Buoyancy and metacentric height GM

Checks the vertical equilibrium and initial transverse stability of a rectangular pontoon, showing G, B and M for a given heel angle.

Rectangular pontoon and reference centres

Eslora L · Manga B · Calado d · Total mass · KG from keel · Liquid density · Momento superficie libre I_fs · Tanques internos parcialmente llenosHeel angle · °Value: 8°Gravedad ·

Metacentric height GM

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Initial condition

Estable

Empuje

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Equilibrium draft

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Metacentric radius BM

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Momento adrizante

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Balance vertical

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Diagrama transversal G–B–M

Initial transverse stability

\[GM=KB+\frac{I_{wp}}{\nabla}-KG-\frac{I_{fs}}{\nabla}\]

\[M_R=W\,GM\sin\phi\]

For a rectangular pontoon: KB=d/2, ∇=LBd and I_wp=LB³/12. The free-surface effect reduces GM.

Metacentric height calculator for pontoons

A body floats in vertical equilibrium when buoyancy equals weight. Its initial transverse stability depends on the relative position of the centre of gravity G and the metacentre M.

Initial stability criteria

GM	Condition	Physical reading
GM > 0	Estable	A righting moment appears at small heel angles
GM = 0	Neutra	There is no initial tendency to return upright
GM < 0	Inestable	The initial heel increases

Free-surface effect

Liquids in partly filled tanks shift their apparent centre of gravity as the vessel heels. The correction I_fs/∇ always reduces the available metacentric height.

Preguntas frecuentes

Is a very large GM always better?

No. It increases stiffness and can produce rapid motions, dynamic loads and poor comfort.

Is the calculation valid at 20° of heel?

Only as an indication. For large angles, full GZ righting-arm curves must be used.

Why compare the entered draft with the equilibrium draft?

A difference shows that mass, density or geometry do not describe exactly the same floating condition.