Calculation
Center of gravity is calculated as follows:
- Determine the weights and arms of all mass within the aircraft.
- Multiply weights by arms for all mass to calculate moments.
- Add the moments of all mass together.
- Divide the total moment by the total weight of the aircraft to give an overall arm.
The arm that results from this calculation must be within the arm limits for the center of gravity that are dictated by the manufacturer. If it is not, weight in the aircraft must be removed, added (rarely), or redistributed until the center of gravity falls within the prescribed limits.
For the sake of simplicity, center of gravity calculations are usually performed along only a single line from the zero point of the reference datum, usually the line that represents the Pitch axis of the aircraft (to calculate fore-aft balance). In complex situations, more than one line may be separately calculated, e.g., one calculation for fore-aft balance and one calculation for left-right balance.
Weight is calculated simply by adding up all weight in the aircraft. This weight must be within the allowable weight limits for the aircraft.
The weight and moment of fixed portions of the aircraft (engines, wings, etc.) does not change and is provided by the manufacturer. The manufacturer also provides information facilitating the calculation of moments for fuel loads. Other removable weight must be properly accounted for in the calculation by the operator.
In larger aircraft, weight and balance is often expressed as a percentage of mean aerodynamic chord, or MAC. For example, assume that by using the calculation method above, the center of gravity (CG) was found to be 76 inches aft of the aircraft's datum and the leading edge of the MAC is 62 inches aft of the datum. Therefore, the CG lies 14 inches aft of the leading edge of the MAC. If the MAC is 80 inches in length, the percentage of MAC is found by calculating what percentage 14 is of 80. In this case, one could say that the CG is 17.5% of MAC. If the allowable limits were 15% to 35%, the aircraft would be properly loaded.
Read more about this topic: Center Of Gravity Of An Aircraft
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