Collisional-cascade relaxation time ($t_c\sim 1/R_{\mathrm{cc}}$)

A bin with mass $m$ loses mass at approximately $m{R}_{\mathrm{cc}}$, so changing an order-one fraction takes $m/(m{R}_{\mathrm{cc}})=1/R_{\mathrm{cc}}$. The catastrophic planetesimal collision rate must be evaluated using the contemporaneous projectile population. It supplies a relaxation scale, not an exact equilibration time for an arbitrary fragment kernel.