Also to add:-
- when calculating speeds (V1/Vr) the performance is always based on losing an engine at V1, so is always "safe".
- most pilots do 6 monthly sim checks, and this always includes practice of engine out on take-off. It is a compulsory item. Usually a cut at V1, which may or may not be a heavyweight departure. We have to get it right, if you are outside of limits in your handling of it then you have to do it again. If you don't get it right the second time you fail. This includes maintaining the flight path (ie keeping straight), following the planned departure, handling the engine problem, notifying ATC if relevant (usually would be!), reaching acceleration altitude, cleaning up and then continuing in the climb to assigned (or requested) safe altitude.
- Airlines are moving over to a new sim regime, ATQP, and that is different to what I just said above!