Free Surface Effect

The free surface effect (FSE) is the apparent reduction in a vessel's metacentric height (GM) caused by the movement of a liquid surface inside a partially filled tank when the ship heels. When the vessel heels, the liquid in a slack tank shifts to the low side, moving its centre of gravity transversely and increasing the heeling moment. This shift is mathematically equivalent to a virtual rise in the ship's overall centre of gravity, reducing the effective GM. The magnitude of the FSE depends on the second moment of area of the liquid surface (breadth cubed divided by twelve) and the density of the liquid, divided by the ship's displacement. A wide, shallow tank with a large breadth produces a much greater FSE than a narrow, deep tank. The chief mate minimises FSE by keeping tanks either full or empty wherever possible and by transferring liquids between tanks rapidly during cargo operations rather than running them half-full for extended periods. Ballast tanks should be pressed up or emptied as early as possible in the loading sequence. The loading computer automatically calculates and deducts FSE from the solid GM to give the corrected effective GM. During Port State Control inspections, stability calculations are verified and any loading condition with inadequate GM—particularly when FSE has been underestimated—is cause for serious concern and possible detention.