Fuel density changes the mass, not the litres
Before a short flight, a piston twin has a basic empty mass of 2,950 kg at 3.95 m; this figure already includes full oil and 10 L of unusable fuel. Pilot and front passenger weigh 170 kg at 2.40 m; baggage is 30 kg at 5.20 m. The usable fuel tanks are filled to 320 L, with the fuel arm at 4.80 m. The fuel supplier's hydrometer shows a density of 0.755 kg/L at the actual fuel temperature of 31°C. The flight-planning system, however, uses a standard density of 0.790 kg/L. The aircraft has a maximum take-off mass of 3,600 kg; the CG envelope is 3.70 m to 4.30 m. The crew wants to know whether the litre-based fuel figure is acceptable and whether the density difference changes the CG check. The fuel gauge reading is in litres and has not been converted to mass on the load sheet.
1. Compute the actual take-off mass and CG using 0.755 kg/L, and compare them with the flight-plan figures using 0.790 kg/L.
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Actual fuel mass = 320 × 0.755 = 241.6 kg. Planned fuel mass = 320 × 0.790 = 252.8 kg; the plan overstates fuel by 11.2 kg. Actual TOM = 2,950 + 170 + 30 + 241.6 = 3,391.6 kg. Moment = 2,950×3.95 + 170×2.40 + 30×5.20 + 241.6×4.80 = 11,652.5 + 408 + 156 + 1,159.68 = 13,376.18 kg·m. CG = 13,376.18 / 3,391.6 = 3.944 m. Using 0.790: mass = 3,402.8 kg; moment = 13,429.94 kg·m; CG = 3.947 m. Both are within MTOM 3,600 kg and the 3.70–4.30 m envelope; the density error changes mass by 11.2 kg and CG by about 3 mm.
2. Explain why a litre figure is not a mass check and how unusable fuel and oil should be treated.
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Litres measure volume, not mass. Fuel mass must be litres × density at the actual temperature, and density can differ from the standard figure. The BEM already includes the 10 L unusable fuel and full oil, so those must not be added again as usable fuel or oil. If oil is topped up after weighing, its mass must be added at the oil arm. A load sheet based only on litres can be under- or over-mass even when the CG looks acceptable.
3. The dispatcher proposes adding 200 kg payload based on the 0.790 kg/L calculation. Check the mass margin and explain the operational decision.
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Planned TOM = 3,402.8 + 200 = 3,602.8 kg, over MTOM by 2.8 kg. Actual TOM = 3,391.6 + 200 = 3,591.6 kg, below MTOM by only 8.4 kg. The flight would be legal on actual density but with a very small margin, so the load should be checked against the actual fuel mass and the CG recalculated with the payload arm. If the actual density later rises, the 8.4 kg margin could disappear; a conservative dispatch decision is to use the actual measured density, not the standard 0.790 kg/L.