Centre of gravity

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Centre of Gravity

The centre of gravity (CG) is the location of the centroid of mass of a vessel. Centres of gravity longitudinally, transversely, and vertically are important to a vessels stability.

Contents

Vertical Centre of Gravity

The vertical centre of gravity (VCG or KG) is the height above the baseline of the centre of gravity. A high VCG is detrimental to stability, the vessels tendency to return to upright when rolled. Too high of a VCG however may make the vessel "stiff" and uncomfortable for crew. With a vertical centre of bouyancy, VCG can be used to determine the metacentric height through the relationship GM = BM - KG. On suitably sized vessels, the VCG will be verified after a vessel launch by either an inclining test or a roll-period test.

Longitudinal Centre of Gravity

The longitudinal centre of gravity (LCG) is the position along the length of the vessel of the centre of gravity. It is generally calculated by considering moments about the aftermost portion of the vessel, however it is often stated as a distance from the ships midship. The placement of the centre of gravity relative to the centre of bouyancy is a factor in vessel trim.

Transverse Centre of Gravity

The transverse centre of gravity (TCG) is the lateral location of the centre of gravity. It is beneficial to maintain the TCG on the centreline of the vessel to maintain a neutral heel.

Calculation

Summation of Moments

This requires knowing the centre of gravity of individual components and their location within the ship. The weight of the component is multiplied by the distance from this components CG to a given reference point (generally, the vessels centreline, after perpendicular, and baseline). This gives the components moment. Summing these moments, and dividing by the total weight of the components, gives the distance from the reference point to the centre of those components. This can be used to aggregate related components, or used for the entire vessel if sufficient information is available.

Weight Curve

For components of irregular shape, a sectional approach can be used to generate a weight curve. For ships with regular framing systems, this can also be used to generate a complete weight curve. The area under the weight curve is a close estimation of the actual weight (see weight study). The centroid of this weight curve will be the LCG. Taking vertical centres of gravity for the sections used and plotting these can be used to determine the magnitude of the VCG, whose position will then be at the LCG.

Direct Observation

With knowledge of the hull form, the location of the LCG and TCG can be determined through a lightship survey. When the vessel is in static equilibrium, the CG of the vessel will be aligned with the CB; thus, by determining the CB for a vessel the CG can be determined. Additionally, to determine the VCG, an inclining test can be performed.

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