Hi Robini:
I can not speak definitively about the 747-400 per se,
but your question as I understand it revolves around TO performance
There are three main things that limit the amount of weight that may be carried from a particular runway: they are limits in case of an engine failure
I. the take off field length ---
---with a question such as this it is best to specify for the responders the so called balanced field distance---
balanced field means that:
---- the distance to accelerate to the critical decision speed V1 ---V1 mean that THE VERY FIRST stopping action must already be complete BY V1 like thrust levers then brakes/spoilers/ reversers-----and then come to a stop
----is equal to the distance required to climb with an engine failed to a height of 35' above the end of the runway while accelerating to safe speed specified by certification [V2]
that condition is the balanced field----
the actual runway length required depends on other important factors
1. the outside Temperature and pressure altitude
2. the slope of the runway [downslope better for acceleration of course]
3. winds
3. runway condition
4. controllability or brake energy requirements
II. climb requirements with a failed engine
III Air carrier obstacle clearance requirements with a failed engine
The weight at which any of those three conditions becomes limiting becomes the highest weight possible to carry from the runway
Perhaps a more useful way to phrase you question is so as to include the actual limitation
what is the minimum balanced field length specified in your approved AFM standard day, filed length limited from a paved level dry runway, with zero runway slope, V1 = to Vmcg and 0---15 knot headwinds---?
and whats the weight specified?
I would add--- what is the maximum zero fuel weight of a 747-400 with xxxxx-engines?-- and what is the typical fuel flow with reserves?
Otherwise it gets too murky
----honestly
PA