Replies

1. 
   stonebm | Oct 21, 2003 06:18pm | #1

   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.

2. 
   WOODEXPERT | Oct 21, 2003 06:20pm | #2

   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

3. 
   Don | Oct 21, 2003 11:18pm | #3

   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

   The GlassMasterworks - If it scratches, I etch it!
1. 
   TLJ | Oct 21, 2003 11:23pm | #4

   Don, is a secant a line that connects any two points on an arc?

4. 
   Joe_Fusco | Oct 22, 2003 01:18am | #5

   Rich,

   This question as been asked 100's of times here and answered just as many.

   To find the radius of a known arc you can use this formula: R = ((((L/2)²)/H) + H) / 2

   1. Where L is the length of any chord that touches the arc.
   2. Where H is the length of a line from the center of the chord L to the arc.
   3. Divide L by 2 then square it.
   4. Then divide the answer by the value H.
   5. Then add the value of H to the answer.
   6. Then divide the answer by 2 and thats the radius.

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5. 
   RobKress | Oct 22, 2003 01:29am | #6

   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

1. 
   Joe_Fusco | Oct 22, 2003 03:02am | #7

   Rod,

   That's a pretty decent method for finding the radius, but there can be some problems with it. What happens if the position of the arc doesn't lend itself to being "hooked"? What happens if the position of the arc doesn't allow you to "pull the tape straight down"? What happens if it a really big arc? All of those could make finding the radius very cumbersome.I use this method in the field if I don't feel like using a calculator.

   Cut a straight piece of wood that will fit "inside" the arc and mark its center with a line.

   Place inside the arc and measure from the marked center to the arc square with the wood.

   Place the piece of wood on a plywood floor or sheet of plywood and use it to draw a line.

   From the center draw a line square the distance you measured to the arc.

   Draw a line connecting the all end points. This forms a triangle.

   Extend the line for the height as far down as possible.

   Mark the center of one of the line that from a side of the triangle.

   Using a square line it up with the mark and square to the side and draw a line until it intersect the height line.

   The length of the line is equal to the radius.

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   Edited 10/21/2003 10:03:01 PM ET by Resurrected

1. 
   Piffin | Oct 22, 2003 05:26am | #8

   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!

1. 
   Joe_Fusco | Oct 22, 2003 05:49am | #9

   Piffin,

   You lost me. . . . ;-).View Image

1. 
   Piffin | Oct 22, 2003 06:18am | #10

   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!

2. 
   Joe_Fusco | Oct 22, 2003 07:54am | #11

   Piffin,

   When I first read your post I thought that’s what you had in mind, but dismissed it because it’s quite difficult to do the way you described. You say something about finding the midpoint of the arc which would be a challenge in itself let alone trying to measure each end to find the “same” height.

   A much better approach to finding the radius of a convex arc would be to:

   1

   2

   3

   Nail a small piece of 2x4 (about 6 inches) onto a larger piece of 2x4 (24-30 inches depending on how big the arc is) at its end.

   Place the long 2x4 on the convex side of the arc and roll it until the small 2x4 touched the arc.

   Measure the distance from the end of the 2x4 with the small on it to where the large 2x4 touched the arc.

   Now you have H (6") and L (whatever the measurement is) to use in either the formula of by the construction method.

   You will have to miter the edge of the small 2x4 to get a good location on the arc though.Like this:

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3. 
   Piffin | Oct 22, 2003 03:12pm | #12

   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!

4. 
   Joe_Fusco | Oct 22, 2003 04:21pm | #13

   Piffin,

   No problem. You really don't need to be parallel either and you can also do this with a sqaure depending one how large the arc is . . .

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6. 
   BowBear | Oct 22, 2003 06:57pm | #14

   Here is an easy to remember formula

   An ex-boat builder treading water!

   
1. 
   IMERC | Oct 22, 2003 07:34pm | #15

   I thought you were going to post the arc formula..

   So were is it? 

   Who ever invented work didn't know how to fish....

7. 
   lostarrow | Oct 22, 2003 08:03pm | #16

   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.

   Be not afraid of going slowly.  Be afraid only of standing still.   chinese proverb
1. 
   johnharkins | Oct 22, 2003 10:44pm | #17

   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

8. 
   mike1 | Oct 23, 2003 01:51am | #18

   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