Back cross arch

Now the cycloid and catenary curves worked well together on the belly, but they won't work on the back in the C bouts where the thickness isn't even...will they? Yes they still work well together. The outside of the back can still have cycloid cross arches, and the inside is still basically a catenary curve in the beginning. The whole inside of the back and belly can be roughed out to an amazing degree of accuracy with just an outline, a couple of drilled holes (you could even get by without them), and a chain.
The outside can then be roughed to size and shape. In the beginning the procedure is just like carving from the outside first. Then I use a thickness marker to point out the thick points as a guide, so I don't go to thin. This will only work so far. This is because there is a fundamental difference between the two curves. The catenary is strictly concave (convex when viewed as above), whereas the cycloid is concave and convex. Through the middle of the instrument the curves are similar and the arching on the outside can go along quite close to finishing. At the point of inflection, where the cycloid changes from convex to concave you have to leave it thicker and blend in the recurve. This point is easy to figure out. From the centerline move out half the distance from the centerline to the low point of the arch and add half of the arch height. Coincidentally(?) this line of inflection is right in line with the f holes. All this will be easy to see when I start making chips.