Dynamic pressure maps for wings and tails of pigeons in slow, flapping flight, and their energetic implications
Concord Field Station, Harvard University, 100 Old Causeway Road, Bedford, MA 01730, USA
* Author for correspondence at present address: Structure and Motion Laboratory, The Royal Veterinary College, Hawkshead Lane, North Mymms, Hatfield AL9 7TA, UK (e-mail: jusherwood{at}rvc.ac.uk)
Accepted 26 October 2004
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Summary |
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Key words: aerodynamics, bird, pigeon, Columba livia, flight, power, lift, pressure, flapping
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Introduction |
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Power models considering vortex structures have been developed for animal
flight (Rayner, 1979a,
1993
;
Ellington, 1984
). Rayner
develops power models based on a view of vortex structures derived from wake
visualisations (e.g. Spedding et al.,
1984
; Spedding,
1986
,
1987
). However, more recent
wake visualisation experiments using Digital Particle Image Velocimetry (DPIV)
for bird flight under highly controlled wind-tunnel conditions (Spedding et
al.,
2003a
,b
)
suggest that quite complex wake vortex structures must be considered before
appropriate force balances -including the support of body weight - are
achieved. Thus, while methods based on assumed vortex structures have provided
one route for extending power calculations for flapping flight to slower
speeds, direct methods for calculating aerodynamic powers are most
appealing.
Blade-element techniques, found to be effective for propellers and
helicopters, have been extended to flapping flight for hovering
(Osborne, 1951;
Ellington, 1984
; Usherwood and
Ellington,
2002a
,b
)
and ascending (Wakeling and Ellington,
1997
; Askew et al.,
2001
) bird and insect flight. However, these techniques are
reliant on the knowledge of appropriate values of lift and drag coefficients
for each, or some form of average, spanwise wing section or `element'. These
coefficients can be determined, even for revolving wings (in which case they
can be quite different from steadily translating wings; Usherwood and
Ellington,
2002a
,b
),
given accurate information on wing shape and, critically, the speed and angle
of incidence of the local air. While these details may be found for birds
during fast flight within the confines of a wind tunnel
(Hedrick et al., 2002
), during
which locally induced air velocities are relatively low compared with flight
or wing velocities, these techniques become progressively less reliable for
flight at lower speeds. Induced velocities of the air near the wings are
relatively high during slow flight, and so dynamic calculations of the angle
of incidence of each wing chord to the air, and the speed of the air with
respect to the aerofoil, become uncertain, resulting in unreliable
calculations of time-varying aerodynamic pressures and forces from kinematic
observations only.
Mechanical and mathematical modelling of aerodynamic forces and power
requirements are proving effective for analysing flapping insects (e.g.
Ellington et al., 1996;
Liu et al., 1998
;
Liu and Kawachi, 1998
;
Dickinson et al., 1999
;
Wang, 2000
;
Ramamurti and Sandberg, 2002
;
Sun and Tang, 2002
; for a
review of insect techniques, see Sane,
2003
). However, the relative complexity of vertebrate wing
morphology and kinematics has limited mechanical model approaches, and
numerical computational fluid dynamics approaches are currently additionally
limited by the computing power required for 3-dimensional, unsteady flows at
higher Reynolds numbers.
Measurement of the forces and strains experienced by the major flight
muscles of birds (the pectoralis) allows direct calculation of the mechanical
power requirements, which include both the inertial power associated with
accelerating the wings and the aerodynamic power
(Biewener et al., 1998;
Tobalske et al., 2003
;
Hedrick et al., 2003
). While
this technique has considerable appeal, as it gives a direct indication of the
force requirements of the pectoralis, and may allow relative, if not
quantitative, changes in power requirements to be determined (e.g.
Tobalske et al., 2003
), the
calibration of pectoralis-induced bone strain recordings to provide reliable
forces over the full range of wing motion can be problematic. This arises from
the fact that in situ simulations of muscle force transmission used
to calibrate force via a bone strain gauge mounted on the
deltopectoral crest (DPC) of the humerus are sensitive to the direction of
muscle pull and the bending moment applied to the DPC.
We present in the current study a novel experimental approach for
determining the contributions of the wings and tails of pigeons in slow flight
to weight support, and their aerodynamic power requirements. Pressure
transducers can be applied between or through bird feathers (developing on
from Usherwood et al., 2003)
to provide measurements of differential pressures at a range of points along
and across wings and tails. Using these point pressures as representative of
pressures for appropriate sections, the aerodynamic forces on wings and tail
can be inferred. With simple kinematic measurements of orientation and
velocity, the aerodynamic power requirements associated with aerodynamic
forces on wings and tails can then be calculated.
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Materials and methods |
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The signals used to provide the mean ± S.D. (for N=3 pigeons) for each sensor position for each pigeon are means of 15-20 flights; the S.D.s indicate variability among pigeons (and applications of the sensors), not the variability from flight to flight.
