Sometimes it’s useful to know the radius of an arch or head casing long before the shop work takes place. I have found the formula above provides precise dimensions and takes advantage of the simple calculators on the market today. Even calculators without a square-root function can handle this one.
For instance, let’s assume that an arched opening leading from a dining room to the great room has 84-in. tall sides, the span is 96 in. and the center of the arch is to be 96 in. above the floor. The rise is then 12 in., as shown in the drawing. When you substitute the numbers and reduce the formula you get:
The radius is 102 in., with no errors resulting from inadvertent stretching of chalklines or other mechanical limitations, such as trying to lay out a curve with a 102-in. radius on a piece of plywood that’s only 96 in. long.
Charles W. Davis, Watsonville, CA
Edited and Illustrated by Charles Miller
From Fine Homebuilding #112
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I do not see a formula.
No Ed, they screwed up again. This has happened several times where the most important part of the "how-to" is omitted. They should really have someone review these BEFORE they post it
I "Could Probably" figure it Out Myself, but for Some Reason this "Comment" does NOT Show the Equation that You use?
I "Try" clicking on your Formula "Link" but Nothing shows up?
Here is what I use to find the radius (r) of an arch of width (L) and height (h) above the vertical sides:
r = (4*h*h + L*L)/(8*h)
You really need to proofread what you post. Once again, it's messed up (there is no formula, which is the point of the tip).
I, too, clicked on this to see how he goes about it.
Not that I wanted to find a technique other than the one I use:
Who cares about the radius, I want the correct curve!
Two nails driven in at the spring points, one driven in at the apex, and two boards screwed together at that apex to touch all three points.
Nestle a pencil into that apex juncture of the two boards, and swing the whole thing both left and right. Make sure to always maintain contact between the boards and the apex nail and each spring-point nail in turn, the left spring-point nail as you swing to the left, likewise with the right.
No need to look around for a 30' trammel arm, if that's what the job theoretically requires –– As I said, who really cares what the radius is?
My formula is: Radius= (Width^2/(8 x Rise)) + Rise/2
which is the same formula as njbobcat23 but in a different form. The radius is 102 inches.
How many more times are we going to get a messed up "Tip of the Day?" Fine Home Building should be ashamed.
I find the information helpful, on more than one occasion I have found myself searching the internet trying to find a formula to solve the very problem.
I saw the formula and understood it, but I didn't understand how it translates into the curve of the arch. I like the idea though. I don't always have the luxury of laying it out subfloor or a piece of plywood that's longer than 96" either.