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First published online March 14, 2008
Journal of Experimental Biology 211, 1120-1130 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.010413

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Kinematics and power requirements of ascending and descending flight in the pigeon (Columba livia)

Angela M. Berg^* and Andrew A. Biewener

Harvard University, Concord Field Station, Department of Organismic and Evolutionary Biology, 100 Old Causeway Road, Bedford, MA 01730, USA

View larger version (9K): [in this window] [in a new window]   Fig. 1. (A) Experimental setup (not to scale) and (B) anatomical points measured on the bird for kinematic analysis. (A) The height of the perches and the distance between them were adjusted to encourage birds to fly at prescribed angles of ascent and descent (Table 2). Three high-speed cameras, one dorsal, one nearer to the tall perch, and one to the side of the arena, were used to record flights (x-axis: horizontal direction between the perches; y-axis: mediolateral; and z-axis: vertical). (B) Birds were marked at several anatomical locations. The shoulder, wrist, wingtip and rump marks were digitized, as was the point on the trailing edge of the wing, directly behind the wrist in the x-coordinate. The position of the center of mass (CoM) was estimated by averaging the x- and z-coordinates of the rump and shoulder and using the y-coordinate of the rump.

View larger version (8K): [in this window] [in a new window]   Fig. 2. The calculation of stroke plane angle (SPA). SPA is the angle corresponding to the slope of the linear regression of the x- and z-coordinates of wingtip position relative to the shoulder.

View larger version (13K): [in this window] [in a new window]   Fig. 3. The thin-airfoil model (A), the normal-forces model (B) and parameters used in calculation of Pind (C). In all panels, FR is the resultant aerodynamic force. (A) The thin-airfoil model for a wing in steady flow (e.g. Norberg, 1990), modified for non-horizontal flight. FL is lift, and FD is drag. β is the angle between the resultant aerodynamic force and the direction of wing movement. (B) The normal-forces model on a static wing in steady flow [after Usherwood and Ellington (Usherwood and Ellington, 2002a)]. The direction of the aerodynamic force is assumed to be normal to the surface of the wing. Fh and Fv are the horizontal and vertical forces acting on the wing, respectively. global is the angle of the wing relative to the horizontal. (C) Schematic of parameters used in calculation of Pind. The area of the stroke plane is projected, using the angle , onto the actuator disc, which is defined as normal to FR. disc is the angle of the actuator disc in the global reference frame. ' is the angle between the flight velocity V and the actuator disc. As they are shown here, both disc and ' have negative values [following Stepniewski and Keys (Stepniewski and Keys, 1984)]. Vx is the horizontal component of the flight velocity. Use of the term Vxsindisc eliminates PPE from the Pind calculation.

View larger version (20K): [in this window] [in a new window]   Fig. 4. (A) Observed flight paths of the four birds, (B) average overall and vertical flight speeds during the digitized wingbeat and (C) wingbeat frequency versus vertical flight angle. (A) Average paths traveled by the pigeons for each flight angle during one wingbeat, with starting position normalized to the origin. Vertical distances traveled were similar between 30° and 60° flights, and also between –30° and –60° flights. Birds traveled greater horizontal distances for ±30° and 0° flights than for ±60° flights. (B) Overall flight speed (squares) showed an increase from –60° to reach a maximum at –30°. Speed decreased from –30° descent to 60° ascent. The vertical component of flight velocity (triangles) showed the greatest differences between ±30° and 0° flights, and was not significantly different between –30° and –60° descents (P=0.11). (C) Wingbeat frequency (WBF) ranged from 6.1 Hz to 9.6 Hz with greater variability observed among individuals for ascending flight. WBF did not differ significantly across vertical flight angles (P=0.053, F=3.77). In B and C, as well as in subsequent figures, each point is the data for a standard wingbeat, lines connect means of adjacent flight angles, and asterisks indicate significant differences. Data for individual birds are color-coded.

View larger version (42K): [in this window] [in a new window]   Fig. 5. Illustration of flight kinematics for each flight condition. Gray broken lines represent the horizontal. (A) From top down: stroke plane angle relative to the horizontal, stroke plane angle relative to body angle, and body angle for each condition. The body angle lines do not exactly correspond to the bird outlines because the outlines were made from actual (non-averaged) images from oblique camera views. (B) Lateral views of wingtip and wrist kinematics and mean observed flight angle for the setup condition. The wingtip path is more craniad for steeper flights. (C) Dorsal view of the wingtip and wrist kinematics. Mid-downstroke posture varied little across conditions, and the outline for level flight is shown for all.

View larger version (10K): [in this window] [in a new window]   Fig. 6. (A) Center of mass (CoM) potential energy change (PE) per wingbeat, and (B) CoM PE flight power (PE/twingbeat) versus vertical flight angle. PE/wingbeat cycle values were similar for ascending flight angles (means for 60°=1.41±0.14 J; 30°=1.10±0.11 J), and also similar for descending flight angles (means for –60°=–1.55±0.09 J; –30°=–1.53±0.08 J). PE flight power values were significantly different among all flight angles except between steep and shallow descent (P=0.073 for –60° vs –30°; P0.012 for all other comparisons).

View larger version (11K): [in this window] [in a new window]   Fig. 7. (A) Stroke plane angle (SPA) relative to horizontal and (B) angle of attack (AoA) at mid-downstroke versus flight angle. SPA was more inclined for level and shallow ascent and descent, and more horizontal for steep ascent and descent. Values of AoA decreased from steep descent through shallow ascent, and then increased slightly from shallow to steep ascent.

View larger version (17K): [in this window] [in a new window]   Fig. 8. Powers of flight versus flight angle. (A) Ptot, PPE, Pind and PKE. Ptot is the sum of PPE, Pind, Ppar, Ppro and PKE. Because of the relatively small magnitudes of Ppar and Ppro, they are not shown on the figure. PPE is the same as shown in Fig. 6B. The slope of the regression of PKE versus flight angle did not differ from zero (P=0.11). (B) Estimated Ptot for all conditions, and the value of Plev+PPE for ascending and descending conditions, with standard error bars. The broken line indicates the value of Plev, which is the value of Ptot for level flight without the PPE for level flight. For every non-level flight condition, Ptot and Plev+PPE were similar (paired t-tests, P=0.134 for –60° and P0.411 for all other conditions).

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