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First published online April 8, 2004
Journal of Experimental Biology 207, 1689-1702 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.00933

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Wing inertia and whole-body acceleration: an analysis of instantaneous aerodynamic force production in cockatiels (Nymphicus hollandicus) flying across a range of speeds

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

Concord Field Station, Museum of Comparative Zoology, Harvard University, 100 Old Causeway Road, Bedford, MA 01730, USA

View larger version (23K): [in a new window]   Fig. 1. These images, taken from a high-speed recording of a cockatiel flying at 1 m s–1, show the tip-reversal upstroke. In the first frame, the wing has already reversed direction and the humerus has been elevated. In the second frame, the primary feathers have rotated slightly to create gaps between successive feathers. Between the second and third frames, the rotated primaries sweep upward as the wrist joint extends. By the third frame, the primaries have been rotated back into their standard orientation and the wing has begun to move forward as well as upward.

View larger version (27K): [in a new window]   Fig. 2. (A) This schematic gives an operator-side lateral view of the experimental setup with the cockatiel in position in the Concord Field Station wind tunnel flight chamber and the data cable leading from the bird to the recording equipment. The dorsally positioned Photron camera is shown; the two laterally positioned Redlake cameras were placed on the far side of the tunnel, one lateral to the bird and one posterior-lateral, and are not shown in the figure. (B) A cockatiel with the accelerometers attached to the animal with the accelerometer axes superimposed and the position of the whole bird center of mass (CT) and body center of mass (CB) indicated.

View larger version (22K): [in a new window]   Fig. 3. (A) This histogram shows the contribution of each wing section to the overall mass moment of inertia (I) of the wing. The moment of inertia calculation employs the sum of the actual and virtual masses shown in B. Each wing section was 1.3 cm wide. (B) This histogram shows the mass and estimated virtual mass of the individual wing sections. Total mass of the standard wing was 8.32 g; the S.D. between the masses of the three original wings was 0.66 g. (C) A silhouette of the standard cockatiel wing divided into 18 sections. The sections incorporating the elbow and wrist joints are labeled.

View larger version (38K): [in a new window]   Fig. 4. Here, we superimpose some of the typical instantaneous acceleration vectors from mid-downstroke and mid-upstroke on the lateral-view high-speed video footage. The same cockatiel is used in all frames and the vector scale is the same in each case. Note that the inertial acceleration vectors are small in size here because the wing is typically at maximum velocity when near mid-stroke; inertial accelerations were much more pronounced at other points in time such as the ends of upstroke and downstroke. In upstroke at faster flight speeds, lift and drag forces tended to vary together and were either both small, as shown in the 7 m s–1 upstroke, or both larger, as shown in the 13 m s–1 upstroke. The scale bar indicates an acceleration of 10 m s–2, equivalent to a force of 0.81 N applied to the cockatiel's whole body mass. Note that the aerodynamic acceleration vectors include drag from the data cable and accelerometers.

View larger version (39K): [in a new window]   Fig. 5. A set of inter-individual mean curves showing the patterns of acceleration and wing movement across a single wingbeat from the start of upstroke to the end of downstroke across a range of speeds. Light gray regions denote downstroke. Solid lines indicate the inter-individual mean response, while broken lines show the mean ± 1 S.D. A, B and C correspond to results from flight speeds of 1 m s–1, 7 m s–1 and 13 m s–1, respectively. None of the birds in this study was able to sustain faster flight speeds with the recording equipment attached. Note that the aerodynamic acceleration vectors include drag from the data cable and accelerometers. Removing drag would not change the mean horizontal acceleration over a wingbeat cycle but would probably reduce the instantaneous magnitude of the acceleration. The maximum drag measured on the accelerometer and cable (at 13 m s–1) would generate an acceleration of approximately 2.6 m s–2, much less than the observed acceleration magnitudes.

View larger version (22K): [in a new window]   Fig. 6. Mean vertical and horizontal accelerations during downstroke and upstroke resulting from aerodynamic forces plotted versus flight speed. The values shown are means ± 1 S.D. for the four birds. Vertical and horizontal upstroke and downstroke accelerations differed significantly between stroke phases (P<0.001, paired t-test), and vertical accelerations differed significantly across speeds. Note that maintaining position in the wind tunnel requires that aerodynamic forces produce a mean vertical acceleration of +9.81 m s–2 (to counter gravity) and a horizontal acceleration of 0 m s–2; there was a slight tendency toward forward acceleration in the cockatiels, especially at faster flight speeds.

View larger version (18K): [in a new window]   Fig. 7. Mean inertial work (A) and inertial power (B) associated with wing acceleration during upstroke and downstroke plotted versus flight speed. Note that while inertial work in upstroke is less than in downstroke at all speeds, this is not the case for inertial power. The reduced duration of upstroke at slower flight speeds increases the upstroke inertial power to the point where it is nearly equal to the downstroke power. As we found previously in cockatiels (Hedrick et al., 2003), changes in wingbeat duration were entirely due to changes in upstroke duration, as downstroke duration did not vary.

View larger version (21K): [in a new window]   Fig. 8. A comparison of the measured cockatiel pectoralis mass-specific muscle power output (black) reported by Tobalske et al. (2003) with three measures of the mass-specific inertial power requirements of flapping flight. The upstroke mass-specific inertial power (red) is the peak wing kinetic energy developed in upstroke divided by the mass of the upstroke musculature and the wingbeat duration. This is the best measure of the muscle power required for upstroke. The downstroke mass-specific inertial power (green) is the peak wing kinetic energy developed in downstroke divided by the pectoralis mass and wingbeat duration. The downstroke excess inertial power is the peak wing kinetic energy in downstroke with the aerodynamic work done during wing deceleration subtracted, i.e. Ek,rd. This sum was converted to a mass-specific power by dividing by the pectoralis mass and wingbeat duration. The muscle masses used to calculate mass-specific powers are given in Table 1.