You don't have to use software unless your going for a very specific finished result.
Once you have a jig built to cut your segments at the correct angle then the only dimension left to decide is the segment width which determines the overall diameter of each ring. I generally stick to 12 segments per ring and 22mm width = 80mm diameter and 41=150 (roughly). The height of the rings can be varied for added effect. Decide on your desired finished shape and create the rings accordingly. You can either start with a rough idea and see how it turns out or you can start with a specific goal in mind and go from there.
Here is a recently completed project where I wanted a specific look to the finished pieces.