Mass and Balance
Mass and Balance is arithmetic with a purpose: every question reduces to moments about a datum, and the marks come from careful units and correct sign conventions.
Definitions to know cold
- BEM/OEM: aircraft plus crew, unusable fuel, engine oil and fixed equipment.
- DOW = BEM + crew + crew baggage; traffic load = passengers + baggage + cargo.
- ZFM = DOW + traffic load; MZFW is the structural limit before fuel is added.
- MTOM, MLW and MRW are structural or performance limits; the take-off mass used is the lowest applicable figure.
- CG position is measured from a datum (arm) or as a percentage of the mean aerodynamic chord: %MAC = (arm - LEMAC) / MAC length × 100.
Mechanics
- Moment = mass × arm. Total moment divided by total mass gives the CG arm.
- Adding mass behind the CG moves the CG aft; adding mass forward of the CG moves it forward. The movement is proportional to mass × distance from the CG divided by the new total mass.
- Loading must respect floor limits, running-load limits and compartment maximums as well as the CG envelope.
Worked example
BEM 30 000 kg at arm 12.0 m; crew 200 kg at 5.0 m; payload 8 000 kg at 18.0 m; fuel 6 000 kg at 15.0 m. Moments: 360 000 + 1 000 + 144 000 + 90 000 = 595 000 kg·m. Mass = 44 200 kg. CG = 595 000 / 44 200 = 13.46 m. If the envelope is 11.0-17.0 m, the load is inside it, provided fuel and payload were also checked against ZFW limits.
Traps
The datum is often ahead of the nose, so arms can be large; watch for inches versus metres and kilograms versus pounds. Do not add fuel to a ZFW calculation. %MAC increases towards the aft limit: an aft CG reduces static stability and stick force per g, while a forward CG increases take-off distance and reduces elevator authority at the flare. Always re-check the CG after a last-minute hold-load - a small aft baggage change can put you outside the envelope.