Sensors and sensor attachment
Two small, disc-shaped (diameter=6.4 mm, depth=2.6 mm) differential
pressure sensors (Entran EPA-EO1-2P, ± 2PSI full range; Entran Devices
Inc., Fairfield, NJ, USA) each had a pennib glued with epoxy over the single
gauge-port, resulting in a unit with a mass of 0.5 g and the shape of a
thumb-tack or drawing pin. At the most distal pressure sensor site (see
below), the sensor mass contributed an additional 13% to the wing moment of
inertia (taking the value of 172.7x10-6 kg m2 for
the moment of inertia of a pigeon wing from
Van den Berg and Rayner,
1995). The hollow pen-nib (of length 4.4 mm) provided a conduit
through which pressures could be transmitted to the membrane in the sensor
unit. The nib was also narrow enough (0.64 mm o.d.) to be inserted through
feather shafts, and held firmly (though reversibly) in place with hot-glue
with minimal disruption to the feather. When attached through a feather shaft,
the pen-nib projects a little way through the dorsal surface of the tail or
wing, and the disc of the sensor body lies flat along the ventral surface. A
difference in pressure between the upper surface, to which the pen nib is
exposed, and the ventral wing surface, to which an array of holes on the flat
bottom of the sensor is exposed, results in a deflection of the membrane in
the sensor, and the production of a voltage signal.
Two ±250 g accelerometers (Entran EGAX-250) of dimensions 4 mmx4 mmx7.5 mm, and two ±50 g accelerometers (ICSensors 3031-050; San Jose, CA, USA) had 7 mm steel pins mounted with epoxy glue at the centre of the sensor, parallel to the direction of sensitivity (individual masses of 0.8 g and 0.5 g, respectively). These pins could then be inserted through a feather shaft and held in place with hotglue, firmly mounting the accelerometers directly underneath the same feathers that carried the pressure sensors (Fig. 1).
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Signals from pressure sensors and accelerometers were amplified and recorded at 5000 Hz using National instruments hardware (SCXI-1000DC, National Instruments, Austin, TX, USA). All signals were collected, digitally filtered (150 Hz recursive Butterworth - 19 times the wingbeat frequency), calibrated and analysed using National Instruments LabVIEW 5.1.
The sensitivities of the differential pressure sensors to acceleration were determined by attaching the sensors to the tip of a modified fan blade of length 0.22 m, and ramping the fan speed from zero to approximately 5.6 cycles s-1 and back down again. During this, the pressure sensor being tested was enclosed in a rigid case so that air around the sensor was always still with respect to the sensor. Power and signal connections ran from the sensor to the centre of rotation of the fan via a 4-channel mercury slip ring (Mercotac 430, Carlsbad, CA, USA) to the amplifiers and recording equipment. The frequency of rotation of the fan was identified from the cyclic variation due to gravity: with the fan orientated vertically the acceleration experienced by the sensor oscillated with an amplitude of 1 g on top of the signal imposed due to centripetal accelerations (up to 160 g, around double the peak observed at the base of the feather P8). With this set-up, the response of each pressure sensor to acceleration was measured, and found to be linear and of magnitudes of 1.0 and 1.2 Pa g-1.
Transducer placements
Accelerometers and pressure sensors were attached through feather shafts
while each pigeon was blindfolded and calm; anaesthesia was never required.
For all placements of the pressure sensors along the wing, the pen-nib
projected through the feather shaft, and then through a small (approximately 5
mmx5 mm) tab of surgical adhesive tape, which prevented nearby feathers
from flicking over the port during flight. Wires to the transducers were
controlled, where necessary, with ties of thin cotton thread sewn through
unused feather shafts. Excess transducer wire was collected on the back of the
pigeon and held in place with tape. The total load of all transducers, signal
wires and tape was approximately 15 g, <4% of body mass. The connection
between the sensor wires and the pair of 6-lead shielded cables was also
located on the back and acted as a mechanical fuse in case of snagging of the
cables. The 6-lead cables (carrying a total of two supply lines and five pairs
of signal wires) were arranged so that each passed around one side of the body
between the wings and the tail, from where the two cables joined again beneath
the pigeon. This arrangement permitted a full range of movement for both the
wings and the tail, which were able to spread fully.
The acceleration-compensated trials involved three sets of transducer placements (Table 1; Fig. 1A,B). The first set had pressure sensors and accelerometers on the outer tail, located on the second from outermost feathers [i.e. rectrice conventionally termed R5 - pigeons have 12 rectrices from 1 (central pair) out to R6 (outermost pair)]. The second set had sensors on the `inner tail', located on the 5th tail feathers in from outermost (R2). At these inner tail placement locations, a few under tail coverts were trimmed to prevent the ventral ports from being blocked. The third set of transducer placements were on the right wing (Fig. 1B), one pressure sensor/accelerometer pair on the third primary from the most distal (as primaries are conventionally numbered from proximal to distal, and there are ten visible primaries on an adult pigeon wing, this is termed P8), and one pair on the third secondary from the most distal secondary (secondaries are conventionally counted from distal to proximal, thus this is S3).
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The non-acceleration-compensated trials involved measurements obtained from four sets of pressure sensor placements (Table 1; Fig. 1C) for each pigeon. By time-normalising (allowing wingbeats of slightly different period to be combined) and synchronising with the accelerometer on S3 (to identify a consistent part of the wingbeat cycle), we were able to develop a pressure map of eight sites along and across the wing (Fig. 1C) for multiple wingbeats of take-off, slow level and landing flight.
