Radius of an arc
Formulas for determining the radius of an arc, or "eyebrow"
I would like to know the formula for determining the radius of an arc, or "eyebrow", in cabinetmakers terms. I know it starts with a line connecting two points of the arc and the amount of "rise" within that segment.
I looked for this formula for a long time and found it in a book called "Pocket Ref" by Thomas J. Glover.
Here is the formula if the line connecting the to points is "A" and the distance from a to the edge of the circle is b (at a 90 degree angle to a)
then (^2 equals "squared"):
or half a squared plus b squared divided by 2 times b.
I think the degrees are (atan(a/2)/(r-b))*2
I just draw the horizontal line and then the rise from the midpoint, create a 3 point arc, then ask ACAD what the radius is.
Here is another way:
Square 1/2 of span.
Divide by rise.
Divide by 2.
Rise squared plus half the width squared divided by twice the rise.
The comments below were added after this Forum discussion was archived as a Knowledge Base article (add your comment).
Comment from contributor A:
C= chord length
M= distance from chord to edge of circle
C squared divided by 8M + M/2 = R
Comment from contributor B:
To calculate radius of a circle where:
r = radius and is unknown
C = chord length (a line the crosses any two points on a circle)
B = length of perpendicular line from midpoint of chord to edge of circle
r=((4*Bsquared + Csquared)/8B)