3.2 Centre of Gravity

Centre of Gravity

The centre of gravity (CG) is the point at which the entire weight of a body may be considered to act for the purposes of statics. If you support a rigid body exactly at its CG (or along a vertical line through the CG), it balances with no residual moment. Weight always acts vertically downward through the CG, regardless of the body’s orientation in a uniform gravitational field.

Why CG Matters in Maintenance and Flight

Every force analysis of an aircraft on the ground or in the air uses the CG as the point of application of weight. Jack reactions, weighing on scales, sling angles for hoisting an engine, and the aircraft’s longitudinal stability all depend on where that point lies. If the CG is too far aft, the aircraft may become longitudinally unstable (insufficient nose-down restoring moment). If it is too far forward, the elevators may lack the moment needed to rotate for take-off or flare. The certified CG envelope is a hard operational limit, not a guideline.

CG of a Uniform Simple Body

For a homogeneous body of simple shape, the CG coincides with the geometric centre (centroid):

• Solid uniform sphere or ball — geometric centre
• Rectangular plate — intersection of diagonals
• Uniform rod — midpoint of the length
• Circular disc — centre of the circle

Symmetry is the quick test: if a plane of symmetry exists, the CG lies in that plane; with two or three mutually perpendicular planes of symmetry, the CG is at their intersection.

CG of Composite Systems

Real aircraft are assemblies of major masses (empty structure, engines, fuel, payload) whose individual CGs are known or estimated. The composite CG is the weighted average of the component CGs. With mass mᵢ at longitudinal station xᵢ:

x̄ = (Σ mᵢ xᵢ) / (Σ mᵢ)

If every mass experiences the same g, weights Wᵢ = mᵢ g may replace masses:

x̄ = (Σ Wᵢ xᵢ) / (Σ Wᵢ)

The product Wᵢ xᵢ is the moment of that weight about the chosen reference (often the aircraft datum, which may be forward of the nose or at a wing leading-edge station). Moments aft of the datum are usually taken positive; moments forward are negative — follow the manufacturer’s sign convention.

Worked example — two-mass system. An engine of weight 4 000 N has its CG 2.0 m aft of datum. A propeller assembly of weight 500 N has its CG 0.40 m aft of datum. Combined:

Total weight = 4 500 N
Total moment = (4 000 × 2.0) + (500 × 0.40) = 8 000 + 200 = 8 200 N·m
CG arm x̄ = 8 200 / 4 500 ≈ 1.82 m aft of datum

Adding a lighter mass far forward or aft can move the CG more than adding a heavy mass near the existing CG — that is why ballast and baggage station limits are strict.

Three-dimensional CG

Aircraft also have lateral (y) and vertical (z) CG locations. Lateral CG is normally on the centreline if loading is symmetric; asymmetric fuel or cargo shifts it and affects roll trim. Vertical CG affects ground-loop and tip-over tendencies and the height of the weight vector in side-load analyses. The same weighted-average formula applies independently to ȳ and z̄.

Aircraft Mass and Balance Practice

Weighing procedures place the aircraft on scales (main gear and nose or tail gear), record scale readings, and convert reactions into total weight and CG arm using moments about the datum. Empty-weight CG is established after equipment changes; operational CG is computed for each load sheet before flight. Fuel burn usually moves the CG because tanks are not all at the empty CG station — flight manuals publish CG versus fuel graphs or tables.

Maintenance implications include:

• Recording weight and moment of installed or removed equipment in the weight-and-balance report
• Ensuring jacking and shoring points are compatible with CG so the aircraft does not tip
• Using correct sling attachment points so the suspended engine or component hangs level
• Respecting floor loading and cargo CG limits in freighters

CG Versus Centre of Pressure (Preview)

Centre of pressure (CP) is the point on an aerofoil or aircraft through which the resultant aerodynamic force (primarily lift and drag) may be considered to act. Unlike CG, which is fixed for a given mass distribution, CP moves with angle of attack, Mach number, and configuration (flaps, slats). The horizontal distance between CG and CP determines the pitching moment about the CG:

• If CP is aft of CG, lift produces a nose-up or nose-down moment depending on whether you treat lift as upward through CP — convention and sign must match the course diagram, but the idea is that a moment arm exists.
• Designers place the CG forward of the aerodynamic centre (a related fixed reference for subsonic aerofoils) so that the aircraft has a natural nose-down restoring tendency when disturbed to higher angle of attack, trimmed out by the tailplane.

Module 2 only requires you to distinguish the concepts: CG is a mass property; CP is an aerodynamic property. Confusing them leads to wrong free-body diagrams (drawing weight at the CP, or lift at the CG without justification). Full stability treatment belongs with aerodynamics (e.g. Module 8), but statics already needs correct point of application for weight.

Stability of Equilibrium (Related Idea)

If a body is slightly displaced and tends to return, equilibrium is stable (CG rises when displaced, as with a ball in a bowl). If it tends to move further away, equilibrium is unstable (CG falls). If it stays in the new position, equilibrium is neutral (CG height unchanged, as with a ball on a flat table). An aircraft’s longitudinal static stability is the flight analogue: a nose-up disturbance should produce a restoring nose-down moment when the CG is within limits.

Summary Formula Checklist

• Weight acts vertically through the CG.
• Composite CG: total moment / total weight (or mass).
• Choose one datum and keep arms consistent.
• Operational CG must remain inside the certified envelope.
• CP is not CG; do not swap them on free-body diagrams.