Moments are a combination of force and displacement, or "moment arm." A playground see-saw is a good example. The weight of the child is the force, and the distance between the child and the see-saw pivot point is the moment arm. For the see-saw to balance, the moments on each side of the see-saw must be equal.
A 60-pound child sitting four feet from the pivot point generates a 240 foot-pound (60 x 4) moment. If an 80-pound child were to climb onto the other side of the see-saw at the same distance from the pivot point, the see-saw would be unbalanced because the larger child generates a 320 foot-pound (80x4) moment. To balance the see-saw, the 80-pound child could scoot forward until he's sitting three feet from the pivot point. Now the moments are again balanced (80x3=240 foot-pounds).
Notice how changing the length of the moment arm changes the moment. It works the same way in airplanes.
When you rotate a tricycle-landing-gear airplane for takeoff, the horizontal tail provides the downward force that raises the plane's nose. The moment arm is the distance between the main wheels and the horizontal tail, because the airplane rotates around its main wheels while they are on the runway. So the nose-up pitching moment generated by the horizontal tail is the downward lift times the distance between the tail and the main wheels.
As soon as the main wheels lift off the runway, the moment arm changes because airplanes in flight rotate around their center of gravity (CG). In a tricycle-gear airplane, the CG is located somewhere between the main wheels and the nosewheel. If the CG were anywhere else, the airplane would sit on its tail (while the airplane is on the ground) .
The instant change in the airplane's "pivot point" that occurs when the main wheels leave the runway also means an instant change will occur in the pitching moment supplied by the horizontal tail. The tail's pitching moment is now bigger because the moment arm is suddenly longer. The bigger nose-up pitching moment will rotate the airplane nose-up unless you reduce the downward lifting force of the horizontal tail by relaxing your pull on the yoke.
The same principles apply during landing, only in reverse. As soon as the main wheels touch the runway, the horizontal tail's moment arm becomes shorter, resulting in less nose-up pitching moment. If you intend to use aerodynamic braking, you'll probably have to apply a little more pull to the yoke to compensate for the shorter moment arm, or the nose is likely to drop.
Tailwheel pilots are faced with the opposite compensation. During takeoff the moment arm gets shorter when the main wheels lift off because the center of gravity is between the main wheels and the tailwheel. Here, you'll have to apply a little more back stick to keep the nose from dropping just after takeoff.
Wheel landings in a taildragger can be challenging for a variety of reasons. One of them is the instantly longer pitching moment arm that occurs when the main wheels contact the runway. If the pilot doesn't relax the pull on the stick, a bounce is likely. In fact, some instructors advocate a little "pulse" of forward stick to "stick" the landing, which is nothing more than an adjustment of the pitching moment by changing the tail lifting force to compensate for the change that suddenly occurs in the moment arm.
Before you decide to use a different takeoff trim setting you should be aware that takeoff trim settings can be a compromise. You must have sufficient nose-up trim to allow you to un-stick the nosewheel with a manageable pull force on the yoke, but not so much as to cause an aggressive nose-up pitch after takeoff. The published takeoff trim setting is the result of extensive flight testing by the airplane manufacturer, and pilots should use this setting.
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