gphilips
It all has to do with the probability of something happening during the take off run and making screen height at the end - 50ft. So you are looking at building in a saftey margin into the performance figures.
Take the engine out case: What is the likelyhood of an engine failing? - Quite low actually. What is the likelyhood of the engine failing just at Vef so that you will not make screen height - extremely remote.
That is why the performance figures for the engine out case use Gross performance figures - ie your plane has a 50:50 chance of meeting the performance criteria. That means also that in the really unlikely case of the engine failing at that particular speed you still have a 50:50 chance of meeting your screen height.
Now look at the all engine case:
What is the probability of having all engines working during the take off run and beyond? - Well, if that probability was low then I don't want to be on that airplane. Its the most likely case. Therefore the regulations (JAR25, I think) require the gross performance figures to be adjusted in such a way that you are very likely to make the screen height at the end of the runway. So you adjust the gross figures by a certain factor. JAR25 says that this factor is to be 1.15. This will give you your net performance.
You need to take now the higher of the two required figures to cover your backside.
Cheers
Arnie