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Figures
- Fig. 1.
(A) Depictions of the vortex-ring and continuous-vortex gaits. (B) Cross-sectional view of the wing profile. Lift produced during flapping provides weight support (upward force) and thrust (horizontal force). In the vortex-ring gait, lift is produced only during the downstroke, providing positive upward force and forward thrust. In the continuous-vortex gait, lift is produced during both the upstroke and the downstroke. The downstroke produces a positive upward force and forward thrust; the upstroke produces a positive upward force and rearward thrust. Partial flexion of the wing during the upstroke reduces the magnitude of the rearward thrust to less than that of the forward thrust produced during the downstroke, providing net positive thrust per wingbeat (adapted from Rayner, 1986, 1988).
- Fig. 2.
The Harvard-Concord Field Station (CFS) wind tunnel, designed for use in studies of animal flight.
- Fig. 3.
Velocity profile in the mid-plane of the flight chamber in the Harvard-CFS wind tunnel operating at an equivalent airspeed of 20 m s-1. Airspeed was measured using a pitot-static probe placed at 121 locations in a 10 cm spaced grid pattern (see text for details). Each square represents the center of a 10 cm square in the grid. (A) Variation in airspeed as a paercentage of the mean. (B) Positive and negative deviations from the mean.
- Fig. 4.
A velocity traverse performed at mid-height and mid-plane, using a pitot-static probe, with the equivalent wind speed at 10 m s-1. Boundary-layer effects on flow velocity were not apparent until within 1 cm of the left and right walls of the working section. Filled circles, traverse of left side; open circles, traverse of right side. Note that the width of the flight chamber at mid-plane is 121 cm, 1 cm greater than at the inlet, to accommodate thickening of the boundary layer along the length of the flight chamber. Left side and right side are referenced looking forward from inside the flight chamber.
- Fig. 5.
Average turbulence levels expressed as percentage turbulence at each of nine locations in two planes (A, at 25 % depth from the front of the working section; B, at 50 %) in the flight chamber. These values were obtained using a 30 cm diameter turbulence sphere. Left side and right side are referenced looking forward from inside the flight chamber.
- Fig. 6.
Digital particle image velocimetry (DPIV) was used to measure variations in velocity and turbulence levels with the wind tunnel set at an equivalent airspeed of 5 m s-1 along the x dimension (axis of airflow). The DPIV system uses a YAG laser and synchronized stereo video cameras to measure velocities U, V and W, corresponding to the x, y and z axes, respectively, of particles suspended in the moving air column. Variation in true airspeed (U) was relative to a mean of 5.54 m s-1. Total turbulence (T) varied about a mean of 0.23 %.
- Fig. 7.
(A) Arrangement of the four high-speed video cameras around the flight chamber of the wind tunnel and typical images from each camera. Cameras 1 and 2 (C1, C2) captured dorsal views of the bird, while cameras 3 and 4 (C3, C4) captured either latero-dorsal or -ventral views of the bird and wings. (B) Points marked on each bird that were digitized for three-dimensional reconstruction. 1, back; 2, shoulder; 3, wrist; 4, tip of the ninth (longest) primary; 5, tip of the fourth primary; 6, tip of the first primary. T1 designates the triangle used to represent the proximal wing section; T2 designates the triangle forming the distal wing section.
- Fig. 8.
Lateral view of a dove at the beginning of the downstroke in slow flight (1 m s-1) with vectors showing the components of the induced velocity calculation (equation 3). The vertical induced airflow (Wiv) is calculated from equation 3, incident airflow (Wk+Ve) is measured via kinematics and wind-tunnel velocity, and horizontal induced airflow (Wih) is calculated from Wih=Wivtan(π/2-θ). Note that the vectors shown are not precisely to scale and that Wk acts opposite to the direction of wing motion. Wk, airflow generated by wing motion; Ve, effective wind-tunnel airflow; Wiv, vertical induced airflow (equation 3); Wit, total induced airflow perpendicular to Wk+Ve; Wih, horizontal induced airflow; θ, angle between Wiv and Wk+Ve.
- Fig. 9.
