Fig. 2. Frames of reference and characteristic angles used in the blade-element analysis. (A) The bird at mid-downstroke, along with the bird's right wing from an earlier instant in the stroke, the global and bird coordinate systems, and several orientation parameters. Note that the wing elevation angle, , is shown for the wing position at the prior instant in time as at mid-downstroke is approximately 0°. (B) A wing section and associated angles. Note that , the wing spanwise rotation angle, is slightly negative as shown. Additionally, has been transformed to the body coordinate system to give (see List of symbols and abbreviations).