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Why does automatic trim exist only in the pitch axis? For example, a flight computer can hold the current pitch automatically when engine thrust is applied.

Why automatic trim not lies in roll and yaw axis?

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    $\begingroup$ I'm a little confused, "automatic trim" for the roll/yaw axis is usually referred to as the autopilot or wing leveler. What are you basing the assumption that aircraft don't have automatic control over those axis on? $\endgroup$ – Ron Beyer Mar 8 '17 at 17:00
  • $\begingroup$ @RonBeyer on some aircraft, trim is always computer assisted and does not require autopilot engagement. $\endgroup$ – kevin Mar 8 '17 at 17:08
  • $\begingroup$ In Airbus (A320+), the computer holds flight path angle (not pitch; the plane will pitch up to maintain flight path angle if you retard the power levers) and roll. And I am not aware of any other widespread civilian aircraft with auto-trim. $\endgroup$ – Jan Hudec Mar 9 '17 at 19:06
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The pitch requires trim because pitch is related to airspeed and engine power. As both of these change quite frequently (except for the cruising phase of a flight), it is convenient to adjust the aircraft's "natural pitch" during climbs or descends, or after changing flaps.

Most aircraft* will not exhibit a tendency to roll / yaw to one side in flight, hence, it is already stable in these axis and trim is not required.

Automatic yaw trim does exist on some multi-engine aircraft. When one engine quits, the flight computer will automatically adjust rudder to compensate the undesirable yaw due to asymmetrical thrust. On an aircraft without such system, the pilot must manually use the rudder pedals, and the amount of rudder has to be adjusted as engine thrust or airspeed changes.

* Small single-engine airplanes do exhibit roll and yaw moments due to the torque and p-factor of the propeller, but these aircrafts are marketed for affordable price and easy handling, so auto-trim is not implemented.

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