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)
1 Concord Field Station, Museum of Comparative Zoology, Harvard University,
Old Causeway Road, Bedford, MA 01730, USA
2 Department of Biology, University of Portland, 5000 N. Willamette
Boulevard, Portland, OR 97203, USA
* e-mail: thedrick{at}oeb.harvard.edu
Accepted 4 March 2002
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Summary |
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Key words: cockatiel, Nymphicus hollandicus, ringed turtle-dove, Streptopelia risoria, flight, kinematics, vortex, gait
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Introduction |
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These studies revealed two basic gait types used by birds and bats during
free flight: a `vortex-ring' gait employed in very slow flight and a
`continuous-vortex' gait used in faster forward flight. In slow-speed flight
(3 ms-1 or less), birds and bats employ the vortex-ring gait in
which each downstroke produces a single vortex ring shed from the wing into
the wake at the end of the downstroke. The upstroke appears to be
aerodynamically inactive at slow speeds, with little or no vortex shedding and
lift generation (Fig. 1A,B). In
faster flight (approximately 7 ms-1), several bird and bat species
employ a continuousvortex gait in which each wingtip sheds a separate vortex
trail during both the upstroke and downstroke
(Fig. 1A)
(Rayner, 1986;
Spedding, 1987
). This implies
that a constant bound circulation is maintained over the airfoil (wing)
throughout the entire wingbeat cycle and that lift is generated during both
the upstroke and downstroke (Fig.
1B) (Rayner,
1993
).
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Transitions between terrestrial gaits are abrupt and occur within a narrow,
repeatable range of speeds. Energetic and mechanical factors appear to mediate
the speed at which terrestrial gait changes occur in different species, but
the exact basis for this is uncertain
(Hoyt and Taylor, 1981;
Farley and Taylor, 1991
). In
the case of flapping gaits during flight, two-dimensional kinematic analysis
suggests that transitions may be gradual because most of the parameters
measured in two-dimensional studies vary gradually over the range of flight
speeds (Tobalske and Dial,
1996
; Tobalske,
2000
). The factors that mediate gait changes in flapping flight
are also unknown, although a mathematical model of flapping gaits suggests
that the continuous-vortex gait may generate excessive induced drag at low
speeds (Rayner, 1993
),
indicating that energetic considerations may also influence gait selection
during flight.
The flow visualization experiments originally used to describe the
vortex-ring and continuous-vortex gaits employed a cloud of neutrally buoyant
helium-filled soap bubbles suspended in still air (e.g.
Spedding et al., 1984;
Spedding, 1987
). Multiple
cameras photographed the vortices produced by the bird or bat as it flew
through the bubble cloud, and the three-dimensional movement of the bubbles
was used to quantify the magnitude and direction of the wake vortices. This
technique permits direct visualization of the vortices created by flying
animals, but also allows the animal to control its own forward velocity. As a
result, analysis is often restricted to a few preferred flight speeds chosen
by the animal in question. In these previous studies, only slow to moderate
speeds (3-7 ms-1) were available for study. Training the animal to
fly in a variable-speed wind tunnel allows experimental manipulation of flight
speed and much higher resolution of wing and flight kinematics. However, wind
tunnels greatly increase the difficulty of direct flow observation. These
difficulties have prevented vortex visualization in wind tunnels, but previous
studies (Brown, 1963
;
Tobalske and Dial, 1996
) have
linked kinematic observations from wind-tunnel flight to particular gaits.
These kinematic studies, however, have been limited to two-dimensional
analysis and do not allow characterization of the airfoil surface or close
examination of the aerodynamic forces that differentiate flapping gaits. These
studies inferred gait transitions from various kinematic variables,
particularly vertical or horizontal projections of the wing path and changes
in wing span or wing posture during the upstroke
(Tobalske, 2000
). Such
variables, however, do not provide quantitative predictions for circulation,
which defines the two gaits in question.
In the present study, we used a high-speed three-dimensional kinematic analysis of cockatiels and ringed turtle-doves flying in a variable-speed wind tunnel to examine gait changes over a broad range of flight speeds, from 1 ms-1 to a maximum speed of 15-17 ms-1. Three-dimensional kinematic reconstruction allows characterization of the shape and orientation of the wing surfaces, permitting an estimation of the airflow past the wing and the circulation generated during a wingbeat cycle. These airflow and circulation estimates can be compared with the within-wingbeat flow patterns predicted by vortex-gait theory. Unlike flow visualization, three-dimensional kinematic analysis is not difficult to employ in a wind-tunnel environment and, therefore, allows examination of a complete range of flight speeds and of brief bursts of acceleration or deceleration. The three-dimensional kinematic analysis also includes the information available in two-dimensional kinematic studies, and three-dimensional changes in airfoil shape and estimates of airflow can be related to simpler two-dimensional kinematic parameters.
The goals of our analysis are to identify the speeds at which gait
transitions occur in both species and to test whether gait transitions during
flight are gradual or abrupt. We also seek to evaluate what key kinematic
changes underlie the aerodynamic basis of a gait change during flapping
flight. The two species involved in this study differ in body mass, wing shape
and wing loading (body weight/wing area). Ringed turtle-doves have
approximately twice the body mass of cockatiels and have shorter, broader
wings with a proportionately larger wing area proximal to the wrist joint;
cockatiels have longer and more pointed wings with a greater distal wing area.
Species with a high wing length-to-width ratio (aspect ratio) are expected to
shift to a continuous-vortex gait at lower speeds than similarly sized species
with shorter or broader wings (Rayner,
1991). Species with lower wing loading should also shift to a
continuous-vortex gait at lower flight speeds because the magnitude of
circulation developed during the upstroke and downstroke required to support
the body weight should be lower. Because cockatiels have approximately two
thirds the wing loading of ringed turtle-doves as well as longer, more pointed
wings, we expected cockatiels to adopt a continuous-vortex gait at lower
speeds than ringed turtle-doves.
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Materials and methods |
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Design of the wind tunnel
The Harvard-Concord Field Station (Harvard-CFS) wind tunnel is an
open-circuit tunnel with a closed jet in the flight chamber, designed and
constructed in 1998-1999 (Fig.
2). It has a working section 1.2 mx1.2 m in cross section
and 1.4 m in length and can operate at wind speeds from 0 to 28.5 m
s-1. Air is moved through the tunnel by a 55.9 kW (75 horsepower)
direct current motor (General Electric, Inc.) and 1.4 m diameter fan assembly
(AFS-1.4 Series axial flow fan, SMJ Inc.) equipped with a built-in silencer
(1.4 LCP series) to reduce noise levels. Barlow et al.
