Fuel Mass and Fuel Loading

Fuel is bought and pumped by volume, in litres or gallons, but the load sheet, the performance charts and the fuel plan all work in mass. Converting one into the other needs the fuel's density, and getting it wrong puts an error into the take-off mass, the centre of gravity (CG) and the endurance at the same time. In a light aeroplane, full tanks and full seats often cannot be carried together, so the fuel mass decides how much else can go on board.

Where the fuel sits matters as much as how much there is. Each tank has its own arm, and the order in which the tanks are filled and emptied moves the CG throughout the flight. Airliners fill and burn their tanks in a set sequence for structural reasons, and some types move fuel into a tail tank in the cruise purely to shift the CG.

Specific gravity and density

Density is mass per unit volume, in kilograms per litre (kg/l) or kg/m³. Specific gravity (SG), also called relative density, is the ratio of the mass of a volume of fuel to the mass of the same volume of pure water, so it has no units. Because a litre of water has a mass of 1 kg, an SG of 0.8 means a density of 0.8 kg/l, and the conversion is direct:

mass (kg) = volume (l) × SG and volume (l) = mass (kg) ÷ SG

2,250 litres at an SG of 0.82 is 1,845 kg. Working backwards, if 100 kg of useful load is left for avgas at an SG of 0.72, the most that can be uplifted is 100 ÷ 0.72 = about 139 litres. Multiplying where one should divide is the classic slip: 120 litres of avgas is 86 kg, not the 167 kg that dividing gives.

Typical values are about 0.72 for avgas and about 0.79 to 0.82 for Jet A-1 and other kerosene fuels. The SG falls as the fuel warms, so a given tank volume holds less mass of warm fuel than of cold.

Under the EASA rules the operator determines the fuel mass using the actual density, normally from the fuel supplier's delivery note, or, where that is not known, a standard density specified in the Operations Manual. Airliner fuel quantity systems measure mass rather than volume: capacitance probes sense the fuel, and the system corrects for its density, on the A320 using a densitometer in each inner wing tank. Flight crew manuals quote tank capacities at a stated reference density, 0.785 kg/l for the A320 and 0.8029 kg/l for the Boeing 737 NG (see fuel quantity and temperature indication).

Imperial and US gallons

Two different gallons survive in aviation. The imperial gallon is 4.546 litres; the US gallon is 3.785 litres. One imperial gallon is therefore about 1.2 US gallons: multiply imperial gallons by 1.2 to get US gallons, and divide US gallons by 1.2 to get imperial.

The imperial system has a convenient property: an imperial gallon of water weighs 10 lb, so

mass (lb) = imperial gallons × 10 × SG

50 imperial gallons of avgas at an SG of 0.72 weigh 50 × 10 × 0.72 = 360 lb, or 7.2 lb per imperial gallon, and 100 imperial gallons at an SG of 0.7 weigh 700 lb. A US gallon of water weighs about 8.35 lb, so the same method in US gallons multiplies by 8.35 × SG. For avgas at 0.72 that gives almost exactly the FAA's standard 6 lb per US gallon.

Standard fuel and oil masses

For light aircraft weight and balance the FAA uses standard weights: 6 lb per US gallon for avgas, 7.5 lb per US gallon for oil (1.875 lb per quart) and 8.35 lb per gallon for water. Jet fuel is heavier, at about 6.7 lb per gallon, and applying that figure to avgas is a common error. With a basic empty weight of 1,650 lb and a maximum take-off weight of 2,550 lb, the useful load is 900 lb; 40 US gallons of avgas weigh 40 × 6 = 240 lb, leaving 660 lb for occupants and baggage.

EASA's rules set no universal figure: the operator uses the actual density or its own Operations Manual standard, and exam questions give the SG to use. Engine oil is normally inside the empty mass already. Modern light aircraft definitions include full engine oil and other operating fluids in the basic empty mass, whereas the older "licensed empty weight" included only the oil that cannot be drained, so the records must be read with care before adding oil (see aircraft weighing).

