Datum and Balance Arm Calculations
Datum and stations
The datum is an arbitrary reference plane from which all balance arms are measured, usually forward of the nose. A station is a location defined by its distance from the datum. The balance arm is the distance from the datum to the CG of a component or to the aircraft CG. Arms aft of the datum are positive; forward arms are negative.
Moment calculations
The fundamental relationship is moment = mass × arm. Total moment is the algebraic sum of all individual moments. CG arm = total moment ÷ total mass. Some aircraft publish index units to simplify large numbers: index = (mass × arm) ÷ constant, plus a reference constant. Candidates must be able to convert between moment and index using the aircraft's stated conversion factor.
Traps
- Using the wrong datum: a datum change shifts all arms by a constant, not the moments.
- Forgetting to include the aircraft's basic moment (the empty aircraft already has a moment about the datum).
- Mixing lb·in with kg·m.
- Index conversions: adding the constant rather than subtracting, or vice versa - follow the aircraft's convention exactly.
- Reading arms from the wrong column of a loading table.
Worked example
Datum at nose. Empty aircraft: 6,000 kg at arm 5.0 m → moment 30,000 kg·m. Pilot 80 kg at 2.5 m → 200. Front passenger 80 kg at 2.6 m → 208. Rear passenger 80 kg at 4.2 m → 336. Fuel 800 kg at 5.5 m → 4,400. Total mass = 7,040 kg. Total moment = 35,144 kg·m. CG = 35,144 ÷ 7,040 ≈ 4.99 m.
Rule of thumb
Set out a table with columns mass, arm, moment; sum the columns; divide. This method eliminates most arithmetic errors.