Appreciate any input, ideas, experience. Keep them polite though
I am not sure if this is what you are talking about but I'll blunder on.
Assuming the take off weight at the time is based upon an individual runway analyses chart. If there are no significant obstacles such as taking off towards water, the runway analyses will probably assume a company standard third segment acceleration height. The minimum is normally 400 feet and can vary depending on many variables including the chief pilot's personal opinion.
On the other hand, if obstacles encroach the straight out or curved flight path the pilot has no choice but to rely implicitly on the performance engineer's calculations. Keep in mind at night or in IMC, obstacles may not been seen; especially with high body angles involved. Once the pilot deviates from the published runway analyses tracking or turning information, he could be be in unknown territory and becomes entirely responsible for his own obstacle clearance. At night or in IMC this could prove foolhardy indeed.
I have seen runway analyses charts that give only a minimum flap retraction (acceleration segment) height and leave the rest to the pilot to decide where to go once the flaps are up. The pilot thus assumes there are no obstacles to concern him and all he has to do is climb to above the MSA and decide where to go from there. Good airmanship would dictate he has a nearby published holding pattern in mind to allow breathing space for decision making at a known safe height.
I well recall one European operator had a special procedure involving a Greek island airport that required a curved track through 90 degrees towards the sea if an engine failed on take off. The flap retract height was published as a standard 800 ft. Once the curved procedure was completed the pilot was on his own. The only problem was the presence of an island 2000 ft high barely seven miles ahead dead on the final track after the 90 degree curved turn.
This island was not accounted for by the company performance engineers and the aircraft would have hit the hill during the third segment. The reason given for not including the island terrain, was that the the foreign State who originally supplied the obstacle charts to the company did not survey beyond 10,000 metres. In other words the pilot was very much on his own once the aircraft was beyond 10,000 metres from take off. This bordered on criminal neglect.
The ideal runway analyses chart would publish safe flight path information until the aircraft reached a safe altitude from which it could conduct an instrument approach to return to the departure airport. This may have to include tracking to various fixes all of which would have been surveyed as part of the OEI flight path. Of course once the pilot has reached the published safe altitude the next course of action is up to him.
In most cases, I understand the runway analyses chart design is based upon the worst case of engine failure at V1 and continue in IMC. If VMC is encountered, then it becomes entirely the responsibility of the captain to stay with the runway analyses published track and any restrictions - or - deviate from the published information and go it alone taking personal responsibility for terrain clearance.
All the above is a bit generalised but I hope it covers some of your questions.