  Reversed von K\'arm\'an streets are responsible for a velocity surplus in the
wake of flapping foils, indicating the onset of thrust generation. However, the
wake pattern cannot be predicted based solely on the flapping peak-to-peak
amplitude $A$ and frequency $f$ because the transition also depends sensitively
on other details of the kinematics. In this work we replace $A$ with the
cycle-averaged swept trajectory $\mathcal{T}$ of the foil chord-line. Two
dimensional simulations are performed for pure heave, pure pitch and a variety
of heave-to-pitch coupling. In a phase space of dimensionless $\mathcal{T}-f$
we show that the drag-to-thrust wake transition of all tested modes occurs for
a modified Strouhal $St_{\mathcal{T}}\sim 1$. Physically the product
$\mathcal{T}\cdot f$ expresses the induced velocity of the foil and indicates
that propulsive jets occur when this velocity exceeds $U_{\infty}$. The new
metric offers a unique insight into the thrust producing strategies of
biological swimmers and flyers alike as it directly connects the wake
development to the chosen kinematics enabling a self similar characterisation
of flapping foil propulsion.