(1999) and other sources cited
therein were used to design the tunnel.
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Air is first pulled through a settling section, measuring 9.36 m2 in cross section, constructed with a 10.2 cm deep aluminum (ACG) honeycomb panel (Hexcel Corp.), with >95 % open area and a cell diameter of 9.5 mm, followed by a series of six stainless-steel screens (16 mesh; 72 % open area; wire diameter 0.2 mm; McMaster-Carr, Inc.) spaced 3.8 cm apart. These produce laminar airflow that is accelerated via a settling chamber and inlet with a 6:1 contraction ratio before entering the working section of the tunnel. Air is moved out from the working section and through a first diffuser, providing a transition from a square to a circular cross section. To improve efficiency via recovery of static pressure, the fan exhausts air through a second diffuser. The inner diameter of the diffuser's outlet is 1.8 m.
The working section consists of Lexan wall panels, 6.4 mm thick, mounted to
an aluminum frame that bolts onto the contraction section in front and the
first diffuser section at the rear. A barrier composed of tensioned 250 µm
gauge vertical stainless-steel wires spaced 2 cm apart is located between the
contraction and working sections to prevent the birds from flying out of the
working section. This is an unavoidable design limitation of any tunnel
suitable for studies of animal flight. Flow separation and turbulence
downstream in the working section resulting from the barrier screen, however,
are minimal (see below). The working section flares out very slightly at 0.5
° to allow for boundary layer thickening in order to maintain a
functionally constant inner diameter
(Barlow et al., 1999). The top
panel of the working section has a small (1 cm diameter) port located midway
along its length, allowing for light-weight cabling to transmit and record
signals (electromyography, strain gauge, sonomicrometry) from the animal
during flight. The left wall has an opening 0.25 m wide located 75 % along its
depth (Fig. 2) that can be used
to introduce the animal to the working section. A clear Lexan door can be
closed to seal the port from unwanted air intake during flight trials. The
floor of the working section also has a small (0.3 mx0.5 m) door that
can be opened to allow an investigator access to the inside of the working
section for the purposes of flight training, animal retrieval and cleaning.
Again, to avoid disrupting airflow and introducing turbulence, this door
remains closed during flight trials. The rear of the working section is
separated from the diffuser and motor-fan assembly by a wire screen to prevent
the animals from being sucked into the fan.
A significant problem with obtaining good kinematic recordings of flight movements is reflection from incident lighting located outside a clear acrylic wall. To solve this problem, the working section of the tunnel is equipped with 300 W halogen lamp mounts positioned in six of its eight corners. In practice, depending on camera position, 4-6 of the mounts were used at any one time (providing 1200-1800 W of total illumination) to achieve the lighting necessary for obtaining high-speed digital video recordings of the animal (see below). Although the lamp mounts necessarily introduce local turbulence in the corners of the working section, the benefit of the lighting quality far outweighs any problems that this may cause. In fact, the birds never fly in these extreme regions of the tunnel (see below), choosing to avoid the lights when they are turned on.
To monitor true wind velocity (Vo) in the tunnel, the
dynamic pressure (q) is obtained from the pressure measured between
two ports located in the front and rear of the contraction section using a
differential pressure transducer (Setra 239; nominal precision 0.3 Pa), where:
![]() | (1) |
To make our measurements, obtained under the atmospheric conditions of the
tunnel's location in Bedford, Massachusetts, USA (58 m above sea level; mean
air temperature during data collection was 26.5 °C and air pressure was
100.9 kPa), comparable with measurements obtained from studies involving wind
tunnels at other locations, we follow Pennycuick et al.
(1997) in reporting equivalent
wind speed (Ve) rather than true wind speed:
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Performance of the wind tunnel
We conducted tests to evaluate the quality of airflow in the tunnel.
Measurements of wind speed were made at 121 locations (11x11; 10 cm
grid) at the mid-plane (0.7 m depth from the front) of the working section;
with the wind tunnel operating at 20 m s-1
(Fig. 3). Measurements were
obtained using a digital manometer (Dwyer Series 475 Mark II) connected to a
pitot-static probe (Dwyer Series 160-36) mounted on a 0.635 cm diameter sting
positioned 20 cm upstream from a ring stand that supported the probe in the
working section. The probe and sting were positioned using scale markings on
the ring-stand support and a calibration grid placed on the floor of the
working section. In nearly all (97 %) locations, the variation in flow
velocity was less than 2.5 % of the mean wind speed
(Fig. 3A), averaging 1.03 %
(i.e. 20.00±0.21 m s-1). In general, the relative
distribution of higher versus lower velocity flow showed no
consistent pattern (Fig.
3B).
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A detailed side-to-side transect of wind velocity was also carried out at mid-height (0.6 m) and mid-plane of the working section. This transect was performed to evaluate boundary layer effects on local air velocity close to the walls (Fig. 4); the wind tunnel was set at an equivalent wind velocity of 10 m s-1. Boundary effects on wind velocity were not appreciable until the probe was positioned within 1 cm of the wall; velocity remained within 1.5 % of mean wind speed over the span of the section to within a distance of 2 cm of the right and left side walls.
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To measure mean air turbulence, we used a 30 cm diameter turbulence sphere
(Barlow et al., 1999). We
computed a turbulence factor by dividing an assumed ideal Reynolds number
(Re) of 385x103 by the observed critical Re
of the turbulence sphere. The critical Re of the sphere matched the
point on a fitted line (polynomial fit) at which the pressure coefficient was
1.22. We computed percentage turbulence from our observed turbulence factor
using the regression provided in Fig. 6.7 of Barlow et al.
(1999
).
Measurements of turbulence were obtained at nine locations spaced evenly across the test section in two different planes (A and B, Fig. 5) located at 25 % (0.35 m) and 50 % (0.7 m) depth from the front of the working section. Turbulence was found to be less than 1.28 %, averaging 1.10±0.08 % (mean ± S.D., N=18) at all 18 locations for which measurements were obtained.
