Centre of Gravity
Definition and limits
Centre of gravity (CG) is the point through which the total mass of the aircraft acts. It is expressed as a percentage of mean aerodynamic chord (% MAC) or as a station/balance arm from the datum. Every type has a forward CG limit and an aft CG limit, and the CG must remain inside these throughout the flight, including after fuel burn.
Why limits exist
- Forward limit: ensures sufficient elevator authority to rotate and flare, and adequate longitudinal stability margin.
- Aft limit: ensures static and dynamic stability and prevents tail-heavy handling; an aft CG reduces stick-force stability and can make stall recovery difficult.
Calculating CG
CG position = Σ(mass × arm) ÷ Σ(mass). This is the moment equation. Moments are added about the datum; the resulting arm locates the CG.
Traps
- Mixing units: arm in inches, mass in kg - convert to a consistent system.
- Sign conventions: arms forward of the datum may be negative.
- Fuel burn shifts CG; check both take-off and landing CG.
- Passengers moving seats changes moments without changing total mass.
- A CG within limits at TOM may be outside at LM after fuel burn.
Worked example
Mass A = 3,000 kg at arm 4.0 m; mass B = 2,000 kg at arm 8.0 m. Total mass = 5,000 kg. Moments = 12,000 + 16,000 = 28,000 kg·m. CG = 28,000 ÷ 5,000 = 5.6 m from datum. If the forward limit is 5.0 m and aft limit is 6.5 m, the CG is valid.
Rule of thumb
Move a mass aft and the CG moves aft; the shift is proportional to (mass moved × distance moved) ÷ total mass.