(A) Dorsal view of a dove in a medium-speed upstroke (7 m s-1) posture showing the three markers on the wing (shoulder, wrist and ninth primary tip) used to establish the position of the wing leading edge and the incident airflow and effective wing length. As shown in the figure, an extended proximal wing and slightly flexed distal wing (with effective length less than geometric length) are typical of a medium-speed upstroke. (B) Dorsal view of a cockatiel in mid-upstroke configuration in fast flight (11 m s-1). Note that, although overall wingspan is similar in both species, mean dove body mass is 83 % greater than that of the cockatiels, leading to a much higher wing loading in doves.
- Fig. 10.
Representative results for several kinematic and aerodynamic variables obtained for two wingbeats of dove 2 flying at (A) 1 m s-1, (B) 5 m s-1, (C) 9 m s-1 and (D) 17 m s-1. Each plot shows (i) vertical (z direction) motions of the wrist and wing tip, (ii) distal and proximal effective wing lengths (b), (iii) distal and proximal incident airflow (Wt), (iv) distal and proximal wing angles of attack (α) and (v) distal and proximal circulation (Γ). The y-axis and x-axis scales are the same for all speeds. Shading indicates downstroke periods, which were determined from the z-axis (vertical) wrist motion.
- Fig. 11.
Representative results obtained for kinematic and aerodynamic variables similar to Fig. 10 but shown for two wingbeats of a cockatiel flying at four different flight speeds. A, B and C are taken from cockatiel 2, whereas D is taken from cockatiel 1, which achieved a greater speed during experimental recordings. The y-axis scales are identical to those used in Fig. 10; the x-axis scale is the same in all plots but extended relative to those for the dove to account for the slightly lower wingbeat frequency employed by the cockatiels.
- Fig. 12.
A comparison of the mean proximal wing circulation during the upstroke and the mean distal wing circulation during the downstroke for the doves (A) and cockatiels (B) over the full range of flight speeds examined. Values are means± S.D. (N=2). for each species at each speed. The shaded region indicates the range of speeds in which downstroke and upstroke circulation are approximately equivalent, resulting in a continuous-vortex wake.
- Fig. 13.
A comparison of estimated circulation resulting from translational and rotational sources for two wingbeats of a dove at flight speeds of 1, 3 and 9 m s-1. Shaded regions indicate downstrokes.
- Fig. 14.
The reduced frequency for all birds over the range of experimental speeds studied. Values greater than 0.3 indicate that unsteady aerodynamic effects may have a significant influence on airflow and lift generation (Spedding, 1993). Results are presented as inter-individual means ± S.D. (N=4).
- Fig. 15.
A comparison of mass-specific whole wingbeat impulses obtained from calculations of distal and proximal wing circulation with those determined from measurements of the bird's vertical acceleration of its center of mass. Inter-individual means and standard deviations are presented separately for doves (A) (N=2) and cockatiels (B) (N=2).
- Fig. 16.
Gait transition results obtained for dove 1 flying at 7 m s-1 over several wingbeat cycles lasting 2 s. (A) The vertical (z direction) motions of the distal and proximal wing sections; (B) the mean vertical acceleration achieved during each complete wingbeat (not including acceleration to counteract gravity); (C) the mean distal wing circulation produced during the downstroke (squares and solid line) in relation to the mean proximal wing circulation produced during the subsequent upstroke (circles and dashed line). The lines plotted in B and C represent cubic spline fits to the data points. The shaded regions indicate wingbeats in which the bird employs a vortex-ring gait.
Tables
- Table 1.
Comparison of gait aerodynamics
Species Speed (m s-1) Circulation (m2 s-1) Wing loading (kg m-2) Gait Source Kestrel (Falco tinnunculus) 7.0 0.55 4.04 c.v. 3 Ringed turtle-dove (Streptopelia risoria) 7.0 0.41 3.71 c.v. 4 Cockatiel (Nymphaticus hollandicus) 7.0 0.32 2.51 c.v. 4 Pigeon (Columba livia) 2.4 1.72 5.65 v.r. 1 Jackdaw (Corvus monedula) 2.5 0.82 3.86 v.r. 2 Ringed turtle-dove (Streptopelia risoria) 3.0 0.79 3.71 v.r. 4 Cockatiel (Nymphaticus hollandicus) 3.0 0.41 2.51 v.r. 4 -
Gait: c.v., continuous vortex; v.r., vortex ring.
1, Spedding et al. (1984); 2, Spedding (1986); 3, Spedding (1987); 4, present study.
Circulation magnitude in the continuous-vortex gait is an average of circulation over the entire wingbeat cycle; circulation in the vortex-ring gait is an average of circulation during the downstroke.
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