Guys, please wake Up. This is basic performance.
And the type of aircraft is irrelevant in this matter.
Er, not a very constructive contribution? Also, type
is relevant. While the same regulatory limitations to the definition of V1/Vr/V2 apply to all types, for most takeoffs there will be a range of possible speeds allowed.
Airbus and Boeing for example go about performance calculations very differently, and it also varies by type: on an A321 V2 may be the result of a complex optimization calculation involving V1/Vr and V2/Vs ratios, and take available runway length and obstacles into account, while on a B747-400 V2 is calculated simply as a function of weight and flap setting, nothing else.
In addition operators are free to modify performance numbers (within allowed parameters), such as using a lower (more "go-minded") V1, thus adding further complexity to the issue.
If VR was limited by 1.05 Vmca, V2 would increase with it
then it is unlikely that VR is limited by 1.05 Vmca
Not sure what you mean Gysbreght, but strictly speaking there is no direct relationship required between Vr and V2, except that the latter must be greater or equal to the former. Both however are limited by their relationship with VMCA.
The OP asked why FMS precalculated Vr changes significantly when a different thrust rating is selected in his FMS. Every thrust rating comes with its own VMCA, with the most de-rated having the lowest VMCA of course, thus allowing for a substantially lower Vr than the highest thrust rating.
Precalculated V2 instead will not change (on a B744) as it is always dependent on weight and flap setting
only (although this V2 does of course always satisfy the 1.1 VMCA and 1.2 Vs requirements, at all possible thrust ratings).
Ergo, when you first look at FMS precalculated speeds on a B744 FMS (when the default full TO thrust rating is still in the system), V2 will be spot-on provided weight and flap settings are correct, while Vr could be several knots higher than the Vr you will actually use. As soon as you "tell" the FMS that the rating you will use that day will be lower, say the maximum de-rate or TO2 as it's called on the Boeing, Vr may drop accordingly.
DISCLAIMER, I am just a line guy with an interest in performance, so if anyone has a better explanation of why the OPs Vr is changing with a change in selected thrust rating then by all means let us know!