Mutt hi there,
its also worth to mention that the emergency turn was initially designed to be commenced during the second segment as to avoid close in obstacles. The distanced one can be avoided by an early commence of turn during acceleration and clean up.
6.0 Turn Analysis
In many cases a turn will eliminate the need to consider limiting obstacles, increasing maximum takeoff weight (increasing payload and/or range). However, a turn may introduce new obstacles in the flight path
and may limit V2 to maintain a turn radius. EOSIDs usually involve a turn during the second segment takeoff climb phase. Sometimes the turn may be
continued into the third segment. A note of caution should be made when considering turns in the third segment. Third segment distance will be extended due to the reduction of the acceleration capability (gradient capability) of the aircraft from the gradient loss in the turn. This may need to be compensated with a weight reduction or by an equivalent alternative means as the regulatory gradient capability must be restored.
Turns in the third segment can be penalizing for obstacle clearance and should only be used for clearance turns to avoid obstacles rather than flying over obstacles.
If it becomes necessary to execute more than one turn like in HKG I can imagine we will have to implement GNSS EOSID to be flown.
Cheers.