Video and kinematics
Two flights were filmed at 250 frames s-1 (Photron Fastcam-X
1280 PCI; Photron USA Inc., San Diego, CA, USA) for each pigeon and sensor
positioning. For the acceleration-compensated experiments, the camera was
placed at 8 m lateral to the line of flight, to give a perpendicular lateral
view of the middle of the flights, from which tail angles
tail, flight velocities V, and the inclination of
the stroke plane to the horizontal ß were calculated
(Fig. 2A). For the
nonacceleration-compensated experiments the camera was placed 4.8 m beyond the
landing perch, providing a view of the middle portion of flight at a distance
of 8.3 m. From this view the angle of the left wing, taken as the angle
subtended between a line from the shoulder to the alula, and the horizontal,
was measured for the downstroke of the three middle flaps of each flight
filmed. We term this the downstroke angle
x-z, indicating it
is the projection of the downstroke angle
on to the x-z plane
(Fig. 2B). Given the relatively
large distance between camera and subject, we ignore parallax effects for both
camera positions.
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Weight support and power requirements from the tail
The precise pressure distribution along and across the tail is currently
unmeasurable. However, if the differential pressure measurements for outer and
inner sites are averaged, and
taken as representative
for the whole tail surface Stail, which is then considered
as flat and inclined at an angle
, the aerodynamic force from
the tail can be calculated, and the force components in the direction of
weight support
calculated
assuming that the force acts perpendicular to the thin surface:
![]() | (1) |
![]() | (2) |
The force per unit area is conventionally related to air density
(taken to be 1.2 kg m-3), wing area and velocity with the use of
force coefficients, in this case the resultant force coefficient
CR. Using the same assumptions as above:
![]() | (3) |
![]() | (4) |
Weight support from the wings
If the measured pressures for similar chordwise sites (we take the five
sites located towards the leading edge of the wing) can be taken as
representative of the mean pressures for appropriate section areas
(Fig. 1), then the aerodynamic
forces on each wing element, and so on the whole wing, can be calculated. At
each instant, each wing element of area S and measured differential
pressure dP, the aerodynamic force F' is simply
![]() | (5) |
Assuming that the net aerodynamic force for each section acts perpendicular
to the wing surface - an incorrect but close assumption for attached flow, and
very close to true for detached flow and high force coefficients
(Dickinson, 1996;
Dickinson et al., 1999
;
Usherwood and Ellington,
2002a
) - then, with an outstretched, untwisted wing in which all
wing chords are horizontal (appropriate for downstroke), the vertical force
contribution from each wing element Fz' can be
calculated:
![]() | (6) |
During upstroke, the differential pressures are slight
(Fig. 3), and the wing is
brought close to the pigeon's body during slow flight
(Fig. 7d). Thus, although some
degree of weight support may be achieved during the upstroke, it is unlikely
to be large. Further, our kinematic data do not provide sufficient resolution
to indicate upstroke weight support accurately from the pressure measurements.
Because of this we assume that weight support from the wings occurs entirely
during the downstroke during slow, level flight. For a pair of wings over a
complete cycle time 1/f, adding the contribution of each (of five)
wing sections from the wing base (r=0) to the wing tip
(r=R), where r is the distance from the shoulder
and R is the wing length, and over the duration of the downstroke
(ds; from t=0 to t=Tds, the period of
the downstroke), the mean vertical force from the wings
is given by:
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During level flight, the loaded body weight of the pigeon should be completely supported by aerodynamic means. Consequently, determining the percentage of weight support achieved by the vertical components of force calculated for both the wings and the tail provides a check on the accuracy of the force calculations obtained from our differential pressure measurements.
Calculating aerodynamic power from differential pressure measurements
Given the same assumptions as those used above in the calculation of weight
support, that a point pressure measurement is representative of an average
section pressure, and that the resultant aerodynamic force acts against the
motion of the wing in the x-z plane (because the forces act
perpendicular to the wing section, and each chord is horizontal), then a
direct calculation of the mean aerodynamic power
required to move the wing can be
made:
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While some aerodynamic forces may be acting in different directions - for instance as thrust overcoming body drag - and there is certainly motion of the wing out of the x-z plane, it appears reasonable, at least for slow flight, to expect the dominating force on the wings to be associated with weight support, and the dominating force requirement of the pectoralis to be to pull the wing down.
The effective moment arm Reff of the total aerodynamic
force on the wing, or the distance of the centre of pressure from the
shoulder, can be a useful term for understanding the derivation of power
requirements. As a proportion of wing length,
![]() | (9) |
Thus, a value of Reff/R=0.5 indicates that the
centre of pressure is halfway between shoulder and wingtip. Also, the power
for both wings at any instant can then be described as:
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Results |
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Acceleration compensation
Acceleration compensation has relatively little effect on the differential
pressure signals for inner and outer tail positions, and even the two wing
positions (Figs 3 and
4). During level flight
(Fig. 4), a consistent
deviation is identifiable at the distal wing site during the `clap' at the end
of upstroke/beginning of downstroke, a period of high acceleration (up to 80
g) and relatively low differential pressure. A second
consistent deviation between acceleration-compensated and non-compensated
pressure measurements, though in the opposite direction and of smaller
proportional significance, occurs towards the end of downstroke. During this
time, the wing is rapidly decelerating (accelerating upwards; note the
accelerometer trace) as the wing slows towards the end of downstroke.
Generally, though, nonacceleration compensated signals provide an adequate
representation of the differential pressures. This supports the use of our
more detailed 8-site non-acceleration-compensated pressure map of the wing for
interpreting the aerodynamic forces developed under these flight
conditions.
Tail lift, drag and power
The average differential pressure across the tail for a whole wing stroke
cycle increases during take-off, is level during the middle three flaps, and
reduces as the pigeons come into land (Fig.
