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According to Wikipedia the definition of taxiing is:
the movement of the aircraft on the ground under its own power [however] push-back is not considered taxiing
In contrast, Eurocontrol seems to define it as:
any movement on the ground including push-back
Any other reliable sources to look up for the correct definition?
Definitions always depend on their context, that is why documents often included a list of definitions. It allows authors to define terms in the context of the document. A definition context is not always a document, it could for example be a field of expertise as well.
The Commercial Aviation Safety Team / International Civil Aviation Organization (CAST/ICAO) Common Taxonomy Team (CICTT) taxi is defined as:
The aircraft is moving on the aerodrome surface under its own power prior to takeoff or after landing
More detail can be found in the phase of flight definition document. This is definition can be applied in many situations.
The Eurocontrol definition you link to comes from the Air Traffic Flow & Capacity Management (ATFCM) and Airport Collaborative Decision Making (A-CDM) domains where statistics about gate-to-runway time play an important role for planning purposes.
In that context it is not really interesting to distinguish the time that was spend in pushback from the time spend actually taxiing to the runway. The taxi-out time is hence defined as the time between off-blocks and take-off.
The FAA definition is in 14 CFR 135.100 and the pilot/controller glossary (quoted here):
TAXI- The movement of an airplane under its own power on the surface of an airport (14 CFR Section 135.100 [Note]). Also, it describes the surface movement of helicopters equipped with wheels.
Interestingly, "pushback" is not in the glossary at all.
This matches the Wikipedia definition that you mentioned, although not the ICAO one from DeltaLima. I think this definition makes sense, because taxiing doesn't necessarily have to be before a takeoff or after a landing. It's possible that the aircraft is simply taxiing from one point to another on the airport surface, e.g. from the fuel pumps to the hangar. That might be more common in GA, though: when I see airliners repositioning on the ground they're usually being towed.
You also didn't mention air or hover taxiing, but I think it's fairly obvious in that case that the helicopter is under its own power. Here are the FAA definitions, for completeness, both from the P/CG:
AIR TAXI- Used to describe a helicopter/VTOL aircraft movement conducted above the surface but normally not above 100 feet AGL. The aircraft may proceed either via hover taxi or flight at speeds more than 20 knots. The pilot is solely responsible for selecting a safe airspeed/altitude for the operation being conducted.
HOVER TAXI- Used to describe a helicopter/VTOL aircraft movement conducted above the surface and in ground effect at airspeeds less than approximately 20 knots. The actual height may vary, and some helicopters may require hover taxi above 25 feet AGL to reduce ground effect turbulence or provide clearance for cargo slingloads.
any movement on the ground including push-back
This definition of taxiing is more specific to controllers. Once the aircraft has commenced its pushback it is normally infringing a controlled movement area and will be under the control of the ground or tower controller.
the movement of the aircraft on the ground under its own power and push-back is not considered taxiing
I believe this to be the more correct definition. Movement of an aircraft under its own power is important in a regulatory sense for aircraft operators. There are a number of matching definitions, relating to compliance with the Minimum Equipment List(MEL), ETOPs despatch - relating to weather minima and the definition of a sector, which is important for calculating the allowable flight duty period(FDP).
Extended range Twin Operations
Dispatch Dispatch is when the aircraft first moves under its own power for the purpose of taking-off.
Dispatch is also used in relation to an aircraft meeting the requirements of the Minimum Equipment List (MEL) for a "flight"(defined below).
'Sector' The time between an aircraft first moving under its own power until it next comes to rest after landing, on the designated parking position.
Definition of Flight - ref to MEL
"Commencement of flight" The point when an aircraft begins to move under its own power for the purpose of preparing for take off.
The time you leave the apron (GATE/RAMP position) and arrived at your takeoff strip (Piano key-marked Takeoff zone), the journey in between is well-known as taxiing. I am sure that this is correct because I have experience with runways and aircrafts. It's a common sense that taxii means no ground power/air cart, and also no support. You taxi your way to the takeoff zone. No disupte about this.
