Acoustic Guitar Construction

I asked Michael Dunn, a fabulous luthier who builds mainly gypsy style guitars, a question about getting more overtones and smoothness from a ladder-braced instrument, and he gave me some good pointers. He suggested that I use a much smaller dome than the exaggerated 'pliage' style that is traditional.

He suggested, in fact, that the top of the dome in the lower bout be about 1/4" (he actually stated 6-7 mm) above the rim.

What, in flattop terms, would be the top radius that would result in that 1/4"?

Thanks.

It depends on the width of the lower bout.. If you tell me that I can calculate it. It is still much smaller, bigger arch, than a typical flattop. For a 14.25" lower bout width that would be an 8.5 foot radius.

It will be either 15 or 15 1/2", if you would figure those I'd appreciate it John.
Thanks

After all my cipherin', figurin', calculatin', scribblin', and number punchin', I think I came up with answers.
Since I had to go waaayyy back for this by looking at a 30-year-old geometry text, it's probably better to condense all of the above terms into one word. So this is my guess.

chord of 15" with a sagitta of .25" has a radius of 112.625", or 9.39'
chord of 15.5" with sag of .25" has a radius of 120.25", or 10'

Calculating the Sagitta of an arc is clumsy at best for older minds like mine who have forgotten or have not used the math for a long time...all I got was a complicated answer to my questions...I knew there had to be an easier way...I searched for months until I found this on-line calculator...all you need to know is the distance from the straight to the top of the curve of the arch at a given length...or two of the measurements ...like length and height..duh? why so mysterious then? I have no clue... just use the calculator :>)

http://www.handymath.com/cgi-bin/arc18.cgi?submit=Entry

Just enter the required info and wowow...there's your answer! Hope this helps.

Ray

Thanks Gents!

I'm a little embarrassed that, had I used the 'search' function for the word 'sagitta' , I would have found that I had asked a similar question a while back and gotten a link to a formula.

The bright side is that the answers all agree. :-)

Anyway, that little 1/4" rise above the rim turns out to be one heckuva dome. That means one heckuva neck angle, especially when a tall, free-floating bridge is taken into account.

Decisions, gentlemen, must be made by yours truly. Go full gypsy, or go blues-style flattop ladder brace, etc. I'm going to give this some more thought.

Thanks again...