EASA 031 Mass & Balance cheat sheet

Mass is a scalar quantity of matter measured in kg; weight is a force (W = m × g) measured in newtons, with g ≈ 9.81 m/s². EASA mass and balance work uses mass in kg, but structural loads are forces.

Unit conversions to memorise: 1 kg = 2.2046 lb; 1 lb = 0.4536 kg; 1 in = 2.54 cm; 1 ft = 0.3048 m; 1 Imp gal = 4.546 L; 1 US gal = 3.785 L; 1 L of fuel ≈ 0.72 kg at density 0.72 kg/L.

Empty mass (basic empty mass) = airframe + engines + fixed equipment + unusable fuel + full oil + trapped fluids; it excludes crew, passengers, baggage, usable fuel and removable equipment.

Dry operating mass (DOM) = basic empty mass + crew + crew baggage + catering + potable water + removable service equipment; it is the aircraft ready for a specific operation, without usable fuel, payload or traffic load.

Take-off mass (TOM) = DOM + take-off fuel + traffic load (passengers + baggage + cargo); landing mass (LM) = TOM − trip fuel; zero-fuel mass (ZFM) = TOM − total fuel on board = DOM + traffic load.

Payload (traffic load) = passengers + baggage + cargo + mail; useful load = traffic load + usable fuel, i.e. the difference between MTOM and empty/basic mass.

Operating mass = DOM + take-off fuel; it is the lowest mass at which the aircraft can be dispatched and is used to check minimum-fuel and performance cases.

Centre of gravity is the point where the total weight acts; its position is expressed as a distance from the reference datum, normally in metres or inches aft of the datum, or as % of mean aerodynamic chord.

Moment = mass × arm; total moment ÷ total mass = CG position; the datum is an arbitrary fixed reference plane chosen by the manufacturer, and arms aft of it are positive.

Maximum take-off mass (MTOM) is a structural (certificated) limit; maximum landing mass (MLM) and maximum zero-fuel mass (MZFM) are also structural limits that must never be exceeded.

Maximum zero-fuel mass (MZFM) = MTOM − maximum usable fuel; it protects the wing root bending moment and the fuselage structure when fuel is in the wings, so ZFM = DOM + traffic load must be ≤ MZFM.

Regulated (certificated) masses come from the type certificate and are fixed; performance-limited masses (e.g. field-length-limited TOM, climb-limited TOM, obstacle-limited TOM, tyre-speed and brake-energy limits) vary with conditions and may be lower.

The actual take-off mass must be the lowest of: MTOM, performance-limited TOM, and the mass consistent with the runway, obstacle, climb and tyre/brake limits.

Landing mass must not exceed MLM; if the planned landing mass exceeds MLM, fuel must be offloaded or the traffic load reduced before departure.

MTOM is not always the limiting value: at high altitude/high temperature the climb-limited or obstacle-limited mass may be far below MTOM, so the load sheet must reflect the performance mass actually used.

Exceeding MZFM overstresses the wing/fuselage junction; exceeding MTOM affects take-off performance and tyre/brake energy; exceeding MLM affects landing gear and landing performance.

Operational limits (company/operator) may be more restrictive than the certificated limits; the more restrictive value always governs the loading decision.

Forward CG limit is set by elevator authority (nose-up control) and by the ability to flare and rotate; the aft limit is set by static/dynamic longitudinal stability and by tail-load/stall-recovery considerations.

Moving the CG forward increases the nose-down moment, raises stick force, increases trim drag and fuel burn, lengthens the take-off run and increases the landing distance; stall speed increases slightly because more tail downforce is needed.

Moving the CG aft reduces tail downforce and trim drag, giving slightly better cruise performance and lower fuel consumption, but reduces static stability and can cause pitch-up or deep-stall tendencies beyond the aft limit.

CG envelope: a graph of CG position against mass; the permitted region is bounded by forward and aft limits that may vary with mass, and the loaded point must lie inside it for take-off, in flight (after fuel burn) and at landing.

Fuel burn moves the CG: fuel in wing tanks burns near the CG, fuel in fuselage or tail tanks has a large arm, so check the most forward and most aft CG cases across the whole flight, not only at take-off.

Stall speed rises with mass (V_S ∝ √m at constant load factor) and with forward CG; the aft CG limit gives the lowest stall speed but the least margin to pitch instability.

CG is expressed as % MAC = ((CG − LEMAC) / MAC) × 100; LEMAC is the leading edge of the mean aerodynamic chord.

A CG outside limits is not corrected by performance calculation: the load must be redistributed (move load, ballast, or fuel) to bring the point inside the envelope.

Weighing is done with calibrated scales or load cells under the wheels (or jack points); the aircraft must be in the specified configuration: empty, cleaned, no removable equipment except that listed in the basic empty mass.

Preparation: defuel to unusable fuel, drain or fill oil to a stated level, remove loose equipment, check tyre pressures, and level the aircraft to the specified attitude (longitudinal and lateral) before reading.

Three-point weighing: record each wheel/scale reading, sum to get the mass, multiply each reading by its arm from the datum to get moments, sum the moments and divide by total mass to obtain the empty CG.

Reading errors: parallax on analogue scales, zero/tare not set, hysteresis, scale not calibrated, aircraft not level, and undetected friction or load-cell drift; repeat readings and cross-check the total against the type's expected empty mass.

Weighing results are corrected for equipment changes; any modification or repair affecting mass must be entered in the mass and balance record and the empty mass/CG amended.

