Explanation on take-off performance:
All aircraft are certified with a maximum take-off weight. Light aircraft right up to large transport planes. The maximum take-off weight for a B747-400 is 397,200kg. To be able to use this weight requires a very long runway, usually up around 4,000 metres long, and also close to mean sea level and cool temperatures. Even at sea level on a 40 deg C day with a 4,000 metre runway, a B747-400 will be unable to take-off at that weight due to runway limitations and enviroment limitations.
I don't have room here to explain the ramifications of environment limitations, but if you live near sea level and then travel to the mountains , for example skiing, you will find you will breathe slightly faster. In fact you can go so high where you'll need oxygen. Ever hear of altitude sickness.? It is caused by the amount of oxygen in the air being less with altitude.
Aircraft suffer from the same limitations. Jet engines create power by giving a mass of air an enormous acceleration. If the air is less dense, as it is at high altidues, then the engine does not provide the same amount of power as it does at seal level. High altitude airports such as Mexico City and Jo'Berg on hot days make it impossible for large planes to take-off at maximum structural weights.
This video is taken on a maximum weight take-off at Jo'Berg in summer. That is the maximum weight that could be calculated on this day, it is significantly less than the max structural weight.
Here are the facts as best I can recall. Runway 21R at Jo'Berg is nearly 5,000 metres long, the temperature was 27 deg C and we needed a minimum of 8 kt headwind to take-off at the max weight we calculated at 364,000 kgs. Jo'Berg is about 5,000 feet amsl.
Take-offs are calculated such that you accelerate to such a speed we call V1, and up to 1 knot less you can abort the take-off and stop on the runway. At V1 you are committe;, and if you should suffer an engine failure at the same time (worse case senario) you will still have ample performance to lift off before the end of the runway.
Notice how long it takes to the rotate speed. You can hear a nose wheel shimmy (out of balance as the nose wheel lifts off the runway.) I estimate that the main wheels crossed the end of the runway at about 35 feet above the surface!!
Notice the slow acceleration. It seemed to take for ever. At the end of the day Boeing performance engineers were right. It worked out fine.
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