Metacentric Height & Ship Stability

Marine Engineering

How It Works

Transverse ship stability depends on the relative positions of the center of gravity (G), the center of buoyancy (B), and the transverse metacenter (M). When waves or wind induce a roll angle (θ), the submerged hull shape becomes asymmetric, causing the center of buoyancy to shift laterally to B'. This creates an internal righting lever arm (GZ = GM · sin θ) that produces a restoring torque returning the vessel upright, provided the metacentric height GM is positive.

Governing Equation
GZ = GM · sin θ , GM = KB + BM - KG , BM = I_T / ∇