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I was looking at the path of the MH-17 flight that crashed in the Ukraine on FlightRadar24 and noticed it was flying at FL310 (31,000ft), then because of the Ukrainian NOTAM which went up to FL320 (32,000ft) and below, it then ascended to FL330.

Why wouldn't it be flying at FL330 already from the start? Doesn't a higher altitude mean less air resistance (because the air is thinner) and therefore better fuel efficiency?

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This is normal.

A 777 on the AMS-KUL route cannot climb to FL330 right after takeoff - this would only be possible maybe 3-5 hours into the flight.

Airliners fly as high as the available thrust (and ATC) allows, because the thinner air allows to fly at a higher lift coefficient and less drag overall. The limit is given by the combination of available thrust and the actual mass of the aircraft, and it will climb higher during a trip as fuel is burnt off. The maximum range is possible at one particular lift coefficient, and to maintain this during a long trip means to increase altitude, so the lower density compensates the lower aircraft mass. Engine thrust is normally sized during design such that this optimum altitude can just be reached in normal operation.

On eastbound routes in controlled airspace, pilots are encouraged to fly at odd thousands of feet (depending on the local rules), so the climb will not be continuous, but stepwise. See this answer for more on separation rules.

For a rather lengthy answer with more background on the theory how to pick the ideal flight condition for maximum range, see this link.

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  • $\begingroup$ An interesting example of this is the cruise-climb that was used by the Concorde. As there were no other aircraft that could fly at the desired altitudes, it was given a block altitude and would gradually climb as it got lighter, allowing for an increased range. $\endgroup$ – Adam Mar 27 '19 at 19:05
  • $\begingroup$ Also, to add to Peter's answer. Winds change with altitude. So, if the wind happens to be a strong headwind at a higher altitude, it can be more efficient to stay lower, depending on the specifics of the airplane and the wind profile. Note that I have no looked at the specific winds that were present during MH-17. $\endgroup$ – Adam Mar 27 '19 at 19:09
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As Peter correctly notes, airliners which take off heavily laden with fuel and passengers struggle to reach their maximum altitude capability until they have burned off sufficient fuel. They achieve this by a technique known as a "step climb".

In this technique, they keep stepping up from one altitude to a higher one as their performance allows.

Prior to reaching Ukrainian airspace, MH17 would have flown through rather dense airspace over Europe where they may have had quite strict altitude stipulations, so that even if it had the performance to climb higher that may have been limited by other traffic inbound to Europe flying over the top of them.

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