⚖️ Mass & Balance
How heavy the aeroplane is, and where that mass sits, decide whether it can fly safely at all. This guide follows the order of the practice topics: the operator's rules and standard masses first, then why the limits exist, the mass names, weighing, fuel, light aircraft load sheets, % MAC, moving the CG, cargo floors and the airline load and trim sheet. Each chapter opens with the one idea to hold on to, then the numbers, the formulas and worked examples you can open.
🧰 Quick tools & cheat sheet play with the numbers
Eight small calculators for the sums this subject asks for again and again, and a one-screen list of the numbers worth knowing by heart. Arms forward of the datum are negative.
⚖️ Loaded mass and CG
📐 CG and % MAC
↔️ Moving mass already on board
➕ Adding or removing mass
⛽ Fuel volume to mass
📦 Traffic load and underload
🧱 Floor loading
🧍 Standard passenger masses
📋 Cheat sheet — numbers worth knowing
| Idea | Number / rule |
|---|---|
| 🧑✈️ Standard crew | flight crew 85 kg · cabin crew 75 kg |
| 🧍 Passengers, 20+ seats | 88 male · 70 female · 84 all-adult (30+ seats) · child 35 |
| 🏖️ Holiday charter | 83 · 69 · 76 kg |
| 🛩️ Small aeroplanes (male/female) | 1–5 seats 104/86 · 6–9 96/78 · 10–19 92/74 |
| 🗣️ Verbal statements | fewer than 10 seats only |
| 🧳 Checked bag per piece (20+ seats) | domestic 11 · European 13 · intercontinental 15 · other 13 |
| 🏗️ Reweighing | 4 years (individual) · 9 years (fleet) |
| 📏 Re-establish DOM/CG | ±0.5% of max landing mass · 0.5% MAC |
| 🧮 Fleet weighings | 2–3: n · 4–9: (n+3)/2 · 10+: (n+51)/10 |
| 🔩 Ultimate load | DUL = 1.5 × DLL |
| ⛽ Final reserve | jet 30 min · piston 45 min |
| 🛢️ Gallons and litres | US 3.785 L · imperial 4.546 L · 1 kg = 2.205 lb |
| 📐 % MAC | (CG − LEMAC) ÷ MAC × 100 |
| ↔️ Moving mass | m × d = M × Δcg |
| ➕ Adding mass | m = M(Y − X) ÷ (Z − Y) |
| 📦 Traffic load | lowest of MZFM − DOM · RTOM − DOM − TOF · RLM − DOM − landing fuel |
1 Mass and Balance Rules Chapter 1
An airline may not simply guess how heavy its passengers are. The rules say which masses it may use for crew, passengers and bags, when it must weigh the aeroplane again, and what the paperwork must show before every flight.
Actual or standard — never less than real. The operator may use weighed masses or the standard tables, and a survey may set its own values, but where the survey gives higher figures than the tables, the higher ones must be used.
Crew and passengers
- 🧑✈️ Crew: 85 kg flight crew and 75 kg cabin crew, both including hand baggage. Extra crew baggage changes the DOM and the CG, so its position must be used.
- 🗣️ Verbal statements (the passenger says how heavy they are, plus a fixed constant for hand baggage and clothing) only on aeroplanes with fewer than 10 passenger seats.
- ⚖️ Weighed passengers are weighed with belongings and hand baggage, immediately before boarding and close to the aeroplane.
- 👶 An infant on an adult's lap is inside the adult's standard mass; an infant in its own seat counts as a child (35 kg).
| Seats | Male | Female | All adult | Child |
|---|---|---|---|---|
| 1–5 | 104 | 86 | — | 35 |
| 6–9 | 96 | 78 | — | 35 |
| 10–19 | 92 | 74 | — | 35 |
| 20+ (all flights except holiday charter) | 88 | 70 | 84 (30+ seats) | 35 |
| 20+ holiday charter | 83 | 69 | 76 (30+ seats) | 35 |
- 🎒 On aeroplanes up to 19 seats, 6 kg may be taken off the male and female values when no hand baggage is carried in the cabin (an overcoat, umbrella, small handbag or camera does not count as hand baggage). Children are not reduced.
