# Metacentre M (initial transverse metacentre)

When a ship floating at rest in still water is inclined by an external force to a small angle fi, the centre of buoyancy shifts from B to the new position – B_{fi}. The point where the new line of buoyancy force intersects the initial line is denoted as the initial metacentre M. For practical purposes, in normal merchant ships the point M does not change in position for inclination up to about 7-15 degrees.

- **KM** – The height of the initial metacentre M above the base plane. It depends on a geometrical form of ship’s submerged part.

**KM = KB + BM**

where:

- **KB** – The height of the centre of buoyancy above the base plane denoted as vertical centre of buoyancy (VCB),

- **BM** – Metacentric radius = Moment of inertia of the waterplane/Volume of displacement= I/V.

- **GM **– The vertical distance between G and M is referred to as the metacentric height.