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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.
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