Router Forums banner

Laying Out Large Arcs Without a Compass

1 reading
3.5K views 12 replies 9 participants last post by  harrysin  
#1 ·
HERE is a trick that I use to layout large arcs
 
#10 ·
Very cool, good trick. I have often done circles needing a large radius and fortunately I have always had the room, but this could be easier. As I think about it you could probably even jig a router onto it.
The other advantage is if you know width and height you want the arch, you don't have to know the radius. I have always used a formula to get the radius, but this don't need it.(y)
 
#12 ·
If you know the radius that you want and the distance between the outside points on the arc, here is how you calculate the middle point location.

C = radius
L = length between end points on the arc

Run a line from the center point of the circle through a point that bisects L, That line will intersect the third point on the arc.
To simplify the math, use A as 1/2 L, C as the radius and B as the line from the center to the cord line.

A² + B² = C ²
B² = C² - A²

B = The distance from the line to the arc is C - B

Example:
Radius = 20
Length between points = 6

From center point of circle to line is:

20² - 6² = 400 - 36 = 364

B =
398114

= 19.078

Distance from center point of line to arc is 20 - 19.078 = .922 Ft = 11.064 inches