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We also obtained velocity and turbulence measurements using a digital
particle image velocimetry (DPIV; Raffel
et al., 1998) system on demonstration loan from TSI Incorporated
(courtesy of S. Anderson). This system involved the use of TSI dual-pulse YAG,
frame-straddling lasers (50 mJ) that illuminated neutrally buoyant particles
of olive oil suspended in the air stream
(Fig. 6). Stereo cameras were
used to reveal particle (and, hence, air) velocity (U, V and
W) in three dimensions (x, z and y, respectively)
defined within the flight chamber, based on illumination of a 10 cm plane. For
these tests, mean U in the x dimension corresponded to
Ve=5 m s-1. At this Ve, the
free-stream true velocity U was 5.54±0.06 m s-1
(range 5.30-5.71 m s-1), V was 0.09±0.03 m
s-1 (range 0.85-0.22 m s-1) and W was
-0.87±0.09 m s-1 (range 0.72-0.56 m s-1) (means
± S.D., N=4275). Total turbulence was 0.23±0.12 %
(range 0.024-1.034 %), and turbulence measured in each component plane was
x=0.07±0.04 % (range 0.001-0.319 %),
z=0.04±0.02 % (range 0.001-0.163 %) and
y=-0.21±0.12 % (range 0.001-1.016 %) (means ± S.D.,
N=4275).
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Potential effects of wind tunnels on bird flight performance
Conditions within a wind tunnel undoubtedly affect bird flight performance
(Rayner, 1994). The unusual
surroundings, noise and lights have unknown effects upon performance, and we
tried to minimize these effects with adequate acclimation and training of the
birds. In addition, the wake of the bird may circulate within the flight
chamber, reflect off the walls of the closed-section flight chamber and
interact with the bound circulation on the wings. Because of this phenomenon,
flight speeds and mechanical power requirements are expected to be lower in a
closed flight chamber compared with free flight without ground effects
(Rayner, 1994
). The effects of
wake reflection are expected to decrease with increasing flight speed.
Wind-tunnel effects are well documented for fixed-wing models
(Barlow et al., 1999
) but not
for birds engaged in flapping flight. One study that compares wind-tunnel with
free-flight performance in a bird suggests that mean wingbeat frequency is
lower in the field and that other wing kinematics exhibit slight differences
between tunnel and free flight (Tobalske
et al., 1997
).
Aerodynamic corrections for bird flight in a closed-section wind tunnel
take into account the ratio of the diameter of the flight chamber to the wing
span and also the position of the bird inside the chamber. The chamber
diameter:wing span ratio was 2.48 for the cockatiels and 2.56 for the doves.
In a cross-sectional view, the birds of both species generally flew near the
horizontal mid-plane or slightly above. This position equates to h/H
values that ranged from 0 to 0.25, where h is the altitude of the
body above the midline of the chamber and H is the vertical height of
the chamber (Rayner, 1994).
Using Rayner's (1994
) model,
for these animal dimensions and positions, minimum power and maximum range
speeds may have been reduced by 3 % and mechanical power at these speeds may
have been reduced by 10 % relative to the same speeds in free flight.
Lacking comparable field data, it is not possible at present to assess the effects of the tunnel upon flight kinematics in the cockatiel and dove; nonetheless, the potential that tunnel conditions may exert a certain systematic effect on our results should be kept in mind.
Three-dimensional coordinate reconstruction
Flight trials were recorded using four synchronized, high-speed digital
video cameras (Redlake PCI 500) operating at 250 frames s-1 with a
shutter speed of 1/1250 s and, in some cases, 1/2500 s. The cameras were
arranged in an arc around the wind-tunnel flight chamber such that the bird
was in view from different angles throughout the wingbeat cycle
(Fig. 7A). Two cameras were
positioned above and behind the animal, and the other two cameras were
positioned to obtain two lateral views. Ventral wing surface views were
available only from the right side of the bird. The cameras were calibrated
with the modified direct linear transformation (DLT) technique using a
19-point calibration frame (measuring 0.420 mx0.340 mx0.285 m in
xyz coordinate space) recorded at the start of each set of trials
(Hatze, 1988). Trials were
recorded at flight speeds of 1-17 m s-1 in 2 m s-1
intervals. Flight speed sequence was not restricted to a particular order, and
the birds were allowed to rest between trials as necessary to maintain
satisfactory performance (typically 2-5 min of steady flight). Cockatiel 1,
which was the first training and test subject, was flown at speeds of 1, 3, 6,
9, 12 and 15 m s-1, rather than at the 2 m s-1 intervals
subsequently used to record from the other individuals.
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Five points: the dorsal and ventral surfaces of the tips of the first, fourth and ninth (or longest) primary feathers, the shoulder and the wrist, were identified on the right wing of each bird using 5 mm diameter circles of white tape marked with a black center dot (Fig. 7B). In addition, a four-point cross of 3 mm wide white tape with black dots at the tips was attached to the dorsal midline between the wings (Fig. 7B). The five points were selected to divide the wing into proximal and distal functional sections: the proximal section consisted of the shoulder, wrist and first primary tip and the distal section consisted of the wrist, ninth primary tip and fourth primary tip. These sets of three points define two distinct planes and effectively separate the wing into distal and proximal sections, allowing an examination of the relative aerodynamic function of these two wing regions in relation to circulation developed over the course of the wingbeat cycle. The four-point dorsal midline cross was used as a proxy for the center of mass to calculate changes in whole-body position, velocity and acceleration during flight. Individual sequences of flight consisting of three successive wingbeats with minimal lateral and vertical movement within the wind-tunnel flight chamber (within-chamber velocity <0.3 m s-1) were selected from the video data and digitized using custom-designed software written in Matlab v5.3. In cases where sequential wingbeats with minimal change in wind-tunnel position were not available, we selected additional wingbeats from the recorded flight sequence, digitizing at least three wingbeats for each individual at each speed.
The raw coordinate data obtained from the digitized trials were resolved
into a single three-dimensional space using the DLT coefficients derived from
the calibration frame (Hatze,
1988). In addition to resolving the multiple two-dimensional
camera views into a single three-dimensional space, the DLT algorithm also
corrects for parallax and other lens distortions. Individual points having a
DLT root mean square (RMS) error two standard deviations greater than the
median error for that point (approximately 5 % of the points) were removed
prior to analysis. Median RMS errors ranged from 2.3 mm for the dorsal midline
marker to 3.2 mm for the ninth primary tip. Occasionally, a point was not in
the view of at least two of the four cameras, resulting in a gap in the
reconstructed point sequence. However, because of the number and placement of
the cameras, such gaps were uncommon. Point interpolation and filtering were
accomplished with a quintic spline fit to known RMS data using the generalized
cross-validatory/spline (GCVSPL) program
(Woltring, 1986
). This method
uses the RMS error from the DLT reconstruction to filter the positional data
and then fills any gaps with a quintic spline interpolation. The results from
this technique were similar to those obtained by smoothing the positional data
using a 37 Hz digital Butterworth low-pass filter. However, the quintic spline
method also allows direct calculation of velocity and acceleration derivatives
from the spline curves, providing the most accurate method for obtaining
higher-order derivatives from positional data
(Walker, 1998
). As a test of
the accuracy of the three-dimensional reconstruction, filtering and derivation
methods, a 5 mm ball bearing was bounced in the video recording field.
