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The elevator trim tab should move trailing edge down when nose up trim is applied and up when nose down trim is applied. It does this because the elevator is not mass nor aerodynamically balanced. This means the center of mass of the elevator is aft of the hinge line, the same is true of the trim tab. These two factors together mean the trim tab has to push up on the trailing edge of the elevator in a nose up trim situation and that can only be done by pushing down on the air flow. The opposite force is necessary for trim down. Often there is a secondary motion applied to the trim tab giving it a dual purpose, it can move in the direction of the trailing edge as the elevator is deflected, this an an anti-servo tab, to increase control loading and is common on planes with stabilators (flying horizontal stabs like on a piper archer). The tab movement can also move opposite the trailing edge direction to decrease control loading, this is called a servo tab), and is common in the configuration on the mu-2. https://www.boldmethod.com/learn-to-fly/systems/4-types-of-trim-tabs/

 

hope that answers you question

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