An aircraft has its datum at the nose. The front seats are 65 inches aft of datum, the rear seats are 105 inches aft and the separate baggage compartment is 145 inches aft. The aft limit is 149 inches aft. The current mass is 2570 lb.
Three passengers are in the rear seats, with the baggage compartment full, and they all want to sit together so the front seat is empty. However, the pilot is very light and, in this situation, the Centre of Gravity (CG) of the aircraft is 3 inches behind the aft limit.
How much luggage must be moved and secured in the front seat to bring the CG to the authorised limit?
Refer to figure.
The CG is currently behind the AFT limit and needs to move forward. This distance is 152 to 149 = 3 inches
In order to move the CG into limits, we will need to move baggage from the baggage compartment (station 145) to the front seat (station 65) 145 - 65 = 80.
Step 1. Establish the parameters:
m = mass to be moved (?)
M = total mass (2570 lb)
d = CG movement required (3)
D = relevant distance, between the baggage compartment and the front seat (distance between 145 and 65 = 80)
Step 2. Time for the formula:
m/M = d/D
m/2570 = 3/80
m = 96.4 lb
By moving 96.4 lb of baggage to the front seat, the CG is moved forward into limits.
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