Fig. 2. Schematic diagram of the computational system of a fruit fly Drosophila melanogaster. (A) The local wingbase-fixed (x, y, z) and the global earth-fixed (X, Y, Z) coordinate systems. The origin O' of the wingbase-fixed coordinate system lies at the wing base, with the x-axis normal to the stroke plane [the yz plane as defined by Ellington (Ellington, 1984b)], the y-axis vertical to the body axis and z-direction parallel to the stroke plane. (B) The wing kinematics are described by the positional angle , the feathering angle (angle of attack of the wing) , the elevation angle , and the stroke plane angle β; the link to the earth-fixed frame of reference comes through the body angle . We assume a body angle of 45° and a stroke plane angle β of 0° (Fry et al., 2005). (C) Instantaneous positional angle , feathering angle , and elevation angle of the fruit fly wing over one complete flapping cycle. Green solid, orange broken and blue dash-dot lines represent the positional angle , the feathering angle and the elevation angle , respectively. Red points a–g: (a) mid pronation, (b) early downstroke, (c) mid downstroke, (d) late downstroke, (e) early upstroke, (f) mid upstroke and (g) late upstroke. T, dimensionless period of one flapping cycle.