vector. The lift vector Lcan be decomposed into
two components: LV1and LV2. The component LV1is in the plane
of the speed vectors, while the component LV2is perpendicular to
that plane. This means that LV1is doing work and, thus, exerts an
effect on the total energy. By contrast, LV2is doing no work so it
has no effect on the total energy.
Fig.12B shows the lift and drag vectors, as seen from above on
the plane of the speed vectors. Thus, the force LV1and the drag vector
East (km)
Flight direction
0–2.0 –1.0
–3.0
0
1.0
–1.0
Flight direction
01.0
01.0 2.0 3.0
0
1.0
2.0
North (km)
0
1.0
Wind speed:
7.8 m s–1
Flight direction
A
B
C
2.0
Wind speed:
16.9 m s–1
Wind speed:
9.2 m s–1
Fig.9. In-flight measurements of large-scale movements. Large-scale
movements are presented for three wind cases. In each case, the large-
scale movement consists completely of dynamic soaring cycles which are
continually repeated. The curving segments are connected to each other
without any straight part in between. (A)Downwind flight at low wind speed;
(B) downwind flight at high wind speed; and (C) upwind flight.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
4229Dynamic soaring in albatrosses
Dcan be made visible. It is shown that LV1has a component LV1sinαW
acting in the direction of the inertial speed vector Vinert which
determines the motion of the bird with respect to the Earth (used as
an inertial reference system). This means that the component LV1sinαW
exerts a propulsive effect on the bird, being equivalent to a thrust
propelling the bird. Therefore, it may be named propulsive force:
As Fpropulsive is doing work, it has an effect on the total energy
state of the bird. To show this, reference is made to the relationship
between the total energy Eand the work done by the forces acting
at the bird along the flight path. These forces are the components
FLsin . (4)
Vpropulsive 1 W
=α
of the lift and the drag vectors parallel to the inertial speed vector:
Fpropulsive=LV1sinαWand DcosαW(Fig.12B). The relationship
between the total energy Eand the work done by the described forces
can be formulated as (with tand τdenoting time quantities):
Differentiation with regard to the time results in the following
relation:
Solving for Fpropulsive yields:
From an analysis of Fpropulsive using data from the albatrosses’
in-flight measurements, the results presented in Fig.13 are obtained.
These results basically show: (1) Fpropulsive is the force that generates
the total energy gain; this takes place in the upper curve; and (2)
the effect of Fpropulsive is very strong.
Positive Fpropulsive values mean that energy is extracted from the
shear wind and transferred to the bird, yielding a total energy gain,
while negative Fpropulsive values cause an energy loss. The range of
positive Fpropulsive values is associated with the upper curve, as
indicated in Fig.13 by the grey shading. The fact that Fpropulsive
reaches its greatest level around the middle of the upper curve means
that it is most effective in the higher altitude region of the dynamic
soaring cycle. This again verifies that the upper curve is the
characteristic flight phase of dynamic soaring for achieving an
energy gain.
As the lift vector is proportional to the airspeed squared, yielding:
the following relation holds for the propulsive force:
This relation shows that a large value of Vand a wide angle αW
between Vinert and Vincrease the propulsive effect of Fpropulsive. The
speed vector relationship presented in Fig.12B shows that the angle
αWis wide when VWis large and highly inclined with regard to
Vinert. Large values of αWand Vinert also contribute to large Vvalues.
This is evidence for the significance of the upper curve for dynamic
soaring because here the wind speed takes on the largest values
during the entire cycle and the angle αWis wide.