- 🏖️ Holiday charter values only if non-revenue passengers use no more than 5% of the installed seats.
- 📈 Many passengers clearly heavier than standard (or many heavy bags) → weigh them or add an adequate increment, and tell the commander.
Worked example — passengers on a 15-seat aeroplane
7 men, 3 women and 2 children, with hand baggage in the cabin. The 10–19 seat row applies.
7 × 92 + 3 × 74 + 2 × 35 = 644 + 222 + 70 = 936 kg. The 6 kg deduction is not allowed, because hand baggage is carried.
Checked baggage
Standard bag masses apply only from 20 seats upward; below that every bag is weighed.
Domestic · 11 kg
Origin and destination inside one State.
European region · 13 kg
The region stretches from 72°N to 27°N and 30°W to 45°E — it includes North Africa and the Canary Islands.
Intercontinental · 15 kg
Origin and destination on different continents (outside the European region).
All other flights · 13 kg
Anything not covered above.
Documentation before every flight
- 📝 Shows the load and its distribution so the commander can confirm the limits are met. It names the aeroplane, flight, commander and preparer, the DOM and its CG, take-off and trip fuel, the load, TOM, LM and ZFM, the CG positions and the limits.
- ✍️ The loading supervisor signs that the load matches; the commander shows acceptance by countersignature or equivalent (for example electronically).
- ⏱️ Last minute changes are told to the commander and entered; new documentation only if the change exceeds the limit in the operations manual.
- 🖥️ Computerised systems are checked at intervals of no more than 6 months; an onboard system as the primary despatch source needs approval; a datalinked copy of the accepted sheet stays on the ground.
Weighing and fleet masses
| Rule | Value |
|---|---|
| Reweigh an individual aeroplane | at least every 4 years |
| Reweigh when fleet masses are used | 9 years |
| Aeroplane changes operator | weigh only if more than 4 years since the last weighing |
| Re-establish DOM/CG (cumulative changes) | DOM ±0.5% of max landing mass, or CG 0.5% MAC |
| Scale calibration | within 2 years (or the maker's period, if less) |
| Fleet tolerance — leave the fleet | DOM ±0.5% of MSLM, or CG ±0.5% MAC |
| Interval between fleet mass evaluations | ≤ 48 months |
If only the CG is outside the fleet tolerance, the aeroplane keeps the fleet DOM with its own CG. A known, accountable difference (galley, seats) can be corrected for instead.
Revised standard masses (surveys)
- 🧾 Needs the authority's approval in advance, a weighing survey plan and a statistical method; the values apply only to that operator and similar circumstances, and are reviewed at least every 5 years.
- 👥 Sample: at least the statistical number and, with 40+ seats, 2 000 passengers (below 40 seats: 50 × seats). Baggage: at least 2 000 pieces.
- 🎯 Accuracy (relative confidence range): 1% for all-adult and baggage, 2% for male/female averages.
- ⚖️ Scale: capacity ≥ 150 kg, graduations ≤ 500 g, accurate to 0.5% or 200 g, whichever is greater. Infants weighed with their adult.
- ➕ Small aeroplane increments: +16 kg (1–5 seats), +8 kg (6–9), +4 kg (10–19). All-adult assumes 80/20 male/female (holiday charter 50/50). Round passengers to 1 kg, bags to 0.5 kg.
Loading and stowage
Loading is supervised by qualified staff and must respect floor strength, running load, compartment and seating limits. Without exact seat allocation, operational margins cover the possible distribution of passengers, cargo and fuel; free seating needs procedures to correct passengers bunched at one end. Cabin items go only where they can be restrained (placarded limits, restraint bars under seats, never in toilets), and are checked before take-off, before landing and when the seat belt signs come on.
