Sagitta momentum uncertainty ($\sigma (p)/p=8p\sigma (s)/(|q|B{L}^2)$)

For a short circular track of chord length $L$, sagitta $s$ and fixed magnetic field $B$, $p=|q|B{L}^2/(8s)$. Differentiating this inverse relation gives $\sigma (p)/p=\sigma (s)/s$. A fixed spatial measurement uncertainty therefore makes the relative momentum uncertainty grow linearly with momentum.