TMOH:
Vmcg must occur before V1, and Vr must be a min of Vmca1.05. So Vmcg will always be less than Vmca since to get airbourne requires in regulation that Vmca is higher than Vmcg.
Sorry, not true. (The part in italics)
Try Vmcg=80kts, Vmca=75kts, V1=Vr=90kts, V2=95kts.
That should meet all the relevant Vmcg and Vmca driven requirements, and is physically plausible. Just because Vrmin is 1.05Vmca
does not mean that Vr=1.05Vmca. You cannot use the regulations to deduce the values of e.g. Vmca, Vmcg, Vs or Vmu, because these are all things which determine the minima - they do not define the values themselves.
To take a really extreme example, V2min is 1.2Vs (or 1.13Vsr, but lets not go there for now). But V2 can be any value greater than that. If I want to define V2 as 200kts, because it's a nice round number, I'm allowed to. The takeoff performance will, of course, be diabolical if I do so, but there is nothing in the regs to stop me.
Apart from anything else, there are many limits placed on the takeoff speeds, and the actual published speed must respect all of them. Without knowing which was the limiting factor for given conditions, simply knowing V2, say, gives at best only a vague idea of the underlying aerodynamics.
A question I came across asked order of V speeds and two of the answers were:
Vmcg, V1, Vmca, Vr, V2
Vmcg, V1, Vr, V2
the later being stated as the correct answer. Weird! I guess you have to ask the CAA for that one.
The reason is that they are testing your grasp of mathematical logic as much as anything. The regulations require the following:
V1>Vmcg
Vr>V1
V2>V1
(if you ignore the possibility of some of these being "greater than or equal to")
The regs also require V2>Vmca
(actually in this as in other cases it may be a factor as well, but the logic is valid anyway)
So the second of the two options is clearly correct. What about the first one. To know that V1<Vmca<Vr I would have to have a requirement (indeed two) placing Vmca relative to those two speeds. Knowing Vmca is less than V2 doesn't help; for all I know it could be <Vmcg, given the regulatory requirements. So while the second set of V-speeds is mandated, and hence must always be true, the first is not mandated, and may or may not be true. That's why they said the second one was the right answer.
And finally...
indeed I do not know the answer, because there is no answer, or rather the answer is the classical engineer's answer: "It depends"
The balance of the factors does tend to result in a higher Vmca than Vmcg for most aircraft. But there is no simple reason why this is so, and therefore there are exceptions, and it would be dangerous to assume otherwise. Of course, since both numbers are required to be demonstrated in test, and are presented in the aircraft pubs, I see no reason to make an assumption; just look the numbers up!
Luke:
Cor blimey. I always presumed that it was a straightforward case of 'VMCG is lower because the traction of the nose wheel helps to keep it straight if an engine fails on the runway'.
Actually, since no credit is permitted for nosewheel steering in the FARs, Vmcg is demonstrated with the nosewheel steering inop'ed and the wheel free to castor. In any event the nosewheel is actually slightly
destabilising, and it is the mainwheels which stabilise the aircraft on the ground (which is why they are fixed and the nosewheel free to move for a tricycle gear)