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With the above mentioned answer, it is pretty much correct except for the twin engine aircraft. For the twin engine aircraft, the critical engine is the one that produces a thrust line closest to the fuselage. Example: if the twin engine aircraft is equipped with 2X engines which have the propeller rotating in a clockwise direction, then the left engine will be the critical engine.

This is because the down going blade on the left engine will produce a line of thrust closest to the fuselage compared to the right engine's propeller. So it is safe to say that if the left engine fails, the aircraft will be harder to control because the thrust line produced by the live engine on the right side has a longer arm from the fuselage causing a higher moment wanting to yaw and roll the aircraft to the left which is harder to control compared to if the right engine fails, such as the Piper Twin Comanche aircraft.

However, if the twin engine aircraft is equipped with counter rotating propellers, meaning, the left engine prop rotating clockwise and the right engine propeller rotating counter clockwise, then there is no critical engine, because both down going blades of the propeller produces a thrust line both equal in distance from the center of the fuselage.

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Q: Do jet engines airplanes have a critical engine?
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