Official Luthiers Forum!

Since I don't have a 56' diameter paint can lying around I thought I'd ask you guys who are math whizzes;

Does anybody know how to figure the amount of offset needed to create and arch for a given amount of length on a straight line in order to get a section of a circle of a given radius? For example, if I wanted to make a dish or a brace making jig for a router table with a radius of 28', and let's say I wanted to know the amount of offset to create an arch on a 24" line that would create a portion of a 28' radius circle. Is there a formula that would let me plug in the length of a straight line and the radius of the circle that would give me the offset? It would be a big help having this info so I could come up with jigs and dishes.

I know there are dishes available, as well as arch templates, but I like making stuff myself when I can...adds to the fun but unfortunately, this fancy math isn't my forte!

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Brad Tucker

If you have excel try this link. http://www.woodweb.com/knowledge_base/_Spreadsheet_Calculation_Program.html

if not http://www.woodweb.com/knowledge_base/Calculating_RadiansChords.html

From the second link:

Arc height when you know the chord length and radius:

B = R - sqrt( R^2 - (A/2)^2 )
(B = Arc Height) (R = Radius) (A = Chord Length)

Said as:
B equals R minus the square root of R squared minus A over 2 squared.


Using the spreadsheet I see the 28' radius in a 24" dish as having an arc height of .2144". The formula delivers virtually the same result.

Thanks, Bob! That makes life much easier for me. I can just plug in the numbers and get what I need. I had searched the net for some info, but came up empty handed.

_________________
Brad Tucker