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I've read in "Optimization of aircraft trajectories over the North Atlantic Airspace" and saw that in the separation standards, the longitudinal separation when changing the flight level is 2.2 minutes. I have not seen this type of separtion before. Can someone tell me where did they get this separation from? And how did they calculate the value "2.2"?

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There is no surveillance radar in oceanic airspace to track aircraft for ATC. This means that we need a way to separate aircraft without knowing exactly where they are at all times. One way to do this is with time-based separation. This means that the lead aircraft will provide periodic position reports and estimates of when they will reach their next waypoint. The aircraft behind them will be instructed to not cross the same points until a certain amount of time after the lead aircraft passed those points. This delay ensures separation between the aircraft. The aircraft are also instructed to fly a specific Mach number as part of their oceanic clearance, so if both aircraft are at the same Mach number the separation will remain fairly constant.

The separation standards you're referencing here are specific to the thesis. The beginning of the paper discusses how lateral separation (between separate tracks) was reduced from 60 NM to 25 NM based on the adoption of new surveillance and communication technologies. They then apply this to aircraft on the same track:

...reducing 25 NM to 20 NM is conceivable since we are considering consecutive flights in the same track.

And then based on an aircraft speed of 600 kts, it would take 2 minutes to fly 20 NM, therefore:

...we assume that the longitudinal separation of consecutive aircraft following the same track can be reduced from 10 minutes to 2 minutes...

And then when discussing flight level changes in 3.2.5, they reference that previous logic:

The separation standards, in this case, become 2.2 minutes (refer to Section 1.2.3).

The justification seems to be that the 10% increase is less than the 50% increase in separation when changing tracks because flight levels are much closer together than tracks. But it's not clear to me where exactly they got the 2.2 minutes from.

Since this paper was written, the North Atlantic separation standards were reduced to 14 NM longitudinally and 19 NM laterally.

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