Empty mass and CG are recorded in the aircraft mass and balance report (weighing report); the datum, arms used, configuration and date of weighing must be documented.

Periodic re-weighing is required by the operator's maintenance programme (typically every few years or after major modification/repaint); the empty CG is the starting point for every load sheet.

A weighing error in the empty CG propagates through every subsequent load calculation, so an unexplained discrepancy between calculated and expected mass must be investigated before flight.

Moment = mass × arm; total mass = Σ masses; total moment = Σ moments; CG = total moment ÷ total mass. Keep arms in the same unit as the moment table (m or in).

Shifting a load: ΔCG = (mass moved × distance moved) ÷ total mass; moving load aft shifts the CG aft by this amount, and the total mass is unchanged.

Adding or removing mass: new CG = (old total moment ± added mass × its arm) ÷ (old total mass ± added mass); adding mass ahead of the CG moves the CG forward.

Fuel burn: treat fuel burned as a mass removed at the tank arm; ΔCG = (fuel mass × (CG − tank arm)) ÷ remaining mass, so check CG at take-off, at landing and at the most critical point.

Loading tables and nomograms give moment for a given mass and arm or index units; read the graph at eye level, interpolate carefully, and always cross-check the arithmetic.

Index method: index = moment / constant (or (moment/C) + K); the load sheet sums indices and converts back to CG, so the constant and sign convention must be applied consistently.

Landing mass = take-off mass − trip fuel; landing CG is calculated from the take-off moment minus the trip-fuel moment, at the trip-fuel tank arm.

Always verify the final point against the CG envelope for take-off, in-flight (fuel burn) and landing, and verify mass against MTOM, MLM and MZFM.

The load sheet (or trim sheet) states DOM, traffic load, fuel, TOM, LM, ZFM and CG position; it is the formal record that the aircraft is within mass and CG limits.

The trim sheet is the working document used to compute the CG; the load sheet is the final signed document given to the flight crew, and the last-minute-change (LMC) procedure covers late changes within defined limits.

The loading supervisor is responsible for the correct loading, mass and balance calculation, and signature of the load sheet; the flight crew must check and accept it before departure.

The commander has final responsibility for the mass and balance of the flight; the load sheet must be signed by the person who prepared it and accepted by the crew.

Loading instructions specify the distribution of traffic load, hold allocation, and any ballast; deviations from the instructions require a new calculation, not an estimate.

Mass and balance records (weighing reports, modification records, load sheets) are retained for the period required by the operator and the authority; they are the audit trail for the empty mass and CG.

Last-minute changes: a defined maximum LMC (often a small percentage of MTOM) may be loaded without recalculating the full load sheet if the CG effect is shown to remain within limits.

If the load sheet does not match the actual load (count, mass or distribution), the aircraft must not depart until the discrepancy is resolved and the documentation corrected.

Floor load limit (kg/m² or lb/ft²) is the maximum load per unit area the cargo floor can carry; area load limit applies to a concentrated load over a small contact area and may require a spreader.

Load spreading: heavy items with small footprints need spreader boards or pallets so that the contact pressure stays below the floor and area load limits.

Hold loading must respect the hold's maximum mass, the floor and area load limits, and the CG effect of each hold's arm; load the holds in the sequence given in the loading instructions.

Tie-down and restraint: cargo must be secured against forward, aft, lateral and vertical loads using approved straps, nets, locks or containers rated for the load; unsecured cargo is a hazard in turbulence or a rejected take-off.

Dangerous goods: check the compatibility, segregation and loading restrictions for each DG item; DG must be loaded where required, secured, and recorded on the NOTOC, and DG mass counts in the traffic load.

Load distribution affects both mass and balance: a heavy item in a forward hold shifts the CG forward, and a full aft hold may breach the aft CG limit even when the total mass is within MTOM.

Unit load devices (containers/pallets) have their own maximum gross mass; never exceed the ULD rating or the aircraft hold structural limit.

After loading, verify that the actual distribution matches the load sheet; a misloaded hold invalidates the CG calculation.

Fuel mass = volume × density; density varies with temperature and fuel type (Jet A-1 ≈ 0.775–0.840 kg/L, avgas 100LL ≈ 0.69–0.72 kg/L), so use the density stated for the actual fuel temperature, not a fixed default.

Volume is usually given in litres, US gallons or Imperial gallons; convert consistently (1 US gal = 3.785 L, 1 Imp gal = 4.546 L) before applying density.

Unusable fuel is fuel that cannot be used in flight; it is included in the basic empty mass and must not be counted as usable fuel in the mass calculation.

Usable fuel is the fuel available for the flight; take-off fuel = taxi fuel + trip fuel + reserve fuel (+ contingency/alternate/final reserve as applicable).

Oil mass: engine oil is part of the basic empty mass at the specified full level; oil consumption during flight is small but must be accounted for if the operator's procedure requires it.

Fuel distribution affects CG: wing-tank fuel has an arm close to the CG, while fuselage or tail-tank fuel has a large arm; fuel burn therefore moves the CG, and the direction depends on tank location relative to the CG.

Fuel loading sequence and tank balancing: fill tanks in the prescribed order, respect tank maximum volumes, and check lateral balance limits when filling asymmetric tanks.

Density check: if the fuel supplier's density differs from the flight-plan density, recalculate fuel mass, because the same volume gives a different mass and a different TOM.