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Assume it is fully loaded (pasengers and cargo) and optimal conditions, almost no wind, etc etc...
How long after takeoff does the plane reaches cruise speed?
If he goes in a straight like on the axis of the airport strip (i.e. makes no turns), how far will have it traveled when it reaches cruise speed?
I did a search on FlightAware for 747-400 aircraft in flight, and sorted by the estimated time enroute. A Qantas flight from KLAX to YSSY came up. I'm assuming that for a 6500 Nm flight, at 13.5 hours, the aircraft is fairly heavy at takeoff.
The flight data shows a departure at 03:28:33, reaching an initial cruise level of FL300 at 03:52:59, after a continuous climb. It was at cruise speed at this point, which gives a time of 25 minutes after takeoff. Comparing the coordinates of these two reporting points gives a distance of about 180 Nm, which from the track is pretty straight.
If you just want to know when it reached a speed around that of cruise, this was about 10 minutes and 80 Nm earlier in the climb, when it reached a ground speed of about 480 knots.
The question is not precise. If you make a 80Nm flight hop between two airports you will never reach cruise speed. Example ZRH-GVA with MD11 each Monday morning (aircraft positioning).
Cruise speed may change during the flight due to unforeseen circumstances prior to take off.
Cruise altitude changes during the flight when ship gets lighter. You start FL310, you may finish the flight at FL370. Or if the wind forecast was wrong, you may decide to fly lower at a different speed.
Computers are calculating during the climb the best speed, thrust setting to climb using temperature, wind forecast, fuel price, cost of operation. So your TOC could be anywhere. If you have engine anti ice on that is changing too.
Since the question is not precise, the answer is not precise either: Make it average 2000 feet per minute and you will have your time to "cruise alt".