The total energy management in the dynamic soaring cycle is
dominated by Fpropulsive. This is confirmed by a comparison with
the contribution of the drag, which is the only other force doing
Et Et F D V( ) ( ) ( cos ) d . (5)
t
t
0 propulsive W inert
0
=−α τ
EF D V( cos ) . (6)
propulsive W inert
=−α
FE
VDcos . (7)
propulsive
inert
W
=+α
LC VS(/2) , (8)
L2
=ρ
FV~sin . (9)
propulsive 2W
α
x (m) y (m)
Flight
over sea
Start
h (m)
0
200
400
600 –100
0
100
20
0
Fig.10. View of dynamic soaring cycles over land. The
coordinate system is referenced to the starting point of the
dynamic soaring trajectory (denoted by x=0, y=0). The solid
line represents the flight path over land, and the dashed arrow
indicates the beginning of the flight over the sea. The bird
performs a number of consecutive dynamic soaring cycles
over land before it reaches the sea. The extension of the
dynamic soaring cycles in the vertical as well as the
longitudinal and lateral directions is of the same magnitude as
the cycles recorded in in-flight measurements over the sea
(as, for example, shown in Fig.4).
Land
Dynamic soaring
trajectory
Start
Sea
0765432 111091 12
Height above sea level (m)
8
Fig.11. Terrain elevation in an area where dynamic soaring cycles over
land were performed, obtained using the SRTM digital elevation model
(Jarvis et al., 2008). The SRTM model provides a grid consisting of
rectangular elements of about 90×90m size for the Kerguelen area.
Coloured bars below the terrain image indicate the altitude above sea level.
The ground track of the dynamic soaring cycles shown in Fig.10 is also
presented. The area is in the land sector of the Kerguelen Archipelago
depicted in Fig.3 where the albatross foraging trip began and ended.
Referencing the dynamic soaring trajectory to the terrain elevation shows
that the flight was performed over flat land. According to the grid element
colouring along the dynamic soaring trajectory, there are no hills or
geometric forms similar to waves. Thus, there cannot be such effects as a
separated air flow region behind wave crests or rising air currents related
to waves.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
4230 The Journal of Experimental Biology 216 (22)
work and influencing the total energy. The analysis of the force
relationship using data from the albatrosses’ in-flight measurements
is also concerned with the drag, yielding an estimation of its
component DcosαW, which is the drag component effective in doing
work (Fig.12B). In Fig.13, the component DcosαWis also shown
(the negative of DcosαWis selected because of its dissipative effect
concerning the energy). Comparison with Fpropulsive reveals that
DcosαWis substantially smaller. This particularly holds for the upper
curve, where DcosαWis practically negligible. Thus, the total energy
behaviour is influenced by the drag to a very small extent only, but
dominated by Fpropulsive.
A comparison with the force characteristics in the lower curve
further deepens the insight into the energy management during
dynamic soaring. In Fig.14, the lift vector in the lower curve is
presented, as seen from above on the plane of the speed vectors. The
lift component LV1sinαWis now acting in the opposite direction to
the inertial speed vector Vinert. Thus, it yields a decrease of the total
energy. However, there is an effect that reduces the size of LV1sinαW.