3). The tail is widely spread during all of the flight between the
two perches, and it is held at a high angle to the direction of travel
(Table 2). While any
contribution to weight-support during slow flight may be valuable, the angling
of the tail near to 45° suggests that the tail acts as a poor lifting
surface with a lift:drag ratio of 1.0, thus any benefit from contributing
to weight support may be offset by an increase in drag; the tail, at least at
these low speeds, does not act as an efficient weight-supporting fixed wing.
Instead, the tail orientates the net aerodynamic force vector required from
the wings forwards: the wings are required to produce less force supporting
weight, but a greater thrust force to overcome the tail drag. Thus, one effect
of the tail is that the wings are required to act in a more
propeller-(versus helicopter-) like manner.
A power requirement for pulling the tail through the air can be calculated assuming that the mean pressure from the four measured sites during level flight (Fig. 5) acts across the whole surface, and the net aerodynamic force acts perpendicular to the tail (Table 2). We do not suggest that this power is contributed by the tail musculature; rather, the aerodynamic drag due to the tail may be treated as a large parasite drag. However, due to some contribution to weight support, tail-drag contributes somewhat to the traditional `induced drag' term. Whatever the distribution of tail-drag between conventional drag terms, the power required to pull the tail through the air is likely to be contributed by muscles that flap the wings, dominated by the pectoralis muscles.
Wing pressures
The mean (± 1 S.D. shown in black, N=3 pigeons)
nonacceleration-compensated differential pressure signals for eight positions
along and across the wing (Fig.
1C) are shown for take-off, level and landing flight
(Fig. 6). While distal sensor
placements measure peak differential pressures that are higher during take-off
and landing than level flight, this is not the case for more proximal
positions. For the innermost site, on secondary S7, peak pressure differential
is slightly higher during the level flaps than take-off and landing. This
agrees with the observations of take-off flight in geese
(Usherwood et al., 2003), and
matches expectations for flapping wings, that distal sites are required to
produce relatively high aerodynamic forces during slower flight, and proximal
sites, with the lower flap velocities, contribute lift forces during higher
speed flight. Negative pressures (indicating relatively higher pressures on
dorsal surfaces than ventral) are observed at all sites during take-off and,
to a lesser extent, during landing. This confirms that the upstroke can
contribute aerodynamic forces during slow flight in the pigeon with a change
in sense of circulation (Alexander,
1968
). It appears reasonable to infer that these forces are
beneficial, as negative pressures could be avoided with slight
changes in either the degree of supination or the path of the wing during
upstroke.
The development of pressure with time during level flight is related to outline tracings (Fig. 7), each separated by approximately 16 ms. More distal sites show higher amplitude signals than more proximal sites, consistent with their higher flapping velocities (Fig. 8A,C). Higher section velocities may increase section pressure differentials both by increasing the angle of incidence of the section to the air (increasing the section force coefficient), and increasing the relative air velocity, thus raising the pressure differential for a given force coefficient. While, at the very end of downstroke the wings supinate [placing each wing chord at an angle to the horizontal (see Fig. 2A)], the wing chords are approximately horizontal throughout the majority of downstroke (Fig. 7a-c). Thus, the wing chords are approximately horizontal during most of the wing motion during which significant pressure is developed.
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Wing forces and powers
Fig. 8 shows a development
of the implications of the differential pressure measurements and the
downstroke kinematics, leading to calculations of weight support and
aerodynamic power. The five sites towards the leading edge of the wing (P8,
P7, P4, S1 and S7), having similar chordwise positions, are included in our
analysis. Two of the middle three flaps are shown, as flap cycles have to be
complete for calculations of mean weight support and power. During downstroke,
the wing stroke angle (Fig. 8B)
varied linearly with time within the x-z plane (x-z)
(i.e. observed from front-on as the animal flew toward the camera,
Fig. 2), indicating a
curvilinear change of downstroke angle within the stroke plane, due to the
inclination of the stroke plane from the horizontal by an angle ß
(35°; Table 2). Variation
in downstroke angle was calculated using the mean kinematic variables given in
Table 3. The geometric velocity
(including forward flight speed, and taking into account the inclination of
the stroke plane) for each wing section
(Fig. 8C), shows that variation
in differential pressures is broadly related to section speeds. Mean section
forces (Fig. 8D) were
determined assuming that the measured point pressures can be taken as mean
pressures for relevant wing sections of known area. These section forces were
then combined, and their orientations to the vertical taken into account when
calculating their contribution to vertical weight support
(Fig. 8E).
Muscle-mass specific aerodynamic powers calculated from point differential
pressure measurements are shown as a function of the wingstroke cycle
(Fig. 8G) and averaged for
appropriate stroke-cycle periods (Table
4). Muscle-mass specific powers are calculated assuming that the
pectoralis dominates downstroke power and constitutes 18% of body mass
(Dial and Biewener, 1993;
Biewener et al., 1998
;
Soman et al., 2005
). Means
± S.D. for vertical weight support, effective aerodynamic
moment arm, and powers are calculated from appropriate individual average
measurements pressure, of differential kinematics and morphology, with
inter-individual averages only determined as the final step.
