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A turbojet aeroplane has a planned Take-off Mass of 190 000 kg. The cargo load is distributed as follows:

Cargo 1: 3 000 kg (3.50 m from reference point)
Cargo 4: 7 000 kg (20.98 m from reference point)
Distance from reference point to leading edge: 14m
Length of MAC: 4.6 m

Once the cargo loading is completed, the crew is informed that the centre of gravity at take-off is located at 38% MAC (Mean Aerodynamic Chord) which is beyond the limits. The captain decides then to redistribute part of the cargo load between cargo 1 and cargo 4 in order to obtain a new centre of gravity location at 31% MAC. Following the transfer operation, the new load distribution is:

  • A
    cargo 1: 4 000 kg; cargo 4: 6 000 kg.
  • B
    cargo 1: 6 500 kg; cargo 4: 3 500 kg.
  • C
    cargo 1: 5 000 kg; cargo 4: 4 000 kg.
  • D
    cargo 1: 4 000 kg; cargo 4: 5 000 kg.

The Centre of Gravity must be displaced by: 38% - 31% = 7% MAC, which corresponds to: 7% of 4.6 MAC = 0.322 m.

The following formula helps to find out how to redistribute part of the cargo load between Cargo 1 and Cargo 4 in order to obtain a new centre of gravity location: Mass Change / Total Mass = Change of CG / Total Distance Moved.

Solving for Mass change we get: Mass Change = (Change of CG x Total Mass) / Total Distance Moved = (0.322 x 190000 kg) / (20.98 m - 3.5 m) = 3500 kg.

CG displacement from 38% MAC TO 31% MAC means that it must be displaced forward, therefore the shifting load 3500 kg must be added to the Cargo 1 (forward cargo) and at the same time the same amount must be removed from Cargo 4 (aft cargo).

After the cargo load redistribution, the Cargo 1 will weigh: 3000 kg + 3500 kg = 6500 kg and the Cargo 4 will weigh: 7000 kg - 3500 kg = 3500 kg.

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