747focal,
Certainly no problem having V1 = VR if the distance geometry fits but would be surprised to see the usual sort of swept wing jet with VR = V2 due to the significant pitch attitude change required for takeoff. I would expect that the time taken for the rotation flare would usually require VR < V2 if the (normal) aim is to hit V2 at or about the screen OEI.
For prop aircraft, having a comparatively small pitch attitude change, it is not a problem to have VR at or near V2.
I take a contrary view regarding obstacles. Presuming adequate ASDA, far better to push V1 up to minimise the takeoff distance by minimising the period of acceleration (and hence distance) OEI between V1 and VR. In general, VR is chosen to suit the rotation speed increase so as to peg V2 at screen and bears a comparatively fixed relationship to V2.
fantom,
Sorry about that, mate ... yes, I have an appropriate background ... just my strange sense of humour .. I should just stick to being a boring old engineer.
As far as I am concerned, both as a pilot and ops engineer, the only difference of significance to the pilot is that, for a flex takeoff, the availability of a bit more thrust after the failure is there for the taking should the pilot have a reasonable need to do so. . .Of far more importance is adequate training of, and understanding by, the pilots within a particular operation so that they have sufficient knowledge and confidence to decide when it is, and is not, appropriate to use reduced thrust takeoff procedures (over and above the routine exceptions one normally sees in operations manuals).
The position you adopt regarding the V1/VR split is not quite so simple as just looking at Vmcg .. but we are all on the same side .. pass, friend.