Natural Period of Roll

The natural period of roll is the period at which a ship oscillates freely in roll after a disturbance, and it is the quantity every roll resonance condition is expressed against. It depends on the roll radius of gyration and the metacentric height, so a stiff ship with a large metacentric height rolls quickly and a tender ship slowly.

The practical difficulty is that the radius of gyration is rarely known, so the period is estimated from beam and metacentric height by an empirical formula. Several are in circulation and they do not agree. The 2008 Intact Stability Code gives a formulation with a coefficient derived from beam, draught and waterline length. ClassNK uses a simpler multiple of beam over the square root of metacentric height, and MARIN’s TopTier guidance uses a different multiple again, while instructing that the period should be measured after departure because rules of thumb based on metacentric height are not always accurate.

On a large container ship at low metacentric height the spread between these formulations is wide enough to move the ship in or out of a resonance band, which makes the choice of formula a safety-relevant decision rather than a matter of convention.

The full article will set out the physical derivation, the competing empirical formulations and their provenance, the measurement of the period by roll decay test and by onboard sensors, the effect of free surface and of loading condition, and the use of the period in resonance avoidance.