Fig. 1. Schematic drawing to show how kinematics were measured from the wingtip trace. (A) Bird in rear view. z_tip 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, z_tip,max and z_tip,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 z_tip,max and z_tip,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.