prb46,
I will try and help. I have over 12,000 hours on this type of aircraft. Unfortunetaly as is so often the case, reality needs to be suspended for dramatic effect. Reality often lacks entertainment value and so the two rarely go hand in hand. You are using a number of terms that don't make much sense in the context you are presenting them, anyway here goes !
From a performance point of view the 757 is something of a star performer. Most takeoffs are derated by anything up to 20% of maximum rated power. Obviously any derated settings are a function of a number of factors. Runway length, runway slope, contamination factors, obstacles in the extended take off area, altitude, temperature, aircraft weight, tire limit speeds, brake energy limits,etc. From a "limiting runway" the ability to derate is obviously reduced as each of these factors impacts on the performance calculation. The information you provide is insufficient to make a meaningful calculation but presumably it would be a full power take off !
You say the crew were expecting 54 pax but 232 turned up. Presumably this was in "extremis" with gun toting bandits at their heals. A 757-200 holds around 34 tonnes of fuel. It has an (empty weight) of around 59 tonnes, a maximum landing weight of 90 tonnes and a maximum take off weight that varies from each certificated aircraft but generally tops out at about 113 tonnes, but bear in mind this is restricted by the factors in the first paragraph.
This aircraft was flying from south east africa to France ? How long is a piece of string ? The fuel capacity of the aircraft would give it a maximum range of around 8 hours with minimum reserves and a very light payload (54pax) that is about 4000 miles. ( You might want to measure the distance ?). On this full fuel assumption, your aircraft with 54 passengers and a standard amount of luggage would weigh around 98 or 99 tonnes! Then another 178 last minute changes turn up ! Well I assume they didn't bring all their worldly chattels with them, so that would be another payload lump of around 14 tonnes. So the take off weight would now be in the order of 113 tonnes ! As you can see this is now at the maximum certified take off mass of the aircraft. However I appreciate that such niceties are of minor concern to our heroes ?
( continued in chapter 2)