Regarding the Vr and V2 speeds on a reduced power take off, and what follows refers to the B737-34 and probably the rest of them too!
We have two types of B737, ones with a dumb FMC where you type in the speeds you are going to climb out with, and another which produces the speeds given a selected weight, flap, and reduction (assumed temp/flex - whatever your language - same thing!)
The first one, we enter the speeds from a card. Done.
The second one - we take the weight, and get an idea of the speeds and bug these from the card. You then go to the FMC, and enter the ZFW, it will come up with the Vr and V2 speeds (V1 down to us). You enter the reducation and the Vr and V2 speeds change (partcularly at light weights). Because....(IMHO)
The idea following standard rate rotation is to achieve V2, following an engine failure at V1. If you use speeds for a full power take off this will be true. However, at a reduced power, because the aircraft is not accelerating as much the V2 will not be achieved at the end of the rotation. You will have to accelerate a little in the air to achieve V2. Hence the FMC will increase the Vr so that at the end of the rotation, you end up at V2. Cunning!
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