This is basically due to the wind speed being small at the altitude of
the lower curve. As a result, the angle αWis also small, yielding a
reduction of LV1sinαW. In Fig.14, it is assumed for comparison
purposes that the same size applies for LV1and for the wind direction
as in Fig.12B, while the wind speed VWis smaller because of the
lower altitude. Comparison of Fig.12B and Fig.14 reveals that
LV1sinαWdiffers considerably in the two cases, showing a significantly
smaller value in the lower curve. This is an indication that the energy
loss in the lower curve is smaller than the energy gain in the upper
V
Vinert
αW
VW
DcosαW
Plane of
speed vectors
LV1
L
D
LV2
LV1
LV1sinαW
A
B
Fig.12. Force and speed vector diagram. (A)View of the bird seen from
behind in the direction of the airspeed vector
V
. The lift vector denoted by
L
is perpendicular to the wings of the bird. It can be decomposed into a
component
L
V1in the plane made up by the speed vectors
V
inert,
V
and
V
W
(appearing as a line), and into a component
L
V2perpendicular to that
plane. The plane made up by the speed vectors
V
inert,
V
and
V
Whas no
fixed relationship to the horizontal, but is continually changing according to
the motion of the bird in the course of the dynamic soaring flight
manoeuvre. (B)View on the plane of the speed vectors: the inertial speed
vector
V
inert, which describes the motion of the bird with respect to the
Earth used as an inertial reference system; the airspeed vector
V
, which
describes the motion with respect to the moving air in the shear wind; and
the wind speed vector
V
W. Furthermore, the lift vector component
L
V1, the
drag vector
D
and the angle αWare presented. The angle αWdescribes the
inclination of the airspeed vector
V
relative to the inertial speed vector
V
inert. There is an inclination (αW0) if the wind speed vector
V
Wis not
parallel to but instead inclined relative to the inertial speed vector
V
inert. The
angle αWcan be determined using the relationship between the speed
vectors
V
inert and
V
W, which are known from the GPS logger in-flight
measurements and the QuikSCAT wind data (as described in Materials
and methods, ‘Wind determination’). The lift vector component
L
V1is, by
definition, orthogonal to the airspeed vector
V
. Because of the inclination
of
V
relative to
V
inert by the angle αW,
L
V1has a component
L
V1sinαW
parallel to the inertial speed vector
V
inert. This component is effective in
terms of a propulsive force Fpropulsive=LV1sinαW. As a result, the work done
by Fpropulsive=LV1sinαWyields an increase in the total energy. The drag
vector
D
exerts a dissipative effect concerning the energy, producing a
negative work due to its component DcosαWacting in the negative direction
of
V
inert. The component
L
V1sinαWand, thus, its propulsive effect, is large
when there is a wide angle αWbetween
V
inert and
V
. The angle αWis wide
when
V
Wis large and highly inclined with regard to
V
inert, as in B. In the
upper curve, the wind speed
V
Wtakes on the largest values during the
entire cycle and the angle αWis wide. This is evidence for the significance
of the upper curve for dynamic soaring as that phase where the energy
gain is achieved.
Upper curve
0
Time (s)
8.06.04.02.0
–0.5
0
0.5
1.0
–1.0
1.5 Fpropulsive
mg
DcosαW
mg
Fig.13. Time histories of the forces doing work, Fpropulsive and DcosαW. The
propulsive force Fpropulsive shows positive and negative values. Where
Fpropulsive is positive, the total energy of the bird is increased, yielding an
energy gain. This part is associated with the upper curve, as indicated on
the diagram using grey shading. Here, Fpropulsive reaches its highest level,
yielding a maximum as large as Fpropulsive,max1.2mg. In the negative
Fpropulsive part, there is a total energy loss. This occurs in the lower curve.
The drag component doing work, DcosαW, yields a dissipative effect
concerning the total energy (indicated by the minus sign). DcosαWis very
small when compared with Fpropulsive. As a result, the total energy behaviour
is dominated by Fpropulsive.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
4231Dynamic soaring in albatrosses
curve so that there is a net energy gain for the complete dynamic
soaring cycle with regard to the effect of Fpropulsive. The described
force difference is confirmed by the time history of Fpropulsive depicted
in Fig.13, where the level of the negative values is smaller than that
of the positive values.
Evidence of non-flapping in dynamic soaring
The results presented in Fig.13 provide evidence that there is no
wing flapping in dynamic soaring. Rather, the bird is in a gliding
condition where the wings are held motionless and in a fixed
position. Evidence for non-flapping is substantiated in the following.
As shown in Fig.13, the propulsive force Fpropulsive approaches
values as high as 120% of the weight so that it is larger than the
weight of the bird, yielding a maximum propulsive force:
A propulsive force this high cannot be generated by wing
flapping. This is because for large birds like wandering albatrosses
with a mass of about 10kg the maximum propulsive force possible
with wing flapping is smaller by an order of magnitude.
