Specifically, the absolute ceiling is the highest altitude that an aircraft can maintain level flight without being affected by the pressure difference between the outside pressure and the in-cabin pressure.
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You'll start losing velocity, and as you do so, also start losing altitude. Nothing fails outright. You just don't have enough energy to climb or even stay level. The engine will work (but flameout is possible).
In aviation weather observation, a description or explanation of the manner in which the height of the ceiling is determined. The different types of ceilings according to this classification are aircraft ceiling, balloon ceiling, estimated ceiling, indefinite ceiling, measured ceiling, and precipitation ceiling.
The biggest reason for flying at higher altitudes lies in fuel efficiency. The thin air creates less drag on the aircraft, which means the plane can use less fuel in order to maintain speed. Less wind resistance, more power, less effort, so to speak.
And that at cabin altitudes above 14,000 feet pilots must use oxygen at all times. And that above 15,000 feet each occupant of the aircraft must be provided supplemental oxygen. All of this is spelled out in Federal Aviation Regulations Part 91.211.