Light Aircraft Weight and Balance

Nothing on the ground tells a pilot that a light aeroplane has been loaded beyond its limits. Four seats, full tanks and a baggage compartment together often add up to more than the maximum take-off weight, and the same people seated differently can move the centre of gravity (CG) outside its envelope while the total weight is legal. Weight and balance is the calculation that catches both before flight.

The arithmetic is the same in Europe and the United States; only the vocabulary and units differ. EASA texts say mass and use kilograms and metres, the FAA says weight and uses pounds and inches, and both treat mass and weight as the same figure for loading purposes. The aerodynamics of the CG limits are covered in centre of gravity and the airline equivalent in load and trim sheet.

Basic empty weight and useful load

Every calculation starts from the aeroplane's own basic empty weight (BEW), the EASA basic empty mass: the airframe, engine and fixed equipment, plus unusable fuel and full engine oil and other operating fluids. Under the GAMA format used in most modern flight manuals, the standard empty weight of the model plus the optional equipment fitted to the individual aeroplane gives its basic empty weight. Older records may give a licensed empty weight, which included only the undrainable oil, so the definition must be checked before oil is added.

The figure and its CG are found by weighing and kept in the aeroplane's weight and balance record, usually section 6 of the flight manual. When equipment is installed or removed, the person doing the work computes and records the new empty weight and CG, and the pilot uses the latest entry, not the type figure or another aeroplane's.

The useful load is the maximum take-off weight minus the basic empty weight: the most that occupants, baggage and usable fuel may weigh together. Take the fuel out and the payload remains. An aeroplane with a basic empty weight of 1,650 lb and a maximum take-off weight of 2,550 lb has a useful load of 900 lb; 40 US gallons of avgas at the FAA's standard 6 lb per gallon weigh 240 lb, leaving 660 lb for people and bags. In kilograms the logic is identical: a basic empty mass of 780 kg, a maximum take-off mass of 1,100 kg, 160 kg of occupants and 20 kg of baggage leave 140 kg for fuel, about 194 litres of avgas at a specific gravity of 0.72.

The trade-off between fuel and payload is constant. With a basic empty weight of 1,750 lb, a maximum take-off weight of 2,550 lb, three occupants weighing 540 lb and 50 lb of baggage, only 210 lb, or 35 of the 53 US gallons of usable fuel the tanks hold, may be loaded.

Some flight manuals also give a maximum ramp weight, slightly above the maximum take-off weight: the difference is the fuel burned during start, taxi and run-up, often about 8 lb in a light single. The pilot still checks that the weight at brake release does not exceed the maximum take-off weight. Some light twins add a maximum zero fuel weight, because fuel in the wings relieves the bending at the wing root that a heavy cabin load would otherwise impose (see aircraft mass definitions).

Datum, arm and moment

The datum is an imaginary vertical plane, chosen by the manufacturer, from which every horizontal distance is measured. It may be the firewall, the nose or a point ahead of the aeroplane chosen so that every arm is positive. It has no aerodynamic meaning, and figures are valid only with the flight manual's own datum.

The arm is the distance from the datum to an item's centre of gravity, positive aft of the datum and negative ahead of it. The moment is weight multiplied by arm, in lb-in or kg m: a 170 lb passenger at 85 in contributes 170 × 85 = 14,450 lb-in. Then:

CG = total moment ÷ total weight

Large moments are often divided by a reduction factor, typically 1,000, to give a moment index: the 14,450 lb-in passenger becomes 14.45. An index must be multiplied back before dividing by weight. A total moment index of 274.5 at 3,050 lb is 274,500 lb-in, so the CG is at 90.0 in. Units are never mixed within one calculation.

The loading graph and moment tables

Flight manuals give the arms of each loading station: the front seats, the rear seats, the fuel tanks and each baggage area. Many also save the multiplication. Moment tables list the moment, or moment index, for given weights or quantities at a station, typically fuel by the gallon or litre. A loading graph draws one sloping line per station on axes of load weight and moment index; entering with the weight at a station and reading off its line gives that item's moment.

The weights and moments are then totalled, and the loaded aeroplane is plotted on the CG moment envelope, a chart of total weight against total moment; where the envelope is drawn against CG position instead, the CG is calculated first. Either way the plot answers two questions at once: is the weight within the maximum, and is the CG within the limits for that weight?

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The CG envelope

The CG envelope is the area of the chart within which the loading is approved. A point on the boundary is acceptable; a point outside is not, whatever the margin. Its edges have different origins. The forward limit, often sloping aft as weight increases, keeps enough elevator authority to rotate and to flare; with the CG forward of it the pilot may run out of nose-up elevator in the landing flare. The aft limit protects longitudinal stability: behind it the aeroplane becomes less stable in pitch, control forces lighten, and recovery from a stall or spin may become difficult or impossible.