For estimating the maximum propulsive force possible with wing
flapping, reference is made to scaling considerations published
previously (Pennycuick, 2008). For this purpose, the following
scaling relationships are assumed to apply: (1) the available power
(Pavailable) generated by the flight muscles increases with mass
according to Pavailablem5/6; (2) the minimum power required for
airborne flight (Prequired) increases with mass according to
Prequiredm7/6; (3) the mass limit for birds capable of powered
horizontal flight is around 16kg. From these assumptions it follows
that for a bird of 10kg mass the estimated surplus of the available
power over the required power is given by:
Fmg1.2 . (10)
propulsive,max
PP1.2 . (11)
available required
The general thrust–power relationship in airborne flight yields for
the propulsive force due to wing flapping:
The flight condition at the minimum power required can be
described by (Brüning et al., 2006):
where VPrequired is the speed at the minimum power required and V*
the speed at the minimum drag-to-lift ratio (CD/CL)min. Using the
relations described in Eqns11–13, the following result is obtained
for the maximum propulsive force due to wing flapping for a bird
of 10kg mass:
For albatrosses, data from various sources for the possible range of
minimum drag-to-lift ratios are available (Sachs, 2005), yielding a
range of:
Applying (CD/CL)min=0.045 as an average, the maximum propulsive
force possible with wing flapping is:
This is smaller by an order of magnitude when compared with the
maximum propulsive force in dynamic soaring Fpropulsive,max1.2mg.
As a result, the energy gain in dynamic soaring cannot be achieved
by wing flapping. Rather, there is another mechanism which is due
Fpropulsive, as described in the preceding section.
The existence of a propulsive force this high (Fpropulsive,max1.2mg
as opposed to Fflapping,max0.06mg) is evidence of the fact that
dynamic soaring is performed without flapping the wings. Instead,
the wings are kept in a fixed position, and hence in the position of
soaring.
LIST OF SYMBOLS AND ABBREVIATIONS
CDdrag coefficient
CLlift coefficient
Ddrag vector
Etotal energy
Fflapping propulsive force due to flapping
Fpropulsive propulsive force
gacceleration due to gravity
haltitude
Llift vector
LV1lift vector component in speed vector plane
LV2lift vector component perpendicular to speed vector plane
mmass
Pavailable available power
Prequired required power
Swing reference area
ttime
tbarbitrary time base (1–3)
tjcurrent time
Vairspeed
Fmg0.06 . (16)
flapping,max
C
C0.04 – 0.05 . (15)
D
Lmin
=
FC
Cmg1.4 . (14)
flapping,max
D
Lmin
FP
V. (12)
flapping =
PC
CmgV
VV
2
27
*
*
3
, (13)
P
required 4
D
Lmin
4
required
=
=
V
αW
VW
Vinert
LV1
LV1sinαW
Fig.14. A view on the plane of the speed vectors in the lower curve is
presented, showing the lift vector components
L
V1and
L
V1sinαWas well as
the speed vectors
V
inert,
V
and
V
W. (The drag vector Dand its component
D
cosαWare not shown to maintain pictorial clarity.) In the lower curve, the
lift component
L
V1effectuates a curvature of the trajectory in such a way
that the flight direction is changed from leeward to windward. This implies
that its component
L
V1sinαWacts in the opposite direction to the inertial
speed vector
V
inert. As the wind speed is small in the lower curve, the angle
αWis reduced. This yields a reduction of
L
V1sinαW.
THE JOURNAL OF EXPERIMENTAL BIOLOGY
4232 The Journal of Experimental Biology 216 (22)
V* speed at the minimum drag-to-lift ratio, (CD/CL)min
Vinert inertial speed
VPrequired speed at minimum power required
VWwind speed
xlongitudinal coordinate
ylateral coordinate
αWwind angle
Δbias
ρair density
τtime
ACKNOWLEDGEMENTS
The authors thank J. Mardon for his help in the preliminary trials of the study, and
Giacomo Dell’Omo, Wolfgang Heidrich, Franz Kümmeth and Alexei L. Vyssotski
for contributing to technical tools as well as for conducting performance tests and
optimizing the equipment.
