Or alternatively
The first step is to calculate the length of MAC. Therefore:
Trailing edge - leading edge = MAC
760.1 - 625.6 = 134.5 (length of MAC)
The old centre of gravity was positioned at 663 aft of datum which needs to be calculated in relation to MAC.
The CG can be found in relation to the leading edge by the following method:
663 - 625.6 = 37.4 aft of the leading edge
To calculate this as a percentage (reference CATS Mass and Balance Book chapter 4)
%MAC = (100% / MAC) x Distance from leading edge
% MAC = (100 / 134.5) x 37.4 = 27.8% (old CG position)
If we are adding a mass into an aircraft we can use the following equation to calculate the new CG position:
CG distance from datum = total moment / total mass
The total mass is the old mass + the additional mass:
41000 kg + 2500 kg = 43500 kg
To calculate a moment use the equation:
moment = mass x arm
moment of the CG = 41000 kg x 663 = 27183000
moment of the cargo = 2500 kg x 360 = 900000
therefore the total moment = 28083000
Using the equation = 28083000 / 43500 = 645.59 aft of datum
We know that the leading edge is 625.6 aft of datum so therefore the CG is 19.986 aft of the leading edge.
19.986 aft of the leading edge can be calculated using the same equation
%MAC = (100% / MAC) x Distance from leading edge
% MAC = (100 / 134.5) x 19.986
% MAC = 14.86%