The original story for the current performance philosophy/requirements is the ICAO Final Report of the Standing Committee on Performance dating back to 1953. One of our posters, a long time colleague and very kindly, passed his personal copy onto me some time ago .. now a valued reference library document on the bookshelf to my side.
Various States then publish their implementation (evolving over the years) of these requirements. Hence we see FAR 23/25 etc.
The point was that the rest of the world pretty much adopted the US certification specifications (in Euroland now CS25 as an example). Still, thank you for that information about the origins of the FARs.
It has nothing to do with obstacle clearance. They demonstrate that the aircraft has a certain climb performance, nothing more, nothing less!
Not quite right.
(b) you are overlooking segment obstacle clearance .. which also is included in the AFM and must be met at planning to establish RTOW compliance.
We have to differentiate between normal ops and engine out scenario. Our take off calculations are taking into account engine out.
For a normal take off (with gear down as the example of the original poster), segment compliance is absolutely not an issue, nor a requirement. In fact there are no segments in a normal takeoff. What you have to comply with during a normal takeoff is the procedural climb gradient. See below...
A complete different authority (ICAO), set a limit for minimum obstacle clearance
Not quite right.
PANS/OPS relates to routine AEO operations, letdowns, etc. Nothing to do with takeoff calculations which are AFM based and OEI.
To be more accurate:
A complete different authority (ICAO), set a limit for minimum PROCEDURAL obstacle clearance (standard and minimum 3.3%).
I.e., they set the standards for what they considered to be a safe clearance of obstacles for design of instrument procedures.
And... EXACTLY... they have nothing to do with an engine out scenario. See above...
In short, so even with gear-down and accelerating, your modern aircraft should have a gradient well above 3.3%
Now that depends entirely on the gross weight and how the aircraft is being operated .. a very long bow to draw, methinks.
Think about it again: An aircraft that does 15-20% climb gradient all engines operating, will have no problems making a 3.3% gradient with the gear extended.