AUTHOR CONTRIBUTIONS
Conception: G.S. Design: G.S., J.T. and F.B. Execution: J.T. and A.P.N.
Interpretation of the findings: G.S. and J.T. Drafting and revising the article: G.S.
and J.T.
COMPETING INTERESTS
No competing interests declared.
FUNDING
The authors are grateful to the Institut Polaire Français Paul Emile Victor, which
supported this work (IPEV, Program No. 354) – the work was performed
according to guidelines established by IPEV and CNRS for the Ethical Treatment
of Animals. The authors are also grateful for the support provided by National
Science Foundation International Research Fellowship for A.P.N. (no. 0700939).
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THE JOURNAL OF EXPERIMENTAL BIOLOGY
... The energy needed to perform such a long duration of flights is gained from the wind in the proximity of the surface. In regions above the sea surface or mountainous areas, the speed of the wind changes considerably with the altitude to yield what is known as "wind shear/gradient" [3,4]. By flying across the wind gradient region periodically, energy is harvested from the spatial wind speed distribution. ...
... Ideally, the dynamic soaring cycle is an energy-neutral (near-neutral) maneuver. It is important to emphasize that, the dynamic soaring phenomenon has been verified and validated experimentally [3,6]. The interest in the albatross flight secret goes back to Leonardo da Vinci and Lord Rayleigh [7] hundreds of years ago. ...
... communities of science and engineering [8,9,10,3]. From physical and engineering points of view, dynamic soaring is an extremely rare -if not entirely unique flight dynamic system. ...
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The albatross optimized flight maneuver -- known as dynamic soaring -- is nothing but a wonder of biology, physics, and engineering. By utilizing dynamic soaring, this fascinating bird can travel in the desired flight direction almost for free by harvesting energy from the wind. This phenomenon has been observed for centuries as evidenced by the writings of Leonardo da Vinci and Lord Rayleigh. Moreover, dynamic soaring biological inspiration has triggered a momentous interest among many communities of science and engineering, particularly aeronautical, control, and robotic engineering communities. That is, if dynamic soaring is mimicked, we will have arrived at a new class of unmanned aerial vehicles that are very energy-efficient during part (or the full) duration of their flight. Studying, modeling, and simulating dynamic soaring have been conducted in literature by mostly configuring dynamic soaring as an optimal control problem. Said configuration requires accurate dynamic system modeling of the albatross/mimicking-object, accurate wind profile models, and a defined mathematical formula of an objective function that aims at conserving energy and minimizing its dissipation; the solution then of such optimal control problem is the dynamic soaring trajectory taken -- or to be taken -- by the bird/mimicking-object. Furthermore, the decades-long optimal control configuration of the dynamic soaring problem resulted in non-real-time algorithms and control solutions, which may not be aligned well with the biological phenomenon itself; experimental observations of albatrosses indicate their ability to conduct dynamic soaring in real-time. Indeed, a functioning modeling and control framework for dynamic soaring that allows for a meaningful bio-mimicry of the albatross needs to be autonomous, real-time, stable, and capable of tolerating the absence of mathematical expressions of the wind profiles and the objective function -- hypothetically similar to what the bird does. The qualifications of such modeling and control framework are the very same characteristics of the so-called extremum seeking systems. In this paper, we show that extremum seeking systems existing in control literature for decades are a natural characterization of the dynamic soaring problem. We propose an extremum seeking modeling and control framework for the dynamic soaring problem hypothesizing that the introduced framework captures more features of the biological phenomenon itself and allows for possible bio-mimicking of it. We provide and discuss the problem setup, design, and stability of the introduced framework. Our results, supported by simulations and comparison with optimal control methods of the literature, provide a proof of concept that the dynamic soaring phenomenon can be a natural expression of extremum seeking. Hence, dynamic soaring has the potential to be performed autonomously and in real-time with stability guarantees.
