Given the following information, what is the minimum additional load in whole kilograms that must be loaded into either compartment 1 or 2, to bring the CG into limits for take-off?
Aircraft take-off mass: 1785 kg
Initial CG position: +2.08 m
Forward CG limit: +2.14 m
Aft CG limit: +2.41 m
Compartment 1: +1.23 m
Compartment 2: +4.76 m
Refer to figure.
The CG is currently in front of the FWD limit and needs to move aft. This distance is +2.08 m to +2.14m = 0.06 m
In order to move the CG into limits, we will need to load this cargo into compartment 2. Compartment 1 is further forward and would give the opposite effect - this removes one answer option already.
Step 1. Establish the parameters:
m = mass to be added (?)
M = total mass (1785 kg)
d = CG movement required (0.06)
D = relevant distance, between the target CG position and the compartment being loaded (distance between +4.76 and +2.14 = 2.62)
Step 2. Time for the formula:
m/M = d/D
m/1785 = 0.06/2.62
m = 40.9 kg
By adding 41 kg into the rear compartment (number 2) the CG is moved back into limits.
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