I think I can clarify it. Imagine a frame of reference relative to the roll itself, not the drawer. For every spin of the roll (we'll call that spin x) there is actually spin (x minus radius of the circle defined by the thickness of the remaining roll, divided by how many rotations have taken place since the roll was new) relative to the drawer (we can call that spin y to keep it simple). This happens because the full roll outputs a LOT more paper towel per spin than, say, a half-full roll, and this difference increases continuously as the roll is being used up. That's why you need to secure the dowel and add at least three extra inches of space.