2 Limitations and Effects of Mass and CG Chapter 2
Why the limits exist: mass limits protect the structure and performance, CG limits protect stability and control. Getting either wrong changes how the aeroplane flies.
Mass → strength and performance. CG → stability and control. The stricter of the flight manual and the operations manual always applies, and the commander must satisfy himself or herself that both are met.
Structural loads
Fatigue is a permanent, cumulative, irreversible loss of strength. Weight is its main cause, so overloading makes parts fail earlier than predicted. The manufacturer sets the maximum taxi, zero fuel, take-off and landing structural masses.
What extra mass does
| Goes up ⬆️ | Goes down ⬇️ |
|---|---|
| Take-off speeds, take-off and stopping distances | Climb gradient, rate of climb, ceiling |
| Stall speed and low-speed buffet speed | Maximum speed and the usable speed range |
| Drag, fuel flow, brake energy, tyre and brake wear | Range and endurance |
| Gear loads, wing root stress, fatigue | Manoeuvrability (less responsive) |
| Rate of descent on the same gradient | Buffet margin |
The centre of gravity
The CG is the point through which the whole weight acts — the balance point and the point the aeroplane rotates about. It moves with fuel burn, flap position and people moving, so it must stay inside the limits on the ground and in the air.
CG forward of the limit
- More tail down load → more drag, more fuel, less range
- Wing carries more → higher stall speed and take-off/landing speeds
- Higher VR, heavy stick forces, harder rotation and flare
- Very stable, less manoeuvrable
CG aft of the limit
- Unstable in pitch, light stick forces → easy to over-stress
- Flat spin more likely, recovery harder
- Pitch-up tendency, steady glide hard to hold
- Constant corrections add drag beyond the limit
3 Mass Definitions and Traffic Load Chapter 3
Every load sheet is built from the same ladder of mass names. Learn what is added at each rung and every traffic load question becomes simple subtraction.
Moment = mass × arm. CG = total moment ÷ total mass. Arms are measured from the datum: forward is negative, aft is positive.
Datum, arms and moments
- 📍 The datum is chosen by the manufacturer on the longitudinal axis (or its extension).
- 📏 The arm is from the datum to the centroid of the mass. 60 kg at −40 in → moment −2 400 kg in.
- 🔢 An index is a moment divided by a constant to keep numbers small: 28 600 000 ÷ 1 000 000 = 28.6.
- ↔️ Lateral CG is assumed zero; only the fore-and-aft position is calculated. CG limits may be in arm or in % MAC.
The mass ladder
| Name | What it contains |
|---|---|
| BEM basic empty mass | Airframe plus standard items: unusable fuel and fluids, engine oil, fire extinguishers, pyrotechnics, emergency oxygen, supplementary electronics |
| DOM dry operating mass | BEM + crew and crew baggage, catering, removable service equipment, potable water, lavatory chemicals. No usable fuel, no traffic load |
| Traffic load (old name payload) | Passengers, baggage, cargo, carry-on specialist equipment — and ballast |
| ZFM | DOM + traffic load |
| Operating mass | DOM + take-off fuel (everything except traffic load) |
| Useful load | Traffic load + take-off fuel = TOM − DOM |
| TOM (brake release mass) | At the start of the take-off run = ramp mass − start and taxi fuel |
| LM | TOM − trip fuel (reserves are still on board) |
| Ramp / taxi / block mass | TOM + start and taxi fuel; may exceed the MSTOM on the ground only |
The regulated take-off mass is the lower of the structural limit and the performance limit of the day (field, climb, obstacle, tyre speed, brake energy).
Traffic load expressions
Worked example — one aeroplane, five numbers
DOM 40 000 kg, traffic load 12 000 kg, take-off fuel 9 000 kg, trip fuel 6 500 kg.
