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I am probably the last person to figure this out, but I spend a lot of time reinventing the wheel and then informing everyone what I just did. This follows that theme.

I want to get one of those Grizzley compound radius fretboard sanders, but I didn't know how the compound radius was calculated. I did know that the compound curvature of the fretboard is the surface of a cone, so while laying in bed trying to go to sleep, I just imagined the simplest cone, one with no depth at all, just a starting point in the center and two concentric circles. You can draw one on a piece of flat paper.

The trick is to make the innermost circle with a radius that you want at the nut, say 16 inches for sake of illustration. So you draw a circle with a radius of 16 inches. (you need lots of paper). Then you decide how wide you want your fingerboard to be at the nut. Perhaps you want it 1 and 3/4 inches. You make two points on that first circle that you just drew that are 1 and 3/4 inches apart. That defines an arc on the circle. The chord of that arc, a straight line between those two points will be 1 and 3/4 inches apart. The curved distance between those two points, the distance that actually follows the circle does not matter.

Now draw two lines. Each line starts at the center of the circle and joins one of those two points that you just made so that now you have a pie shaped slice of the circle. Make the lines go well past the first circle.

The next step is to determine how far from the nut your next reference point will be. All fretboard shapers have at least two points of rotation. One point is at the nut, and the other point may be at the 12th fret, or some other fret. Wherever that second point is, all you need to do is find the with of the fingerboard at that point. Since fingerboars taper, that second width will probably be wider than 1 and 3/4 inches. On my fingerboards the distance at the 12th fret is frequently 2 and 1/4 inchse. So assuming that my Grizzley compound fretboard sanders second point of rotation is at the 12th fret, I would use 2 and 1/4 inches as my second fretboard width.
   On my drawing I find a two points on those two lines that are spreading from the center of the circle that are 2 and 1/4 inches apart. Those two points can be connected with a short chord line to make a second larger triangle. The distance from one of those two points to the center is the second radius of your compound. It is important that the distance of both of those points to the center of the big circle are the same or you have drawn your chord line slanted and it will be longer than it should have been.
    I have not done this yet, but it should work.

Back to bed. Way too much pizza for supper. (which may have been my inspiration)

Hi John
That is pretty much the math and action behind my radius jig. It makes a nice fingerboard however probably not as nice as the grizzly, it does require some sanding to get rid of router marks but not tto much. I got the design from one of your brothers friends, Bo Walker in Texas.

_________________
Tickle your guitar daily, and it'll tickle you back.

That looks cool. is it adjustable for different fingerboard tapers?

I got the real math, its pretty simple.

The second radius = ( nut radius / nut width) x fingerboard width at the second point

I got better math for you...

1 cnc + 1 CAD drawing = Infinite number of perfect compound radiussed fretboards

The Grizzly sander/radius jig will set you back about $1000. That's a nice downpayment on a homemade cnc, whci will do a lot more for you than that one jig. Food for thought.

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"I want to know what kind of pickups Vince Gill uses in his Tele, because if I had those, as good of a player as I am, I'm sure I could make it sound like that.
Only badly."

I looked at the Grizzly radius jig, turned it upside down, and modified it to use a router instead of a sander, then built mine from scrap. It cost me nearly nothing.
When I proudly posted photos and drawings, I found that I had re-invented the one that John How posted.
It works great, and the only cost was a bit of scrap, some glue, and a handfull of drywall screws.

Al