... Because aerodynamic kinetic energy can be obtained through dynamic soaring in powered as well as unpowered flight, pelagic birds that engage in dynamic soaring when the wind is strong will often flap their wings when the wind is weak [19,[102][103][104]. Nevertheless, the great majority of research on avian dynamic soaring has focused on albatrosses [77,78,[105][106][107][108][109][110], which are capable of flying immense distances without flapping, and whose flight morphology is highly specialized for this function [111]. Moreover, because it is challenging to demonstrate empirically which sources of atmospheric energy are being employed in situations where a bird uses flap-gliding flight, or where gradients and updrafts occur together (as they do whenever waves are present), the use of gradient soaring has only been confirmed in albatrosses and (more recently) shearwaters [19]. ...
... Hence, because the wind is expected to be slower closer to a surface, the general principle of flying windward in a wind of increasing speed and leeward in a wind of decreasing speed can be restated more specifically for gradient soaring as climbing windward and descending leeward [100]. An alternating windward rise and leeward fall is therefore diagnostic of gradient soaring [18,108,110,113,114], usually involving an undulating flight path whose sinuosity is expected to vary according to how the overall travel direction relates to the overall wind direction [106,107,109]. This phasing of the horizontal and vertical components of flight can be used to identify dynamic soaring even in cases where the details of the wind field may be unknown [19]. ...
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The use of flying robots (drones) is increasing rapidly, but their utility is limited by high power demand, low specific energy storage and poor gust tolerance. By contrast, birds demonstrate long endurance, harvesting atmospheric energy in environments ranging from cluttered cityscapes to open landscapes, coasts and oceans. Here, we identify new opportunities for flying robots, drawing upon the soaring flight of birds. We evaluate mechanical energy transfer in soaring from first principles and review soaring strategies encompassing the use of updrafts (thermal or orographic) and wind gradients (spatial or temporal). We examine the extent to which state-of-the-art flying robots currently use each strategy and identify several untapped opportunities including slope soaring over built environments, thermal soaring over oceans and opportunistic gust soaring. In principle, the energetic benefits of soaring are accessible to flying robots of all kinds, given atmospherically aware sensor systems, guidance strategies and gust tolerance. Hence, while there is clear scope for specialist robots that soar like albatrosses, or which use persistent thermals like vultures, the greatest untapped potential may lie in non-specialist vehicles that make flexible use of atmospheric energy through path planning and flight control, as demonstrated by generalist flyers such as gulls, kites and crows.
... The energy gain attributes to the vertical gradient of the shear wind and the lift component doing positive work during the dynamic soaring cycle [1]. It has been shown that flying at low or zero mechanical energy cost is made possible through performing dynamic soaring [2]. ...
... ©IJRASET: All Rights are Reserved | SJ Impact Factor 7.538 | ISRA Journal Impact Factor 7.894 | The albatross replenishes the energy from the shear wind field and thus the cycle is almost endless and this enables the albatross to soar for miles and for weeks. One important point to note is that the energy gain for dynamic soaring is smooth and continuous and the energy extraction does not depend on wave soaring or wave lift [12]. ...
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The optimal aerodynamic traits of the natural flyers have always been a foundation for the designing of bionic drones. In this paper, the aerodynamic soaring capabilities of the albatross and eagle are discussed in detail along with the eagle's control surface aerodynamics. The bell shaped lift distribution characteristics exhibited by the albatross are also discussed along with its subsequent sub traits such as proverse yaw, wing-tip vortices and so on. The main soaring dynamics discussed are the dynamic soaring exhibited by the albatross and the utilization of thermal updrafts for thermal soaring by the eagle. Apart from these, the different control surfaces and their actuations along with wing morphing techniques are also highlighted. A proper and near perfect manifestation of the traits of natural flyers could be a harbinger to near perpetual modern aircrafts. Aerodynamics and propulsion system are the areas of research that are of concern in this manuscript.
