Hi Alan,
I don't think sweep can be sensibly related to radii as the radius would be different for each width in each sweep - that's the whole point of the sweeps and sizes, each tool produces a different cut.
Initially I thought it might be the number of twentieths of a complete circle, what with a No10 being half a circle, but that falls down when you find a quarter circle somewhere between a No7 and a No6.
It's not a straight relationship between the depth at the centre and the length of the chord of the curve either, as what works for a No10 falls to bits as a concept as you move down the sizes.
Looking at the charts it would appear that the relationship is non-linear as the sides of the stacked diagrams curve inwards, so pi may be involved in the equation.
At which point I'm happy to define it as "a complicated formula produces a vast selection of unique radii."
Sorry I couln't give you a more definite answer.
Just to make matters worse for you, the continental system is one size off from the Sheffield system, so an English No10 is the same sweep as a continental No9 and so on.