The weight and balance proportion formula is a handy tool to aid in quickly determining the effect of moving an item.
To use the formula, simply apply some basic algebra. Plug in the numbers you have and solve for what you need.
Example One
A 180 pound passenger wants to move from the front seat, at station 110, to the rear seat, located at station 142. How will this effect the center of gravity location? The total weight of the airplane is 2700 pounds.
Weight to be shifted is 180 pounds. Total weight is 2700 pounds. Distance shifted is 32 inches.
Cross multiplication yields:
Weight to be shifted x Distance shifted = Total weight x CG Change
Solve for CG change:
CG Change = Weight Shifted x Distance Shifted / Total Weight
CG Change = 180 pounds x 32 inches / 2700 pounds
CG Change = 5760 pound-inches / 2700 pounds
CG Change = 2.13 inches
Since the passenger is moving aft, the CG will move 2.13 inches aft.
Example Two
The airplane is within its weight limitations. However, the center of gravity is 1.5 inches too far aft. How much weight must be moved from station 167 to station 142, in order to bring the CG 1.5 inches forward. Total weight of the loaded airplane is 3,200 pounds.
Cross multiplication yields:
Weight Shifted x Distance Shifted = Total Weight x CG Change
Solve for weight shifted:
Weight Shifted = Total Weight x CG Change / Distance Shifted
Weight Shifted = 3200 pounds x 1.5 inches / (167 inches - 142 inches)
Weight Shifted = 4800 pound-inches / 25 inches
Weight Shifted = 192 pounds