- ZFM = 40 000 + 12 000 = 52 000 kg
- Operating mass = 40 000 + 9 000 = 49 000 kg
- TOM = 52 000 + 9 000 = 61 000 kg; useful load = 12 000 + 9 000 = 21 000 kg
- LM = 61 000 − 6 500 = 54 500 kg (subtract the trip fuel, not all the fuel)
4 Weighing and the Basic Empty Mass Chapter 4
The basic empty mass and its CG come from putting the aeroplane on scales. Everything else on the load sheet is built on these two numbers.
Add the scale readings for the mass; add reading × arm for the moment; divide. A negative CG is forward of the datum.
The weighing
- 🏠 In an enclosed, draught-free hangar, on calibrated and zeroed equipment, by the manufacturer or an approved maintenance organisation.
- 🧹 The aeroplane is clean, complete, fluids accounted for, and prepared to the same condition as the last schedule; non-basic items (passenger seats, trolleys) are removed.
- 📋 The person in charge compiles and signs the weighing schedule, ending with the BEM and CG. It stays in the technical log until the next weighing.
Platform scales
Electronic platforms under each wheel — light aircraft.
Hydrostatic units
Pascal's law; between the jacks and the jacking points.
Strain gauges
Resistance changes with load — larger aircraft.
Freight is normally weighed (standard freight masses only by special permission). The MEL lists the minimum serviceable equipment and the basic and optional role equipment, which helps define what sits in the BEM and the DOM.
Worked example — CG from three scales
| Wheel | kg | arm (in) | moment |
|---|---|---|---|
| Nose | 400 | −30 | −12 000 |
| Left main | 1 800 | +40 | +72 000 |
| Right main | 1 800 | +40 | +72 000 |
| Total | 4 000 | +33.0 | +132 000 |
CG = 132 000 ÷ 4 000 = +33.0 in (aft of the datum). Treating the nose arm as positive would give 39 in.
5 Fuel Mass and Fuel Terms Chapter 5
Fuel is ordered by volume but loaded by mass. You need the planning terms (what each slice of fuel is for) and the conversions (litres, gallons, pounds, kilograms).
Mass = volume × density. With SG as kg per litre: kg = litres × SG. With imperial gallons: lb = gallons × 10 × SG.
| Fuel | Covers |
|---|---|
| Start and taxi | APU and engine start, taxi — not part of the take-off fuel |
| Trip | Take-off, climb, cruise, descent, arrival, approach and landing at destination |
| Contingency | Unforeseen events; usually a % of trip fuel (5% of 4 600 = 230 kg) |
| Alternate | Missed approach, climb, transit, approach and landing at the alternate |
| Final reserve | Jet 30 min · piston 45 min |
| Additional | Only if the above cannot cover an engine or pressurisation failure at the critical point |
| Extra (discretionary) | Commander's choice: tankering, expected delays |
Conversions
| From | Value |
|---|---|
| 1 US gallon | 3.785 L · water ≈ 8.33 lb |
| 1 imperial gallon | 4.546 L ≈ 1.2 US gal · water ≈ 10 lb |
| 1 kg | 2.205 lb (1 lb = 0.454 kg) |
| 1 quart | 0.25 gallon |
| Fuel at SG 0.72 | ≈ 6 lb per US gallon · 7.2 lb per imperial gallon |
SG has no units: it compares fuel with the same volume of water. It is on the refueller's delivery note; if it is unknown, use the standard density in the operations manual. Tanks keep a small space for venting and expansion.
Worked example — uplift in US gallons
39 000 kg of fuel is needed at SG 0.80.
39 000 ÷ 0.80 = 48 750 L; ÷ 3.785 = 12 880 US gallons. Dividing by 4.546 would give imperial gallons (about 10 720).
6 Loaded Mass and CG for Light Aircraft Chapter 6
A light aircraft load sheet is a table of mass, arm and moment. Fill it from the BEM down, check the masses against their limits, and plot the CG points on the envelope.
If the ZFM and TOM CG points are inside the envelope, the CG stays inside throughout the flight (with fuel used in the right order) — even after a diversion.
- BEM + pilot, passengers, baggage and cargo → zero fuel mass.
