How do concave disk--e.g. very shallow spherical bowl?

I got that and it is an obvious improvement over what I had originally suggested.
We are on the same page then.
With the template method the difficulty lies with the method of producing accurate partial radius templates that will be within the range of hobby accuracy which often appears to be in the .0001" range here.

Spending a good deal of time making a part to tolerances that you can not measure is pointless. (How would you measure such a part)
 
Spending a good deal of time making a part to tolerances that you can not measure is pointless. (How would you measure such a part)
A spherometer is used to accurately measure the curvature of lenses and mirrors. A fairly simple one is made with two points a distance apart and an indicator at the midpoint. The distance above or below the line connecting the midpoints is measured and the radius of curvature can be calculated. The OP did just that in calculating the radius of curvature needed at 55". The more sophisticated spherometers use three points in an equilateral triangle with a micrometer at the center of the triangle to measure the distance above or below the plane through the three contact points.

For the OP's purpose though, I would think that the actual radius of curvature isn't that critical. He got his specification by reverse engineering a commercially available product.
 
Nice diagram Mr Waller. I may try something like this also. I want to make a concave bowl for hammering copper discs.
Question: If the tailstock pivot was offset on the cross slide axis (is that X or Y) what would be the resulting shape?
Robert
 
Nice diagram Mr Waller. I may try something like this also. I want to make a concave bowl for hammering copper discs.
Question: If the tailstock pivot was offset on the cross slide axis (is that X or Y) what would be the resulting shape?
Robert
If the pivot point is off center the tool will reach full depth before or after the center resulting in a radiused groove on the face.
 
If you look at the intended purpose of Euler's disk, a conical profile should work just fine to confine the spinner. There is no particular magic in a spherical surface -- the main thing is to create a radially symmetric inward-pointing bias to the spinner. If you don't have a mill and RT to create the conical profile, you may be able to set your lathe compound over far enough to do the job -- or use the taper-attachment idea mentioned earlier in this thread.

Another idea: go to thinner stock for the disk. Evenly support it at its perimeter, then apply a pull force to the center (from the back). It will deform into a curve, the depth of which depends on the thickness and diameter of the stock, and the magnitude of force applied. The details on how to apply the force are left up to you :).

I personally like the simplicity of a piece that's just turned to produce the desired profile.
 
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