Shifting the CG

One common weight and balance problem involves moving passengers from one seat to another or shifting baggage or cargo from one compartment to another to move the CG to a desired location. This also can be visualized by using a board with three weights and then working out the problem the way it is actually done on an airplane.

Solution by Chart
The CG of a board can be moved by shifting the weights as demonstrated in Figure 2-10. As the board is loaded, it balances at a point 72 inches from the CG of weight A. [Figure 2-11]

To shift weight B so the board will balance about its center, 50 inches from the CG of weight A, first determine the arm of weight B that will produce a moment that causes the total moment of all three weights around this desired balance point to be zero. The combined moment of weights A and C around this new balance point, is 5,000 in-lb, so the moment of weight B will have to be -5,000 lbin in order for the board to balance. [Figure 2-12]

Determine the arm of weight B by dividing its moment, -5,000 lb-in, by its weight of 200 pounds. Its arm is -25 inches.

To balance the board at its center, weight B will have to be placed so its CG is 25 inches to the left of the center of the board, as in Figure 2-13.