Last weekend, the furniture bank had a golfing fundraiser. One of the staff asked if we could make a photo backdrop. The idea was to have a semi-circular top, two pieces 6' tall and one 8' tall, all 4' wide. The other repair guy and I cut some out of particle board normally used for table parts there. She painted two of them and wallpapered the tall one. We used some scrap wood to make braces on the back and tilted them back. Threaded inserts attached them so they could be easily stored.

Anyway, to do the cutting, I used the Rockler ellipse/circle cutting jig. It holds a P-C 390 or compatible router and we cut with a 1/4" straight bit in about 3 passes. I think it worked great.

Before I had it, and needed a larger radius arc, I attached the router to a piece of 1/4" plywood, set a pivot point and cut thru 8/4 oak. Likewise, it worked well. The beds had about a 4' radius.

There are two ways to determine the center of the circle including an arc. Any three points not in a line determine a unique circle.

1. Call the points a,b, and c. (b being in the middle)
   Use a compass or trammel set to a bit more than half the distance between a and b
   Mark an arc from each point that intersects with the other one
   Draw a straight line between the two points of intersection, this will be a radius
   Repeat for points b and c
   Where the two lines intersect will be the center of the circle, set your compass to the distance between that center and any point a, b, or c
   
   2, If the rise in the center of the arc is d and the distance between the two end points is 2f, then
   the distance from the center to the end point e is r, the radius
   the distance from the chord between the two end points and the center is (r-d)
   using Pythagorean theorem
   (r-d)^2 + f^2 = r^2
   r^2 - 2dr + d^2 + f^2 =r ^2
   -2dr + d^2 +f^2 =0
   d^2 +f^2 = 2dr
   (d^2 +f^2) / 2d =r
   
   Then set a compass to the radius and draw intersecting arcs from both end points, that will be your arc's center point.

i was told there would be no math.....

2 hours ago, DAB said:

i was told there would be no math.....

Good one!

Problem with math at my age is if I write it down to keep , then I have to remember where I put in info when I need it. But the real deal is I probably will not even remember I have the math.