Hmmm ... I know of storms (not particularly, but inferred from hail size) that likely had updrafts from 100-140mph with baseball and softball sized hail. I'm thinking the Aurora mega-stone probably came from the storm with a mega-strength updraft, but I'm almost certain that storm structure played a very large role in the growth of that stone, rather than updraft strength alone (hailstone trajectory usually plays a decent roll anyways). But ok, take a 230/250
mph updraft...
Wmax (IDEAL Updraft strength) = SQRT (2*CAPE)
Usually, this is actually: Updraft = [SQRT (2*CAPE)]/2... in other words, in the real world, the actual updraft speed can be / is usually one-half of the square of two times CAPE. Now, this updraft speed in the above formula is in m/s ... So, with the proper conversion, 250mph is about 103 m/s...
Solving for CAPE....
CAPE = (2*Updraft speed)^2 / 2
CAPE = (2*103)^2 / 2 = 21,218 J/KG ...
Yep, that means to support an updraft of 230mph with ONLY bouyancy/CAPE, which isn't exactly fair, the CAPE in the environment must be 21,218 J/KG ... I'll just leave it at that...
Now, there is another signficant source for updraft strength other than bouyancy/instability (CAPE) -- updraft rotation. With a rotating updraft, vertical pressure perturbations, the updraft tends to be 'stronger' than a non-rotating updraft... Thus a supercell in a 4000 CAPE environment (with it's rotating updraft / mesocyclone) can and will have a stronger updraft than a non-supercell in the exact same environment... Thus the reason why the vast majority of "very large" hail reports, say >2.0", are produced from supercells.
EDIT: This only applies to vertical updraft velocity... Check out
http://meted.ucar.edu/mesoprim/cape/print.htm points 6-9 (I think) for other factors that contribute or detract from the CAPE-vertical velocity estimation equation given in this post...