Glossary term
Metacentric Height
Initial stability measure equal to the vertical distance between a vessel center of gravity and metacenter.
Definition
quantityMetacentric height is the vertical distance between a vessel center of gravity and metacenter, used as a first measure of initial stability.
Metacentric height, usually written GM, describes the small-angle stability tendency of a floating body. A positive GM generally creates an initial righting moment, while too small or negative GM indicates poor or unstable initial behavior. Very large GM can also be undesirable because it can produce fast, uncomfortable, and highly loaded roll motion.
Metacentric height is a small-angle stability measure for a floating vessel or platform. It is commonly written as GM, the vertical distance between the center of gravity G and the metacenter M. For small heel angles, a positive GM produces an initial righting tendency.
A common relationship is:
where GZ is righting arm and \phi is heel angle. The corresponding righting moment is:
where \Delta_m is displacement mass. These relationships are useful for initial interpretation, but they do not replace a full righting-arm curve for larger heel angles.
Engineering use
Metacentric height is used in loading manuals, inclining experiments, intact stability review, ballast planning, offshore floating systems, and operational limits. It helps operators understand whether a vessel is tender, stiff, or unsafe in a particular loading condition.
A high positive GM is not automatically good. It can produce short roll periods, high accelerations, cargo loads, crew discomfort, and fatigue demand. A low positive GM may produce slow roll but limited stability margin. Stability design balances safety, operability, reserve stability, freeboard, and mission requirements.
Common mistakes
A common mistake is treating GM as the whole stability answer. It describes initial behavior only. Downflooding angle, range of positive stability, righting-arm area, free-surface effect, damage condition, wind heel, cargo shift, and seakeeping can govern safety. A strong GM review states displacement, center of gravity, tank status, free-surface correction, water density, loading condition, measurement method, and uncertainty.