Radius of arc (I am trying to draw this in CAD)

[gjngss]

Hello,

I have an interesting one... See below image, I know the arc length (10,000mm), the overall "chord" length including the length under the triangles on the sides, and the overall "chord" height. I am trying to draw this in CAD, and need another one piece of info i.e. arc radius, angle in corner etc.

I am thinking there is no mathematical answer...but I thought I would ask.

 

[Ishuda]

Hello,

I have an interesting one... See below image, I know the arc length (10,000mm), the overall "chord" length including the length under the triangles on the sides, and the overall "chord" height. I am trying to draw this in CAD, and need another one piece of info i.e. arc radius, angle in corner etc.

I am thinking there is no mathematical answer...but I thought I would ask.

View attachment 8551

You might want to look at
http://mathworld.wolfram.com/CircularSegment.html
for some ideas. It looks like it might be possible to find out enough to completely describe the circle by combining and/or inverting some formulas there

 

[mmm4444bot]

… need … arc radius …

I am thinking there is no mathematical answer.

Actually, we can find the radius by introducing an xy-coordinate plane and by solving a system of equations, followed by using a trigonometric formula for sine. (I used software, to help with solving the equations.)

I turned the arc upside down, with its lowest point at the origin. I placed the center at (0,r), and I used (h,k) for the tangent point. (This allows working in Quadrant I only.) The distal end of that linear segment is at (6800,1700).

Is this homework?