Calculating Aircraft CG

CG = sum of all moments / sum of all weights

Change in CG = Moment + Change in Moment /Weight + Change in Weight

M1 + M(change) / W1 + W(change)

Any weight added causes a positive moment change

Weight shifted rearward causes a positive moment change

Weight shifted forward causes a negative moment change

For an airplane to be in balance, the CG (center of gravity) must lie somewhere near the point where the lift is produced by the wings. The Weight and Balance section of the POH will list the total weight of the empty aircraft and the corresponding arm, which is the empty weight CG. The arm is the distance in inches from the datum, an arbitrary reference point determined by the manufacturer. The datum is usually located at the tip of the spinner or the firewall. If the chosen datum is the firewall, items located forward of the firewall will have a negative arm and items located aft of the firewall will have a positive arm. An empty aircraft will be balanced, and this condition must be maintained as weight is added in the form of fuel, the pilot, passengers, and baggage. Manufacturers have determined how much weight can be added at different stations (established at various distances in inches from the datum) without compromising the overall balance and weight limits of the aircraft. As weight is added to each station, pilots will need to check and make sure that the total weight and CG still falls within an acceptable “envelope.” 

A simple way to determine the CG of an aircraft after weight is added or removed from different stations is to set up a table with three columns. Under the first column the individual weights at each station should be listed, beginning with the weight of the empty aircraft. The second column should list the corresponding arm of each item listed in column 1. The third column should list the moment of each item, which is its weight multiplied by its arm. The moment of a force is its turning effect, and it depends on two things: the size or magnitude of the force and its moment arm, which is the distance from the point at which the force is applied to the pivot or fulcrum. If the force being applied (weight) is measured in pounds and the arm is in inches, then the moment is expressed in pound-inches (lb.-in.). The same turning effect (moment) is achieved by placing half the original weight at double the distance. For example, a 2 lb. weight with an arm of 10 inches has a moment of 20 lb.-in. (2 x 10 = 20) and a 1 lb. weight with an arm of 20 inches also has a moment of 20 lb.-in. (1 x 20 = 20). This is why stations further from the datum, such as the aft baggage compartment, can be loaded with less weight than stations closer to the datum, such as the pilot and front passenger. When the total of the moments is divided by the total weight, the resulting number is the CG, expressed in inches aft of the datum. This number can then be checked against the forward and aft CG limits listed in the POH. As long as the CG falls within these boundaries the aircraft will be sufficiently balanced. Additionally, the total weight must not exceed the maximum gross weight allowed by the POH.