Fuel burn pulls the CG forward
A twin-engine turboprop is dispatched at a take-off mass of 5,000 kg with a CG at 4.50 m aft of the datum. The forward CG limit is 4.40 m and the aft limit is 5.05 m. Usable fuel at take-off is 800 kg, all in a tank whose arm is 5.40 m. The planned trip burns 600 kg; 200 kg remains as reserve. The load sheet shows 50 kg of cargo at station 2.00 m and 180 kg at station 6.00 m. The operator's SOP requires the landing CG to be checked before dispatch, not only the take-off CG. The cargo is already secured and no ballast is carried. The aircraft has no fuel-transfer system, and the crew cannot change the fuel load without affecting the reserve.
1. Compute the landing CG after the planned 600 kg fuel burn and state whether it is within the forward and aft limits.
Read the worked answer
Landing mass = 5,000 − 600 = 4,400 kg. Moment at landing = 5,000 × 4.50 − 600 × 5.40 = 22,500 − 3,240 = 19,260 kg·m. Landing CG = 19,260 / 4,400 = 4.377 m. The forward limit is 4.40 m, so the CG is 0.023 m (2.3 cm) forward of the limit. The landing case is therefore outside the envelope even though the take-off CG at 4.50 m was within it.
2. Determine the maximum fuel burn that would keep the landing CG at or aft of the forward limit, and compare it with the planned burn and reserve.
Read the worked answer
Let x be the fuel burned. At the forward limit: (5,000 × 4.50 − 5.40x) / (5,000 − x) = 4.40 22,500 − 5.40x = 22,000 − 4.40x 500 = x So the maximum burn that keeps the landing CG exactly at 4.40 m is 500 kg. The planned burn is 600 kg, 100 kg more. A 500 kg burn would leave 300 kg of the 800 kg take-off fuel, which is above the 200 kg reserve, but the planned trip requires 600 kg, so the flight cannot simply burn less without changing the fuel plan.
3. The crew can move 50 kg of cargo from station 2.00 m to station 6.00 m before departure. Compute the new landing CG and decide whether this is an acceptable action.
Read the worked answer
Moving 50 kg from station 2.00 m to 6.00 m adds 50 × (6.00 − 2.00) = +200 kg·m. At the landing mass of 4,400 kg this shifts the landing CG aft by 200 / 4,400 = 0.045 m. New landing CG = 4.377 + 0.045 = 4.422 m, which is 0.022 m aft of the forward limit and therefore acceptable. The take-off CG also shifts by 200 / 5,000 = 0.040 m, from 4.50 to 4.54 m, still below the 5.05 m aft limit. The move must be checked for restraint and compartment limits.