A pilot must be able to accurately and rapidly solve any problems that involve the shift, addition, or removal of weight. For example, the pilot may load the aircraft within the allowable takeoff weight limit, then find a CG limit has been exceeded. The most satisfactory solution to this problem is to shift baggage, passengers, or both. The pilot should be able to determine the minimum load shift needed to make the aircraft safe for flight. Pilots should be able to determine if shifting a load to a new location will correct an out-of-limit condition. There are some standardized calculations that can help make these determinations.
When weight is shifted from one location to another, the total weight of the aircraft is unchanged. The total moments, however, do change in relation and proportion to the direction and distance the weight is moved.
When weight is moved forward, the total moments decrease; when weight is moved aft, total moments increase. The moment change is proportional to the amount of weight moved. Since many aircraft have forward and aft baggage compartments, weight may be shifted from one to the other to change the CG. If starting with a known aircraft weight, CG, and total moments, calculate the new CG (after the weight shift) by dividing the new total moments by the total aircraft weight.
To determine the new total moments, find out how many moments are gained or lost when the weight is shifted. Assume that 100 pounds has been shifted from station 30 to station 150. This movement increases the total moments of the aircraft by 12,000 lb-in.
Moment when at station 150 = 100 lb x 150 in = 15,000 lb-in
Moment when at station 30 = 100 lb x 30 in = 3,000 lb-in
Moment change = 12,000 lb-in
By adding the moment change to the original moment (or subtracting if the weight has been moved forward instead of aft), the new total moments are obtained. Then determine the new CG by dividing the new moments by the total weight:
Total moments = 616,000 + 12,000 = 628,000
The shift has caused the CG to shift to station 78.5
A simpler solution may be obtained by using a computer or calculator and a proportional formula. This can be done because the CG will shift a distance that is proportional to the distance the weight is shifted.
Weight Shifted = CG (change of CG)
Total Weight Distance weight is shifted 100 = CG 8,000
120 CG = 1.5 in
The change of CG is added to (or subtracted from when appropriate) the original CG to determine the new CG: 77 + 1.5 = 78.5 inches aft of datum The shifting weight proportion formula can also be used to determine how much weight must be shifted to achieve a particular shift of the CG. The following problem illustrates a solution of this type.
Aircraft Total Weight . . . . . . . . . . . . . . . . .7,800 lb
CG . . . . . . . . . . . . . . . . . . . . . . . . . . . .Station 81.5
Aft CG Limit . . . . . . . . . . . . . . . . . . . . . . . . . .80.5
Determine how much cargo must be shifted from the aft cargo compartment at station 150 to the forward cargo compartment at station 30 to move the CG to exactly the aft limit.
Weight to be Shifted = �CG
Total Weight Distance weight is shifted
Weight to be Shifted = 1.0 in
7,800 120 in
Weight to be Shifted = 65 lb