Basic Weight and Balance Equation - Know To This Aeronautical Airplane Engineering Knowledge

This equation can be rearranged to find the distance a weight must be shifted to give a desired change in the CG location:

This equation can also be rearranged to find the amount of weight to shift to move the CG to a desired location:
It can also be rearranged to find the amount the CG is moved when a given amount of weight is shifted:
Finally, this equation can be rearranged to find the total weight that would allow shifting a given amount of weight to move the CG a given distance:
Solution by Formula
This same problem can also be solved by using this basic equation:
Rearrange this formula to determine the distance weight B must be shifted:
The CG of the board in Figure 2-10 was 72 inches from the datum. This CG can be shifted to the center of the board as in Figure 2-13 by moving weight B. If the 200- pound weight B is moved 55 inches to the left, the CG will shift from 72 inches to 50 inches, a distance of 22 inches. The sum of the moments about the new CG will be zero. [Figure 2-14]
When the distance the weight is to be shifted is known, the amount of weight to be shifted to move the CG to any location can be determined by another arrangement of the basic equation. Use the following arrangement of the formula to determine the amount of weight that will have to be shifted from station 80 to station 25, to move the CG from station 72 to station 50.

If the 200-pound weight B is shifted from station 80 to station 25, the CG will move from station 72 to station 50.

A third arrangement of this basic equation may be used to determine the amount the CG is shifted when a given amount of weight is moved for a specified distance (as it was done in Figure 2-10). Use this formula to determine the amount the CG will be shifted when 200-pound weight B is moved from +80 to +25.
Moving weight B from +80 to +25 will move the CG 22 inches, from its original location at +72 to its new location at +50 as seen in Figure 2-13.