captainpaddy
...Ah now, ya can't really mean that!..
Oh, I can assure you he does!
...If you feel that a trip to the weeds is inevitable then you are implying that the rudder will hit the stop and control will be impossible....
Yes he is, under the circumstances he has outlined.
...You can't honestly think that possibility has been overlooked by authorities or manufacturers. ...
No, not overlooked. Just discounted, on the basis of probability of occurrence.
In a nutshell, one of the limiting factors in deciding how low V1 may be permitted to go is Vmcg, the minimum speed necessary to keep the aircraft (straight) on the runway between V1 and Vr, following an engine failure at V1.
If Vmcg is established in a zero cross wind situation, as it is on my current aircraft type, then it will be far below the correct value of Vmcg that should be used in a (maximum) 40kt X/W take-off.
Whilst I can't speak to the performance calculations on the A321 which you fly, on my current type the difference in the two Vmcg values is in excess of 53 kts. The nominal correction to be applied to Vmcg is +1.33kts/1kt X/W.
So, if by ill fortune you were using a Min V1, on a limiting cross wind take-off, and suffered an instantaneous upwind engine failure at/after V1, you may well be committed to the take-off some 50 kts below the actual Vmcg pertaining on the day.
Whether Vr, or the edge of the runway, arrives first will then be in the lap of the Gods, but a trip to the weeds seems to me to be a reasonable description of what may happen next!
What john_tullamarine is correctly pointing out is that many pilots misunderstand the parameters surrounding certification, and therefore have an unfounded confidence in their ability to keep the aircraft straight following an upwind engine failure, at light weight, using a Min V1, in a limiting cross wind.
Demonstrations in the simulator, during command courses or on Base Training Captain's courses, quickly induces a sobering sense of reality.
Regards
Bellerophon