= Metacentric height
{title2=$GM=I_{\rm wp}/V_d-BG$}
{wiki}
For a small heel of a floating body in a uniform <fluid>, the metacentre is the intersection of the new vertical <buoyancy> line with the original vertical through the <centre of buoyancy>. With the <centre of mass> a signed distance $BG$ above the original <centre of buoyancy>, the <metacentric height> is $GM=I_{\rm wp}/V_d-BG$. Here $I_{\rm wp}$ is the waterplane <second moment of area> about the heel axis and $V_d$ the displaced <volume (thermodynamics)>. Positive $GM$ gives a restoring small-angle <torque> and negative $GM$ gives instability. The formula describes local static stability, not all large-angle behaviour or effects of free <liquid> surfaces inside the body.
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