Average wrist and wingtip trajectory in the body-referenced coordinate system, normalized by wing chord (top view). Dots indicate successive time increments during downstroke. Solid green line represents virtual leading edge at mid-upstroke, dashed line at mid-downstroke, green stars are wing tip, and hexagons are wrist positions at mid-upstroke and downstroke. Wrist flexion angle, ϕ, is the angle between the two vectors representing the leading edges of the proximal and distal portions of the wing. (a) Speeds below 5.5 m s−1; (b) speeds between 7 and 8.5 m s−1. (Online version in colour.)