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First published online January 5, 2005
Journal of Experimental Biology 208, 355-369 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01359

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Dynamic pressure maps for wings and tails of pigeons in slow, flapping flight, and their energetic implications

James R. Usherwood^*, Tyson L. Hedrick, Craig P. McGowan and Andrew A. Biewener

Concord Field Station, Harvard University, 100 Old Causeway Road, Bedford, MA 01730, USA

View larger version (39K): [in a new window]   Fig. 3. Average acceleration-compensated pressure measurements for inner and outer tail positions (red lines) and two positions along the wings (blue lines), with non-acceleration compensated results (black lines) underlying. The synchronising accelerometer trace (green lines throughout; black lines indicate ±1 S.D.; N=3 pigeons) from an accelerometer placed at the base of secondary S3 allows signals from separate flights to be combined; each cycle is defined by the peak in accelerometer signal, relating to rapid upwards acceleration of the wing towards the end of downstroke. The time-base for each raw signal is normalised to the wing stroke cycle (thus slight differences in frequency do not result in increasing variation through the cycle). In each trace, the signal is split into a take-off flap followed by three full flaps, three full flaps at the middle of the flight, and three full flaps prior to landing followed by a landing flap. Underlying grey bars indicate periods of downstroke throughout.

View larger version (23K): [in a new window]   Fig. 4. An expansion of Fig. 3 for the middle three flaps only, with traced kinematics of the wing stroke included. The effect of acceleration is highlighted (i) for the distal wing position, and relates to the high acceleration (up to 80 g) at the `clap' at the upstroke/downstroke transition. The effects of acceleration-compensation are generally slight for both tail and wing differential pressure signals.

View larger version (29K): [in a new window]   Fig. 5. Mean acceleration-compensated differential pressures for inner and outer tail positions, and distal and proximal wing positions. Also included are acceleration signals for inner and outer tail positions (second pair of traces) and the proximal wing position - the synchronising accelerometer. Tracings of the pigeon through the wing stroke cycle match the timing of the graph. Values are mean ±1 S.D. (shown in black; N=3 pigeons). The vertical red broken lines show the relationship between a peak in both inner and outer tail pressure signal, an upwards acceleration of the wings towards the end of downstroke, and a concurrent downwards acceleration of the tail.

View larger version (51K): [in a new window]   Fig. 6. Mean non-acceleration-compensated differential pressure signals for eight positions (P8, P7, P4, P3, S1, S2, S6, S7) along and across the wing. The traces are ordered from distal sites at the top towards proximal sites nearer the bottom, and the synchronising accelerometer trace again appears as the last trace, in green. Values are mean ±1 S.D. (shown in black; N=3 pigeons). Signals for the five sites near the leading edge of the wing are shown in red. Signals for the three pressure sites towards the trailing edge are shown in blue. Periods of downstroke defined by kinematic observations of the wrist are shown as grey for two of the middle three flaps. This shows the close relationship between downstroke timing and the development of `positive' (ventral-to-dorsal) differential pressures, which are used to define downstroke periods shown with underlying grey boxes for take-off and landing. LE, leading edge; TE, trailing edge.

View larger version (34K): [in a new window]   Fig. 7. Expansion of Fig. 6 for the middle three flaps: non-acceleration-compensated pressures for eight sites (P8, P7, P4, P3, S1, S2, S6, S7) along and across the wing. Six pigeon outlines relate to the same timing as the plots, and are labelled a-f. Each tracing is separated in time by an interval of approximately 16 ms (although the rest of the timing remains normalised to the cycle as defined by the synchronising accelerometer peaks). Positions (a) and (f) are the upstroke/downstroke transition, and occur just after the trough in synchronising accelerometer signal. Position (b) indicates mid downstroke, a period of little wing acceleration, coinciding with peak pressure for sites along the leading edge. Position (c) is towards the end of downstroke, when the synchronising accelerometer is being accelerated upwards. Position (d) relates to a downwards acceleration of the proximal wing, after which the distal wing opens up (position e), completing upstroke. LE, leading edge; TE, trailing edge.

View larger version (31K): [in a new window]   Fig. 1. Positioning of accelerometers (rectangles) and differential pressure transducers (circles) across (A) tail, (B) wing for acceleration-compensated trials, and (C) the non-compensated 8-position map. Following convention we code our feathers R for rectrices (tail feathers), P for primaries and S for secondaries, with numbering for the wing feathers counted from the primary/secondary boundary. The pressures measured at each of five positions along the leading edge are taken as representative for the wing sections demarcated by straight lines in C.

View larger version (15K): [in a new window]   Fig. 2. The axes and measured angles for side view (A) and front view (B) during level flight between two perches. For an explanation of symbols, see List of symbols.

View larger version (24K): [in a new window]   Fig. 8. The implications of the differential pressure measurements of the five sites towards the leading edge of the wing (P8, P7, P4, S1 and S7), and the downstroke kinematics, during the earlier two of the middle three flaps (complete flap cycles are required). (A) Differential pressures. (B) The variation in wing stroke angle during downstroke within the x-z plane, i.e. when observed from front-on (x-z), is shown in black, the angle within the stroke plane () in red. (C) The calculated geometric velocity (including forward flight speed) for each wing section. Mean section forces assuming that the measured point pressures can be taken as mean pressures for relevant wing sections of known area (D) are combined, and their orientations to the vertical are taken into account when calculating contribution to weight (BW) support (E). The effective moment arm for the aerodynamic force on the wing (Reff), or the effective centre of pressure, acts approximately half way along the wing (F). Instantaneous muscle-mass specific powers (G) are calculated assuming that the pectoralis dominates downstroke power, and constitutes 18% of body mass. Means ± S.D. for weight support, effective moment arm and powers, are calculated from appropriate individual average measurements of differential pressure, kinematics and morphology; averaging is performed as the final step.