I know that some of the planes have a strong desire to raise the nose. And some have a strong desire to pull one way or the other. Spits are bad in this. Also, the trim needs to be adjusted according to your speed and altitude and consumption of fuel.
I think the best way to test is to fly straight and level as you say, but also keep the speed the same.
To best see your trim or its affects go into cockpit view and then cycle to the view where the cockpit is invisible but you have guages on the right and left lower corners. You need to have the 'fixed' rectal and the floating one in view. You have good trim when the floating circle stays close to center in the fixed. If not, your flying is a slip fashion (your nose is not pointing in the direction the plane is going thru the air).
Everytime I start a plane (like after crashing) I have to set the trim. Particularly the elevator trim. It seems the game puts it off and then once you move the trim it 'wakes up' so you have to move it again to get the right trim. You may even end up in the exact spot you had it in before you moved it. It is an odd thing. Plus, it does not take long after take off you have to trim again.
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Race you to the Mucky Duck!