Find the radius from a chord

[JohnS]

Originally Posted by Unregistered

The answer using the above Numbers should be 0.0288

Agreed. I must have made an error keying the numbers in. Thanks

Thanks! that formula worked like a charm for automating my radius calculations along a railroad track. It gave pretty much the same results as least squares circel fitting.

Anyone know what the name of the formula is and/or a scientific paper i can refer to it?

[JohnS]

Originally Posted by Unregistered

Thanks! that formula worked like a charm for automating my radius calculations along a railroad track. It gave pretty much the same results as least squares circel fitting.

Anyone know what the name of the formula is and/or a scientific paper i can refer to it?

I have never seen a name given to it. It is included in most math reference books. In the CRC Standard Mathematical Tables, it is covered in the Geometry section, under sector and segment of a circle. (Page numbers vary in different editions)

m^2 + (1/2c)^2 / 2m = r

Originally Posted by Robert Fogt

Just to make sure we are talking about the same thing, c is a straight line between points X and Z, called the cord, the curved line would be called arc length XZ.

Assuming you know c (not XZ) and m then the formula would be:

r = (m² + ¼c²)/2m

brilliant, thankyou , i needed this info too. spot and many many thanks. Andy

The formula your looking for is....
(x/2)squared + Y squared/ 2Y = R

I cant figure out how to write this on the computer but its (X over 2) squared + Y squared and all of that is over 2Y = Radius

Hope that helps.
Its in Circular Work in Carpentry and Joinery on the 9th page

where that formula come from? will you please explain me how to get to that formula r=(m2 +1/4c2)/2m

Find the chord length when we know the diameter of circle

I know the arch length and the radius..need to know the cord length

[JohnS]

Originally Posted by Dale

I know the arch length and the radius..need to know the cord length

Switch calculator to radian mode. The central angle is
theta = arc length/ radius
Chord = 2*R*sin(theta/2)

This only works in radian mode.