The aerodynamics of avian take-off from direct pressure measurements in Canada geese (Branta canadensis)
Concord Field Station, Harvard University, 100 Old Causeway Road, Bedford, MA 01730, USA
* Author for correspondence (e-mail: jusherwood{at}oeb.harvard.edu)
Accepted 22 July 2003
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Summary |
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Key words: flight, flapping, wing, bird, inertia, power, Canada geese, Branta canadensis
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Introduction |
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With the development of more sophisticated techniques in PIV appropriate
for bird flight (Rosén,
2003; Spedding et al.,
2003a
,2003b
),
high-resolution (both spatially and temporally) wake dynamics can now be
observed, allowing a significant step towards understanding the aerodynamics
of avian flight. However, these techniques are currently limited to steady
flight of a highly trained bird within a wind tunnel in near darkness and
require that images of the wake from several wing beats are pieced together to
produce representative wakes for a complete wingstroke cycle at a given flight
speed. In addition, relating flow fields in a wake at some distance downstream
from a bird to the pressures experienced by the bird is not trivial. Imaging
of the flow immediately around the bird and its wings would help this process,
but this has not yet been achieved and is unlikely to be accomplished in the
near future.
Sampling of the downwash of a hovering bat by hot-wire anemometry
(Norberg et al., 1993)
provides an alternative technique for studying the wake of a flapping animal
and can be used to derive a value for induced power. However, neither of the
techniques for studying the wake of a flying bird (PIV or hot-wire anemometry)
is capable of providing direct information on the varying pressures acting
along the wing. Assessments of muscle forces during flight have been possible
using calibrated strain measurements of the deltopectoral crest of the humerus
in the pigeon Columba livia (Dial
and Biewener, 1993
) and magpie Pica pica
(Dial et al., 1997
). However,
even without the difficulties inherent in calibration of the strains to
provide force data (Tobalske et al.,
2003
), this technique provides limited information on the
aerodynamic forces acting along the wing. This is because the confounding
contributions of inertial forces are difficult to identify and remove, and
force distributions along a wing cannot be resolved from limited and local
bone strain measurements. As an intermediate between studies of flapping-wing
aerodynamics focusing on the consequences to the air or consequences to the
muscles and bones, we have developed a direct technique for measuring the
pressure differentials developed across flapping bird wings.
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Materials and methods |
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Acceleration compensation of pressure transducers
Each unit (4.5 g or 7.5 g) consists of a differential pressure transducer
(PX74-0.3DV; Omega, Stamford, CT, USA) with a stiff 3.2 mm-diameter nozzle cut
to project through the feathers to the upper wing surface when tied between
flight feathers (Fig. 1). Each
sensor was relatively light compared with the wing (1-2% of wing mass,
together totaling 9%), each comparable to the mass of 2-4 primary feathers.
While the additional wing mass may have resulted in a slight compensation in
kinematics due to increasing the moment of inertia, I {by
approximately 12% for the outstretched wing, using the scaling relationship
for a single wing I=0.118[(wing mass)x(wing
length)2]1.040, r2=0.997, from
Van den Berg and Rayner,
1995}, we found that the action of the loaded and unloaded wings
was similar. Each differential pressure transducer was attached next to either
one (sites a, c and e; Fig. 1B)
or a pair of (sites b and d; Fig.
