|
| |
|
|
|
|
||||
| Home Help Feedback Subscriptions Archive Search Table of Contents | ||||
First published online May 8, 2007
Journal of Experimental Biology 210, 1742-1751 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.001701
Aerodynamics of wing-assisted incline running in birds
1 Department of Biology, University of Portland, 5000 North Willamette
Boulevard, Portland, OR 97203, USA
2 Flight Laboratory, Division of Biological Sciences, University of Montana,
32 Campus Drive, Missoula, MT 59812, USA
* Author for correspondence (e-mail: tobalske{at}up.edu)
Accepted 12 February 2007
 |
Summary |
|---|
 TOP Summary IntroductionMaterials and methodsResultsDiscussionList of symbols and...References |
|---|
Key words: vorticity, circulation, added mass, lift, digital particle image velocimetry, ontogeny
|
Introduction |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of symbols and...References |
|---|
;
Dial et al., 2006). It is
commonly used by ground-dwelling species such as the Galliformes when they
have access to a sloped terrain (cliff, boulder, tree, etc.), and may also be
common among nestlings of a diverse array of bird species (K.P.D., unpublished
observation). During flapping flight the wings produce lift, normal to the
incurrent velocity on the wing, which functions to support body weight and to
produce thrust that opposes profile and parasite drag on the wings and body
(Rayner, 1988;
Norberg, 1990). As gravity
dominates the force balance even during fast flight in vertebrates, net lift
during steady flapping flight is oriented primarily upward
(Rayner, 1988). In contrast,
during WAIR it is hypothesized that lift from the wings functions primarily as
thrust that accelerates the body toward the surface of the substrate being
climbed, thereby increasing friction and aiding the feet in gaining purchase.
Previous studies using kinematics, accelerometers and force plates have
provided data in support of this hypothesis, but uncertainty remains about the
aerodynamics of flap-running. Stroke-plane angles are oriented toward the
substrate during the early phase of downstroke
(Dial, 2003;
Dial et al., 2006;
Segre, 2006), and the body is
accelerated toward the substrate during most of the wingbeat cycle
(Bundle and Dial, 2003), but it
has not been established whether such acceleration is due to lift, profile
drag or inertia of the wings. One objective of the present study was to reveal
the aerodynamic function of the wings for adults, juveniles, and even baby
birds (6–8 days) during WAIR using digital particle image velocimetry
(DPIV).
Although WAIR is an intriguing escape behavior in adult birds, it emerges
as a particularly fascinating behavior when the implications of flap-running
are considered relative to the ontogeny and, potentially, the evolution of
flight. Like many ground-dwelling birds, chukar partridge (Alectoris
chukar; Gray 1830; hereafter `chukar') exhibit precocial development.
Baby chukar, covered in down, can walk away from their nest upon hatching.
Their flight feathers emerge over several weeks, and they can fly
approximately at 20 days post hatching (d.p.h.) when the flight feathers are
fully emerged (Dial et al.,
2006; Segre,
2006). Within 6–8 d.p.h., baby chukars have partially
emerged, symmetrical wing feathers. These babies will use WAIR even though
they are unable to fly, and they will continue to use WAIR throughout the rest
of their development (Segre,
2006). The majority of bird species are altricial in their
development, so the young leave the nest and fly for the first time using
flight feathers that are nearly identical to those in the adult. Thus, WAIR in
precocial species offers a unique opportunity to study the ontogeny of lift
development in birds. Our second objective with the present investigation was
to test whether the aerodynamics of the developing wing are the same across
age classes of chukar.
If partially developed wings in precocial birds are reasonably analogous to
the incipient wings that the presumed ancestors of modern birds possessed,
then the ontogeny of WAIR in extant species offers a novel, testable
biomechanical model for the origin of powered flight in birds
(Bundle and Dial, 2003;
Dial, 2003;
Dial et al., 2006). This model
assumes that development in external wing morphology is representative of the
transitional adaptive stages (Bock,
1965) that led to the complex structure of the extant avian wing.
An obvious limitation of the model is uncertainty in how extant avian
neuromuscular control and kinematics compare with ancestral forms.
