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Metacentric radius (BM)

B1. Naval Architecture

Definition

I_T/V, transverse moment of waterplane area over volume.

The metacentric radius BM=IT/BM = I_T / \nabla is the height of the transverse metacenter above the center of buoyancy, equal to the second moment of the waterplane area about the centerline divided by displaced volume. It is purely geometric. A wide, full waterplane gives a large ITI_T and so a high BMBM, which is why beam dominates initial stability through this term. BMBM combines with KBKB to give KMKM, from which GM=KMKGGM = KM - KG.