Weight and Balance and Its Effect on Performance
Mass effects
Every performance number is mass-dependent. Take-off distance scales roughly with the square of mass; climb gradient scales inversely with mass. MTOM, MLM, MZFM and the regulated take-off mass are the four limits; the MZFM protects the wing-root bending and the tail-load case with zero fuel. Loading must keep the CG within the certified forward and aft limits.
CG effects
A forward CG increases the tail-down load, raising stall speed, take-off distance and trim drag, and reducing cruise speed and range. An aft CG reduces static stability, shortens take-off distance and can increase cruise speed, but may reduce elevator authority and pitch stability. The neutral point is where stick-fixed static margin is zero; the manoeuvre point is the neutral point with stick-free stability.
Balance mechanics
Moment = mass × arm; the CG is total moment / total mass. Use the index method if the manual gives index units. Zero fuel mass is empty mass + traffic load + payload. Ramp mass includes taxi fuel; take-off mass is ramp mass minus taxi fuel.
Worked example
Empty mass 30,000 kg at arm 18.0 m; fuel 5,000 kg at 20.0 m; payload 4,000 kg at 22.0 m. Total moment = 540,000 + 100,000 + 88,000 = 728,000 kg·m; total mass 39,000 kg; CG = 18.67 m. If the aft limit is 18.5 m, ballast or a load shift forward is required.
Traps
Forgetting to subtract taxi fuel; confusing MZFM with MLM; assuming aft CG always improves all performance; using volume rather than mass for fuel (density!).