Nonetheless, our present effort to document the aerodynamics of WAIR in baby
chukar might provide new insight into how an ancestral incipient wing that was
not capable of supporting flight may have been an exaptation
(Gould and Vrba, 1982)
originally used solely for WAIR.
|
Materials and methods |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of symbols and...References |
|---|
=1.15 kg
m–3), and half took place at the University of Montana
(=1.12 kg m–3). The birds were transported between
institutions using a private jet.
|
|
We used previously established methods for eliciting WAIR and flight
(Bundle and Dial, 2003;
Dial, 2003;
Dial et al., 2006;
Segre, 2006). Inclines, made
of wooden boards, were 15 cmx45 cmx2 cm
(widthxlengthxthickness) for babies and 25 cmx2 mx2 cm
(widthxlengthxthickness) for juveniles and adults. With a refuge
box at the top of an incline and 60-grit sand paper providing for traction,
the birds climbed at the maximum slope for which we could obtain repeated
runs. Average incline angle relative to horizontal was 65±0° in
babies, 74±7° in juveniles, and 80±0° in adults
(Fig. 2). To elicit flight in
adults with a climb angle of approximately 80°, we removed the incline and
released the bird by hand below the refuge box. We sampled the flights in the
middle of the climb during the interval in which the birds were climbing
approximately at a steady rate. We recorded and analyzed 138 WAIR trials and
11 flights.
|
;
Warrick et al., 2005). We
verified the location of the bird and the motion of its wings relative to the
illumination field using a synchronized high-speed video camera (Redlake
PCI-2000, San Diego, CA, USA) sampling at 250 Hz and located dorsal to the
animal's line of travel. We seeded the air with particles of olive oil (<1
µm in diameter) generated at a rate of 7x1010 particles
s–1 using a vaporizer fitted with a Laskin nozzle. Particle
illumination was recorded using a 1376x1040 pixel,
charged-coupled-device (CCD) camera placed perpendicular to the illumination
field, and DPIV samples were obtained at 5 Hz.
To calculate particle velocity, we used cross-correlation of paired images
with an elapsed time between images (
t) of 500 µs for
babies and 325 µs for juveniles and adults. Average particle separation was
6 pixels in the center of the animal's wake. We employed an adaptive multipass
with an initial interrogation area of 64x64 pixels and final area of
16x16 pixels with 50% overlap. Vector fields were post-processed using a
median filter (strong removal if difference relative to average >2*r.m.s.
of neighbours and iterative reinsertion if <3*r.m.s. of neighbours),
removal of groups with <5 vectors, fill of all empty spaces by
interpolation, and one pass of 3x3 smoothing. We estimate minimum error
in velocity measurements was 5.0±0.5%, including contributions due to a
correlation peak of 0.1 pixels, optical distortion and particle-fluid
infidelity (Raffel et al.,
2000; Spedding et al.,
2003b).
Subsequent analysis focused upon vortex cores and the velocity of the jet
between the cores observed in the wake 1–5 chord lengths away from the
base of the animal's wings (Fig.
2 and Fig. 3A). We
used streamlines (Fig. 3B),
drawn with vectors expressed relative to average velocity, to inform our
selection of regions of vorticity. Vorticity (
, in
s–1) was computed using post-processed vector fields as
rotz (dy/dx). We treated as background noise and
masked from subsequent analysis ||<3s.d. of
|| in the free-stream
(Fig. 3C,D). To measure
circulation (
, m2 s–1) in vortex cores, we
initially used one of two methods adapted from Spedding et al.
(Spedding et al., 2003a).
First, we integrated with respect to area for all above-threshold,
contiguous, same-sign about a given peak (max),
giving c (Fig.
3C,D). Second, we integrated all same-sign in a given DPIV
field within 1.5 chord lengths (c) of peak to measure
a. This method involved some subjectivity, and again was
informed by the appearance of streamlines
(Fig. 3B).
|
We considered each negatively signed vortex core deposited in the wake
during early downstroke to represent the cross-section of a starting vortex
(Figs 2,
3) shed from the trailing edge
of the wing, equal in magnitude but opposite in sign from the bound vortex on
the wing as lift development began during downstroke
(Batchelor, 1967;
Norberg, 1990;
Spedding et al., 2003a).
Similarly, we considered each positively signed vortex core deposited in the
wake during late downstroke to represent the cross-section of an ending vortex
shed from the trailing edge of the wing. Observed vortex cores may have
represented portions of trailing tip vortices rather than starting or stopping
vortices (Spedding et al.,
2003a; Warrick et al.,
2005), but the distinction was not relevant for our analyses as we
assumed the wake vortices rolled up into the form of planar elliptical loops
(see estimation of lift, below).
