Parametric roll resonance

A ship in longitudinal seas experiences a completely different shape of the underwater volume as compared with the ship in calm water and in beam seas. The reduction of righting arm GZ at wave crest causes a larger heel under the action of wind and sea. The ship rights again, due to the increased righting arm GZ in the wave trough, when the wave passes the ship. The ship in a seaway behaves dynamically, i.e. she starts rolling, and passes the upright position when returning from the first large roll. If the time of the large roll to the opposite side coincides with a wave crest passing the vessel, then the ship ends up with another reduction of righting arm GZ, and consequently with larger roll. Roll amplification due to the “timing” of the restoring moment variation with the roll motion is called “parametric resonance”.

This resonance can cause the ship to roll to very large angles in a moderate sea, leading to cargo damage, loss of containers and, in extreme cases, capsizing of the ship.

Further reading: ABS Guide for “Assessment of Parametric Roll Resonance in the Design of Container Carriers” (2004), can be downloaded from

Large containerships are prone to parametric rolling because the shape of the fore body and aft body are usually very different, leading to a variation of righting levers as wave crests and trough move alongside the ship. A small initiating force at the right time from the rudder, wind gusts and other influence can set the ship rolling to a large angle. Possible consequences on machinery operation of the ship heeling to very large angles include: loss of cooling water, loss of suction, exposure of lubricating oil sumps and, for resiliently-mounted engines, problems with connection of services – and hence shutdown of the main engine.

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