Fig. 2. Constant-circulation wake. In (A), the effect of the (invisible) bird moving at speed U is to leave behind a pair of undulating vortices with constant circulation (₁=₂=constant), in which case potential cross-stream vortices denoted by broken lines have zero strength. Here the geometry is simplified for convenience so the wake appears as if the downstroke and upstroke portions were approximate ellipses and rectangles, respectively, as drawn in (B). Although the actual geometry assumed in most models (e.g. Rayner, 1986; Spedding, 1987b) is slightly more complicated, the fundamental principle remains that the wake impulse (I) from both down- and upstrokes points upward, contributing to lift, and hence weight support. Because the wingspan is reduced on the upstroke, the projection of area S₁ onto a vertical plane will be larger than that of S₂, and so the net impulse of the whole wake is forward, generating thrust.