As in Spedding et al. (Spedding et al.,
2003a), c produced an estimate of average lift
that was insufficient to support weight (i.e. match gravitational acceleration
of the body at 9.805 m s–2) during flight at a steady rate of
climb (71±3% for 
and
103±26% for 
). During
WAIR and flight, 
was
significantly greater 
within
what we interpreted to be a single vortex loop (paired t-test,
P=0.0193; d.f.=8). We viewed this pattern as being inconsistent with
the Kelvin–Helmholtz Circulation Theorem, which posits that circulation
is constant within a given vortex, regardless of whether the vortex is a
closed-loop or ends on a substrate
(Batchelor, 1967). These
problems were not apparent with
and
, thus, we abandoned further
use of c and hereafter report only a.
Far-field induced velocity (Uind,
Fig. 2 and
Fig. 3A) in the jet between
vortex cores was sampled midway between
and
using an interrogation area
2 cmx2 cm for babies and 4 cmx4 cm for juveniles and adults.
Uind was probably greater, by some unmeasured amount, than
the induced velocity at the wing
(Ellington, 1984;
Sane, 2006). We were unable to
measure Uind at the wing because the wings and body, and
reflection of laser light, obscured near-field flow patterns. Direction of
vortex impulse was considered to be normal to a line including
and
. We report acute angles of
vortex impulse relative to horizontal (
h, in degrees,
Fig. 2) and relative to slope
of incline (s, in degrees) along with the inclination angle
of wake vortex relative to horizontal (ß).
We estimated average lift by coupling our DPIV data with three-dimensional
(3D) kinematic data obtained from the same age classes of chukars and reported
in detail elsewhere (Segre,
2006) (Table 2).
Added mass of the vortex wake was estimated using Dabiri's method
(Dabiri, 2005). We made a
number of simplifying assumptions in this effort, so caution is warranted when
interpreting these estimates. Following Spedding et al.
(Spedding et al., 2003a) and
Warrick et al. (Warrick et al.,
2005), we assumed that a single vortex loop shed per downstroke
was planar and that no contraction occurred during wake development. Thus, the
major and minor axes of an elliptical vortex loop were defined using the 3D
excursion of the wing tips during downstroke. Average lift during the entire
wingbeat (L) was estimated as:
 | (1) |
is added-mass coefficient,
S is vortex width (Fig.
2), Uv is self-induced vortex velocity and
T is wingbeat duration (Dabiri,
2005). To facilitate comparisons with previous accelerometer data
(Bundle and Dial, 2003), we
also computed Ld, the mean lift during downstroke by
substituting Td, downstroke duration (s) for T in
Eqn 1.
|
The most appropriate method for measuring the added mass of the vortex wake
(the second term in Eqn 1) involves the use of a Lagrangian frame of reference
in which the trajectories of fluid particles are tracked over time
(Dabiri, 2005;
Dabiri et al., 2006;
Shadden et al., 2006). This
requires a time series of DPIV images. Our DPIV images were obtained at 5 Hz,
the limit for our system, so we were unable to undertake a Lagrangian
analysis. Instead, we assumed =0.72,
which is the added-mass coefficient reported for an elliptical vortex
(Dabiri, 2005). We measured
S as the average diameter of observed vortex cores, and we measured
Uv as observed rate of translation of
max in the subset (N=39) of our DPIV samples in
which the same vortex core appeared in consecutive images.
Wake vortex ratio (Wa), a dimensionless index of the
relative contribution of vortex added mass to the overall estimate of
L was calculated according to Dabiri
(Dabiri, 2005):
 | (2) |
max and
a, we computed normalized
(Spedding et al., 2003a;
Hedenström et al., 2006),
dimensionless values
maxcUb–1 and
a(cUb)–1, where
c is average chord length (Table
1; m) and Ub is body velocity (m
s–1) as measured from 3D kinematics
(Segre, 2006)
(Table 2).
