  Block-structured AMR meshes are often used in astrophysical fluid
simulations, where the geometry of the domain is simple. We consider potential
efficiency gains for time sub-cycling, or time refinement (TR), on
Berger-Collela and oct-tree AMR meshes for explicit or local physics (such as
explict hydrodynamics), where the work per block is roughly constant with level
of refinement. We note that there are generally many more fine zones than there
are coarse zones. We then quantify the natural result that any overall
efficiency gains from reducing the amount of work on the relatively few coarse
zones must necessarily be fairly small. Potential efficiency benefits from TR
on these meshes are seen to be quite limited except in the case of refining a
small number of points on a large mesh -- in this case, the benefit can be made
arbitrarily large, albeit at the expense of spatial refinement efficiency.