Derivation of gravitational acceleration from the motion of the bearing
resulted in a value of 9.79 m s-2. To assess the effect of
digitizing error and the resulting three-dimensional reconstruction error on
the final estimates of circulation, a single wingbeat was digitized five
times. The standard deviation of the circulation estimate from these five
wingbeats was 2.7 % of the mean for the distal wing section and 5.6 % of the
mean for the proximal wing section.
Aerodynamic calculations of circulation and lift
To estimate the bound circulation over the proximal and distal wing
sections and the aerodynamic lift produced, the following variables were
determined.
Airflow
Airflow over the right wing was initially estimated from the kinematic
results by summing the vectors of (i) three-dimensional movement of the wing
within the coordinate space (Wk) and (ii) airflow produced
by the wind tunnel (Ve). Flow velocities were resolved
separately for the proximal and distal portions of the wing. Proximal wing
section kinematics was determined from the centroid of the triangle formed by
the wrist, shoulder and first primary. Distal wing section kinematics was
based on the centroid of the triangle formed by the wrist, ninth primary and
fourth primary (Fig. 7B). We
also estimated vertical and horizontal induced flow velocity, the velocity
added to the air by the bird. In general, the induced velocity estimates acted
to increase the magnitude of flow over the wing and to decrease the angle of
attack of the wing section. Vertical induced flow velocity
(Wiv) was estimated using the following equation
(Azuma, 1992):
![]() | (3) |
![]() | (4) |
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Effective wing length
The proximal and distal effective wing lengths (b) were calculated
as the length of the wing's leading edge orthogonal to the incident airflow
vector (Wt). Markers placed on the shoulder, wrist and
ninth primary established the leading edge position of each wing section.
Proximal effective wing length was based on the distance from the shoulder to
the wrist and distal effective wing length on the distance from the wrist to
the ninth primary (Fig. 9).
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Angle of attack
Angle of attack () for the proximal and distal portions of the wing
was estimated from the three-dimensional geometric position of the distal and
proximal wing sections and the previously established airflow vectors
(relative wind velocity) over these wing sections.
Coefficient of lift
The coefficient of lift (CL) for the distal and
proximal sections of the wing was estimated from the angle of attack using the
following equation (Norberg,
1990):
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Wing chord
Wing chord (c) for the proximal and distal wing sections was
calculated as the distance from the leading edge markers to the trailing edge
markers in the xy (horizontal and lateral) plane.
Circulation
Circulation () around each wing section was calculated to satisfy
the Kutta condition for finite fluids using the wing chord, fluid velocity and
angle of attack parameters established earlier (equations 3 and 4) based on
the following relationships (Norberg,
1990
):
![]() | (6) |
![]() | (7) |
Lift
Instantaneous lift (L) was estimated from the circulation, airflow
and effective wing lengths of the proximal and distal wing sections according
to Norberg (1990):
![]() | (8) |
![]() | (9) |
![]() | (10) |
![]() | (11) |
Unsteadiness
To assess the potential importance of unsteady flow effects, which are not
accounted for in the quasi-steady aerodynamic analysis used to estimate
circulation (Norberg, 1990),
we calculated the `reduced frequency' (k) characterizing the bird's
flight at each speed (Spedding,
1993
):
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All calculations were performed in Matlab v5.3 for Linux (The Mathworks Inc.). We report the results as means ± S.D.
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Results |
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Effective wing length as a function of flight speed
In both species, we found that effective wing length was more constant at
low than at high speeds (Figs
10A,B,
11A,B). The wing was fully
extended during the downstroke and remained extended through much of the
upstroke, but with the individual primary feathers supinated to permit airflow
between them, a maneuver known as a `tip reversal upstroke' or `upstroke
flick' (Brown, 1963;
Norberg, 1976
;
Tobalske and Dial, 1996
;
Tobalske, 2000
). Both species
gradually abandoned this behavior as speed increased, leading to greater
variation in wing length over the wingbeat cycle as distal effective length
was reduced during the upstroke. Effective wing length during the upstroke
decreased in both species at intermediate and fast speeds (Figs
10C,D,
11C,D) as a result of flexion
at the wrist. Wrist flexion was initiated rapidly at wing turn-around and
typically reached a maximum as the wing passed the level of the shoulder. At
intermediate and fast speeds (Figs
10C,D,
11C,D), the wings of both
species were fully extended for the majority of the downstroke. At these
faster speeds, the variation in effective wing length within the wingbeat
cycle was much greater in the distal wing than in the proximal wing, which
remained fully extended throughout the wingbeat cycle.
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Airflow magnitude as a function of flight speed
In both species, the flapping motion of the wing provided most of the
airflow at slow speed flights (1-7 m s-1), whereas at faster flight
speeds (9-17 m s-1) airflow was increasingly driven by the bird's
overall forward velocity. For example, at a forward flight speed of 1 m
s-1, peak airflow over the distal portion the wing of dove 1
approached 10 m s-1 (Fig.
10A), while at a forward flight speed of 17 m s-1 the
peak airflow during downstroke was only elevated to 19 m s-1
(Fig. 10D). This overall trend
affected the variation in circulation within the wingbeat cycle and over the
length of the wing across the range of speeds studied. Because of the wing's
rotational motion (downstroke depression and upstroke elevation), airflow over
the proximal section of the wing during slow-speed flight was much lower in
magnitude than that over the distal section (Figs
10A,B,
11A,B). In contrast, because
airflow was driven mainly by the bird's forward velocity at high speeds,
considerably less variation in airflow magnitude was observed between the
upstroke and downstroke, and airflows over the proximal and distal portions of
the wing were also of similar magnitude. These trends become more pronounced
as speed increased (Figs
10C,D,
11C,D).
Angle of attack as a function of flight speed
Similar to patterns of airflow over the wing, variation in the wing's angle
of attack over the course of the wingbeat cycle decreased with increasing
speed in both species. Angles of attack () at low speeds (Figs
10A,
11A, with peaks of 52° for
the proximal and 43° for the distal wing sections) were much greater than
those commonly used by aircraft airfoils (0-15°;
McCormick, 1995
). Mean angles
of attack at faster speeds decreased (proximal 9-14°; distal -5 to
14°) to within the range employed by conventional airfoils. Nevertheless,
brief periods of high angle of attack persisted at all but the fastest speeds.
Peak angle of attack for the distal wing section of both species at all speeds
typically occurred at mid-downstroke, as the wrist passed below the shoulder.
