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#21
05-18-2008, 02:29 PM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

What if you know the arc-length, and the chord? Is there anyway to calculate the radius?
#22
05-19-2008, 07:18 AM
 JohnS Double Ultimate Supreme Member Join Date: Dec 2007 Location: SE Michigan, USA Posts: 8,703 Rep Power: 17
Re: Find the radius from a chord

Quote:
 Originally Posted by Unregistered What if you know the arc-length, and the chord? Is there anyway to calculate the radius?
Yes, but it gets ugly:
c must be less than s, and c/s must be accurately measured, even so it works poorly for small central angles, appreciably less than 1 radian (about 58 degrees).

s = R*theta (note: central angle, theta, must be in radians)
c = 2*R*sin(theta/2)

c/s = sin(theta/2) / (theta/2)

You have to solve this transcendental equation for theta, then R = s/theta

Four approaches:
1) Plot the function, enter with c/s, look up theta
2) Prepare table of values and do reverse interpolation
3) Expand the first few terms of Taylor series and solve
4) Use Newton's method to iterate a solution. (Use #3 for initial guess, quite unstable near theta=0, because derivative is 0)
#23
07-09-2008, 05:35 PM
 kasten_rich Guest Posts: n/a
Re: Find the radius from a chord

Here's the formula that I have found that works. This is from the Machinist's Handbook.

R= C squared + 4 h squared / 8 h.

C is the length of the chord; h is the height. As an example:

C= 53.125, h = 3.25, so C squared = 2282.3 + 4 X 3.25 squared or 42.25. 2282.3 + 42.25 = 2864.55. 8 X 3.25 = 26. 2864.55/26 = 101.175. So R = 101.175.

Does that help?
#24
08-15-2008, 04:08 AM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

hate to be the devils advocate here but what happens in the case that the height H (or m) in some formulas is zero, i.e. a point on the arc, shouldn't the formula still result an answer???

Quote:
 Originally Posted by Unregistered I stumbled on this through a google search. I was also looking for the same formula which I couldnt find in any of my study books. It's in the machinist handbook but I dont have one here at home. Here's the Formula R = ((C/2)² + H²)/2H So in your case with a chord of 30m and a height of 10m R = ((30/2)² + 10²)/2*10 R = ((225+100)/20 R = 325/20 R = 16.25m I know I'm a little late on the thread but should help others.
#25
08-15-2008, 05:36 PM
 JohnS Double Ultimate Supreme Member Join Date: Dec 2007 Location: SE Michigan, USA Posts: 8,703 Rep Power: 17
Re: Find the radius from a chord

Quote:
 Originally Posted by Unregistered hate to be the devils advocate here but what happens in the case that the height H (or m) in some formulas is zero, i.e. a point on the arc, shouldn't the formula still result an answer???
No. H isn't a point on the arc. It is the point of maximum height, at the center. If it is zero the "arc" is a straight line and the radius infinite.

You'd have to set up a different equation for an arbitrary point on the arc.
#26
09-25-2008, 03:33 PM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

so i need to find the radius having only the height from the chord to the arch and the arch length.. I do NOT know C or R or an angle? how can this be done?
#27
09-26-2008, 05:12 AM
 JohnS Double Ultimate Supreme Member Join Date: Dec 2007 Location: SE Michigan, USA Posts: 8,703 Rep Power: 17
Re: Find the radius from a chord

Quote:
 Originally Posted by Unregistered so i need to find the radius having only the height from the chord to the arch and the arch length.. I do NOT know C or R or an angle? how can this be done?
Much like #22, you can set up and solve an ugly transcendental equation

s = R*theta (theta must be in radians)
h = R*(1 - cos(theta/2))

2h/s = (1-cos(theta/2))/(theta/2)
Solve above, for theta/2, then theta, then R = s/theta

Expanding the above in Taylor series, first term gives initial guess of theta approx. equal 8*h/s. If this is a common problem, you could assume theta, calculate h/s, and build a lookup table. You could then interpolate between points.
#28
10-30-2008, 04:54 PM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

Thanks. Done!
#29
05-17-2009, 07:04 PM
 Unregistered Guest Posts: n/a
Re: Find the radius from a chord

I have a problem ...tricky for me simple to some

length of wall is 396 inches
the furthest point of the radius away from the wall is 3O inches.

I need to have a supplier crimp and bend my track but I need to provide the radius.(which is not provided on the drawing) Thanks to lazy Mr Architect
I would call the architect for this but this is a long weekend and I need to finish... please help
#30
06-18-2009, 11:39 AM
 amanda dubuisson Guest Posts: n/a
explain to me how the radius and chords are different?

[QUOTE=amanda ]I am not exactly sure what you mean.

The chord meaures the curve of a sector of a circle? so what can u explain to me like in a question for this Circle A has a radius of 3 m. What is the length of the longest chord in circle A? can you help me on that and to show me how you did it.

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