The back long arch

On to the back long arch. On the back I split from the idea held by Torbjörn Zethelius in his "Inside Out" article in the Strad, and came up with an idea I don't think is held by anyone. At least I haven't seen it presented anywhere before. I came up with this idea, and it was really solidified when I read that a viola by Grancino had a back 7.5mm thick. This was the only way I could get that result. The Ole Bull model I made has a 7mm thick back, and is the direct result of how the long arch is formed.
If you make a catenary curve from the end block to somewhere between the far corner and the opposite bout, from both ends, you end up with a shape like two clam shell halves joined in the middle with a thick rib. When you add the back thickness to this arch you get the outside arch which is... a circle. You can change the thickest point of the back by changing where you decide to put the end of the curve. Putting both at the corners will give a thicker back and one that rises faster. Putting both at the bouts works better for a low arch like this Strad. Some models may have the top and bottom arches going to different points. I take the arch given on the poster and copy it on white copy paper with a scanner. I tape that on my light box and then mark the thicknesses and end blocks in. Taking my chain, I move it around until the curve goes from the block to wherever, and goes up to the thickness marks. I mark the end point. Then I do the same to the other end. I find the center of each curve, and the depth at theat point and the long arch is figured out.
The drawing shows the circle in black, catenaries in orange and the outside arch in red. The bottom is to the right.