Center of gravity of an aircraft

The center of gravity (CG) of an aircraft is the point over which the aircraft would balance. Its position is calculated after supporting the aircraft on at least two sets of weighing scales or load cells and noting the weight shown on each set of scales or load cells. The center of gravity affects the stability of the aircraft. To ensure the aircraft is safe to fly, the center of gravity must fall within specified limits established by the aircraft manufacturer.
Ballast Ballast is removable or permanently installed weight in an aircraft used to bring the center of gravity into the allowable range.
Center-of-Gravity Limits Center of gravity (CG) limits are specified longitudinal (forward and aft) and/or lateral (left and right) limits within which the aircraft's center of gravity must be located during flight. The CG limits are indicated in the airplane flight manual. The area between the limits is called the CG range of the aircraft.
Weight and Balance When the weight of the aircraft is at or below the allowable limit(s) for its configuration (parked, ground movement, take-off, landing, etc.) and its center of gravity is within the allowable range, and both will remain so for the duration of the flight, the aircraft is said to be within weight and balance. Different maximum weights may be defined for different situations; for example, large aircraft may have maximum landing weights that are lower than maximum take-off weights (because some weight is expected to be lost as fuel is burned during the flight). The center of gravity may change over the duration of the flight as the aircraft's weight changes due to fuel burn or by passengers moving forward or aft in the cabin.
Reference Datum The reference datum is a reference plane that allows accurate, and uniform, measurements to any point on the aircraft. The location of the reference datum is established by the manufacturer and is defined in the aircraft flight manual. The horizontal reference datum is an imaginary vertical plane or point, arbitrarily fixed somewhere along the longitudinal axis of the aircraft, from which all horizontal distances are measured for weight and balance purposes. There is no fixed rule for its location, and it may be located forward of the nose of the aircraft. For helicopters, it may be located at the rotor mast, the nose of the helicopter, or even at a point in space ahead of the helicopter. While the horizontal reference datum can be anywhere the manufacturer chooses, most small training helicopters have the horizontal reference datum 100 inches forward of the main rotor shaft centerline. This is to keep all the computed values positive. The lateral reference datum is usually located at the center of the helicopter.[2]
Arm The arm is the horizontal distance from the reference datum to the center of gravity (CG) of an item. The algebraic sign is plus (+) if measured aft of the datum or to the right side of the center line when considering a lateral calculation. The algebraic sign is minus (-) if measured forward of the datum or the left side of the center line when considering a lateral calculation.[1]
Moment The moment is the moment of force, or torque, that results from an object’s weight acting through an arc that is centered on the zero point of the reference datum distance. Moment is also referred to as the tendency of an object to rotate or pivot about a point (the zero point of the datum, in this case). The further an object is from this point, the greater the force it exerts. Moment is calculated by multiplying the weight of an object by its arm.
Mean Aerodynamic Chord (MAC) A specific chord line of a tapered wing. At the mean aerodynamic chord, the center of pressure has the same aerodynamic force, position, and area as it does on the rest of the wing. The MAC represents the width of an equivalent rectangular wing in given conditions. On some aircraft, the center of gravity is expressed as a percentage of the length of the MAC. In order to make such a calculation, the position of the leading edge of the MAC must be known ahead of time. This position is defined as a distance from the reference datum and is found in the aircraft's flight manual and also on the aircraft's type certificate data sheet. If a general MAC is not given but a LeMAC (leading edge mean aerodynamic chord) and a TeMAC (trailing edge mean aerodynamic chord) are given (both of which would be referenced as an arm measured out from the datum line) then your MAC can be found by finding the difference between your LeMAC and your TeMAC.