Mass & Balance

The PPL lesson covered mass, moments and the CG of a light aircraft. Commercial aircraft carry dozens of passengers, cargo in several holds and tonnes of fuel, so the calculation is organised on a load sheet, the CG is expressed as a percentage of the wing chord, and structural limits on the floor and the fuselage matter as well.

1. Commercial mass terms

Term	Meaning
Basic empty mass	Aircraft with fixed equipment, unusable fuel and full oil
Dry operating mass (DOM)	Basic empty mass plus the crew and their baggage, catering, and removable equipment – everything except usable fuel and traffic load
Traffic load	Passengers, baggage, cargo and mail – the payload that earns money
Zero fuel mass (ZFM)	DOM + traffic load
Operating mass	DOM + take-off fuel
Take-off mass	ZFM + take-off fuel (block fuel minus taxi fuel)
Landing mass	Take-off mass − trip fuel

2. The limits

• Maximum structural limits from certification: maximum ramp mass, MTOM, MLM and MZFM (fuel in the wings relieves the bending at the wing root, so the mass of everything else is limited).
• Performance-limited masses: the runway, the climb gradient, obstacles, and the landing distance at the destination may all give a lower limit on the day.
• The allowed take-off mass is the lowest of: MTOM (or performance-limited TOM), MZFM + take-off fuel, and MLM + trip fuel.

Example: MTOM 73,500 kg, MZFM 62,500 kg, MLM 64,500 kg; take-off fuel 12,000 kg, trip fuel 9,000 kg. Limits: 73,500 / 62,500 + 12,000 = 74,500 / 64,500 + 9,000 = 73,500. The allowed TOM is 73,500 kg. If the DOM is 42,000 kg, the maximum traffic load is 73,500 − 42,000 − 12,000 = 19,500 kg – and it must also respect the MZFM: 62,500 − 42,000 = 20,500 kg. So the limit is 19,500 kg.

3. Standard masses

Weighing every passenger is impractical, so operators use standard masses approved by the authority. EASA standard values (for 20 seats or more) are, for example, 84 kg for an adult including hand baggage, 35 kg for a child and 15 kg per piece of checked baggage on most flights. Operators may also use their own surveyed values.

4. CG as a percentage of MAC

Airliner CG limits are given as a percentage of the mean aerodynamic chord (MAC), measured from its leading edge (LEMAC):

CG % MAC = (CG position − LEMAC) ÷ MAC length × 100

Example: LEMAC 17.0 m aft of the datum, MAC 4.2 m, CG at 18.3 m: (18.3 − 17.0) ÷ 4.2 × 100 = 31% MAC.

The take-off CG also sets the stabiliser trim for take-off; a wrong value means a heavy or light rotation.

5. The load sheet and trim sheet

• The load sheet lists the DOM, passengers by cabin section, baggage and cargo by hold, fuel and the resulting ZFM, TOM and LM, with the limits.
• The trim sheet (often graphical, using index units instead of moments to keep numbers small) gives the CG at ZFM and TOM.
• Small changes after the load sheet is finished – a few late passengers or bags – are handled as last-minute changes (LMC) within limits set by the operator; larger changes need a new load sheet.
• The commander signs the load sheet (or accepts it electronically) and enters ZFM, ZFM CG and fuel into the FMC.

6. Structural loading limits

• Floor loading: a maximum mass per square metre (distributed load) and per running metre (linear load). A heavy, small item may need a spreader plate.
• Compartment limits: each cargo hold has a maximum mass.
• Cargo and baggage must be restrained with nets or tie-downs so they cannot move in turbulence or on landing.

7. Fuel and the CG

Fuel burn moves the CG during the flight. Many aircraft burn the centre tank first, then the wings, and some long-haul types move fuel to a trim tank in the tail in cruise to keep the CG aft – reducing the tailplane download and saving fuel. The flight crew monitors the CG, and the CG at landing must be within limits.

8. Effects of the CG in airliners

• Forward CG: more stable, higher stall speed, more tailplane download, higher fuel burn, longer take-off (higher rotation force).
• Aft CG: less stable, less fuel burn, risk of tail tipping on the ground when loading (tail stands are used on some types), and reduced control margins.

Flying it at Levant

SimBrief works with the same terms: on the OFP you will find the DOW (dry operating weight), payload, ZFW, TOW and LW with their maximums, and which limit applies. Before departure, load the same figures in the simulator, enter ZFW and ZFW CG in the FMC and set the take-off trim from the CG.

Check yourself

1. What does the dry operating mass include that the basic empty mass does not? Crew and their baggage, catering and removable equipment.
2. ZFM 58,000 kg, take-off fuel 11,000 kg. What is the take-off mass? 69,000 kg.
3. LEMAC 20.0 m, MAC 5.0 m, CG at 21.25 m. What is the CG in % MAC? 25%.
4. Why is there a maximum zero fuel mass? Without fuel in the wings, the load in the fuselage bends the wing roots more.
5. Five passengers arrive after the load sheet is printed. How is this handled? As a last-minute change, within the operator's LMC limits.

Simulation training material with invented figures. Always use the operator's and manufacturer's data.