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Discussion |
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One implication of the second pressure peak experienced by the tail towards
the end of downstroke is the possibility that the tail may act to convert some
of the inertial power required to slow the wings
(Hedrick et al., 2004) into
useful aerodynamic work. Without the tail, the deceleration of the wings at
the end of downstroke would result in a downwards acceleration of the body
(recorded by the accelerometers at the tail base), and both the body mass and
the wing masses would accelerate with respect to the centre of mass. If the
aerodynamic forces from the tail limit this reaction-acceleration of the body,
the internal work is reduced, and energy is given to the air, potentially
providing a useful aerodynamic force and power. To confirm this possibility,
detailed changes in tail orientation and velocity through the wing stroke
cycle have to be related to the differential pressures, but this is beyond the
accuracy of the current techniques.
The tail may have multiple functions during slow flight, and these functions are likely to change as flight speed increases. While a large, widely spread tail may be beneficial during slow flight due to contributing somewhat to weight support, other functions may dominate during slow flight in pigeons. These potentially include a reduction of vertical body oscillations leading to more effective motion of the wings through the air, a conversion of some inertial power to aerodynamic, and a readiness for low-speed manoeuvring.
Wing aerodynamic mechanisms
Sites nearer the leading edge of the wing display approximately
half-sinusoidal waveforms during downstroke, while sites nearer the trailing
edge exhibit a double peak during downstroke
(Fig. 7), similar to that
described for distal positions of a goose wing during take-off flight
(Usherwood et al., 2003). We
suggest that this phenomenon is due to the distance of the sensor from the
axis of rotation of the wing during pronation and supination. In our study of
Canada goose take-off flight, the distal sites that were sampled on the wing
may have been confounded with more caudal positioning of the pressure sensors.
The pressure signal for sites near the trailing edge are interestingly similar
to the force traces produced by models of hovering insects (e.g.
Dickinson et al., 1999
;
Birch and Dickinson, 2003
).
Using their `robofly' model, Birch and Dickinson
(2003
) showed that the peak
towards the end of the half-stroke (i.e. downstroke or upstroke) is related to
an increase in the angle of incidence of the wing. We suggest that, for the
pigeons sampled here, the peak in differential pressure for sites nearer the
trailing edge during the end of each half-stroke may be due to an increased
velocity of the trailing edge during wing rotation prior to the change in wing
direction. This would occur due to the distance of the trailing edge sites
from the centre of longitudinal rotation of the wing. Whether this results in
an increase on the net force for the whole section, however, is unclear.
Our account for the pressure peak towards the ends of each half stroke
cannot explain the peaks observed towards the trailing edge at the start of
downstroke, because pronation at the start of downstroke would result in a
lower velocity at the trailing edge, away from the axis of pronation. In our
study of goose wing pressures during take-off flight
(Usherwood et al., 2003), we
argued that the early peak might be related to an initiation of the downstroke
before the wings are fully pronated, resulting in a higher angle of incidence
and an increased pressure differential across the wing chord. However, we did
not observe this increase in differential pressure at the sites near the
leading edge of the pigeon wings in this study. In the case of a scaled,
mechanical `hovering' Drosophila, Birch and Dickinson
(2003
) show that the first peak
of each half-stroke can be attributed to a wing-wake interaction. For the
pigeons studied here, we propose that a similar wing-wake interaction may be
the cause of the significant, earlier peak during each half-stroke by the
trailing-edge sites. Although the pigeons were not hovering, their advance
ratios were low enough (0.38 for the wing tip during downstroke) that an
interaction between the wing and the flow due to the previous half-stroke
seems likely, and may be expected to influence the pressures across the wing
as it starts to flap. Given that the trailing edge sites, unlike the sites at
the feather bases, experience pressure differentials right up to the end of
each half-stroke, a sudden change in direction at the start of each
half-stroke could result in a local interaction with the fluid that had been
accelerated by the passing of the wing a moment before. To confirm whether
this mechanism acts on the trailing-edge sites of the wing would require flow
visualisation similar to that described for hovering model Drosophila
analysed by Birch and Dickinson
(2003
). However, such
observations of very near-field flow would be very difficult to achieve on
live birds.
Point pressure measurements and weight support
Despite certain assumptions, we believe that the calculation of the
vertical component of the aerodynamic forces experienced by the wings from our
direct differential pressure recordings is fairly robust. On average, a mean
vertical force of 74.5% of the body weight was calculated during the level
portion of the animal's flight (Table
4). With the additional 7.9% of weight support achieved from tail
lift (Table 2) this leaves a
deficit of 17.6% of body weight support. Some of this deficit may be
attributed to body lift, as well as inaccuracy in our pressure or kinematic
measurements, or some failure in the assumptions used in the calculation. In
particular, our assumption that a point pressure should represent the mean
pressure for a wing section should be treated with caution. Pressure profiles
around wing chords rarely show an even pressure distribution. However, our
pairs of measurements at similar spanwise positions (P4 and P3; S1 and S2; S6
and S7), while showing somewhat different waveforms, exhibit similar general
magnitudes in peak differential pressure
(Fig. 6), or time integral of
pressure during downstroke, suggesting that the exact chordwise placements may
not be critical. We therefore feel that an account of 82.4% of body weight
from direct pressure measurements of the wings and tail provides some
confidence in the use of differential pressure sensors for determining section
force contributions, and justifies our development of a novel method for the
calculation of aerodynamic powers.
