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Appeciate an explanation in terms of definition of climb in terms of gradient & an explanation of the reasons behind each percentage condition for the different air craft types: twin engine, three engine, four engine, maybe propeller as well?

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Gradient as percentage is defined as the ratio between vertical displacement and horizontal displacement. For example, a 5% climb gradient means than for every 1 000 meter of horizontal travel, the aircraft climbs 50 meters. If you want to convert it to an angle you have to use the inverse tangent: $\textrm{atan}(0.05) \approx 0.05 \ \text{rad} \approx 2.86 ^\circ $

In take-off configuration with the landing gear retracted, the steady gradient of climb for one-engine-inoperative (OEI) is not less than:

  • 2.4 % for two-engined aeroplanes,

  • 2.7 % for three-engined aeroplanes and

  • 3.0 % for four-engined aeroplanes,

(source EASA CS-25, Amendment 20, CS 25.121)

The reason for the difference is that two-engined aircraft loose 50% of their thrust, while four-engined aircraft loose only 25% of their thrust in a OEI situation.

In other configurations there are similar differences.

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