I've been thinking about ways to insulate the riser in a rocket stove so that it gets hot enough to be efficient. I was thinking that the size of the barrel might limit the thickness of the insulation. The barrel deflecting the exhaust around the outside of the riser also limits the materials you can use for insulation. I got to wondering if there was a reason for this coaxial setup instead of a parallel rig. I realize the falling exhaust in the barrel is hotter than the outside air and probably reduces the need for insulation. If the riser were not in the barrel how much would the heat loss be increased? How much more insulation would be needed to compensate? Right now this is all armchair theory, but I do hope to start tinkering with scrap stoves which may end up heating a barn or garage soon. Attached is a sketch of the idea.
For common sizes of barrel and riser, there is really no benefit to using thicker insulation than fits comfortably inside the barrel. 55 gallon barrels (23" diameter) seem to be the easiest to come by, and 8" i.d. risers are the largest common size, so even at the extreme of 2 1/2" thick firebrick and 2" of rockwool or perlite insulation, you would have 23 - 17 = 6/2 = 3" nominal airspace all around. If the riser is square, this would pinch at the corners, but the insulation can safely be thinner at the corners. In practice, this has been found to work well, and more insulation than this does not make it work noticeably better.
If the barrel were not surrounding the riser, the riser insulation would need to be thicker for heat loss performance, as the greater temperature difference to the room air would increase the loss for the same insulation. This would come close to barrel size, so no space would be saved.