At this time, the distal wing's angle of attack was due primarily to the
motion of the wing relative to the bird's body as the wing chord was oriented
nearly parallel to airflow within the tunnel. In contrast to the distal wing,
patterns of proximal wing section peak angle of attack for both species
changed with speed. In slow-speed flight, the proximal peak angle of attack
occurred at mid-downstroke, concomitant with the peak for the distal section.
Consequently, its timing and magnitude were also due to the wing's motion
rather than to its orientation to airflow within the tunnel (Figs
10A,
11A). At faster speeds,
however, changes in proximal angle of attack were phase-delayed relative to
distal angle of attack, with the result that proximal angle of attack peaked
during the upstroke (Figs
10B-D,
11B-D). This trend was more
pronounced in the doves than in the cockatiels, but clearly occurred in both
species. Because of the lower angular velocity of wing motion during the
upstroke, the angle of attack achieved by the proximal wing section at this
phase was primarily due to a more angled orientation of the wing section
relative to airflow within the tunnel.
Circulation as a function of flight speed
At slow speeds in both species, the distal wing section during the
downstroke provided most of the estimated circulation developed over the
course of the wingbeat cycle. In general, circulation about the proximal wing
section during the downstroke was low and generated little lift (Figs
10A,B,
11A,B). As forward speed
increased, estimated circulation was influenced by two trends: (i) differences
in airflow between the proximal and distal wing sections and between the
upstroke and downstroke declined in magnitude, and (ii) the proximal wing
section's peak angle of attack was phase-delayed into the upstroke. The
interaction between these two trends at faster speeds resulted in the
development of significant circulation about the proximal wing during the
upstroke and a maintained dominance of distal wing circulation during the
downstroke (Figs 10C,
11C). At near maximum flight
speeds, upstroke circulation decreased relative to downstroke circulation.
This resulted from the very low angle of attack of the proximal wing during
the upstroke, which severely reduced its estimated circulation despite the
large magnitude of airflow moving past it (Figs
10D,
11D). In general, circulation
became more constant as flight speed increased, but some intra-wingbeat
variation still occurred. In slow flight, the distal wing downstroke (Figs
10A,B,
11A,B) dominated circulation
patterns. In intermediate and fast flight, circulation switched between the
distal wing during the downstroke and the proximal wing during the upstroke,
resulting in an overall decline in within-wingbeat variation in
circulation.
To examine general patterns of circulation for the full range of flight
speeds studied, we averaged the estimated circulation over half-wingbeat
intervals (mean proximal upstroke versus mean distal downstroke). We
alternated between the distal and proximal wing sections for each phase of the
wingbeat cycle because our intra-wingbeat results (Figs
10,
11) showed that the distal
wing dominated lift production during the downstroke and that the proximal
wing section dominated during the upstroke. This resulted from the interaction
between estimated circulation magnitude and effective wing length during each
phase. In both species at slow speeds, circulation during the downstroke was
much greater than that achieved during the upstroke
(Fig. 12). As speed increased,
mean downstroke circulation decreased and upstroke circulation increased, the
two becoming nearly equivalent at 7 m s-1
(Fig. 12). The match between
downstroke and upstroke circulation was maintained up to nearly the fastest
speeds at which each species flew in the tunnel. At the fastest speeds (>12
m s-1 for the cockatiels and >15 m s-1 for the
doves), circulation developed by the proximal wing section during the upstroke
again began to decline. The decline in proximal wing section upstroke
circulation correlated with the difference in mean maximum speed observed for
the two species (cockatiels 15 m s-1; doves 17 m s-1).
Equivalent circulation during the upstroke and downstroke should result in a
continuous-vortex gait, whereas much greater downstroke circulation relative
to upstroke circulation should result in a ladder-wake gait
(Pennycuick, 1988). Thus, both
species started with a vortex-ring gait and switched to a continuous-vortex
gait at 7 m s-1. Cockatiels maintained a continuous-vortex gait to
12 m s-1 and doves to 15 m s-1
(Fig. 12), whereupon they
appeared to change to a ladder-wake gait.
|
Translational and rotational circulation
We derived our overall estimate of circulation from two different sources:
circulation due to wing translation (t) and circulation due
to long-axis rotation of the wing (
r). We found that
translational circulation made up the majority of the total, providing 90 % or
more of the total circulation at all speeds when averaged over a complete
wingbeat cycle. However, our analysis suggests that a brief period of high
rotational circulation occurs at the transition from the upstroke to the
downstroke in slow flight (Fig.
13). This pulse of rotational circulation was prominent in doves
at speeds of 1, 3 and 5 m s-1 and in cockatiels flying at 1 and 3 m
s-1.
|
Reduced frequency
The quasi-steady aerodynamic analysis that we employed to estimate
circulation assumes steady airflow over the wing during the upstroke and
downstroke phases of the wingbeat cycle. To assess the validity of this
assumption, we calculated the reduced frequency of the bird's flight at each
speed from the angular velocity of the bird's wing during the downstroke with
respect to the bird's forward flight speed
(Fig. 14). In general, flight
conditions involving a reduced frequency of less than 0.3 support the
assumption of steady flow and can be accurately modeled using a quasi-steady
analysis (Spedding, 1993).
This condition was met for both species at speeds of 5.0 m s-1 or
above. The reduced frequency results at 1.0 and 3.0 m s-1 do not
support a quasi-steady analysis. Inter-trial variation in reduced frequency
was much greater at low speeds because the unsteadiness of the bird's position
within the flight chamber at low speeds contributes much more to the overall
unsteadiness of airflow than when the birds flew at higher speeds.
|
Impulse comparison: accuracy of the two-section circulation
model
As a further check of the results that we obtained from our quasi-steady
analysis, we compared the vertical impulse provided by lift calculated from
the circulation results (equation 10) with that determined from the vertical
acceleration of the bird (equation 11;
Fig. 15). These calculations
do not include all the forces acting on the bird; in particular, we omit all
drag and lift from surfaces other than the wings. However, vertical
acceleration to overcome gravity is believed to be much greater than that
required to overcome drag, and the wings are expected to provide the majority
of lift at all speeds (Pennycuick et al.,
2000). Thus, our omission of drag and body or tail lift should
still allow a useful, if approximate, comparison between the impulse provided
by our circulation estimates and the impulse required for weight support. As
expected, the impulse calculated from acceleration changed little with speed,
reflecting the near-constant vertical position that the birds held at all
speeds. The impulse calculated from circulation for both species
underestimated the acceleration derived impulse at speeds below 5 m
s-1, was approximately equal at intermediate speeds (5-11 m
s-1) and exceeded it at speeds above 11 ms-1. This trend
was more apparent in the cockatiels than in the doves. Overall, the impulse
comparison shows that our two-section circulation model provided an impulse
sufficient to maintain altitude at all but the slowest speeds and performed
best at intermediate flight speeds where the gait transitions occurred.
|
Gait transition speed
At 7 m s-1, all four of the birds, and especially dove 1,
adopted a flight pattern of accelerating upward and forward in the tunnel
working section via a series of rapid, high-amplitude wingbeats then
slowly drifting back with a series of lower-amplitude wingbeats
(Fig. 16). The high-amplitude
wingbeats were characteristic of those observed in slower flight, whereas the
lower-amplitude wingbeats were characteristic of those used in fast flight.