- + fuel (converted to mass) → ramp mass.
- − start, taxi and run-up fuel → take-off mass (its moment is subtracted too).
- − trip fuel and oil → landing mass; landing CG = landing moment ÷ landing mass.
- Check each mass against its maximum and each CG against the envelope.
Worked example — a four-seat load sheet
| Item | lb | arm (in) | moment (lb in) |
|---|---|---|---|
| BEM | 1 650 | 85 | 140 250 |
| Front seats | 340 | 80 | 27 200 |
| Rear seats | 300 | 115 | 34 500 |
| Baggage | 80 | 140 | 11 200 |
| ZFM | 2 370 | 89.9 | 213 150 |
40 US gallons at about 6 lb each = 240 lb → ramp mass 2 610 lb. After taxi the TOM is 2 600 lb with a moment of 235 000 lb in: CG = 90.4 in. Averaging the arms (105 in) would ignore the different masses.
- ➖ Removing mass from behind the CG moves the CG forward; from ahead of it moves it aft; exactly at the CG — no change.
- ➗ Moments given as moment/100 must be multiplied by 100 again before dividing by the mass (forgetting gives 0.90 in instead of 90.4 in).
- ➕➖ A negative arm × positive mass = negative moment. Removing a mass with a negative arm makes the total moment more positive: (−3.75 lb) × (−45 in) = +168.75 lb in.
- 🛢️ Oil in quarts: 2 qt = 0.5 US gal; × 8.33 × 0.9 ≈ 3.75 lb.
7 CG as a Percentage of MAC Chapter 7
Airliners give the CG as a percentage of the mean aerodynamic chord, because what matters for stability is where the CG sits relative to the wing's aerodynamic forces.
% MAC = (CG arm − LEMAC arm) ÷ MAC length × 100. 0% is the leading edge, 100% the trailing edge; a bigger % is a more aft CG.
Worked example — both directions
LEMAC 50 in, MAC 160 in, CG 82 in: (82 − 50) ÷ 160 × 100 = 20% MAC.
LEMAC 110 in, MAC 90 in, CG 18% MAC: 0.18 × 90 = 16.2 in → arm 126.2 in.
Negative LEMAC −12 in, MAC 50 in, aft limit +8 in: (8 − (−12)) ÷ 50 × 100 = 40% MAC. Ignoring the sign would give 8%.
8 Repositioning the CG Chapter 8
If the CG is out of limits for any part of the flight, the aeroplane does not take off. You either move mass already on board, or add or remove mass (ballast).
Moving mass: total mass stays the same, only the moment changes. Adding mass: both change, so the new moment is divided by the new mass.
Move mass on board
d is how far the item moves (aft hold to forward hold), not its arm.
Add or remove mass
X present CG, Y target CG, Z arm of the item — all from the datum.
Mass carried only to fix the CG is ballast, and it is part of the traffic load. The minimum correction brings the CG just onto the nearest limit; afterwards check take-off and landing CG and that no mass limit is now exceeded.
Worked example — bring the CG to mid-range
M = 18 000 kg, CG 121.5 in, limits 117–121 in (mid 119), so the CG is aft of the aft limit. Freight can move from +160 to −90.
Δcg = 121.5 − 119 = 2.5 in; d = 160 − (−90) = 250 in. m = 18 000 × 2.5 ÷ 250 = 180 kg.
Worked example — adding ballast
2 000 lb at 82 in; target 85 in; ballast at 135 in.
(2 000 + m) × 85 = 2 000 × 82 + 135m → 6 000 = 50m → m = 120 lb. The divisor is Z − Y = 50, not Z − X.
Graphs: mass is always the vertical scale; the horizontal shows CG position, moment or % MAC. Swept-wing jets use % MAC; some light singles plot moment/100 as slanted lines.
9 Cargo Handling and Floor Loading Chapter 9
Cargo holds have limits per compartment, per unit length and per unit area. A heavy box can be legal one way round and illegal the other.
