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Metacentric radius (BM)

B1. Naval Architecture

Definition

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

The metacentric radius $BM = I_T / \nabla$ 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 $I_T$ and so a high $BM$, which is why beam dominates initial stability through this term. $BM$ combines with $KB$ to give $KM$, from which $GM = KM - KG$.