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Are there situations where the fly-by-wire system of a commercial passenger aircraft will use differential thrust to yaw? Or is that even possible at all (i.e. do the necessary interfaces exist)?

I imagine it could for instance be useful in the case of a crosswing landing, to maintain full yawing capabilities. Also, I guess the connection between flight controls and the engine control system exists, as it is shown for example by the envelope protection of an Airbus.

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First, you need to understand what fly-by-wire is. In layman's terms, FBW separates pilot input from direct mechanic actuation over anything. Yes, control surfaces are still moved due to hydraulic work, but such work is not exercised by the crew over the hydraulic lines which means pilots don't need to apply different "strength" levels over the sidestick or any other input mechanism.

That said, the FADEC (Fully automated digital engine control) does not apply differential thrust to control yaw in situations where crosswinds are encountered. Yaw is a rudder-controlled motion. Applying differential thrust would put too much strain on the airframe and wing structure, not to mention that in addition to inducing yaw, differential thrust also induces a roll along the longitudinal axis of the aircraft

The only reason differential thrust would be encountered on an airliner is more closely related to non-normal operations in which an engine is idled or shutdown and in those cases the yaw motion induced by the asymmetric thrust would be countered with rudder input.

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