That explains it very nicely. (And a lot easier than k factor.)
And it comes pretty close to working out - I was just tacking on a couple of mm to the πr length for a hemisphere, and since the thickness of the material was running about 3.3-3.5 mm, that was pretty close to half the thickness. Maybe a little extra, but it wound up not stretching much, which kept the wood intact.
Good to know why it was working though. Now I can easily modify it for thicker/thinner materials.