Constant-force spatially gated motor ($⟨f⟩\simeq f_0(x_2/\Delta )(1-e^{-k_1{x}_1/u})$)

A prescribed-speed molecular motor model in which a head attaches only within a phase window of width $x_1$, stays bound to phase $x_2$, and then detaches at a constant rate before the next period $\Delta$. If the binding window and detachment tail are short relative to the bound plateau, the phase-average force is the plateau fraction multiplied by its attachment probability and bound-head force $f_0$.

With positive opposing load magnitude $L$ and positive viscous drag coefficient $\gamma$, steady contraction requires $L=N⟨f⟩-\gamma u$. A decreasing motor force curve and an increasing drag-magnitude line have a unique intersection for each load below the limiting stall force. Using $+\gamma u$ as the signed drag would instead make drag assist forward motion, reversing its physical role.