Aerodynamic powers from point pressure measurements
The results for the distribution of section forces exerted on the wing show
that the effective moment arm for the aerodynamic force on the wing, or the
effective centre of pressure, acts approximately half way along the wing
(Fig. 8F). This reflects the
fact that the higher differential pressures recorded at more distal sites are
offset by their narrower chords. The constancy of
Reff/R=0.5 throughout the downstroke suggests
that lift coefficients vary for each wing position through time; otherwise,
the centre of pressure should become biased towards the wing tip at
mid-downstroke, when the wing tip is moving relatively fast
(Fig. 8C). While the
measurement of Reff/R is somewhat limited by the
distribution of the pressure sensors, direct pressure measurements allow the
assumption of constant spanwise lift and drag coefficients (common in
blade-element analyses of slow and hovering flight; see
Dickson and Dickinson, 2004) to
be avoided.
The mean muscle-mass specific power for a complete flap cycle of 272.7 W
kg-1 is high compared with both theoretical analyses and previous
direct measurements of pectoralis muscle power output obtained using
deltopectoral crest (DPC) bone strain measurements and sonomicrometry
(discussed below). The muscle-specific induced power requirement (the power
associated with changing the momentum of a finite mass of air) for a
fixed-wing flier with the flight speed, wingspan, and weight shown in Tables
2 and
3 (using the default induced
power factor k of 1.2 and following
Pennycuick, 1989) is only 79.5
W kg-1. This suggests that induced power is only responsible for
29% of the aerodynamic power requirements of slow flight in pigeons. Thus, our
measurements indicate that the pigeon wings experience a very high profile
drag, and that induced power is only a relatively small component of the
aerodynamic power requirements of slow flight (when it is
conventionally expected to dominate).
Given the high profile drag coefficients observed for bird wings
(Usherwood and Ellington,
2002b) when operating at high incidences and high force
coefficients (appropriate for slow flight, especially when profile drag forces
contribute to weight support), the dominance of profile power is perhaps not
surprising. Indeed, the view of the profile drag coefficient as being some
simple, low, and even constant, value is questionable for analyses of the
power requirements of bird flight, as has been identified for calculations of
the power requirements of insect hovering
(Ellington, 1999
). Thus, power
calculations using profile drag coefficients for steady, attached flow are
likely to vastly underestimate power requirements for rapidly flapping
flight.
The values of muscle-mass specific aerodynamic power calculated in more
theoretical analyses of pigeons in slow flight by Pennycuick
(1968) and Rayner
(1979b
) of 110 W
kg-1 and 87 W kg-1, respectively, are close to the
induced powers alone but are markedly lower than the 273 W kg-1
calculated in this study. This supports the suggestion that profile drag
coefficients conventionally derived from studies involving attached
(pre-stall) flow may be misleading. A `rule of thumb' profile drag coefficient
of 0.02 is often used (e.g. Askew et al.,
2001
; following Rayner,
1979a
; Pennycuick et al.,
1992
), which would make profile power relatively insignificant for
slow flight. With profile drag coefficients for revolving bird wings
potentially >2 (Usherwood and
Ellington, 2002b
), and the direct aerodynamic power calculations
presented here, an undiscriminating use of CDpro=0.02 now
appears to be inappropriate.
The value of muscle-mass specific power of 273 W kg-1 (for the
pectoralis) appears physiologically reasonable, but is higher than the value
of 207 W kg-1 recently quantified for the pectoralis of White
Carneau pigeons flying under nearly identical conditions
(Soman et al., 2005), based on
DPC strain measurements and detailed muscle sonomicrometry. It is also much
higher than the value of 108 W kg-1 reported in an earlier study by
Biewener et al. (1998
) for
Silver King pigeons flying at slightly faster free-flight speeds (6-7 m
s-1). The lower values obtained from measurements of DPC strain,
however, may reflect difficulties with aspects of calibration of the in
vivo technique (see Tobalske et al.,
2003
). The in situ `pull' calibrations applied to the
whole muscle beneath its attachment to the DPC may produce a greater bending
moment compared with the in vivo distribution of force transmitted by
the pectoralis to the DPC. Adopting an aerodynamic correction for estimates of
pectoralis power based on DPC strain-force measurements, Tobalske et al.
(2003
) observed pectoralis
mass-specific power outputs that ranged from 80 to 150 W kg-1 for
cockatiels Nymphicus hollandicus and ringed-turtle doves
Streptopelia risoria flying at 3-5 m s-1 in a wind
tunnel.
Some uncertainty similarly exists in our estimate of muscle power based on
direct wing pressure recordings, which depend on assumptions about both the
pressure distributions and the orientation of net aerodynamic forces across a
limited number of wing sections. Nevertheless, these measurements indicate
that peak forces due to aerodynamics of 5.7 N are centred halfway down
the wing (see Fig. 8), which
implies a peak pectoralis force of 59 N and a peak pectoralis stress of 79.9
kN m-2 (calculated based on muscle fibre area of 7.39
cm2, given muscle parameters and bone geometries for pigeons used
in previous studies; Dial and Biewener,
1993
; Biewener et al.,
1998
). Again, these values are physiologically reasonable but
higher than those previously measured in vivo in smaller wild-type
(Dial and Biewener, 1993
) and
Silver King pigeons (Biewener et al.,
1998
) under similar flight conditions. The lower values of peak
muscle force and power output obtained from calibrated measurements of strain
recorded at the deltopectoral crest, however, may reflect difficulties with
aspects of the calibration of the in vivo technique (see
Tobalske et al., 2003
).
