Fuel and Oil: Mass, Density and Balance Effects
Fuel mass from volume and density
Fuel is bought and loaded in litres (or US gallons) but mass and balance work in kilograms. Mass = volume × density. Jet A-1 density is typically 0.775–0.840 kg/L at 15 °C, with about 0.80 kg/L a common planning figure; avgas 100LL is about 0.72 kg/L. Density falls as fuel warms (roughly 0.0008 kg/L per °C), so a given volume weighs less when warm. Convert consistently: 1 US gal = 3.785 L, 1 kg = 2.2046 lb.
Unusable fuel, oil and distribution
Unusable fuel is part of the basic empty mass and must never be counted as usable. Oil in the engine and tank is also part of the BEM and is not a traffic-load item; on small aircraft a full oil tank can be 8–10 kg and may sit far enough from the CG to matter. Fuel in the wings sits near the CG, so burning it changes the CG only slightly; fuel in a fuselage or tail tank can shift it significantly. Tank imbalance limits and transfer/sequencing procedures exist because fuel position, not just fuel mass, affects the CG.
Worked example
Uplift 3 200 L. At density 0.79 kg/L, mass = 2 528 kg; at 0.81 kg/L, mass = 2 592 kg - a 64 kg difference on the same volume. If the aircraft is already 40 kg below MTOM, the warm-day figure will breach the limit while the planning figure does not. Always use the density actually applicable to the fuel delivered, not an assumed 1 kg/L.
Traps that cost marks
Treating 1 L as 1 kg; using a planning density when the fuel supplier's density is on the delivery note; ignoring temperature; adding unusable fuel to usable fuel; forgetting oil in the BEM; and assuming that burning fuel never moves the CG.