I want to make a table top with a slight arc along the edge. I know the length of the side (the chord) and I know the height of the arc above the chord. Anyone know the formula to calculate the radius of the circle?
TIA Ron
Geometry question
Sep 05, 2003
13 Replies
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to XL spreadsheet (watch out for line wrap)
http://216.239.51.104/search?q=cache:6GIlO2OZGFMJ:
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Man, this web thing takes the joy out of trying to remember old HS geometry!
Anyways, came up with the same thing, R = (x^2 + y^2)/(2*y), where y is half the length of the chord and x is the height above the chord...
i.
Norm Abrams wrote:
You think the web's bad? Try AutoCAD. Draw the chord. Draw the height. Draw a 3 point arc. Select the arc and right click properties. Gives you the radius, arc length, etc.
Let l be the length of the chord h be the chord-arc height
r the radius and d the distance from the centre to the chord
Then r = ( (l^2 / 4) + h^2 ) / 2h
d = ( (l^2 / 4) - h^2 ) / 2h
That's easy. AutoCAD.
UA100
Thanks everyone. You saved me a lot of research time and I never even thought of using AutoCad...
Ron
You could make a string compass and draw that part of the arc on a sheet of cardboard. Go out on the driveway if you need room. Done.
[top-posting fixed]
I was more thinking along the lines of how, but Bruce's suggestion is a good one.
todd
The optimized formula is: chord squared, divided by 8 times the height, then add half the height.
example: chord: 10 height: 2
radius = ((10*10)/(8*2)) + 2/2 radius = (100 / 16) + 1 radius = 6.25 + 1 radius = 7.25
The derivation of the above gets messy.
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