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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?

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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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