Metacenter and ship stability

We address the location of the metacenter M of a floating body such as a ship. Previous studies of M in relation to the stability of a ship have mainly used geometrical approaches and were limited to near equilibrium. We develop a quantitative approach to the location of M for a general shape of the cross-section of a floating body in a rolling/pitching motion and for an arbitrary heel angle. We show that different definitions of M refer to one and the same special point of the floating body. We discuss the relation between the height of M with respect to the line of flotation and the contribution of the buoyancy force to ship stability. We provide expressions and graphs of the buoyancy, flotation, and metacentric curves for some simple shapes of floating bodie