As I'm studying PPL theories, I've encountered with this kind of a question below and it would be great to understand the principle behind the calculation of the 'CG'

Calculated take-off mass = 2300 lbs, calculated CG = 95.75 in, fuel burn = 170 lbs on station 87.00 in. Where is the CG situated after the landing?


Not too much theory, just simple math. You find the spot where the sum of all torques (mass x distance) = zero. Where you would balance the plane on a see-saw. That is your CG

If you start out with 2300 lbs at 95.75 inches and remove 170 lbs at 87.00 inches, the torque of 170 x 8.75 = 1487.5 inch pounds has been removed. The new weight is 2130 lbs.

The new CG is 1487.5 inch pounds/2130 pounds = 0.70 in the OTHER direction. So new CG is at 96.45 inches.

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