... Trajectory of the CA ESC system represented by Equation (2.1).37 3. Simulink Diagram for Control-affine ESC-like controller. In this sec-38 tion, we present the structure of the ESC-like system used as a real-time autonomous39 controller for dynamic soaring. The model of dynamic soaring takes two control in-40 puts C L and φ. ...
Preprint
For centuries, soaring birds -- such as albatrosses and eagles -- have been mysterious and intriguing for biologists, physicists, aeronautical/control engineers, and applied mathematicians. These fascinating biological organisms have the ability to fly for long-duration while spending little to no energy, as they utilize wind for gaining lift. This flight technique/maneuver is called Dynamic Soaring (DS). For biologists and physicists, the DS phenomenon is nothing but a wonder of a very elegant ability of the bird's interaction with nature and using its physical ether in an optimal way for better survival and energy efficiency. For the engineering community, said DS phenomenon, is a source of inspiration and an unequivocal promising chance for bio-mimicking. In literature, significant work has been done on modeling and designing control systems that allow the DS maneuver to take place. However, the DS phenomenon in literature has been configured as an optimal control problem that utilized developments in numerical optimization algorithms along with control systems methods to identify/find the optimal DS trajectory taken -- or to be taken -- by the bird, or the mimicking UAV. Nevertheless, all said methods are non-real-time. In this paper, we provide a novel differential geometric control formulation and analysis of the DS problem, which allow us to introduce a control system structure similar to extremum seeking systems. The introduced control system is proved to be controllable and able to conduct real-time DS, which hypothesizes that our framework captures more of the biological behavior of soaring birds. It also allows for practical mimicking of them. Simulation results are provided along with comparisons with powerful optimal control solvers to demonstrate the effectiveness of the introduced approach.
... Previous studies have identified the vertical motions that are generated by surface-based thermals [5][6][7][8][9][10][11] as the most favored by birds for climbing and soaring over land. Dynamic soaring (responding to the vertical shear of the horizontal wind [12][13][14][15][16]) is another atmospheric feature that is used by the albatross to maintain prolonged flight over the ocean. Orographic uplift or slope (soaring at a low altitude over complex terrain) has also been evaluated [8,10,17,18]. ...
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One-second-processed three-dimensional position observations transmitted from an instrumented golden eagle were used to determine the detailed long-range flight behavior of the bird. Once elevated from the surface, the eagle systematically used atmospheric gravity waves, first to gain altitude, and then, in multiple sequential glides, to cover over 100 km with a minimum expenditure of its metabolic energy.
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Effects of deployment of miniaturized transmitters and loggers have been well studied in penguins, but much less so in flying seabirds. We examined the effects of satellite tag (platform terminal transmitter, PTT) deployment in Black-browed (Thalassarche melanophris) and Gray-headed (T. chrysostoma) albatrosses at South Georgia and reviewed the recent literature for other albatrosses and petrels. In our study, although a few individuals may have slightly extended their foraging trips, overall there was no significant difference in trip duration, meal mass, breeding success, or rate of return in the next season between birds with PTTs and controls. By comparison, most other studies of albatrosses and petrels recorded extended trip durations and, in some cases, high rates of nest desertion following PTT attachment. That occurred particularly where transmitter loads exceeded 3% of adult mass. Extended trip durations may result from reduced flight efficiency, as well as the effect of capture and temporary restraint, but affected birds seem nonetheless to commute to representative foraging areas. To minimize device effects, we suggest that transmitter loads be reduced to a minimum, use of harnesses be avoided (particularly for breeding season deployments when tape attachment to feathers is an effective alternative), and careful attention be given to limiting handling times during incubation when some species are particularly sensitive to disturbance.
