Centre of gravity

031 Mass & BalanceChapter 3

The centre of gravity (CG) is the point through which the total weight of the aircraft acts vertically. All loading calculations revolve around moments about a datum.

Datum & stations

Definition — Datum

A fixed vertical plane chosen by the manufacturer — reference for all arm distances. May be at the nose, firewall, or any convenient point; not necessarily on the aircraft. Given in the AFM/loading manual.

Definition — Station

A numbered location relative to the datum — identifies where a mass acts (e.g. hold, seat row, fuel tank).

Definition — Arm (balance arm)

Horizontal distance from the datum to the point where a mass acts. Moments ahead of datum (nose side): negative arm, negative moment. Aft of datum: positive arm, positive moment. If datum at nose, all moments are typically positive aft.

Moment & CG

Formula — Moment

Moment (Nm) = Mass × Arm
            = Force × distance from datum

Formula — Centre of gravity

CG (arm) = Total moment ÷ Total mass

Key fact

CG is computed along the longitudinal axis only. Weight always acts parallel to gravity (vertically downward). CG position is NOT affected by stabiliser trim or horizontal stabiliser setting — trim changes tailplane load but the actual CG stays where the mass is.

Key fact

If no datum is given in a question, choose one and apply signs consistently. Actual datum position and CG limits are in the AFM.

Sign conventions

Key fact

In many loading manuals: clockwise (aft) moment = positive; anticlockwise (forward) moment = negative. This gives the distance from datum to the actual CG along the longitudinal axis.

Key fact

Gear deployment moves the CG. Undercarriage extending forwards moves CG forward; gear retracting rearwards moves CG aft. Tailwheel aircraft must be weighed in the flight (level) attitude.

Indexes

Definition — Index

A scaled-down figure without units representing a moment — simplifies arithmetic. DOI (dry operating index) = DOM × CG arm ÷ constant. Fuel index tracks CG shift as fuel burns from different tank locations.

Key fact

Indexes decrease the magnitude of moments, making load sheets manageable. For fuel index not tabulated, use the next highest index value (conservative).

Load documentation

Key fact

The Mass & Balance document must be signed. Last-minute changes (LMC) must be documented and within approved limits. Traffic load must remain fixed in flight — only pre-calculated fuel-burn CG movements are permitted.

Key fact

Tie-downs prevent cargo shifting — unplanned CG movement can exceed limits and damage the aircraft.

Equilibrium

Key fact

Moments determine whether a body is in equilibrium. Sum of moments about a point = zero when balanced. In flight, the CG must remain within the approved envelope for all phases.

Exam trap

Stabiliser trim does not move the CG — it changes tailplane download/upload. Exam questions often trap you with “trim moves CG aft.”

Exam trap

Datum at nose → aft arms positive. Datum ahead of nose → nose-side arms negative. Always check the manual’s sign convention before calculating.