With RSTP the tree needs to converge which takes appr. 4-6 seconds. If you need a faster converge rate you'd need to look at something like SPB or various proprietary alternatives.
Additionally, arranging the switches in a ring may save ports but isn't the best approach. The image linked by user4565 provides a better way with two redundant core switches (which you set up with the lowest STP priority) and the rest arranged into a fabric. This will also ensure the fastest possible converge rate with RSTP.
Still additionally: you should consider providing redundancy through L3/IP multipathing instead of through L2 spanning tree. For IP multipathing you provide (usually) two independent L2 and L3 paths through the fabric.
Without redundant bridge loops you can deactivate spanning tree(!), which saves dead reconvergence time and also has the benefit that all physical links can actually be utilized. In the cisco example, you'd connect all left switches to each other for one path and all right switches to each other for the other path.
Of course, you don't need to do the split in half on the physical switch level, you can also do it on the logical VLAN level.