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First published online November 5, 2004
Journal of Experimental Biology 207, 4255-4268 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.01283

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The relationship between wingbeat kinematics and vortex wake of a thrush nightingale

M. Rosén^1,*,, G. R. Spedding² and A. Hedenström^1,

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

View larger version (13K): [in a new window]   Fig. 1. Schematic drawing to show how kinematics were measured from the wingtip trace. (A) Bird in rear view. ztip is the vertical position of the wingtip at any instance of the wingbeat. When the wingtip is at a maximum vertical distance from the horizontal, ztip,max and ztip,min are defined. The amplitude A1 (m), was derived from fitting a single frequency sine function to the wingtip trace, hence 2A1 represents the peak-to-peak swing of the wingtip over a full wingbeat. The projected wingspan, b', is measured from tip to tip. When the wing is in the horizontal position at downstroke b'd is measured. Similarly, b'u is measured in horizontal position for the upstroke. The span ratio R=b'u/b'd. (B) Side view of the flight path through still air. The inclination angle of the wingtip path to the horizontal line was calculated from a line fitted between ztip,max and ztip,min for the upstroke kin,u and downstroke kin,d separately. Stroke wavelength is the distance the wingtip travelled during downstroke, d, and upstroke, u.

View larger version (9K): [in a new window]   Fig. 2. Schematic drawing of the vertical centreplane cross section of a wake generated by a downstroke at low speed. The positive start vortex and the negative stop vortex are indicated as circles. The inclination angle of the wake plane, trace, with respect to the horizontal was obtained by fitting a straight line between the start (+) and stop vortex (–) at low speeds and a line parallel to the wake trace at intermediate and high speeds. The direction of the induced downwash was estimated from an average in a rectangular box in the centre of the wake just above the wake trace. The inclination angle of the induced downwash (ind) was then calculated relative to the vertical.

View larger version (97K): [in a new window]   Fig. 3. Rear view of the thrush nightingale in the wind tunnel. Consecutive frames spaced at 0.008 s intervals showing a complete wingbeat at U=5 m s–1 (A), 7 m s–1 (B) and 10 m s–1 (C), starting with the upstroke (a) to the transition between upstroke/downstroke (e,f) and through the downstroke (j) to the transition between downstroke/upstroke.

View larger version (34K): [in a new window]   Fig. 4. Eight wingbeats of the thrush nightingale in steady level flight at U=10 m s–1. Here, one typical wingtip tracing is presented as wingtip trace ztip and projected wingspan b'. Downstroke regions are hatched.

View larger version (10K): [in a new window]   Fig. 5. Amplitude A1 (m) derived from a single frequency sine fit to the wingtip trace. 2A1 represents the peak-to-peak swing of the wingtip over a full wingbeat. There is no significant dependence of A1 on U. (ANOVA: A1=0.0009U+0.073; N=28, r2=0.06, P>0.05). For details see Table 2. Values are means ± S.E.M.

View larger version (8K): [in a new window]   Fig. 6. Wingbeat frequency f (Hz) as function of flight speed U. The variation between maximum and minimum f is small, only 7%. (ANOVA: f=0.060U2–0.73U+16.25; N=28, r2=0.18, P<0.05). For details see Table 2. Values are means ± S.E.M.

View larger version (26K): [in a new window]   Fig. 7. The solid line shows the Fourier series approximation of the projected wing tip trace (filled circles). The coefficient amplitudes (in m) are given by An. The normalised acceleration is shown by the broken line.

View larger version (11K): [in a new window]   Fig. 8. Reduced frequency k (diamonds), and advance ratio J (circles), as function of flight speed U (m s–1).

View larger version (63K): [in a new window]   Fig. 9. Wingtip trace ztip (open circles) and projected wingspan b' (filled circles; mean values for both wings are mirrored), over a series of wingbeats at U=5, 7 and 10 m s–1. The bird is flying from right to left and all data is to scale on a 2 mx2 m grid. The start and end of a stroke phase is determined by maximum or minimum wingtip position, ztip,max and ztip,min. The downstroke phase is hatched. Data sampled at 1/125 s intervals.

View larger version (10K): [in a new window]   Fig. 10. The downstroke fraction of the wingbeat cycle versus flight speed, U (m s–1). (ANOVA: =–0.011U+0.55; N=28, r2=0.31, P<0.005). Values are means ± S.E.M.

View larger version (11K): [in a new window]   Fig. 11. Span ratio R versus flight speed, U (m s–1) (circles, ANOVA: R=–0.009U+0.34; N=28, r2=0.28, P<0.005) Values are means ± S.E.M. The mid-upstroke wingspan (triangles; ANOVA: N=28, r2=0.38, P<0.001) and the mid-downstroke wingspan (diamonds; ANOVA: N=28, r2=0.06, P>0.05) are shown for comparison.

View larger version (115K): [in a new window]   Fig. 12. Composite colour-coded spanwise vorticity with superimposed velocity field vectors for flight speeds U=5, 8 and 11 m s–1. Data are from the vertical centreplane. Velocity vectors are shown at half resolution. The vorticity is mapped symmetrically about a 10-step colour bar. The resolution of the colour bar matches the worst-case uncertainty in the measurement, so all visible features exist. The colour bar is rescaled to local absolute maxima at each different flight speed; these are ±700, 280 and 200 s–1, respectively. The regions corresponding to a starting and stopping vortex are indicated by a (+) and (–) arrow, respectively. The stroke wavelength is shown as a black bar and the wingspan, 2b, and mean chord, c, is shown for reference. For more details and examples of wakes at other speeds (4, 7 and 10 m s–1; see Spedding et al., 2003a).

View larger version (17K): [in a new window]   Fig. 13. (A) Inclination angles for downstroke: kin (squares; N=28, see equation 8) and ind from body centre position (diamonds, N=63) and mid-wing position (triangles; N=95) with a mean value of (circles; N=158). (B) trace from downstroke measured at body centre position (diamonds, N=28) and mid-wing position (, N=86) and mean values (circles; N=122). (C) Upstroke inclination angles for: kin (squares; N=28) and ind from body centre position (circles; N=47). (D) trace for downstroke measured at body centre position (circles; N=52). Values are means, and means ± S.E.M.

View larger version (21K): [in a new window]   Fig. 14. Summary of wake geometry data (abstracted from Fig. 13). (A) Downstroke, (B) upstroke. Squares, kin; circles, ind; diamonds, trace.