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Does the roughly 1" plate height stay the same regardless of body width? Just wondering if the curves look better scaled up as the body width gets bigger.

I use the 1" thickness for all my sizes 16",17" and 18".

I will go as low as 7/8" thickness if that's all I can get ,but no thinner.

I think you’ll find that if you draw a curtate cycloid across the lower bout at 17 x 1, scaling it to 18” or 16” won’t make much of a difference in the height. There was a site that would generate corves for you that you could use as templates, but I can’t find it now so I’m guessing. Still, my impression is that the height is a forgiving enough dimension that if you are within 1” and 7/8” you will have a traditional sounding instrument at the range of sizes you are talking about.


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The site with the curtate cycloid calculator is R.M. Mottola's:

https://www.liutaiomottola.com/formulae/curtate.htm

I'm sure you'll spend some quality time looking around. There's a treasure trove of great information there.

I made mine a bit differently. I'm always like that. I wanted it to rise fast from the edge. I formed the arch from two long catenary arches on the inside in a cross pattern. Then catenary cross arches. I got what I wanted with that, but a curtate cycloid wouldn't work on the outside, they rise up much slower from the edge, and the inflection point would be much further in. For the back I used curtate cycloids on the edges, with an area 30-60 mms wide that was just a catenary arch in the middle. So it is a curtate cycloid that is stretched in the middle. It is 16 1/8" wide, and about 1 1/8" arch height from the bottom. So about an inch form the top surface.

The belly is done the same way on the inside, but since there is less difference in thickness between the middle and the edge (3.0 -about 4 mm compared to 2.5 - 6 mm), I just made the outside basic arches following the inside, joined with an inflection point through the f holes. It's about 1" arch from the bottom. It's supposed to be what GB Guadagnini would have done in response to seeing his sons guitar. His archings are quite full. It's supposed to be the first arch top, from1780 or so.

I'm guessing that the arch height was set by the available wood, just like in violins, to a point. Some cellos have backs with low arches, and I'd bet that it was just a thinner piece of wood they wanted to use. Why waste wood that you have? Adjust the arching to suit, and it should be fine.

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Why be normal?

Some years ago I made a couple of nylon string archtops that didn't work out well. To keep the top weight down I used a rather high arch and made the graduations thin. Since I was using a 15 mm arch on the top (measured from the rib top) I raised the arch height on the guitars to 22 mm, to take into account the longer box. The sound was loud and carried well, but was not suitable for the Classical repertoire. I also had problems getting good looking 'closed' Ring modes, ending up with pairs of modes that were 'open' in different ways.

At one point I was reading John Schelling's paper on 'The Violin as a Circuit' from the electrical engineering journal. He had put in a footnote that said, in effect, that if you wanted the plates to vibrate the same way you should scale the arch height to the thickness of the plate, not to the length of the box. Since I was making the tops about 3 mm thick, similar to the average thickness on a violin top, that implied an arch height the same as a violin; 15 mm. I made two that way and the worked fine. I had no more problems with 'open' modes, and figured that the thin, highly arched plates were not stiff enough around the edges to resist buckling in the 'ring' mode.

It just goes to show that you can pick up information from all sorts of places.

Alan, I've never used Chladni patterns, so I can't really comment on how mine are! The top does seem pretty resonate. I glued it on yesterday, well halfway, I only have 8 clamps, and 4 wood screws; could easily use 8 more. The neck block, and the bass upper bout are still loose, but they are practically tight right now so only a knife will fit in. Before gluing I did some measurements on the free plate. Just using an online tone generator, and tapping, and listening, I found 6 main ringing notes, and a bunch of others that don't really ring.
90Hz, 112Hz, 156Hz, 200Hz, 300Hz, and 360 Hz. 2 octaves from the top to the bottom. It is still 240 grams, not as light as the 220 I was going for. The back is only 330 grams.

Glued on, the belly has very little movement. I'm not sure how much movement you should feel at the bridge; but it isn't very much.
Tapping the belly in the center it sounds about 116Hz. Blowing in the f hole it resonates at 133Hz. I don't know what "normal" is.

It is nice to finally have a (almost) closed box, and to hold it up like a guitar. It has the satisfying "swoosh" of sound when you slide your fingers across its surfaces. It's my first one so I am clueless.

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Why be normal?

Thanks for the replies. I used that calculator on the Motolla site and using those control points I made a 17" cross section that was 1" high in my CAD program. I scaled this up in 3D to 18" and it only added just under 1/16 of an inch in height. Funny, in my mind I thought the vertical increase would have been much greater.

Ah yes; nobody has enough clamps. I made a box of about 50 spool clamps years ago, using a drill press, thread rod, 1" dowel, and cork. It took about an afternoon. Invaluable.