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First published online December 28, 2007
Journal of Experimental Biology 211, 215-223 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.007823

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The implications of low-speed fixed-wing aerofoil measurements on the analysis and performance of flapping bird wings

G. R. Spedding^1,*, A. H. Hedenström², J. McArthur¹ and M. Rosén²

¹ Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA
² Department of Theoretical Ecology, Lund University, SE 223-62, Lund, Sweden

View larger version (7K): [in this window] [in a new window]   Fig. 1. Reynolds number Re based on wing chord c as a function of body mass m for birds. Data collected and selected by C. J. Pennycuick (personal communication). The different symbols represent different orders, and passerines are noted by filled upright triangles.

View larger version (13K): [in this window] [in a new window]   Fig. 2. Section lift:drag (Cl:Cd) polars for the Eppler 387 aerofoil (black silhouette), for angle of attack from –4° to +11°. Replotted from data in Lyon et al. (Lyon et al., 1997).

View larger version (49K): [in this window] [in a new window]   Fig. 3. Spanwise vorticity, y(x,z) for a mid-wing slice taken at x=17c for the thrush nightingale in the Lund wind tunnel. The reference frame moves with the mean flow, as for flight from right to left through still air. A sequence of four frames from consecutive wing beats is collected to cover just over one wake wavelength (). + signs show patches positive vorticity shed at the beginning of the downstroke; there are two in this sequence. The equivalent patch of negative vorticity, noted by the – sign, is much more diffuse. From the same dataset (but a different sample) as Spedding et al. (Spedding et al., 2003b).

View larger version (74K): [in this window] [in a new window]   Fig. 4. Spanwise vorticity, y(x,z) for two fixed wings, shown at midspan. The left column shows the wake for a thin cambered plate, with circular arc, and the right column is for the Eppler 387. The silhouettes are shown below. The top row is for a measurement station where the left margin is at x=1c (immediately behind the trailing edge), and the symmetric colour bar is scaled to ±8U/c. The bottom row is taken at x=10c, and the colour bar is scaled to ±2U/c. The field of view is 3.2cx1.5c in x and z. The aerofoils are at fixed angle of attack, =4°, and the chord Reynolds number is 11.7x103.

View larger version (7K): [in this window] [in a new window]   Fig. 5. Normalised circulation, , of the largest coherent wake structure in the wake of a thrush nightingale (TN, squares), two robins (RO, circles and triangles) a house martin (HM, diamonds), and a redstart (RED, shaded triangles) as a function of normalised flight speed (U/Ump). The solid line is from Eqn 5. Data compiled from Rosén et al. (Rosén et al., 2007) and Hedenström et al. (Hedenström et al., 2006b).

View larger version (13K): [in this window] [in a new window]   Fig. 6. Normalised vertical wingtip speed plotted over two wing-beat periods (t/T), as reconstructed from the two largest Fourier modes of a series interpolation to kinematic data of the house martin at four flight speeds (U4, U6, U8, U10) from Rosén et al. (Rosén et al., 2007).

View larger version (9K): [in this window] [in a new window]   Fig. 7. Local wing section Reynolds number (Reloc) over two wing-beat cycles (t/T) for U=6 m s–1 at three spanwise locations; r=0.2b (red, upper curve), 0.5b (green, middle curve) and 0.8b (blue, lower curve), where b=wing semispan).

View larger version (15K): [in this window] [in a new window]   Fig. 8. Lift:drag polars for the Eppler 387 wing at Reynolds numbers ranging from approximately 1x104 to 6x104. Each CL (CD) curve is plotted twice, for increasing and decreasing from –12°–19°. The two sets of curves cannot be distinguished. Blue horizontal line marks the preferred CL of the wing.

View larger version (14K): [in this window] [in a new window]   Fig. 9. CL as a function of angle of attack, , for the Eppler 387 wing. Blue horizontal line, see Fig. 8.

View larger version (2K): [in this window] [in a new window]   Fig. 10. The local wing section angle of attack depends on the ratio of wtip to U, and on a local rotation, which depends on the stroke plane angle and local twist. Silhouette shows a generic wing cross section at same span location.