Making round wooden spheres [balls]

For a spheres that is 4" in diameter:

Here is a way that I have acually used.  Cut 4" cube. Drill a hole
2" in diameter into a piece of plywood and mount you router underneath.
Put in a router bit with good bottom cutting ability.  (A dovetail bit is
excellent).  Place the router bit (2- sqrt(3)) inches below the top surface
of the plywood.

It looks like this

======================           ========================== (plywood)
                           _
                          \ /  
                           | (router bit)

The edge of the circle and the top of the router bit describe a circle
with a radius of 2". Feed the corners of the cube into the hole. Keep feeding
any high spot in until there aren't anymore.  Careful, the bit can easily
catch the work. (I usually start with the bit down farther and work up to
the measurement given above.) 

In general:

For a hole h" is diameter and you want to make a sphere D" in diameter.
The depth of the router bit (d) should be:

          d = D/2 - SQRT( (D/2)^2 - (h/2)^2)

(For a D = 4 and a  a h = 2  the depth  is  2 - SQRT(3)

The bigger h is the less error, however if h ever gets bigger than D the ball
will fall through.  I am comforable with h = D/SQRT(2).  I would use what ever
drill bit I have that makes h some where between D/2 & D/SQRT(2).

Try it It really works.

Dave Van Ess