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So you want the upper edge of each circle to be exactly on the hemisphere?
Yes, ideally, although anything approximating that would be good
moocher-
Well see the sketch, with that formula, you can calculate it to whatever precision you require, certainly with Excel. :)
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r will be constant; r = 20.
h however will increase 1 x by each circle (n); hence h = 5*n
I.e. The first d will be d1 = (20^2-(5x1)^2)^(1/2)
Second one, d2 = (20^2-(5x2)^2)^(1/2)
Solve that and you'll get your disc radius, d for n, n+1 ...
SwissChap
coventry_eagle
So you want the upper edge of each circle to be exactly on the hemisphere?
See this (sorry for the quick and dirty sketch), where h is the height of all the discs up to that point (including the one you want to find the radius of), and r is the radius of the hemisphere you're looking for.