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Service ceiling
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In aeronautics, a ceiling is the maximum density altitude an aircraft can reach under a set of conditions.
Service ceiling The service ceiling attempts to capture the maximum usable altitude of an aircraft. Specifically, it is the density altitude at which flying in a clean configuration, at the best rate of climb airspeed for that altitude and with all engines operating and producing maximum continuous power, will produce a 100 feet per minute climb.

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Encyclopedia
In aeronautics, a ceiling is the maximum density altitude an aircraft can reach under a set of conditions.
Service ceiling The service ceiling attempts to capture the maximum usable altitude of an aircraft. Specifically, it is the density altitude at which flying in a clean configuration, at the best rate of climb airspeed for that altitude and with all engines operating and producing maximum continuous power, will produce a 100 feet per minute climb. Margin to stall at service ceiling is 1.5g.
The one engine inoperative (OEI) service ceiling of a twin-engine, fixed-wing aircraft is the density altitude at which flying in a clean configuration, at the best rate of climb airspeed for that altitude with one engine producing maximum continuous power and the other engine shut down and feathered, will produce a 50 feet per minute climb.
However some performance charts will define the service ceiling as the pressure altitude at which the aircraft will have the capability of climbing at 50 ft/min with one propeller feathered.
Absolute ceiling A less often used term is the absolute ceiling – the highest altitude (calculated on the ground and which will never be reached in flight) an airplane can sustain level flight, which means the altitude at which the thrust of the engines at full power is equal to the total drag at minimum drag speed, with other words: the altitude where maximum thrust available equals minimum thrust required, so the altitude where the maximum sustained (with no decreasing airspeed) rate of climb and angle of climb reach 0. Most commercial jetliners have a service (or certificated) ceiling of about 42,000 feet (12,802 m) and some business jets about 50,000 feet while their absolute ceiling is much higher even if it isn't used for operational puroposes because it is impossible to reach (because of the vertical speed asymptotically approaching to zero)without afterburners or other devices temporary increasing thrust and it isn't economically advantageous due to the low indicated airspeed which can be sustained. Finally, must be noticed that the absolute ceiling varies with the air temperature and, overall, the aircraft weight (usually is calculated at MTOW).
Combat ceiling
It is the highest altitude at which an aircraft is expected to have a 500 feet per minute climb
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