I had to replace rotted trim around a curved roof. There wasn’t a semi-circle which would have given me a diameter, only the arc of the circle. Is there a way to figure out the radius of a circle from just the arc.
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I think you can do it if you measure the perimeter (i.e., along the curve) and then the chord (straight across from one end of the arc to the other) and then trial and error it using CAD or on paper. There may be a formula but don't know if off the top of my head.
rich,
i had the same problem as you
i needed to make some curved stair nosing for a job
check out this website
http://www.mathforum.org/dr.math/faq/faq.circle.segment.html
lee
Rich: If you have enough of the arc available, and you KNOW it is an arc from a circle. Do the following: Draw two secants as far apart on the arc as you can. Draw a perpendicular bisector for each secant. They meet at the center. Best accuracy is if the secants are 90 degrees apart. Shorter the arc, more slop in the answer.
Don
Don, is a secant a line that connects any two points on an arc?
Rich,
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Here's how to do it in the field....
take one tape measure and hook it at the top of the arch. Pull straight down. Take a second tape measure and hook it on one of the far ends of the arch. Pull it towards the other tape measure. Keep the first one straight down from the top and pull both tape measures until they cross at the same measurement. You now have the radius of the circle.
Rob Kress
Rod,
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Edited 10/21/2003 10:03:01 PM ET by Resurrected
What you guys are describing works for working within the arc - say in an arched doorway openning.
Rich2 is looking at this from the outside of the arc - the perimeter edge of a roof.
In this situation, I think he would need to place a straightedge against the outside of the curve, measuring square to the ends of it equally toa point of contact on the curve. When both measurements are equall, he has the height for your formula, Joe, as well as the length of the chord..
Excellence is its own reward!
Piffin,
You lost me. . . . ;-).View Image
Sorry, I'm sure it must have been a payback.
Take your chord in the drawing.
It is on the inside of the arch.
That is where you would be physically (inside) when finding the radius of an arched openning.
But he is on th eoutside of the arc - a roof edge.
To draw a chord thru that he has to use his chainsaw.
But draw a line parrallel to your chord in contact with the outside of the arch at it's midpoint.
At the two ends of that line, draw two other lines perpendicular to it to intersect the circle at the same intersection with your first chord.
The length or either of these lines is equal to the height for your formula.
But he is working it all from the outside of the arc.
It would take two people though probably..
Excellence is its own reward!
Piffin,
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I didn't mean the midpoint of the arc, I meant the midpoint of the parrallel chord.
Your detail is the practical one-man solution, though it took three of us to get there.
;o).
Excellence is its own reward!
Piffin,
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Here is an easy to remember formula
I thought you were going to post the arc formula..
So were is it?
Who ever invented work didn't know how to fish....
I used to make the arch forms for the masons on the job. I have used the two tape method that Kress talked about and I also used the following formula to find the radius of the arch , given the the width and the rise . The rise was usually determined by the number of brick courses the mason needed to achive a full first course of brick across the top of the arch.
A = base of arch(chord)
B= height of arch
( A divided by 2) squared + B squared.
Divide the sum of those two calulations by 2B = Radius of the arch.
hey Bob I've treaded water around arches like that before too thanks for the scenery my neanderthal bent takes better to lost arrow's explanation though
Hey Rich if you have excel on your computor I can send you a great arch moulding program. It will tell you what you need to know quickly and easily.
Mike