jtr,
A good argument never hurt anyone ....... bit hard to answer your question, though.
Fact is that Vmca sometimes is higher than Vmcg. The problem with the "arm" theory alone is that it ignores a bunch of other considerations.
Be aware that Mr Boeing's aft limit is a lot further aft than 22 percent .. the typical takeoff CG has not much to do with the certification values of Vmcg and Vmca. Very definitely influences the real world value on the day .. but the real world has never had all that much to do with certification ....
There is no simple relationship between the two figures .. sorry about that ......
Cap'n,
Be relaxed, good sir ... we all knew that it was a deliberate mistake put in intentionally to check if BIK was on the ball .....