Ball Geometry

After making quite a few balls, I decided I wanted to understand the relationship between the material thickness, the ball diameter and the size of the resulting hole. It would be nice to have a simple formula to figure out how thick the stock should be for a certain size ball or if I found a nice piece of wood, how big could I make a ball with it. Looking at the balls that I had already made, I looked closely at the ones that had a nice size hole for the size of the ball and took measurements. So it was trial and error to find what I liked and then to develop the math behind it.

For this example I will use a material thickness of .750”. Easier to work in decimals at this point. The ball I made with this material was 4 5/16” or 4.335

Knowing those 2 pieces of information gives me the proportion of the material thickness to the ball diameter.

EF ÷ (2CF) = X       EF= Material thickness      CF= Ball radius    2CF = Diameter

.750” ÷ 4.335” = .173     This number was generated by trial and error.

(.173)  x  (2CF)  =  EF     Use this to find material thickness

2CF = (EF) ÷ .173            Use this to find ball diameter for given material thickness.



So if you want a 6” ball , The material thickness = (.173)  x  (6”) = 1.038” or  1  1/32”

If your material thickness is 1.750” , the box size would be 1.750” ÷.173 = 10.116” or 10 1/8”.

I figure I lose about 1/8” in diameter in the making of the ball so if you want to get close to a certain size, factor that into the initial box size and size your material accordingly.

The hatched area in the drawing is the plan view of the opening and how it was generated. I would need a mathematician to prove if my drawing is correct but it seems to work in the real world.

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