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I am new to "luthierism" or lets build our egos a bit, "luthierology". Yes that sounds much better.

I am planning a dreadnought build and as my grandfather always taught me, "measure twice, cut once".

I have been investigating building a radius dish for the radius on the back and top typical in dreadnought guitars made popular by such manufactures such as Martin, Gibson, Taylor etc.
As I do with anything, after doing some research on the net, I decided to put some pencil to paper and just see what kind of radius we were talking about. It seems that common top radii are 25', 28', or 30'. Furthermore most of these radius discs that you can purchase on the net are usually about 24'' in diameter, or 2'. So I sorted through my brain to remember my old trig formulas. I wanted to see just how much radius that is. It seems at first thought that a 2' length arc on the circumference of a 25' (for example) radius circle sure wouldn't be much. So I calculated.

Long story short (if you want to know the math, I will be happy to mail or post it) the difference the arc length of a 2' chord on a 25' circle is .0005'. Or in other words, there is less than 1/2 a thousandth of an inch in "arcing".

However, with that said, seeing pictures on the net of these radius dishes there appears to be definite visible arcing. So therefore, I plead, "am I missing something?"

Thanks, Larks

Actually it's about .240".

I draw it in CAD and measure the distance. My trig is getting pretty rusty these days.

That's for a 25' radius.

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Horton, MI

I couldn't do the maths (not the s!!) either.......

you've gone wrong somewhere, there's more dip than that. at a rough guess from memory id say about 1/4"

I don't use dishes, I sand the braces to shape then glue them it with BIG clamps to pull the top round to meet them

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Its also more than just an arc, its a dome. Think of it as taking a guitar shaped piece off a 25' beach ball.

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Lance@LuthiersForum.com

Actually, I think we are talking about different measurements. However, thanks to your reply I reevaluated my logic.
I was comparing the difference between the length of the arc (arc length) and the length of the 2' (chord) which is precisely 2.005' vs 2'. However that is probably not what I was looking for. I actually need what is called the segment height which would amount to the maximum depth of the dish created. This measurement actually comes out to 0.020008'.
Still a small number, however, now I can see that it is much more in the ballpark of significant.

Thanks for your reply, now I understand.

Math is why I made these the old fasioned way, screwing together a 30' trammel and carefully swinging arcs.

The arc is on both sides of the forms and shows the approx difference between. There's a bridge pin on the table for some perspective.

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http://www.chassonguitars.com

Yup somethings wrong with your math.



R=h+d therefore

h=R-d

d=

so, h=R-

here we go

R=300" (25' radius)

h=300"-1/2*sqrt of {(4*300^2)-24^2}

h=300"-1/2*sqrt of {359,424}

h=300"-1/2*599.5198078

h=300"-299.7599039

h=0.240096"

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"There's really no wrong way, as long as the results are what's desired." Charles Fox

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Just read your post, seems you were calculating a different thing.

Anyway, hope my simple pictures help.

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My Facebook Guitar Page

"There's really no wrong way, as long as the results are what's desired." Charles Fox

"We have to constantly remind ourselves what we're doing....No Luthier is putting a man on the moon!" Harry Fleishman

"Generosity is always different in the eye of the person who didn't receive anything, but who wanted some." Waddy Thomson

There's the long compass way of drawing it, this link from Jon Sevy's site.

http://gicl.cs.drexel.edu/people/sevy/luthierie/luthierie.html

Useful after figuring the rise (or drop in this case) using his arc calculator.

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now known around here as Pat Foster
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Some luthier genius on this forum posted a technique involving the placement of a shim a determined distance from the mouth of a plane throat, marking the center of the brace to be planed, then planing that brace either side until a radius is formed.

I used this technique on #3, and I am very pleased with the results, using cam clamps to glue on the braces.

Kudos to whoever posted that technique!!