These two wingbeat styles also corresponded to very different estimated
circulation patterns. High-amplitude, high-acceleration wingbeats showed a
much greater mean circulation over the distal wing during the downstroke than
over the proximal wing section during the upstroke
(Fig. 16C). However, in the
lower-amplitude and slightly decelerative wingbeats, circulation over the two
wing sections and between the upstroke and the downstroke was approximately
equal. In all these cases, proximal wing section upstroke circulation was
maintained relatively constant, whereas distal wing circulation varied greatly
depending on whether a slow-speed (high-amplitude) or a fast-speed
(low-amplitude) wingbeat kinematic pattern was adopted.
|
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Discussion |
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Analysis of aerodynamic gaits: vortex-ring versus continuous-vortex
gait
Our present measurements allowed us to investigate the use of these two
aerodynamic gaits over a broad range of speeds. We found that, during
slow-speed flight (1-5 m s-1), both species produced a much greater
bound circulation during the downstroke than during the upstroke, indicating
the use of a vortex-ring gait. At 7 m s-1, both species produced
approximately equivalent circulation during the downstroke and upstroke
(Fig. 12), indicative of a
continuous-vortex gait. At faster speeds, the cockatiels (7-12 m
s-1) and doves (7-15 m s-1) appeared to sustain a
continuous-vortex gait.
Our three-dimensional kinematic and quasi-steady aerodynamic analysis
revealed a slightly different gait transition speed (7 m s-1) for
the doves from that suggested by a more traditional two-dimensional kinematic
analysis (9 m s-1; B. W. Tobalske, personal observation). Both
two-dimensional (B. W. Tobalske, personal observation) and three-dimensional
analysis indicate a similar transition speed of 7 m s-1 for
cockatiels. The discrepancy between the two-dimensional and three-dimensional
results for doves highlights the difficulty of precisely inferring gait
transitions from two-dimensional kinematics (Brown,
1953,
1963
;
Scholey, 1983
;
Aldridge, 1986
;
Tobalske and Dial, 1996
;
Tobalske, 2000
). By examining
variables directly related to the formation of circulation around the proximal
wing section during the upstroke, three-dimensional kinematic analysis
doubtless provides a more reliable estimate of the changes in circulation that
underlie the shift from a vortex-ring to a continuous-vortex gait. This is not
possible using a two-dimensional approach, which is largely limited to
measurements of the tip-reversal angle and wing span during the upstroke to
infer changes in flight gait. Ultimately, flow visualization studies of a
species across a broad range of flight speeds will be needed to evaluate
circulation directly and to confirm our three-dimensional kinematic estimates
of circulation in relation to gait use.
Gait transitions during acceleration and high-speed flight
In both species, estimated upstroke circulation declined as each approached
the fastest speed (cockatiels 15 m s-1, doves 17 m s-1)
that it would sustain in the wind tunnel. The loss of circulation during the
upstroke and corresponding increase during the downstroke
(Fig. 12) suggest that at
their very fastest flight speeds these two species do not employ a
continuous-vortex gait. At these fastest flight speeds observed in our wind
tunnel, both species retracted their wings to an increasing degree in an
apparent attempt to reduce profile drag. The presumed loss of a
continuous-vortex wake structure during very fast, forward flapping flight has
not been observed previously, although it is a recognized possibility
(Rayner, 1993). We interpret
this decline in upstroke circulation as a relative shift in the aerodynamic
requirements of the wing from the need to generate lift at low and
intermediate speeds to a rapidly increasing need to reduce drag and produce
thrust in order to achieve a very fast forward flight speed.
In addition to this high-speed gait change, we also found that the birds
employed a similar change when accelerating upwards and forwards at speeds at
which they normally employed a continuous-vortex gait
(Fig. 16). In both the
high-speed and acceleration cases, estimated upstroke circulation was non-zero
but was less than downstroke circulation. These conditions match those of
Pennycuick's proposed ladder wake
(Pennycuick, 1988). Hence, we
believe that these species employ a ladder-wake gait during very fast flight
and during bouts of acceleration at intermediate speeds. Both acceleration and
very fast flight require increased forward thrust in comparison with normal
cruising flight, either to accelerate the center of mass or to act against
profile and parasite drag at high speeds (which increase in proportion to
Ve2). Thus, in these two species, the ladder-wake gait
appears to be the preferred means of generating additional thrust at medium
and fast flight speeds.
Two properties of flapping flight further explain the shift away from the
continuous-vortex gait at very fast flight speeds: (i) use of the distal wing
as the primary source of thrust, and (ii) negative thrust production during a
lifting upstroke. Most of the thrust in flapping flight is produced by the
distal wing during the downstroke (Brown,
1963). Therefore, increasing thrust production requires the
distal-wing-bound circulation to increase. Consequently, if the proximal
circulation during the upstroke does not increase to match the distal
downstroke circulation, a bird will necessarily shift into a discontinuous
vortex-ring or ladder-wake gait. The difficulty for a bird flying at high
speed and attempting to sustain circulation and lift during the upstroke is
that upstroke circulation necessarily generates negative thrust (i.e. lift has
a rearward component; Fig. 1B).
Therefore, increasing proximal wing circulation during the upstroke to match
distal downstroke circulation and maintain a continuous-vortex gait would
actually diminish the bird's forward acceleration by increasing negative
thrust production. Our results obtained during periods of acceleration
(Fig. 16) and very fast flight
(Figs 10D,
11D,
12) confirm this, showing
that, although estimated upstroke circulation does not cease, it does not
increase to match the elevated downstroke circulation, resulting in the loss
of continuous circulation and a shift to a ladder-wake gait.
Accuracy of the quasi-steady analysis
Our estimations of circulation and lift rely on an assumption of
quasi-steady flow and simple airfoil behavior in which a constant
configuration is maintained and the plane of the airfoil is nearly parallel to
the incoming airflow. In short, a quasi-steady assumption permits analysis of
flow patterns without reference to the time history of these flow patterns.
