Here's my understanding -
Typically, on tricycle gear aeroplanes... Cessna 406, PA34, 737, A320, 747 etc, and for
exam purposes, VMCG can be considered, generally, to be higher than VMCA.
As Mr Tullamarine pointed out, it's very bank dependant, but hopefully I can answer the basis on which your question lies!
So we have a tricycle gear aeroplane, going from front to back, first we have the nosewheel, then (typically) the CG, then the mainwheels, then the rudder/vertical stabiliser. As JT pointed out, nosewheel steering is disconnected for VMCG testing, effectively free castoring.
It all lies in the moment arm, that is, the stabilising/directional force supplied by the rudder/vertical stabiliser, and it's distance from the fulcrum. In the air this is the CG, which is generally ahead of the mainwheels. So to produce a given moment (that which will render the aeroplane directionally controllable with loss of critical engine), there will be some force 'X' required at the rudder. However, whilst the wheels are still in contact with the ground, again 'generally' speaking (because the faster you go, the more the fulcrum moves from the wheels to the CG as the weight gradually moves off the wheels and onto the wings), there will be a shorter arm between the fulcrum (now the wheels) and the rudder. Hence, to produce the same moment over a shorter distance, a greater directional force needs to be supplied at the rudder. At full deflection, the only other variable is our CAS, which must be increased. That's where your VMCG > VMCA comes from!
However, this is only relevant for an aeroplane with a CG situated ahead of the mainwheels (technically the centre of radius of turn to be precise, but good enough), so it is convenient for us to imagine this being a tricycle gear aeroplane.
Going by the same theory, everything is reversed for a taildragger, for which
in theory, VMCG would be less than VMCA...
But as JT has written above, there are so many external and type specific factors to be considered, this is all theoretical - I'm no aeronautical engineer, but I hope this has helped you with the basic understanding as I have it.