While the brief pigeon flights described in this study are unlikely to be
near maximal efforts - the pigeons were capable of 80-100 flights in a day
with no apparent loss of performance -we do not expect the pigeon flight to be
entirely aerobic. Burst muscle-specific powers have been calculated for quail
in rapid ascending take-off flight (Askew
et al., 2001). Without any aerodynamic assumptions,
simply calculating the rate of change of potential energy, these flights reach
315 W kg-1, and the total aerodynamic power for the quail is likely
to be considerably above this value. Thus, our measured values for the power
requirements of pigeon flight do not appear extreme, lending some support to
the technique. In addition, this suggests that more anaerobic, near-maximal
pigeon muscle performances may be studied with a development of the current
technique for ascending flight, or loaded flight experiments, and higher
calculations of pigeon muscle powers may be expected in the future.
While our calculations of the aerodynamic power requirements for slow, level flight in pigeons are considerably above those derived from both aerodynamic models and in vivo muscle measurements, we believe that each component for the power calculation is reasonable. (1) Pressures are low at start and end of the downstroke and high at mid downstroke; (2) net wing forces are close to those required for weight support; (3) wing kinematics are sensible (Table 3) and match those of recent 3-D kinematic measurements of wing stroke plane and amplitude (B. W. Tobalske, T. L. Hedrick and A. A. Biewener, unpublished); and (4) the position of the centre of pressure (the effective moment arm length) occurs approximately half way along the wing (Fig. 8). While a variety of additional aspects may be considered in the calculation of power requirements - for instance additional forces and motions outside the x-z plane, or a multiplication factor to scale the forces to support body weight exactly - most of these additions contribute complications that appear to us to be unjustified at this stage, and would indicate even higher power requirements. Thus, we conclude that slow, level flight in pigeons is energetically demanding, and aerodynamically inefficient.
Future work
The direct pressure measurements along and across flapping bird wings
reported here for pigeons and previously for Canada geese during take-off
flight (Usherwood et al.,
2003) have the potential to contribute significantly to the
understanding of many aspects of bird flight. The aerodynamic implications of
both wing morphology and kinematics can be determined with pressure sensors on
bird wings of diverse species flying with a variety of flight styles.
Telemetered or data-logged pressure data have the potential to provide insight
into the aerodynamic contributions to the physiological implications of
free-flight behaviours such as foraging and migration (e.g. following
Bishop et al., 2002
), or
specific flight strategies such as formation flying (following
Weimerskirch et al., 2001
) or
dynamic soaring (Weimerskirch et al.,
2000
).
List of symbols
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Alexander, R. McN. (1968). Animal Mechanics. Seattle: University of Washington Press.
Askew, G. N., Marsh, R. L. and Ellington, C. P.
(2001). The mechanical power output of the flight muscles of the
blue-breasted quail (Coturnis chinensis) during take-off.
J. Exp. Biol. 204,3601
-3619.
Biewener, A. A., Corning, W. R. and Tobalske, B. W.
(1998). In vivo pectoralis muscle force-length behavior
during level flight in pigeons (Columba livia). J. Exp.
Biol. 201,3293
-3307.
Birch, J. M. and Dickinson, M. H. (2003). The
influence of wing-wake interactions on the production of aerodynamic forces in
flapping flight. J. Exp. Biol.
206,2257
-2272.
Bishop, C. M., Ward, S., Woakes, A. J. and Butler, P. J. (2002). The energetics of barnacle geese (Branta leucopsis) flying in captive and wild conditions. Comp. Biochem. Physiol. 133A,225 -237.
Dial, K. P. and Biewener, A. A. (1993).
Pectoralis-muscle force and power output during different modes of flight in
pigeons (Columba livia). J. Exp. Biol.
176, 31-54.
Dickinson, M. H. (1996). Unsteady mechanisms of force generation in aquatic and aerial locomotion. Am. Zool. 36,536 -554.
Dickinson, M. H., Lehmann, F.-O. and Sane, S. P.
(1999). Wing rotation and the aerodynamic basis of insect flight.
Science 284,1954
-1960.
Dickson, W. B. and Dickinson, M. H. (2004). The
effect of advance ratio an the aerodynamics of revolving wings. J.
Exp. Biol. 207,4269
-4281.
Ellington, C. P. (1984). The aerodynamics of hovering insect flight. V. A vortex theory. Phil. Trans. R. Soc. Lond. B 305,115 -144.
Ellington, C. P. (1999). The novel aerodynamics
of insect flight: applications to micro-air vehicles. J. Exp.
Biol. 202,3439
-3448.
Ellington, C. P., Van den Berg, C., Willmott, A. P. and Thomas, A. L. R. (1996). Leading-edge vortices in insect flight. Nature 384,626 -630.[CrossRef]
Hedrick, T. L., Tobalske, B. W. and Biewener, A. A.
(2002). Estimates of circulation and gait change based on a three
dimensional kinematic analysis of flight in cockatiels (Nymphicus
hollandicus) and ringed turtle-doves (Streptopelia risoria).
J. Exp. Biol. 205,1389
-1409.
Hedrick, T. L., Tobalske, B. W. and Biewener, A. A.
(2003). How cockatiels (Nymphicus hollandicus) modulate
pectoralis power output across flight speeds. J. Exp.
Biol. 206,1363
-1378.