Comparison of our results obtained for the aerodynamic impulse derived from
our circulation analysis with the impulse based only on measurements of the
bird's whole-body acceleration (Fig.
15) suggests that our quasi-steady analysis, while accurate over a
broad range of intermediate speeds (5-11 m s-1), underestimates
overall circulation at low speeds and overestimates it at high speeds.
Consistent with this, reduced frequency analysis
(Fig. 14) indicates that
quasi-steady flow assumptions are invalid from 1 to 3 m s-1,
explaining the impulse discrepancy during slow flight. At fast speeds, the
discrepancy in aerodynamic impulse is more likely to reflect our use of a
simplified wing model and the absence of profile and parasite drag estimates.
We modeled the wing as consisting of two simple (proximal and distal) plates.
By treating the distal portion of the wing as a plate with uniform orientation
and no span-wise bending, our analysis ignores the loss of circulation that
may well be incurred by increased bending of the wing, particularly over its
distal section. This is likely to be most prominent at faster flight speeds as
aerodynamic forces increase (i.e. according to a classic U-shaped curve;
Combes and Daniel, 2001). The
discrepancy between our calculation of circulation and acceleration models
could also result from parasite and profile drag which, because of
uncertainties regarding suitable drag coefficients (e.g.
Pennycuick et al., 1997
), were
not added to the acceleration-based impulse results
(Fig. 15). These drag forces
should increase rapidly at high speeds and may account for some of the
`excess' circulation impulse that we estimated at the fastest speeds at which
the birds flew in the wind tunnel.
Comparison with direct measurements of circulation
Despite the limitations of our quasi-steady analysis, the circulation
magnitudes that we observe here compare favorably with those reported in
previous studies based on direct visualization of the wake structure behind
the wing (Table 1). Circulation
magnitude at a particular flight speed should increase linearly with wing
loading for species of similar size and wing shape, including all of those
listed in Table 1. Circulation
magnitude should also be lowest at intermediate flight speeds at which the sum
of induced, parasite and profile drag is minimized
(Pennycuick, 1975;
Rayner, 1995
). Both these
trends are evident in Table 1.
The value for a pigeon (1.72 m2s-1) flying at 2.5 m
s-1, which is 2-5 times greater than that of the other species,
probably reflects its much higher (60% greater than the mean of the other
species) wing loading and relatively shorter and broader wings (lower aspect
ratio), especially in comparison with the cockatiel. Both these factors will
necessitate a larger magnitude of circulation to support the bird's body
weight.
|
Intra-wingbeat variation in circulation
Although the use of a `continuous' vortex gait suggests uniformly
maintained circulation over the course of the wingbeat cycle when birds fly at
moderate to fast speeds, our estimates of instantaneous circulation indicate
that significant variation in circulation magnitude occurred over the course
of the wingbeat cycle at all speeds when birds used this aerodynamic gait
(Figs 10,
11). Variation in circulation
was greatest at wing turn-around, as a result of the decrease in distal and
proximal wing section circulation magnitude at these times (Figs
10C,
11C), and generally decreased
as speed increased. Theoretical analysis of the continuous-vortex gait based
on previous flow visualization experiments suggests that instantaneous
circulation should be constant throughout the entire wingbeat cycle
(Rayner, 1993). However, this
does not correspond to our findings. As noted above, we found that mean
circulation remained constant between halves of the wingbeat cycle (between
upstroke and downstroke) but was not constant within the half-cycles. These
brief shifts in circulation magnitude should lead to energy loss and airflow
along the wing from root to tip (span-wise vorticity), reducing aerodynamic
efficiency (Rayner, 1986
).
However, given the time-varying nature of both incident airflow over the wing
and wing configuration in flapping vertebrate flight, variation in circulation
over the course of the wingbeat cycle may be unavoidable. Our results for
cockatiels and doves suggest that this is the case over much of their speed
range when using a `continuous'-vortex gait (Figs
10C,
11C).
Because of limitations inherent to our quasi-steady kinematic analysis and
the current lack of time-varying visualized changes in circulation and wake
structure, it is likely that our results based on an evaluation of the
circulation achieved over each half-wingbeat
(Fig. 12) more accurately
reflect the overall pattern of the bird's vortex wake than our analysis of
instantaneous changes in circulation (Figs
10,
11). Although our kinematic
analysis does record rapid changes in wing configuration (such as those that
occur especially during wing turn-around), it is not clear that circulation
changes instantly in response to changing wing configuration. Spanwise
vorticity of sufficient magnitude to create a vortex-ring wake rather than a
continuous-vortex wake may occur only if bound circulation on the wing is
completely arrested and must be re-initiated
(Rayner, 1993). Also, it is
important to recognize that the vortex wake observations that have laid the
foundation for vortex gait theory reflect patterns produced by complete
wingbeats and are not a direct recording of the instantaneous circulation
within the time span of one wingbeat
(Spedding et al., 1984
;
Spedding, 1986
,
1987
). While intra-wingbeat
changes do occur and may reduce aerodynamic efficiency, they do not alter the
fundamental patterns of aerodynamic gait versus flight speed that we
find here and which have been previously hypothesized
(Rayner, 1986
) and described
(Spedding et al., 1984
).
Aerodynamics of flight gait transition: establishing upstroke
circulation
The species in this study established equivalent circulation during the
upstroke and downstroke (the continuous-vortex gait requirement) primarily by
increasing estimated circulation during the upstroke, although some reduction
in downstroke circulation did occur (Fig.
12). As the circulation produced during the downstroke is easily
diminished by a reduction in flapping velocity, the key changes that lead to a
gait transition occur during the upstroke. Cockatiels and doves established
upstroke circulation by meeting the following two conditions: (i) a phase
delay in the peak proximal wing section angle of attack from mid-downstroke
into upstroke, and (ii) a reduction in intra-wingbeat variation in airflow
(Wt), especially during the upstroke, by increasing
overall forward velocity. Variation in estimated circulation over the course
of a wingbeat cycle was due primarily to two sources: changes in the magnitude
of airflow and changes in the angle of attack.