Usable and unusable fuel

Unusable fuel is the fuel left in the tanks when the engine can no longer draw on it. The pick-up is deliberately placed above the bottom of the tank so that water and sediment, heavier than fuel, settle below it and are drained at the pre-flight fuel check; tank shape leaves further pockets. The unusable quantity is specified for each tank in the aircraft's manuals.

Unusable fuel is part of the basic empty mass and has no place in the fuel plan. Only usable fuel may be counted for trip fuel, reserves and endurance, and the endurance entered on the ICAO flight plan is the usable fuel expressed as time. Airliner quantity indications, such as the Boeing 737's, show usable fuel; light aircraft gauges measure volume, are inaccurate in manoeuvres and cannot be relied on away from empty, which is why the FAA teaches pilots to check the quantity visually or with a calibrated dipstick and to manage fuel by time and known consumption.

Fuel arm and tank positions

Each tank has a fuel arm, the distance from the datum to the CG of the fuel in it. In a light aeroplane with wing tanks the arm is close to constant, and burning fuel is simply a mass removal. An aeroplane takes off at 2,400 lb with its CG at 44.0 in and burns 30 US gallons, 180 lb, from tanks at 48.0 in. The landing moment is 105,600 − 8,640 = 96,960 lb-in on 2,220 lb, so the CG moves forward to 43.7 in. Fuel behind the CG moves the CG forward as it burns; fuel ahead of it moves the CG aft.

On a swept-wing airliner the arm of the fuel on board changes with the quantity, because the tanks fill and empty in sequence and the fuel moves along the sweep. The load and trim sheet therefore reads a fuel index from a table rather than using one arm. If the zero fuel CG and the take-off CG are both within limits, the CG stays within limits throughout the flight, provided the fuel is used in the prescribed sequence.

Lateral balance matters too. Fuel is loaded symmetrically, and imbalance between the wing tanks is limited: on the Boeing 737 NG an imbalance of more than 453 kg between the main tanks triggers an alert, and crossfeed is used to correct it unless a leak is suspected.

Fuel loading and burn sequence

The loading and burn sequences on a transport aeroplane are set by the wing structure. Lift bends the wing upwards; fuel in the wing tanks bends it downwards and relieves the bending moment at the wing root, which is also why a separate maximum zero fuel mass exists (see maximum structural and regulated masses). The rules follow from that:

• Fuel loading sequence: the wing tanks are filled first and the centre tank last. The A320's manual refuelling order is wing tanks, then centre tank, then additional centre tanks. On the Boeing 737 NG the main tanks 1 and 2 must be full if the centre tank contains more than 453 kg.
• Fuel burn sequence: the centre tank is used first, then the wing tanks. Within each wing the inboard fuel is used before the outboard, and the outboard tanks stay full as long as possible for bending relief and to help damp flutter.

The sequence is built into the systems. On the Boeing 737 the centre tank pumps deliver a higher pressure than the wing pumps, so they override them and feed both engines until the centre tank is empty. On the A320ceo the centre tank pumps feed the engines directly, and sequence valves on the wing tank pumps give them priority; on the A321ceo jet pumps transfer the centre tank fuel into the wing tanks, which feed the engines. Either way the centre tank empties first. The outer tank fuel is transferred to the inner tank only when the inner tank falls to a low level, about 750 kg on the A320.

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Trim tank CG management

An aft CG reduces the tailplane download, and with it the extra lift the wing must make and the trim drag. Some long-range types exploit this with a trim tank in the horizontal stabiliser. The A330, A340, A380 and MD-11 carry one. In the cruise, fuel is transferred aft to move the CG towards the aft limit, which saves roughly 1 to 2 per cent of fuel; before landing it is moved forward again. Concorde also trimmed by transferring fuel between forward and aft trim tanks.

Transferring fuel to trim the aeroplane is an alternative to deflecting a control surface. Moving the CG closer to the centre of pressure reduces the out-of-balance pitching moment, so less surface deflection, and less drag, is needed to trim. The same principle appears in some Mach trim systems, which can counter the nose-down tuck at high Mach number by transferring fuel to a rear trim tank and so moving the CG rearwards. The price of an aft CG is reduced longitudinal stability and lighter stick forces, which is why the CG is moved towards the aft limit, never beyond it (see centre of gravity).

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.