Many trainers are certified in both the normal and utility categories, and the utility envelope is smaller: lower maximum weight, narrower CG range and often front seats only. Intentional spins and other utility manoeuvres are approved only inside it. Baggage compartments carry their own placarded weight limits, set by the floor and the restraints, and a compartment can be overloaded while total weight and CG are legal. Weight, CG and each compartment limit are three separate tests.

Worked example

A four-seat aeroplane is loaded with two front occupants, one rear passenger, 40 US gallons of avgas and 50 lb of baggage. Its flight manual gives a maximum take-off weight of 2,550 lb and, for this example, CG limits of 41.0 and 47.3 in aft of the datum at every weight up to that maximum.

The CG is 99,760 ÷ 2,300 = 43.4 in, inside the 41.0 to 47.3 in range, and the weight is 250 lb below the maximum. The common slips each produce one of the wrong options in exam questions: omitting the baggage gives 42.2 in, counting the fuel as 40 lb instead of 240 gives 42.9 in, and averaging the arms gives 58.4 in.

The same loading must be checked at the other fuel states. After 30 gallons (180 lb) are burned, the landing weight is 2,120 lb with a moment of 99,760 − 8,640 = 91,120 lb-in, a CG of 43.0 in. With no usable fuel left the zero fuel weight is 2,060 lb and the moment 88,240 lb-in, a CG of 42.8 in. Both lie inside the same limits.

Fuel burn and CG movement

Fuel burned is weight removed at the tank's arm. When the tanks are aft of the CG, as in the example, the CG moves forward as fuel is used; when they are ahead of it, aft. An aeroplane taking off at 2,400 lb with its CG at 44.0 in that burns 30 US gallons, 180 lb, from tanks at 48.0 in lands at 2,220 lb with a moment of 105,600 − 8,640 = 96,960 lb-in, so its CG is at 43.7 in.

Because the CG travels along a line from the take-off point towards the zero fuel point as the tanks empty, take-off and landing alone do not prove that it stays within limits. The zero fuel condition is checked too, since a diversion or a longer flight than planned could otherwise carry the CG out of the envelope in the air. Landing weight is the take-off weight minus the fuel burned, converted to weight: 20 gallons are 120 lb, not 20.

Weight shift and adding or removing weight

Two formulas handle changes to a loading without recalculating the whole table (see centre of gravity).

Moving weight, the weight shift formula: the total weight does not change, so

weight moved × distance moved = total weight × CG shift

An aeroplane at 2,400 lb with its CG at 46.5 in and an aft limit of 46.0 in needs a 0.5 in shift. With baggage compartments at 120 and 90 in, 30 in apart, 2,400 × 0.5 ÷ 30 = 40 lb must go forward. In metric units, a 20 kg bag moved 2.40 m forward in a 1,200 kg aeroplane moves the CG 20 × 2.40 ÷ 1,200 = 0.04 m forward.

Adding or removing weight changes the total, so the new CG is the new total moment over the new total weight, or, as a shift, weight added × (its arm − old CG) ÷ new total weight. A 100 lb bag added at 95.0 in to 2,200 lb at 42.0 in gives 101,900 ÷ 2,300 = 44.3 in. A 150 lb rear passenger at 73.0 in leaving an aeroplane of 2,500 lb at 47.0 in moves the CG forward to 106,550 ÷ 2,350 = 45.3 in. Weight added behind the CG moves it aft; weight removed from behind it moves it forward.

The same equation finds limits. At 2,400 lb with the CG at 44.5 in and an aft limit of 46.0 in, baggage at 106 in must satisfy weight × (106 − 46.0) = 2,400 × (46.0 − 44.5), so only 60 lb may be loaded, although 150 lb would still be within the maximum take-off weight. Ballast corrects a CG that is too far forward: at 2,100 lb with the CG at 38.5 in and a forward limit of 40.0 in, ballast at 115 in must satisfy ballast × (115 − 40.0) = 2,100 × 1.5, so 42 lb, secured.

When the CG is outside the envelope but the weight is not, the cure is normally redistribution rather than offloading: removing fuel can even move the CG the wrong way if the tanks lie forward of it. An overweight aeroplane needs load removed, and every change is followed by a fresh check of weight, CG and compartment limits. Flying overweight lengthens the take-off run, reduces the rate and gradient of climb, raises the stalling speed and lengthens the landing, while eroding the structural margin.

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.