Hedrick. T. L., Usherwood, J. R. and Biewener, A. A.
(2004). Wing inertia and whole-body acceleration: an analysis of
instantaneous aerodynamic force production in cockatiels (Nymphicus
hollandicus) flying across a range of speeds. J. Exp.
Biol. 207,1689
-1702.
Liu, H., Ellington, C. P., Kawachi, K., Van den Berg, C. and
Willmott, A. P. (1998). A computational fluid dynamic study
of hawkmoth hovering. J. Exp. Biol.
201,461
-477.
Liu, H. and Kawachi, K. (1998). A numerical study of insect flight. J. Comput. Phys. 146,124 -156.[CrossRef]
Osborne, M. F. M. (1951). Aerodynamics of flapping flight with application to insects. J. Exp. Biol. 28,221 -245.[Medline]
Pennycuick, C. J. (1968). Power requirements for horizontal flight in the pigeon Columba livia. J. Exp. Biol. 49,527 -555.
Pennycuick, C. J. (1975). Mechanics of flight. In Avian Biology, vol. 5 (ed. D. S. Farner and J. R. King), pp. 1-75. London: Academic Press.
Pennycuick, C. J. (1989). Bird Flight Performance: a Practical Calculation Manual. Oxford: Oxford University Press.
Pennycuick, C. J., Heine, C. E., Kirkpatrick, S. J. and Fuller, M. R. (1992). The profile drag coefficient of a Harris' hawk wing, measured by wake sampling in a wind tunnel. J. Exp. Biol. 165,1 -19.
Ramamurti, R. and Sandberg, W. C. (2002). A
three-dimensional computational study of the aerodynamic mechanisms of insect
flight. J. Exp. Biol.
205,1507
-1518.
Rayner, J. M. V. (1979a). A vortex theory of animal flight. Part 2. The forward flight of birds. J. Fluid Mech. 94,731 -763.
Rayner, J. M. V. (1979b). A new approach to animal flight mechanics. J. Exp. Biol. 80, 17-54.
Rayner, J. M. V. (1993). On the aerodynamics and the energetics of vertebrate flapping flight. Cont. Math. 141,351 -400.
Sane, S. P. (2003). The aerodynamics of insect
flight. J. Exp. Biol.
206,4191
-4208.
Soman, A., Hedrick, T. L. and Biewener, A. A. (2005). Regional patterns of pectoralis fascicle strain in the region Columba livia during level flight. J. Exp. Biol. 208, in press.
Spedding, G. R. (1986). The wake of a jackdaw (Corvus monedula) in slow flight. J. Exp. Biol. 125,287 -307.
Spedding, G. R. (1987). The wake of a kestrel (Falco tinnunculus) in flapping flight. J. Exp. Biol. 127,59 -78.
Spedding, G. R., Rayner, J. M. V. and Pennycuick, C. J. (1984). Momentum and energy in the wake of a pigeon (Columba livia) in slow flight. J. Exp. Biol. 111,81 -102.
Spedding, G. R., Rosën, M. and Hedenström, A.
(2003a). A family of vortex wakes generated by a thrush
nightingale in free flight in a wind tunnel over its entire natural range of
flight speeds. J. Exp. Biol.
206,2313
-2344.
Spedding, G. R., Rosën, M. and Hedenström, A. (2003b). Quantitative studies of the wakes of freely-flying birds in a low-turbulence wind tunnel. Exp. Fluids 34,291 -303.
Sun, M. and Tang, J. (2002). Unsteady
aerodynamic force generation by a model fruit fly wing in flapping motion.
J. Exp. Biol. 205,55
-70.
Tobalske, B. W., Hedrick, T. L., Dial, K. P. and Biewener, A. A. (2003). Comparative power curves in bird flight. Nature 421,363 -366.[CrossRef][Medline]
Usherwood, J. R. and Ellington, C. P. (2002a).
The aerodynamics of revolving wings. I. Model hawkmoth wings. J.
Exp. Biol. 205,1547
-1564.
Usherwood, J. R. and Ellington, C. P. (2002b).
The aerodynamics of revolving wings. II. Propeller force coefficients from
mayfly to quail. J. Exp. Biol.
205,1565
-1576.
Usherwood, J. R., Hedrick, T. L. and Biewener, A. A.
(2003). The aerodynamics of avian take-off from direct pressure
measurements in Canada geese (Branta canadensis). J. Exp.
Biol. 206,4051
-4056.
Van den Berg, C. and Rayner, J. M. V. (1995). The moment of inertia of bird wings and the inertial power requirement for flapping flight. J. Exp. Biol. 198,1655 -1664.[Medline]
Wakeling, J. M. and Ellington, C. P. (1997).
Dragonfly flight. III. Lift and power requirements. J. Exp.
Biol. 200,583
-600.
Wang, Z. J. (2000). Two dimensional mechanism for insect hovering. Phys. Rev. Lett. 85,2216 -2219.[CrossRef][Medline]
Weimerskirch, H., Martin, J., Clerquin, Y., Alexandre, P. and Jiraskova, S. (2001). Energy saving in flight formation. Nature 413,697 -698.[CrossRef][Medline]
Weimerskirch, H., Guionnet, T., Martin, J., Shaffer, S. A. and Costa, D. P. (2000). Fast and efficient? Optimal use of wind by flying albatrosses. Proc. R. Soc. B 267,1869 -1874.[CrossRef][Medline]
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