Mass and Balance: moments, CG envelope and %MAC
Definitions
Mass and balance uses a datum, arms measured from it, moments (mass × arm), and the CG as total moment divided by total mass. Know BEM/DOW, MZFW, MTOW, MLW, MRW, and the difference between maximum and operating masses. The CG must stay inside the certified forward and aft limits for every phase; limits are expressed in metres or as %MAC.
%MAC
Mean aerodynamic chord is the chord between LEMAC and TEMAC: %MAC = (CG distance from datum − LEMAC)/(TEMAC − LEMAC) × 100. Aircraft with variable-incidence tailplanes may have separate takeoff and landing CG limit schedules.
Loading discipline
Load and trim sheets must be checked and signed; last-minute changes require recalculation. Fuel is a moving mass - tank sequencing, burn and refuelling change both mass and CG. Floor loading, compartment limits and ULD tie-down are structural checks, not just arithmetic. A dripstick or dip table converts volume to mass using density; use the density quoted, not 0.8 kg/l by habit.
Effects
Forward CG: longer takeoff run, higher stick forces, better stall recovery. Aft CG: lower stall speed and trim drag, but degraded stability; the aft limit is critical for controllability and tail load in a stall.
Worked example
BEM 40 000 kg at 18.0 m; traffic load 12 000 kg at 22.0 m; fuel 9 000 kg at 20.0 m. Moments: 720 000 + 264 000 + 180 000 = 1 164 000 kg·m. Total mass = 61 000 kg. CG = 1 164 000 / 61 000 = 19.08 m from datum. Check against the envelope before dispatch.
Traps
Forgetting that zero-fuel mass and takeoff mass have different limits; mixing kg with lb; using the wrong sign when the datum lies behind the nose.