Shannon airport

The rotate point in normal operations is irrelevant, they may not even be using full power, the critical factor is the V1 engine failure distance, the point at which if an engine fails, it can still get off safely on the remaining runway, at which point it also has to be able to climb away without falling foul of any obstacles. Fortunately, engine failures on long haul aircraft are rare, but when they happen, they get the attention of all involved very rapidly, and the pressure on all involved is significant. An engine failure on a twin is usually more significant than on something like a 747, if for no other reason than the 747 has lost 25% thrust, the twin loses 50%, and this is one of the reasons why any twin jet climbs a lot better than the larger 4 engine aircraft, the thrust reserve is that much higher, and if it's being used, the twin will climb faster or steeper than the 4 engine. That's one of the reasons for the standing joke about the early 340's only being able to climb because of the curvature of the earth, and why they can fly so far once they get to height, the twin has to have power reserves for operational safety that go way beyond the 4 engine.

Take a look at some of the performance of the early jets, and at the long range piston aircraft. Their climb performance fully loaded was not exactly sparkling, which was the reason that many of the control zones around places like Heathrow were so large, in the early days of long haul, they had to be in order to provide separation from the traffic that needed a lot longer to climb away effectively.