Hi Beirut pilot
It's common that certification requirements are being mixed up with procedural requirements. I am kind of a geek when it comes to this topic, so a rather long reply follows...
Certification requirements:
The different segments, and corresponding gradients, of a take off are
certification requirements (FAR 25). Hence, the manufacturer of your aircraft has to demonstrate that your aircraft will met these requirements or your aircraft would never have been allowed to fly.
These are just ways for the authorities to ensure, that the aircraft being certified, is able to get away from the ground somewhat at all. They (FAA originally) deviced these manoeuvres and set the requirements, that needs to be demonstrated, to a level that they decided was to be considered safe.
It has nothing to do with obstacle clearance. They demonstrate that the aircraft has a certain climb performance, nothing more, nothing less!
Procedural requirements:
A complete different authority (ICAO), set a limit for minimum obstacle clearance during (all engines operating/normal/standard/day-to-day) takeoffs. This is described in ICAO Doc 8168: Procedures for Air Navigation Services (PANS OPS), currently 5th edition.
Their assessment of what is safe resulted in a minimum required gradient of 3.3%. For our modern high-performance aircrafts with gradients in the 15%+ range, this is not a problem (remember these requirements were set in the 60'ies and applies to propeller/general aviation aircrafts as well).
What further adds to the confusion, is that previous versions (up to 3rd edition), there was indeed a level segment for acceleration in PANS OPS procedure design. This was because Lockheed Constellations, DC-3s etc. didn't have all that great performance. But still it's shouldn't be confused with the certification requirements in FAR25. A level segment for acceleration is obsolete since 1993 with the 4th edition of PANS OPS.
In short, so even with gear-down and accelerating, your modern aircraft should have a gradient well above 3.3%
Engine failure:
ICAO procedures (PANS-OPS/Doc 8168) are ALWAYS assuming all engines operating:
So if your engine subsequently fails, your brake cooling becomes a secondary issue and you retract the gear. There after you "apply the note", in the quote above = follow the engine failure procedure established by your operator: You and your company are on your own! It's YOUR responsibility to clear obstacles and no agency is guaranteeing you anything.
P.s.
For go-around the same misconceptions exists. The reply above is partly copied from a recent reply I made to that topic in
http://www.pprune.org/tech-log/55733...ormance-2.html . Maybe it will interest you to read my replies there too.