1B) single-axis accelerometers (SA20; Sensor One, Sausalito, CA,
USA). The response of both accelerometers and pressure transducers to
acceleration was determined by steadily (thus avoiding pressure differentials)
orientating the units vertically upwards (+1 g, +9.81 m
s-2), horizontally (0 g, 0 m s-2) and
vertically downwards (-1 g, -9.81 m s-2). This was
done so that the confounding effect of acceleration (because of flapping) on
the pressure signal, due to the inertial deflection of the membrane integral
to the pressure transducer, could be removed. The units with a pair of
accelerometers allow the effects of wing rotation (pronation or supination)
and the slight (12.5 mm) separation between pressure transducer and
accelerometer to be assessed. The traces for sites b and d in
Fig. 2 consist of two lines,
one for each accelerometer signal removal. However, the two lines are barely
distinguishable, appearing occasionally as a thickening of the trace, showing
that the impact of separation between pressure transducer and accelerometer
was negligible. Acceleration compensation of the pressure signal was, however,
significant. At positions of peak acceleration (around ±;75
g or 750 m s-2, at the beginning/end of downstroke
and upstroke at the most distal transducer placement), a false signal of up to
±;350 Pa was removed. While the frequency response of each transducer
was high (>1 kHz), both high-frequency noise and limitations in the
kinematic data made high-frequency signals difficult to interpret. As a
result, acceleration-compensated pressure signals were low-pass filtered at 25
Hz (2nd order Butterworth), approximately five times that of the wingbeat
frequency.
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Results and discussion |
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Upstroke and `gaits' in avian flight
Studies by PIV of the wake left behind flying birds have led to the
description of two distinct flight `gaits'
(Spedding et al., 1984;
Rayner, 1986
,
1991
,
1995
; Spedding,
1986
,
1987
;
Tobalske, 2000
): the
`vortex-ring gait', in which the upstroke results in minor aerodynamic forces,
and the `continuous-vortex gait', in which aerodynamic lift is maintained
during the upstroke. The concept of `gaits' in flight is useful in
distinguishing between slow, sparrow-like flight and fast, gull-like flight,
but the transition between the two gaits as a function of speed, for most
birds, is likely to be continuous (e.g.
Spedding et al., 2003a
), with
the aerodynamic role of the upstroke gradually increasing with increasing
flight speed. Whether the term `gait' should be dropped because of this lack
of discontinuity with speed (although `walking' and `running' are normally
termed gaits even in birds that can show continuous variation in kinematics
with speed; Gatesy and Biewener,
1991
) and `flight style' should be adopted, the concept of
different flight techniques, largely defined by force production during the
upstroke, remains useful. In this context, the results for the goose through
upstroke during take-off are interesting. Pressures along the wing divide into
three regions: (1) `positive' (a vertral-dorsal sense) at the wing base; (2)
near-zero for the center portion of the wing; and (3) `negative' (a
dorsal-ventral sense) at the wingtip (Fig.
3). The maintenance of ventral-dorsal pressure at the wing base,
and the reversal at the wingtip, adds a new flight `style' to those previously
described based on upstroke function; again, however, discontinuity between
take-off flight style and other flight styles (whether closer to the
`vortex-ring' or `continuous-vortex' gaits or styles) should not be
inferred.
Wingtip pressure reversal
Circulation (and pressure-sense) reversal at the wingtip during the
upstroke has been reasonably argued for take-off flight in the pigeon
(Alexander, 1968): wingtip
attitudes, and presumed low induced air velocities, are likely to result in
the wingtips operating at negative aerodynamic angles of incidence. The
bending of the primaries (Corning and
Biewener, 1998
) also suggests that they experience forces
orientated upwards and forwards during the upstroke. This phenomenon is
difficult to infer, however, for many other cases, both due to the unknown and
potentially high local induced velocities and to the relatively low angles at
which the air meets the wing (the angles of incidence). Indeed, it is often
difficult to determine whether any significant aerodynamic forces are produced
during the upstroke or even whether the aerofoil is operating at a positive or
negative angle of incidence (see, for instance, the analysis of a hovering bat
described by Norberg,
1976
).
