Load Sheet and Centre of Gravity on a Charter Flight
A four-seat light aircraft is being loaded for a charter flight. The empty mass is 760 kg and the empty centre of gravity is 0.78 m aft of the datum. The pilot and front passenger together weigh 160 kg at a moment arm of 0.40 m. Two rear passengers weigh 150 kg at 1.60 m. Baggage of 30 kg is loaded in the rear compartment at 2.10 m. Fuel is 120 litres at a density of 0.72 kg/L, in tanks whose arm is 0.90 m. The maximum takeoff mass is 1,100 kg. The centre of gravity envelope is 0.72 m to 1.02 m aft of the datum at all masses up to maximum takeoff mass.
1. Calculate the takeoff mass and the centre of gravity, and determine whether the aircraft is within limits.
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Fuel mass = 120 × 0.72 = 86.4 kg.
Moments (kg·m):
- Empty: 760 × 0.78 = 592.8
- Front: 160 × 0.40 = 64.0
- Rear: 150 × 1.60 = 240.0
- Baggage: 30 × 2.10 = 63.0
- Fuel: 86.4 × 0.90 = 77.8
Total mass = 760 + 160 + 150 + 30 + 86.4 = 1,186.4 kg. Total moment = 592.8 + 64.0 + 240.0 + 63.0 + 77.8 = 1,037.6 kg·m.
Centre of gravity = 1,037.6 / 1,186.4 = 0.874 m aft of datum.
Mass: 1,186.4 kg exceeds the 1,100 kg maximum by 86.4 kg - the aircraft is overweight. CG: 0.874 m is inside 0.72–1.02 m, so the CG is within the envelope, but that is irrelevant while the mass limit is breached.
2. The pilot must reduce mass. Evaluate two options and recommend one, with calculations.
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Option A - reduce fuel. Each litre removed saves 0.72 kg and 0.72 × 0.90 = 0.648 kg·m. To lose 86.4 kg, remove 86.4 / 0.72 = 120 L, i.e. all the fuel. That is not viable: the aircraft would have no fuel. Even removing 60 L (43.2 kg) leaves the aircraft 43.2 kg overweight.
Option B - offload baggage and a rear passenger. Removing the 30 kg of baggage saves 63.0 kg·m and 30 kg, leaving 1,156.4 kg. Removing one rear passenger (75 kg) saves 120.0 kg·m, leaving 1,081.4 kg - under 1,100 kg. New moment = 1,037.6 − 63.0 − 120.0 = 854.6 kg·m. New CG = 854.6 / 1,081.4 = 0.790 m - still inside the envelope, and the CG moves forward, which is generally the safer direction for handling.
Recommendation: offload the baggage and one rear passenger, then re-run the load sheet. This preserves full fuel and keeps the CG within limits. Removing fuel alone cannot solve the problem without emptying the tanks.
3. Explain why an aft centre of gravity near the rear limit is a handling concern even when the CG is 'legal'.
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As the CG moves aft, the moment arm between the CG and the tailplane/elevator shortens, so the same elevator deflection produces less pitching moment. The aircraft becomes less stable in pitch and requires more control input to recover from a disturbance. Stick force per unit of load factor decreases, so the pilot can overstress the airframe with less effort, and stall recovery is slower because the nose must be pushed further. An aft CG also raises the risk of an inadvertent stall or spin entry and makes the stall less recoverable. Being inside the envelope is necessary but not sufficient: a CG close to the aft limit leaves no margin for fuel burn, passenger movement or a gust upset. In this case the original 0.874 m was legal but only 0.146 m from the rear limit, and the correction to 0.790 m improved that margin. The pilot should verify the CG after the correction, not just the mass.