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First published online May 21, 2007
Journal of Experimental Biology 210, 1912-1924 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.002063

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Low speed maneuvering flight of the rose-breasted cockatoo (Eolophus roseicapillus). II. Inertial and aerodynamic reorientation

T. L. Hedrick^1,*, J. R. Usherwood² and A. A. Biewener³

¹ Department of Biology, CB 3280 Coker Hall, University of North Carolina, Chapel Hill, NC 27599-3280, USA
² Structure and Motion Laboratory, The Royal Veterinary College, North Mymms, Herts, AL9 7TA, UK
³ Concord Field Station, MCZ, Harvard University, Old Causeway Road, Bedford, MA 01730, USA

View larger version (63K): [in this window] [in a new window]   Fig. 1. Characteristic wing orientation at (A) the start of downstroke, (B,C) mid-downstroke, (D) the end of downstroke and (E) mid-upstroke. We judged downstroke to begin when the tips of the primaries were rapidly accelerated by downward angular acceleration beginning at the shoulder, as is visible in the tips of the right wing primaries in A. Mid-downstroke was the moment of greatest angular extent between the two wings. The end of downstroke was judged to occur as just prior to the wrists beginning an upward trajectory. Finally, we considered mid-upstroke to be the frame in which the angle defined by the wrists first reach their maximum upward excursion.

View larger version (14K): [in this window] [in a new window]   Fig. 2. Frames of reference and characteristic angles used in the blade-element analysis. (A) The bird at mid-downstroke, along with the bird's right wing from an earlier instant in the stroke, the global and bird coordinate systems, and several orientation parameters. Note that the wing elevation angle, , is shown for the wing position at the prior instant in time as at mid-downstroke is approximately 0°. (B) A wing section and associated angles. Note that , the wing spanwise rotation angle, is slightly negative as shown. Additionally, has been transformed to the body coordinate system to give (see List of symbols and abbreviations).

View larger version (9K): [in this window] [in a new window]   Fig. 3. Individual points are the average response of a bird for a given wingbeat number and turn direction, N=68. Net roll torque was estimated via a blade-element analysis, among-wingbeat roll acceleration from the second derivative of a quintic spline fit through the series of mid-downstroke roll measurements.

View larger version (5K): [in this window] [in a new window]   Fig. 4. Inter-individual mean fraction of body weight supported during each wingbeat of the turn (N=6 for each wingbeat). Fraction of body weight supported was calculated by dividing the estimated mean upward force generated each bird by its body weight. The overall average fraction supported was 0.89. The fraction supported reaches a local minimum at the 0th wingbeat, the middle wingbeat of the turn and also the one with the greatest average body roll.

View larger version (7K): [in this window] [in a new window]   Fig. 5. Inter-individual centripetal force and estimated mean inward aerodynamic force for each wingbeat during the turn. Across all wingbeats and birds the estimated inward force accounted for 72±18% of the observed centripetal force (N=67).

View larger version (6K): [in this window] [in a new window]   Fig. 6. Pectoralis mass specific aerodynamic power estimated from the wing kinematics at mid-downstroke, stroke duration and wrist arc during downstroke, shown as the inter-individual mean ± s.d. Across all birds and wingbeats, power averaged 238.24±80.85 W kg–1 (N=58). Note that data for wingbeat –3 were not available because a stroke duration, measured from mid-upstroke to mid-upstroke, was not available from 4 of the 6 birds.

View larger version (30K): [in this window] [in a new window]   Fig. 7. Predicted versus measured change in roll during the four phases of the wingbeat cycle. (A) Mid-upstroke to the start of downstroke, (B) the start of downstroke to mid-downstroke, (C) mid-downstroke to the end of downstroke, (D) the end of downstroke to mid-upstroke. Because the inertial predictions do not take into account any initial roll velocity, we high-pass filtered the measured roll angles with a cut-off frequency of 3.5 Hz prior to computing the change in roll for comparison with the inertial predictions.

View larger version (8K): [in this window] [in a new window]   Fig. 8. Predicted versus estimated inertial change in roll for an entire wingbeat. As in Fig. 6, roll measurement was subjected to a high-pass filter prior to extracting the measurement. Note that this particular regression includes three points (marked by asterisks) that are more than three standard deviations from the mean of at least one of the axes. Removing these points would reduce the r2 of the regression to 0.089 and the P value to P=0.02.

View larger version (27K): [in this window] [in a new window]   Fig. 9. Electromyogram correlates to different components of the estimated aerodynamic torque and the predicted change in roll due to inertial reorientation. Normalized EMG measures were normalized by dividing by the standard deviation of the measurement for the individual muscle. (A) Pectoralis activation intensity versus Cr, the aerodynamic force coefficient. (B) Biceps activation duration versus wing spanwise rotation at mid-downstroke. (C) Supracoracoideus activation duration versus the estimated inertial change in roll in late upstroke. (D) Biceps impulse versus the estimated inertial change in roll in early downstroke.

View larger version (12K): [in this window] [in a new window]   Fig. 10. (A) A depiction of how the assumptions used in extending the instantaneous measures of torque (or force) act over the course of a single wingbeat from the beginning of downstroke to the end of the subsequent upstroke. In the model, torque from the right wing is greater than that from the left wing during the entire downstroke. Note that torque due to upward force on the right wing has a negative sign; it was inverted to facilitate comparison with the left wing. (B) The square of the wrist velocity magnitude, an important part of our force and torque estimates. Note that the relationship between right and left torques at mid-downstroke does not persist through the entire stroke. The shading indicates downstroke in both modeled and recorded data; kinematic mid-downstroke does not occur at the temporal midpoint of the downstroke but downstroke did end at exactly 0.6 wingbeats in this instance.

View larger version (8K): [in this window] [in a new window]   Fig. 11. Among-wingbeat change in roll versus the estimated aerodynamic effect, taking into account initial roll velocity and roll damping. The measured change in roll shown here is the total measured change, rather than the measured change in the higher frequency portion of the signal as was shown in Fig. 7 and compared with the predicted inertial reorientation.