Statistical analysis
We used one-way analysis of variance (ANOVA, d.f.=2,6) to test for an
effect of age class upon observed differences in mean max,
a, s and Uind,
Uv and S during WAIR. We used a paired
t-test (d.f.=1) to test for significant differences between these
same variables measured in adults during WAIR and flight. Values are reported
as means ± s.d.
|
Results |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of symbols and...References |
|---|
and
;
Fig. 3). Beginning at 7 d.p.h.
(Fig. 4A,B), babies
consistently exhibited wake structures similar to those of juveniles and
adults (Fig. 4C–F). In
contrast, at 6 d.p.h. (Fig. 6),
the babies obviously struggled to climb the slope (65°) and exhibited a
wake with less (40.5%). During
WAIR, impulse from the downstroke was directed upward relative to the ground
(average h, 45±6°) and also toward the surface of
the slope that the animal was climbing, with s varying from
23±6° to 31±9°. Average s was slightly
lower in babies compared to juveniles and adults, but the observed differences
were not significant (Table 3).
During flight, impulse was nearly normal to the ground (85.0±0.5°;
Fig. 4). Considering the ground
to represent substrate during flight, there was a significant difference
between mean s during WAIR and flight (P=0.0235).
Consistent with large differences in body mass and wing size,
and
varied significantly among age
classes (P=0.0002; Table
3). Comparing babies and adults engaged in WAIR,
varied from
–0.18±0.06 m2 s–1 to
–1.8±0.3 m2 s–1, and
varied from 0.20±0.04
m2 s–1 to 1.6±0.1 m2
s–1. Normalizing to remove the effects of c
and Ub, removed the significant effect of age class during
WAIR (Fig. 7A). Among all three
age classes, normalized was
14±3 and was
14±4. An average of 54±28% more was present in the
vortex cores during flight compared with WAIR in adults
(Table 3;
Fig. 7A), but the differences
between means were not statistically significant (P=0.3431 for
and P=0.3130 for
).
|
|
|
|
|
Age class did not have a significant effect upon absolute or normalized
and
(Table 3). Average
was –724±192
s–1, and average
was 652±189
s–1. Normalized mean
and
were 41±18 and
37±17, respectively.
Induced velocity in the center of the vortex loops varied significantly among age classes (P=0.0052) with a minimum of 2.1±0 m s–1 in babies to 8±2 m s–1 in adults. Compared with Uind during WAIR, Uind during flight was slightly higher (8.1±0.1 m s–1), but the difference between means was not significant (P=0.8233). Significant differences were also observed among age classes for wake vortex velocity (Uv, P=0.165) and width (S, P=0.0067).
Wake vortex ratio, Wa, varied from 0.03±0.01 in
babies to 0.08±0.02 in both juveniles and adults during WAIR. The
observed differences among the age classes were significant when either
(P=0.0285) or
(P=0.0156) were
employed as the denominator of Eqn 2. Wa averaged
0.05±0.00 during chukar flight.
Expressed relative to body weight, estimated average lift was least in
babies during WAIR (Fig. 6B) at
6±2% of body weight when L was calculated using
and 7±1% when
L was calculated using
in Eqn 1. Relative L
was slightly greater in juveniles compared with adults
(Fig. 6B). For example, based
on , relative L in
adults was 60±2% and 88±37% in juveniles. The percentage of body
weight supported during flight was estimated as 101±12% employing
and 118±37% when using
. Given the downstroke
fractions within the entire wingbeat
(Segre, 2006)
(Table 2), average lift during
downstroke Ld=2.3L among the three age classes
when engaged in WAIR, and Ld=2.2L during flight
in adults.
|
Discussion |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of symbols and...References |
|---|
;
Dial et al., 2006;
Segre, 2006), our results
revealed a wake dominated by the effects of lift production as in flapping
flight in birds (Spedding et al.,
2003a; Spedding et al.,
2003b; Warrick et al.,
2005) (Figs 3,
4,
5,
6) rather than a drag-based
wake such as might be produced by a paddling motion (Johannson and Lauder,
2004). This is because observed impulse angles (h and
s, Figs 2,
3,
4,
5,
6) were nearly perpendicular to
the path of wing motion. Specifically, Segre measured stroke plane angles
during WAIR at 61° relative to horizontal
(Segre, 2006), and our measure
of vortex inclination angle (ß; orthogonal to h and
s, Fig. 2)
was 45±6°. If the wake was being generated solely by drag, we would
have observed shear layers in the flow manifest as a street of opposite-sign
parallel with ß (Johannson and Lauder, 2004;
Spedding et al., 2003b).
