Semi-layman's opinion. Hear me out. The above explainations have been far too complex. It is simply a case of common sense....

The center of Gravity of a plane is a bad name. It is really the Center of Mass (CoM). In reality, the mass of the plane is distrubuted throughout the plane, BUT, "averaging" the mass to one point means that we can deal with a single point with ALL the mass of the plane, and our calculations will be right. Center of Mass is a mathematical convenience, but it works.

So, the center of mass (CoM) is a point somewhere in the vacinity of the plane that represents all the mass of the plane in one place.

Now, "Balanced" is a state where all forces are at equilibrium. Unequal forces would cause acceleration in some direction according to Newton, so, a balanced plane is in equilibrium.

A Pivot is a place where two bodies meet. All the forces a body exerts on another are applied at the point of the pivot.

So, balancing planes means that we put the plane on a pivot, and move it around until it is balanced.

There are two forces involved with our balancing act. The force of gravity that mathematically can be modeled as being a vertically dopwnward force applied to the center of mass of the plane, and the force (pressure) which is vertically upward that the pivot is applying to the plane. These forces will be the same regardless of whether the plane is upright or inverted.

If the CoM is BELOW the pivot, for example, it is 1inch below the pivot, and 1/4 inch in front of the pivot, then there is a "torque" force applied to the pivot. The magnitude of the force will be the *component* of the gravitational force perpendicular to the line between the pivot and the CoM. This line is called the "Moment Line". The greater the torque, the greater the angular accelleration. As our plane pivots, the center of mass moves closer to being underneath the pivot, and the unbalancing force is REDUCED because the component of the gravitational force is reduced. As the CoM comes directly underneath the Pivot there is NO torque force because there is NO horizontal component to the Gravitational Force. Thus, the CoM becomes a pendulum beneath the pivot. Due to air resistance there is a "dampening" force, and the plane will settle in to a balanced position where the CoM is directly below the pivot (It *may* not be horizontal, but it *will* be balanced). The nature of the above process can be described as Negative feedback. The more the system is out of balance, the more the torque forces attempt to bring the system in to balance. Also, to re-iterate, when the CoM is Below the pivot, the gravitational force on the plane is balanced by the pressure force of the pivot on the plane.

If the CoM is ABOVE the pivot, for example, it is 1 inch above the pivot, and 1/4 inch in front of the pivot, then there is a torque force applied to the pivot, and the plane will rotate (see a pattern here?). As the plane rotates, the component of the gravitational force perpendicular to the moment line Increases. The plane is therefore in a "Positive Feedback" state, and will not balance. The Only way to balance a plane with the CoM above the pivot is to start with the CoM exactly above the pivot. That way, the plane has no rotating forces on it, and it will not leave it's state of equilibrium. Unfortuanately, you had better hope your room is breeze free..... the moment a breath of wind applies force to the plane, the CoM will shift slightly from above the pivot, and the plane will rotate off the pivot.

This is why we blance Low-winged planes inverted, because for almost all low winged planes, the CoM will be below the pivot when we do.

Regardless, whether we can get the plane to balance inverted or upright, the CoM will be somwhere on the section of the plane that is vertical and goes through the pivot point. The CoM is NOT exactly where the pivot meets the plane. It is somewhere vetically above or below the pivot.

Anyway, there's my 0.02.

In retrospect, I should have just asked why people carry their suitcases hanging from their arms instead of balancing them above their heads .... It is all pretty much common sense.

gus