Running load protects the frames; area load protects the floor panels. Both must be met, plus the compartment maximum.
Containers
Standard sizes that lock in, each with its own mass and floor-loading limit. Moved by floor power drive units from a door panel joystick.
Pallets
Held with nets or straps; often in the front of the forward hold.
Bulk
Loose items at the rear of the aft hold, behind a restraining net.
Lower holds have fire-resistant linings, are usually pressurised and heated, and normally have fire detection. Overloading a floor creases panels and speeds up fatigue that can end in collapse with little warning.
Worked example — a box on its three faces
720 kg box, 2 ft × 3 ft × 10 ft. Running limit 25 kg/in, area limit 100 kg/ft².
- Running: 2 ft (24 in) → 30 kg/in ✗ · 3 ft (36 in) → 20 kg/in ✓ · 10 ft (120 in) → 6 kg/in ✓
- Area: 2 × 3 = 6 ft² → 120 kg/ft² ✗ · 2 × 10 = 20 ft² → 36 ✓ · 3 × 10 = 30 ft² → 24 ✓
Lay it on a large face with the 10 ft side fore and aft.
- 🪵 Concentrated or sharp loads need approved load spreaders (for example 2 in thick timber). 400 kg on 0.5 m² = 800 kg/m²; with a 500 kg/m² limit a spreader of at least 0.8 m² (plus its own mass) is needed.
- 🔁 kg/ft ÷ 12 = kg/in · 1 m² = 10.76 ft² · uniformly distributed loads still obey running and compartment limits.
10 Large Aircraft Loading and Load Sheets Chapter 10
On an airliner the questions are: how much traffic load can we take today, what spare capacity is left for last minute changes, and is the CG inside the envelope at zero fuel and at take-off?
The allowed traffic load is the lowest of the structural, take-off and landing limits. Underload = allowed − actual, and it sets the limit for last minute changes.
Stations, flaps and trim
- 📏 Positions are given as station numbers, water lines and buttock lines. After a fuselage plug is inserted, stations behind it keep their numbers but their arms grow (a 100 in plug adds 100 in), so a conversion chart is used.
- 🪶 Flaps travelling aft move the CG slightly aft: a −15 000 kg in moment change at 60 000 kg moves the CG 0.25 in forward on retraction.
- 🎚️ The take-off stabiliser trim comes from CG (% MAC), mass and flap: a more forward CG needs more nose-up trim units.
Planning the traffic load
Worked example — which limit bites?
DOM 35 000 · MZFM 52 000 · RTOM 64 000 · RLM 55 000 · TOF 13 000 · trip 8 500 (so 4 500 kg remains at landing).
- Structural: 52 000 − 35 000 = 17 000 kg
- Take-off: 64 000 − 35 000 − 13 000 = 16 000 kg
- Landing: 55 000 − 35 000 − 4 500 = 15 500 kg ← lowest
With 14 800 kg booked, the underload is 700 kg. The same answer comes from the allowable TOM: lowest of MZFM + TOF (65 000), RTOM (64 000) and RLM + trip (63 500) → 63 500 − operating mass 48 000 = 15 500 kg.
The load and trim sheet
- Part A (left): masses — section 1 sets the limiting TOM, maximum traffic load and underload before LMC; section 2 distributes the load (TR transit, B baggage, C cargo, M mail, Pax F/C/Y); section 3 summarises and cross-checks.
- Part B (right): start at the dry operating index, move along each row of boxes by the load in that zone (each box has a pitch and an arrow).
- Drop a line to the ZFM — the point must be in the zero fuel envelope.
- Apply the fuel index and drop to the TOM — the point must be in the take-off envelope. Then the CG stays within limits throughout, including diversions.
Centre tank fuel is normally used before wing fuel, which keeps the wings loaded longer and relieves wing root bending. A DOM CG at 18% of a 134 in MAC starting at 625 in is 625 + 24.1 ≈ 649 in from the datum.