Undoubtedly, the wings were producing lift and experiencing profile drag
simultaneously (Shultz and Webb, 2002), but the overwhelming pattern of
lift-induced wake vortices obscured any measurable traces of profile drag in
the wake.
Although our data from direct visualization of the wake are in general
agreement with the conclusions of previous experiments that include kinematic
and accelerometer measurements (Bundle and
Dial, 2003; Dial,
2003; Dial et al.,
2006; Segre,
2006), some discrepancies refine our understanding of the
mechanics of WAIR and present questions for further study. The DPIV data
support the hypothesis that the wings contribute to hindlimb function during
WAIR. For adult chukar during WAIR, accelerometer measurements indicated an
average force from the wings at 220% of body weight and oriented at 28°
relative to the substrate being climbed at an incline of 54° [average
taken among four phases of downstroke in table 3 of Bundle and Dial
(Bundle and Dial, 2003)]. In
comparison, our estimate of Ld in adult WAIR was less at
146±21% of body weight when we used
to estimate
Ld and 134±4% when we used
, but the impulse angle
(s, 29±2°) was within 1 s.d. of that measured by
Bundle and Dial (Bundle and Dial,
2003). The accelerometer and DPIV data both serve to revise prior
estimates from 2D kinematics (Dial,
2003) that lift is directed perpendicularly toward the
substrate.
There are several potential explanations for our lower estimate of
Ld compared to the body accelerations measured by Bundle
and Dial (Bundle and Dial,
2003). Foremost, the contribution of wing inertia was not
subtracted from total acceleration in the earlier publication
(Bundle and Dial, 2003), so
their measures include the effects of both aerodynamic forces and wing inertia
acting upon the body. Future modeling of wing inertia using detailed 3D
kinematics (Hedrick et al.,
2004; Segre, 2006)
should test whether the average force acting on the body due to wing inertia
is approximately 80% of body weight, as suggested by the difference between
accelerations in the earlier publication
(Bundle and Dial, 2003) and our
estimate of Ld.
Another important consideration is that our estimates of L and
Ld were developed with only limited insight into the true
3D geometry of the wake. As described in Materials and methods, the most
appropriate method for measuring the spatial distribution of wake vortices
requires sampling a time-series of DPIV samples for a Lagrangian analysis in
which flow trajectories are measured
(Dabiri, 2005;
Dabiri et al., 2006;
Shadden et al., 2006), ideally
in 3D or, more realistically given current DPIV technology, using multiple 2D
transects of the wake (Spedding et al.,
2003a; Warrick et al.,
2005). Our DPIV system samples at a maximum of 5 Hz, so a
time-series analysis of individual vortices was not feasible. Additionally,
WAIR in chukars is an explosive, short-duration activity with finite
repeatability before the birds tire and refuse to cooperate, so it is far from
amenable to use the same transect-sampling methods used for DPIV measurements
of the wake of highly trained passerines (Passeriformes) flying toward a light
source in a wind tunnel (Spedding et al.,
2003a; Hedenström et al.,
2006) or hummingbirds (Trochilidae) hovering at an artificial
feeder (Warrick et al.,
2005).
There may also have been a deficit in in the wake relative to the
bound on the wings due to rapid decay of in the wake resulting
from turbulence (Tytell and Ellington,
2003). Based upon measurements of the onset of turbulence and the
corresponding decay of in experimentally induced, laminar vortex
rings, Tytell and Ellington (Tytell and
Ellington, 2003) suggest that a vortex-ring Reynolds number
(Re; equal to /
, where is kinematic viscosity, Pa
s–1) of approximately 5000 is a practical limit below which
wake measurements may accurately represent initial impulse and of a
shed vortex ring. A ring Re of 5000 would be typical of hovering
hawkmoths (Manduca spp.) or hummingbirds. For comparison, ring
Re during WAIR varied from approximately 10 000 in baby chukar to 100
000 in adults, and it was approximately 150 000 during flight in adults.
An argument of an effect of rapid wake decay appears to be undermined by
recent observations, including our data from chukars (Figs
5 and
7), that sufficient circulation
is present in the wake of flying birds to account for weight support
(Spedding et al., 2003b;
Warrick et al., 2005;
Hedenström et al., 2006).
