calculating a curve

[rocket]

I've been asked to make a smaller size arch top guitar, and have been looking at plotting the correct shape arch to suit the instrument using David Cohens' curtate cycloid calculator.
I wasn't sure if i should use the dimensions across the lower bout or the dimensions from neck to tail, so i did a test on Bobs' archtop neck to tail pattern and got conflicting results.
My lower bout calc. matched his neck end but not his tail end ,and when i used the neck to tail dimensions the curve was nothing like Bobs, mine was much flatter.
Can anyone shed some light on the curve?
Rod.

[Nick]

Graham or Peter would be your men I'd say Rod being the mando guru's & I think both have done extensive research on arching. Personally I would just scale down the arching templates to fit the new size, but never having done anything smaller then a 17 I'd tend to fall back more on Graham & Peter's collective wisdom first before going down the scaling road.

[rocket]

Thanks Nick , i could probably do just that because the half span is only 13mm smaller, i just thought i'd try the exercise out .
Cheers

Rod.

[graham mcdonald]

The thing to consider on a guitar is that the recurve is going to be a different width depending on the length of the overall curve if the arching is based on curtate cycloids. Its not so bad on a mandolin as the body is basically a circle with an extension at the neck end. I am working up to my first archtop jazz guitar at the moment and I will probably plot out several curves - length and across at a few points and average out the recurve from them. I do think you should take the curtate cycloid as a guide rather than anything else. I certainly haven't read all the violin literature, but I always had the idea that it was someone fairly recently who noticed that Strad arching curves were very close to curtate cycloid curves, and so they have become fashionable because of that. I don't know if anyone has evidence that such shapes are actually acoustically superior. Graham Caldersmith wrote an article some years ago one their use in violin making, but I think he liked them for their mathematical elegance as much as anything else.

cheers

graham

[rocket]

THanks Graham, you opinion is very helpful in that i'd already played around with my outcomes, both lineal and lateral and what Bob is using and decided to find a happy medium there somewhere, keeping in mind the neck angle and tail piece extension over the belly.
Rod.

[matthew]

I use curtate cycloids as a starting point for my double bass arching. They seem to work well. I start by laying out the long arch which is made up of two curtate cycloids joined together (I do this by eye and there are various choices to make) then I measure the arching height at several points along the arch (3-4 places, at least centre of upper bout, waist, and lower bout) and plot curtate cycloids using these arching heights and corresponding arch widths. Then make the templates and off we go. I try to keep the recurve distance the same all around the plate, I think this looks nice.

[rocket]

Thanks Mathew, i'll take your ideas onboard too.
Cheers,,
Rod.