How to find a Radius with chords?

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Okay, so we had this problem show up at work.Company wanted a new panel for their RV/Coach, had a radius-ed corner.All we have is a 2" and 6" od pipe die (8'long for bending some of our light boxes)2" and 6" didn't work.I know the chord theories can make this problem go away (part has already gone away, we declined the job)I think the section I could measure was about 3" (the part of the radius).I've been scouring youtube and google, but every equation I can find lists the chord length, and the distance TO the CENTER of the circle. So that equation does me no good.So The only two numbers i would have are the length of my chord and the distance from the chord to the inner/outer radius of the piece. How would I solve this puzzle?
Reply:You are looking for the circular segment formula. The version you need is Radius = (center height of chord / 2) + (( chord length^2) / (8 * center height of chord))The other versions are not solvable with the data you have.Irving, TX. Epicenter of the Metroplex!Using Tapatalk
Reply:Cool beans.  Just something else to add to my arsenal of math problems lolSent from my SAMSUNG-SM-G935A using Tapatalk
Reply:

Originally Posted by AdVirMachina

You are looking for the circular segment formula. The version you need is Radius = (center height of chord / 2) + (( chord length^2) / (8 * center height of chord))The other versions are not solvable with the data you have.Irving, TX. Epicenter of the Metroplex!
Reply:

Originally Posted by Oscar

Oohhh, that's a good formula right there.  I should try to derive it, just for the heck of it.  


Reply:

Originally Posted by Oscar

Oohhh, that's a good formula right there.  I should try to derive it, just for the heck of it.  


Reply:

Originally Posted by neuralsnafu

....The only two numbers i would have are the length of my chord and the distance from the chord to the inner/outer radius of the piece. How would I solve this puzzle?
Reply:

Originally Posted by Oscar

Oohhh, that's a good formula right there.  I should try to derive it, just for the heck of it.  


Reply:

Originally Posted by ManoKai

You have the arc length and the sagitta. This online calculator will allow you determine your radius, chord length, and sagitta if you know two of three variables. After you solve for the radius, the arc length is simply the radius x subtended angle (in radians).
Reply:Sorry wrong formula.Sincerely, William McCormickLast edited by William McCormick; 11-20-2016 at 10:01 AM.If I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.
Reply:

Originally Posted by AdVirMachina

You are looking for the circular segment formula. The version you need is Radius = (center height of chord / 2) + (( chord length^2) / (8 * center height of chord))The other versions are not solvable with the data you have.Irving, TX. Epicenter of the Metroplex!
Reply:I knew there was a dirt bag simple way to do this. And I found it. The rule is that if two cords intersect within a circle that if you multiply the two pieces of the same line split at the intersection, that the resulting area of a rectangle will equal the rectangle created by the other lines multiplied segments. That means the formula is half the cord times half the cord, divided by the height of the circular segment. That amount is actually the length of the diameter of the circle when added to the height of the circular segment. In the example below if we multiply 1.496272 times 1.496272 we get 2.238829897984 if we divide 2.238829897984 by the height 0.399775 we get 5.600224871450191 the length of the other line segment short of the height of the circular segment if we add the height 0.399777 to 5.600224871450191 we get the diameter of the circle or there about 5.999999871450191 if we divide that by 2 we get the radius that is threeThe slight difference is because of the base ten system not the formula.

Sincerely, William McCormickIf I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.
Reply:^ why are you carrying 6+ significant digits? What tool are you using to mensurate these tolerances?"Discovery is to see what everybody else has seen, and to think what nobody else has thought" - Albert Szent-Gyorgyi
Reply:

Originally Posted by ManoKai

^ why are you carrying 6+ significant digits? What tool are you using to mensurate these tolerances?
Reply:We need Minnesota Dave to confirm this formula. Sincerely, William McCormickIf I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.
Reply:

Originally Posted by William McCormick

We need Minnesota Dave to confirm this formula. Sincerely, William McCormick
Reply:Here you go guys

William has a valid solution.If the pic isn't clear, the formula ends up to be:a = 1/2 cord lengthh = height from cord to circle edger = radiusradius = (a^2 + h^2) / (2h)  


Last edited by MinnesotaDave; 11-21-2016 at 02:24 PM.Dave J.Beware of false knowledge; it is more dangerous than ignorance. ~George Bernard Shaw~ Syncro 350Invertec v250-sThermal Arc 161 and 300MM210DialarcTried being normal once, didn't take....I think it was a Tuesday.
Reply:

Originally Posted by MinnesotaDave

Here you go guys

William has a valid solution.If the pic isn't clear, the formula ends up to be:a = 1/2 cord lengthh = height from cord to circle edger = radiusradius = (a^2 + h^2) / (2h)  



Reply:

Originally Posted by William McCormick

I am just demonstrating the formula not the actual measurement. I usually go two or three places max....
Reply:

Originally Posted by MinnesotaDave

Here you go guys

William has a valid solution.
Reply:

Originally Posted by neuralsnafu

Okay, so we had this problem show up at work.Company wanted a new panel for their RV/Coach, had a radius-ed corner.All we have is a 2" and 6" od pipe die (8'long for bending some of our light boxes)2" and 6" didn't work.I know the chord theories can make this problem go away (part has already gone away, we declined the job)I think the section I could measure was about 3" (the part of the radius).I've been scouring youtube and google, but every equation I can find lists the chord length, and the distance TO the CENTER of the circle. So that equation does me no good.So The only two numbers i would have are the length of my chord and the distance from the chord to the inner/outer radius of the piece. How would I solve this puzzle?
Reply:Manokai, the equation William Mcormick used is the second equation in your link post #7.http://www.mathopenref.com/sagitta.htmlYou should use a different color text when using those macros. It would stand out and be easier to use IMO.The nomenclature is different than WM's. Your link used S for sagitta , lower case l for half length (L) and r is standard.  I will have to look it up in my machinist handbook to see what they use for nomenclature.
Reply:@ Insideride -check. However, cool that William McCormick and MinnesotaDave derived/illustrayed the formulae in action. And yes, your suggestion to bold the variables for visual contrast in the future is a good one. Thanks."Discovery is to see what everybody else has seen, and to think what nobody else has thought" - Albert Szent-Gyorgyi
Reply:This is another dirt bag simple formula. The square of half the cord times pi equals the donut shaped area for any two circles with the same center point.

Sincerely, William McCormickIf I wasn't so.....crazy, I wouldn't try to act normal, and you would be afraid.