However, during WAIR, it is likely that the proximity of the substrate
affected wake dynamics (Doligalski et al.,
1994; Han and Cho,
2005) and may have increased vortex instability in ways that are
not straightforward to estimate given that the ramps we used for WAIR
experiments were relatively narrow and parts of the wings always extended over
the edge of the substrate.
Regardless of the potential limitations of our estimate of L, our
observations of similar wake structure
(Fig. 4) and normalized
(Fig. 7A) for WAIR among age
classes provides novel insight into the aerodynamics of the developing avian
wing. DPIV evidence from four species of passerines in flight
(Hedenström et al., 2006)
similarly indicates that normalized circulation is not sensitive to wing shape
(Hedenstrom et al., 2006).
Even though baby chukars cannot fly at 6–8 d.p.h.
(Dial et al., 2006;
Segre, 2006), they were able
to generate using their wings as an airfoil in the same way as
juveniles and adults. Variation in the magnitude of was associated
with learning to effectively perform WAIR during the critical transition stage
that occurred at days 6 and 7 post-hatching
(Fig. 6). Although absolute
increased with increasing size among the three age classes
(Table 3;
Fig. 7A), normalizing
and, thereby, controlling for the effects of c and
Ub, revealed that the dramatic differences in feather
morphology between baby and adult chukar
(Fig. 1) did not have a
significant effect upon (Fig.
7A). It is imperative to note that large variance within age
classes meant that the power was extremely low (
0.08) for this test of
statistical significance. Thus, a larger sample size is needed to confirm that
no true difference exists among age classes.
Instead of a deficit of , the comparatively poor performance of baby
chukar with respect to L (Fig.
7B) may be attributed to their wing kinematics that we used to
calculate A and T in Eqn 1
(Segre, 2006)
(Table 2). During WAIR, baby
chukar have wingbeats of lower frequency and amplitude than juveniles and
adults (Segre, 2006), which
led to relatively small A and large T
(Table 1). In contrast, the
expected trend derived from interspecific scaling of wingbeat kinematics with
body size in galliform birds would suggest that babies should have a
relatively higher frequency and approximately the same amplitude of wingbeat
as the larger birds (Tobalske and Dial,
2000). Ultimately neuromuscular control and the ability to
generate work and power using the primary downstroke muscle, the pectoralis,
drives the motion of the wing (Dial,
1992; Tobalske et al.,
2003; Hedrick et al.,
2003). Thus, the observed similarity in normalized among
age classes (Fig. 7A) leads us
to predict that the performance of the developing wing during WAIR is
constrained primarily by control or the ability to generate power rather than
shape of the animal's aerofoil.
Understanding the function of morphing structures during transitional
stages is critical to evaluating adaptation in ecological and evolutionary
time (Bock, 1965;
Dial, 2003;
Dial et al., 2006). Our data
show that a developing wing with symmetrical, partially emerged feathers can
develop similar to a wing with asymmetric feathers on an adult wing
(Figs 1 and
4). Although understanding the
neuromuscular control and power output of the muscles moving these wings
awaits further study, the aerodynamics that we report should aid in providing
a new model for developing hypotheses about the role of feathers and flight
ability of the ancestors of modern birds
(Padian and Chiappe, 1998;
Prum, 1999;
Padian, 2001;
Zhou, 2004).
|
List of symbols and abbreviations |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of symbols and...References |
|---|
h
s
a
c
max
|
Acknowledgments |
|---|
|
References |
|---|
|
TOPSummaryIntroductionMaterials and methodsResultsDiscussionList of symbols and...References |
|---|
Batchelor, G. K. (1967). An Introduction to Fluid Dynamics. Cambridge: Cambridge University Press.
Bock, W. J. (1965). The role of adaptive mechanisms in the origin of the higher levels of organization. Syst. Zool. 14,272 -287.
Bundle, M. W. and Dial, K. P. (2003). Mechanics
of wing-assisted incline running (WAIR). J. Exp. Biol.
206,4553
-4564.
Dabiri, J. O. (2005). On the estimation of
swimming and flying forces from wake measurements. J. Exp.
Biol. 208,3519
-3532.
Dabiri, J. O., Colin, S. P. and Costello, J. H.
(2006). Fast-swimming hydromedusae exploit velar kinematics to
form an optimal vortex wake. J. Exp. Biol.