At all speeds, airflow (Wt) was greater during the downstroke than during the upstroke. Thus, establishing equivalent circulation across the entire wingbeat cycle required a greater angle of attack during the upstroke than during the downstroke. We found that, at low speeds (1 and 3 m s-1) in both species, distal and proximal wing section peak angle of attack occurred during the downstroke (Figs 10Aiv, 11Aiv). Whereas the distal wing's peak angle of attack occurred during the downstroke at all flight speeds, at 5 m s-1 and faster, both species adopted a phase delay in the proximal wing section peak angle of attack, so that it peaked during the upstroke rather than the downstroke. However, airflow at this speed was insufficient to create a continuous-vortex gait (Figs 10Biii, 11Biii, 12). Both the motion of the wing and the bird's forward velocity contributed to airflow over the wing during the downstroke. In contrast, wing motion during the upstroke added little to the flow provided by the bird's overall forward velocity. Thus, the flow available for establishing upstroke circulation was determined almost exclusively by the bird's forward velocity. It was not until both species flew at 7 m s-1 that the flow magnitude over the wing, in combination with the proximal wing section angle of attack, was sufficient to produce the substantial upstroke circulation necessary to establish a continuous-vortex gait.
Aerodynamics of gait transition: fast flight, acceleration and
morphology
After making a transition into a continuous-vortex gait at 7 m
s-1, both species progressively decreased the angle of attack of
the proximal and distal sections of the wing at faster speeds. At the same
time, however, both species maintained the phase delay in the proximal wing
section's angle of attack relative to the distal wing. Because of the extreme
reduction in the proximal wing section angle of attack (2°) at the fastest
speeds (cockatiels 15 m s-1, doves 17 m s-1) that either
species would sustain in the wind tunnel, estimated upstroke circulation
declined substantially relative to that generated by the distal wing during
the downstroke, resulting in the loss of a continuous-vortex gait. As noted
above, however, this reduction in angle of attack was apparently necessary for
reducing profile drag for the birds to sustain these very fast flight speeds.
This resulted in a second gait transition, in which both species appeared to
adopt a ladder-wake gait.
The phase delay in the proximal wing section's angle of attack that developed at a steady forward flight speed of 5 m s-1, prior to the transition into a continuous-vortex gait, was also observed when the birds accelerated within the wind tunnel at intermediate flight speeds (Fig. 16). Incident airflow velocities developed during the use of such rapid, highamplitude downstrokes were much greater than those developed during the upstroke. Consequently, estimated downstroke circulation was much greater than that achieved during the upstroke, resulting in brief shifts between the use of a ladder-wake gait during the acceleration burst and a continuous-vortex gait when the bird returned to a steady flight speed.
Contrary to our prediction that the cockatiels would switch to a continuous-vortex gait at a lower speed than the doves because of their 33% lower wing loading, the transition speed was identical for both species. We had anticipated that the cockatiels' lower wing loading would result in their requiring a lower overall circulation at any given flight speed and that this should enable them to shift to a continuous-vortex gait at a lower speed than the doves because it would require less upstroke circulation to match that produced during the downstroke and establish a continuous-vortex gait. Although the mean magnitude of circulation produced by the cockatiels was indeed approximately 50% of that of the doves, this difference was apparently insufficient to enable them to adopt a continuous-vortex gait at 5 m s-1, despite the presence of a phase delay in the proximal wing's angle of attack at that speed.
Vortex wake gaits in comparison with terrestrial gaits
Terrestrial gait transitions are typically correlated with changes in
footfall and shifts in muscle use patterns
(Hildebrand, 1959;
Goslow et al., 1981
).
Different terrestrial gaits can be distinguished by distinct patterns of
whole-body center of mass energy fluctuations and mechanical work
(Cavagna et al., 1977
). In the
present study, we found that both cockatiels and ringed turtle-doves gradually
switched from a discontinuous vortex-ring to a continuous-vortex gait, finally
making the transition at a similar distinct speed (7 m s-1). The
use of the vortex-ring or ladder-wake gaits at speeds above 7 m s-1
was associated with brief periods of acceleration, whereas the use of a
continuous-vortex gait at slow speeds was associated with brief periods of
deceleration. The gradual nature of vortex gait transitions that we observe
here for these two avian species and previous two-dimensional kinematic
results (Tobalske and Dial,
1996
; Tobalske,
2000
) suggest that vortex gaits should not be viewed as distinct
locomotor gaits similar to those used by terrestrial animals but simply the
aerodynamic consequences of changes in speed.
However, the gradual change in aerodynamic gait that we observed probably
reflects the constraints that a wind-tunnel environment places on a flying
animal's forward velocity. We found that shifting from a vortex-ring to
continuous-vortex gait required adjustment of both peak angle of attack timing
and overall flight speed. By restricting flight speed (i.e. by having the
birds fly in a relatively constricted space, 1.4 m in length), we may
constrain the birds to use a gradual gait transition. The flight chamber in
our wind tunnel is large enough to allow the species we examined in this study
some freedom of movement and, as noted above, individual animals occasionally
used this space to alternate rapidly between gaits, accelerating with a
ladder-wake gait and decelerating with a continuous-vortex gait. Such a
pattern of acceleration and deceleration is evident in the 7 m s-1
trial shown in Fig. 16, where
gait changes apparently occur within two wingbeats. Similar oscillations have
been observed to occur in magpies flying in a wind tunnel and in the field
(Tobalske et al., 1997). It
would be interesting to test whether such variation in gait use is
characteristic of cockatiel and dove flight in the field or whether birds in
the wild tend to avoid flying at such transition speeds. Under natural,
free-flight conditions, both the timing of angle of attack and overall flight
speed are under the direct control of the bird. As a result, the switch from a
vortex-ring gait at 5 m s-1 to a continuous-vortex gait at 7 m
s-1 may occur within the duration of a few wingbeats.
Concluding remarks
Our analysis of wing kinematics combined with a quasisteady airflow
analysis shows that cockatiels and ringed turtledoves both shift from a
vortex-ring to a continuous-vortex gait at 7 m s-1. Both species
also shift to a vortex-ring gait in situations calling for maximal thrust
production such as acceleration and very fast flight. We expected that
differences in wing shape and body size would result in different circulation
levels and different gait transition speeds between cockatiels and ringed
turtle-doves. While estimated circulation magnitude did differ as expected,
gait transitions occurred at the same speed (7 m s-1), although
greater resolution in speed near the transition might show some difference.
Vortex gait transitions occur gradually in the wind tunnels, but may occur
rapidly in free flight where the bird is free to vary its flight speed, e.g.
when reaching cruising flight speeds from take-off. Thus, further
investigation of gait transition speed would benefit from free-flight
conditions where the experimental apparatus (wind-tunnel or still-air
corridor) does not constrain flight behavior. Finally, the use of flow
visualization in a variable-speed wind tunnel remains the best prospect for
further investigation of the aerodynamic effects of flight gaits and is more
likely to resolve the variability in circulation experienced by a bird
employing a continuous-vortex gait.
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Acknowledgments |
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