Chapter
A lecture or a course of lectures on ‘Aircraft’ would put approximately equal emphasis on aerodynamic, structural and power-plant aspects; whereas lectures on ‘Aerodynamics of Aircraft’ would concentrate principally on aerodynamic matters while referring to just the basic elements of what limitations are imposed by structural and power-plant considerations. Similarly this lecture on the ‘Aerodynamic Aspects of Animal Flight’ will concentrate on the aerodynamic forces, and the resulting dynamic interactions, between the movements of a flying animal relative to the air and the associated air movements; and include only brief references to fundamental limitations imposed by the strength and stiffness of the skeleton of the animal and other structural considerations, or by the power-plant capabilities of the animal’s musculature and metabolism. Equally it will give only a highly condensed account (see section on Evolution) of the biologically fundamental questions of how systems for animal flight evolved in response to environmental demands and opportunities.
Chapter
To quantitatively describe and forecast the state of the boundary layer, we turn to the equations of fluid mechanics that describe the dynamics and thermodynamics of the gases in our atmosphere. Motions in the boundary layer are slow enough compared to the speed of light that the Galilean/Newtonian paradigm of classical physics applies. These equations, collectively known as the equations of motion, contain time and space derivatives that require initial and boundary conditions for their solution.
Chapter
At first glance, the large number of equations developed in Chapters 3-5 would suggest that we have a fairly complete description of turbulent flow. Unfortunately, a closer examination reveals that there are a large number of unknowns remaining in those equations. These unknowns must be dealt with in order end up with a useful description of turbulence that can be applied to real situations. In this Chapter, the unknowns are identified, and methods to parameterize them are reviewed. Simulation techniques such as large-eddy simulation are discussed in Chapter 10.
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Albatrosses fly long distances over the Southern Ocean, even around the world, almost without flapping their wings: this has raised interest in how they perform such a feat. On a cruise to the South Atlantic I observed albatrosses soaring in a characteristic swooping zigzag flight that appears to combine two soaring techniques to gain energy wind-shear soaring (dynamic soaring) using the vertical gradient of wind velocity and wave-slope soaring using updrafts over waves. The observed characteristic swooping flight is shown in a new illustration and interpreted in terms of the two soaring techniques. The energy gain estimated for "typical conditions" in the Southern Ocean suggests that wind-shear soaring provides around 80-90% of the total energy required for sustained soaring. A much smaller percentage is provided by wind shear in light winds and significant swell when wave-slope soaring dominates. A simple dynamical model of wind-shear soaring is proposed based on the concept of a bird flying across a sharp wind-shear layer as first described by Lord Rayleigh in 1883 and later developed with Pennycuick's (2002) description of albatrosses "gust soaring." In gust soaring a bird exploits structures in the wind field, such as separated boundary layers and eddies in the lee of wave crests, to obtain energy by climbing headed upwind and descending headed downwind across a thin wind-shear layer. Benefits of the model are that it is simple to understand, it captures the essential dynamics of wind-shear soaring, and it provides reasonable estimates of the minimum wind shear required for travel velocity in different directions with respect to the wind. Travel velocities, given in a travel velocity polar diagram, can be combined with tacking to fly in an upwind direction faster than the wind speed located at the top of the wind-shear layer.
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SUMMARY Cine films of brown pelicans flying in formation were used to measure altitudes and wing tip spacing (WTS, distance perpendicular to the flight path between wing tips of adjacent birds at maximum span) for birds flying in ground effect, and vertical displacements and WTS for birds flying out of ground effect. Views were near coplanar with the plane of flight paths, and maximum wing span was used for scale. Induced drag savings in ground effect averaged 49% for gliding. Average WTS varied considerably with no evidence for systematic positioning near an optimum. There were also no differences in average WTS between flapping and gliding in or out of ground effect. Vertical displacements out of ground effect varied less than WTS but more than vertical displacements in ground effect. Few birds had wing beat frequencies similar to the bird ahead as would be needed to track vertical variation in trailing wing tip vortex positions. Imprecision in WTS may be due to unpredictable flow fields in ground effect, and difficulty in maintaining position under windy conditions out of ground effect.