Determining the CG

One of the easiest ways to understand weight and balance is to consider a board with weights placed at various locations. We can determine the CG of the board and observe the way the CG changes as the weights are moved.

The CG of a board like the one in Figure 2-4 may be determined by using these four steps:

1. Measure the arm of each weight in inches from the datum.
2. Multiply each arm by its weight in pounds to determine the moment in pound-inches of each weight.
   
3. Determine the total of all weights and of all the moments. Disregard the weight of the board.
   
4. Divide the total moment by the total weight to determine the CG in inches from the datum.

In Figure 2-4, the board has three weights, and the datum is located 50 inches to the left of the CG of weight A. Determine the CG by making a chart like the one in Figure 2-5. As noted in Figure 2-5, A weighs 100 pounds and is 50 inches from the datum: B weighs 100 pounds and is 90 inches from the datum; C weighs 200 pounds and is 150 inches from the datum. Thus the total of the three weights is 400 pounds, and the total moment is 44,000 lb-in.

Determine the CG by dividing the total moment by the total weight.

To prove this is the correct CG, move the datum to a location 110 to the right of the original datum and determine the arm of each weight from this new datum, as in Figure 2-6. Then make a new chart similar to the one in Figure 2-7. If the CG is correct, the sum of the moments will be zero.

The new arm of weight A is 110 - 50 = 60 inches, and since this weight is to the left of the datum, its arm is negative, or -60 inches. The new arm of weight B is 110 - 90 = 20 inches, and it is also to the left of the datum, so it is - 20; the new arm of weight C is 150 - 110 = 40 inches. It is to the right of the datum and is therefore positive.

The board is balanced when the sum of the moments is zero. The location of the datum used for determining the arms of the weights is not important; it can be anywhere. But all of the measurements must be made from the same datum location.

Determining the CG of an airplane is done in the same way as determining the CG of the board in the previous example. [Figure 2-8] Prepare the airplane for weighing and place it on three scales. All tare weight, that is, the weight of any chocks or devices used to hold the aircraft on the scales, is subtracted from the scale reading, and the net weight from each wheel weigh point is entered on the chart like the one in Figure 2-9. The arms of the weighing points are specified in the Type Certificate Data Sheet (TCDS) for the airplane in terms of stations, which are distances in inches from the datum. Tare weight also includes items used to level the aircraft.

The empty weight of this aircraft is 5,862 pounds. Its EWCG, determined by dividing the total moment by the total weight, is located at fuselage station 201.1. This is 201.1 inches behind the datum.