209,2025
-2033.
Dial, K. P. (1992). Activity patterns of the wing muscles of the pigeon (Columba livia) during different modes of flight. J. Exp. Zool. 262,357 -373.[CrossRef]
Dial, K. P. (2003). Wing-assisted incline
running and the evolution of flight. Science
299,402
-404.
Dial, K. P., Randall, R. J. and Dial, T. R. (2006). What use is half a wing in the ecology and evolution of birds? BioScience 56,437 -455.[CrossRef]
Doligalski, T. L., Smith, C. R. and Walker, J. D. A. (1994). Vortex interactions with walls. Annu. Rev. Fluid Mech. 26,573 -616.[CrossRef]
Ellington, C. P. (1984). The aerodynamics of hovering insect flight. V. A vortex theory. Philos. Trans. R. Soc. Lond. B Biol. Sci. 305,115 -144.[CrossRef]
Gould, S. J. and Vrba, E. S. (1982). Exaptation; a missing term in the science of form. Paleobiology 8,4 -15.[Abstract]
Han, C. and Cho, J. (2005). Unsteady trailing vortex evolution behind a wing in ground effect. J. Aircr. 42,218 -227.
Hedenström, A., Griethuijsen, L. V., Rosén, M. and Spedding, G. R. (2006). Vortex wakes of birds: recent developments using digital particle image velocimetry in a wind tunnel. Anim. Biol. 56,535 -549.[CrossRef]
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.
Johansson, L. C. and Lauder, G. V. (2004).
Hydrodynamics of surface swimming in leopard frogs (Rana pipiens).
J. Exp. Biol. 207,3945
-3958.
Norberg, U. M. (1990). Vertebrate Flight: Mechanics, Physiology, Morphology, Ecology and Evolution. New York: Springer.
Padian, K. (2001). Stages in the origin of bird flight: beyond the arboreal–cursorial dichotomy. In New Perspectives on the Origin and Early Evolution of Birds (ed. J. A. Gauthier), pp. 255-272. New Haven: Yale University Press.
Padian, K. and Chiappe, L. M. (1998). The origin of birds and their flight. Sci. Am. 278, 38-47.[Medline]
Prum, R. O. (1999). The development and evolutionary origin of feathers. J. Exp. Zool. 285,291 -306.[CrossRef][Medline]
Raffel, M., Willert, C. and Kompenhans, J. (2000). Particle Image Velocimetry: A Practical Guide. Berlin: Springer-Verlag.
Rayner, J. M. V. (1988). Form and function in avian flight. Curr. Ornithol. 5, 1-66.
Sane, S. P. (2006). Induced airflow in flying
insects I. A theoretical model of the induced flow. J. Exp.
Biol. 209,32
-42.
Schultz, W. W. and Webb, P. W. (2002). Power
requirements of swimming: do new methods resolve old questions?
Integr. Comp. Biol. 42,1018
-1025.
Segre, P. S. (2006). A 3-dimensional evaluation of wing movement in ground birds during flap-running and level flight: an ontogenetic study. MS thesis, University of Montana, USA.
Shadden, S. C., Dabiri, J. O. and Marsden, J. E. (2006). Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18, 047105.[CrossRef]
Spedding, G. R., Rosén, 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., Hedenström, A. and Rosen, M. (2003b). Quantitative studies of the wakes of freely flying birds in a low-turbulence wind tunnel. Exp. Fluids 34,291 -303.[CrossRef]
Tobalske, B. W. and Dial, K. P. (2000). Effects of body size on take-off flight performance in the Phasianidae (Aves). J. Exp. Biol. 203,3319 -3332.[Abstract]
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]
Tytell, E. D. and Ellington, C. E. (2003). How to perform measurements in a hovering animal's wake: physical modelling of the vortex wake of the hawkmoth, Manduca sexta. Philos. Trans. R. Soc. Lond. B Biol. Sci. 358,1559 -1566.[CrossRef][Medline]
Warrick, D. R., Tobalske, B. W. and Powers, D. R. (2005). Aerodynamics of the hovering hummingbird. Nature 435,1094 -1097.[CrossRef][Medline]
Zhou, Z. (2004). The origin and early evolution of birds: discoveries, disputes, and perspectives from fossil evidence. Naturwissenschaften 91,455 -471.[CrossRef][Medline]
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