The orientations of the significant negative pressures observed at the wingtip during upstroke in the flapping Canada goose are impossible to determine precisely from the kinematic data in this study (accurate three-dimensional kinematics are not possible with such unconstrained flight). The pressure does, however, appear to be orientated to provide a predominantly thrust force, as the primaries are approximately vertical during the upstroke (Fig. 3, snapshots 10-12), perhaps with some component acting downwards. Any component against weight-support is presumably detrimental to an animal seeking to gain altitude in take-off flight. The thrust component, however, would be beneficial: the wing in upstroke would act as a conventional propeller, increasing the velocity of the bird, both directly aiding escape and increasing the weight-supporting aerodynamic forces from the inner wing and body. An alternative, although not mutually exclusive, view is that the negative pressures during the upstroke are a physical inevitability related to either kinetic or morphological constraints. Pronation cannot be instantaneous, and negative pressure may be due simply to beginning pronation before the end of upstroke. Alternatively, there may be some morphological constraint prohibiting sufficient supination during the upstroke. Whether the phenomenon should be viewed as a beneficial, thrust-producing action or as an inevitable consequence of using flapping wings in slow flight (and resulting in an `undesirable' downwards force) is impossible to determine at this stage, and the truth may well fall somewhere between these two extremes.
Implications of the double pressure peaks
The timing of the double pressure peaks observed at the distal sites is a
consistent phenomenon after lift-off (Fig.
2). The first peak occurs just after downstroke begins. Positive
pressure then falls off briefly over mid-downstroke. The second peak occurs
near the end of downstroke, possibly associated with a `flaring' of the wing
due to supination before the end of downstroke, resulting in an increased
angle of incidence. The initial pressure peak may be related either to
initiation of the downstroke before the wing is fully pronated or to `added
mass' effects associated with rapid wing accelerations. This is followed by a
brief drop in pressure when the wing is flapping fastest and presumably
operating at some favorable aerodynamic lift-to-drag ratio. The significance
of the second pressure peak is not certain at this stage but may best be
described in the context of management of the kinetic energy of the wing.
`Inertial power', due to repeated investment into the kinetic energy of
flapping wings, need not be metabolically costly, even in the absence of
elastic mechanisms, if the energy can be transferred to useful aerodynamic
work (Weis-Fogh, 1972;
Pennycuick and Lock, 1976
;
Ellington, 1984
;
Dudley and DeVries, 1990
;
Van den Berg and Rayner, 1995
;
Askew et al., 2001
). An
appropriate timing of such energy transfer might result in the pressure record
indicated here. Towards the end of downstroke, the wings need to be
decelerated quickly with minimal metabolic cost, and at the same time a high
aerodynamic drag would provide some contribution to weight-support. By using
the air to `brake' the wing, a peak in pressure differential is created that
may also result in an aerodynamic force useful for weight-support.
Future research with direct pressure measurements
Key future improvements of the technique described here may include:
onboard data logging (e.g. Tucker,
1999), thus removing the necessity of trailing signal wires;
lighter transducers; flight through a more constrained volume, from which
accurate three-dimensional kinematics can be recorded; and improved
time-resolution of the pressure signal. Such developments will permit research
into the aerodynamics of controlled, steady flight of smaller birds in wind
tunnels and near-natural maneuvering, turning, gliding, soaring, hovering,
stooping and landing flight in trained or imprinted birds. The current study
shows results low-pass filtered at 25 Hz (2 pole digital Butterworth), which
limits the temporal resolution: a signal occurring above 20 Hz (or under 0.05
s) is likely to be missed. While this permits variations to be identified
throughout a wingbeat cycle lasting approximately 0.2 s, flight at 8.5 m
s-1 would result in pressure variations for an average chord (0.2 m
width) to be neglected for anything less than two chord lengths of travel. As
a result, interesting transient effects may be averaged and overlooked. With
accurate three-dimensional kinematics and improved, less-filtered pressure
signals (the transducers themselves have frequency responses around 1 kHz),
transient aerodynamic phenomena, potentially important for slow or unsteady
flight, may then be related to details of wing motion.
In conclusion, direct pressure measurements, with appropriate compensation for the sensitivity of pressure transducers to acceleration, allow the aerodynamics of flapping bird wings to be studied without the need for combining data from many wingbeats. Such observations produce direct evidence for both novel aerodynamic features and phenomena previously inferred from kinematics but uncertain due to unknown local induced flow-fields. This technique of direct pressure measurement provides an important link between the properties and consequences of the near-field wake and the physiologically important stresses and strains experienced by muscles and bones developed to generate and transmit the mechanical power necessary for flapping flight.
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Acknowledgments |
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