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Parametric Rolling Motion – a twist in the tail!

Fleetweather was recently contacted by a journalist and asked whether it was possible to forecast the possibility of parametric rolling and so for this blog we thought that we would give a brief explanation of this phenomenon and explain how ship routing can take it into consideration.

Let’s start with a warning. Although the results of ‘auto parametrically excited motion’, or Parametric Rolling Motion (PRM) are headline grabbing and the World Shipping Council estimate contribute to the loss of around 1000 containers a year; the underpinning physics are pretty dry. Describing a 4 dimensional phenomenon in words is challenging and we recommend you watch this video of a wave tank experiment which is worth a 1000 words!

In February 2017 Svendborg Maersk lost 517 containers in the Bay of Biscay. Photo: Maersk Line A/S via DMAIB

Here goes with the words……PRM is usually associated with containerships and car carriers which have hull forms with wide, flat sterns and pronounced bow flare. However the phenomenon can also occur in other vessels in quarter seas.

PRM is a mixture of pitching and rolling occurring simultaneously, resulting in a twisting, dipping motion – very uncomfortable to humans and very stressful for ships and deck cargo. A transversely symmetrical ship, moving in pure head or following long-crested seas will have motions of pitch, heave and surge, but will experience no transverse roll moment. However, under certain conditions of wave encounter frequency, a rolling motion can exist.

This motion results from changes in the water plane as a wave passes through the vessel, the resulting changes in submerged hull geometry relative to time, leads to time varying changes in buoyancy and metacentric height, i.e. in the static roll stability. When the wave encounter period is resonant with the natural roll frequency then a sudden and severe rolling motion can result with an angle of more than 40 degrees rapidly developing, even in a moderate sea, leading to cargo damage, loss of containers and, in extreme cases, capsizing of the ship.

On 1 January 2019 MSC Zoe lost 342 containers in the North SeaPhoto: Image Courtesy: Havariekommando; Kustwacht

The key to safe ship routing is to avoid course and speed combinations which lead to a resonant wave encounter frequency.

The Fleetweather routing system calculates the wave encounter frequency by combining the expected course and speed of the vessel between Estimated Positions (EPs) for the next 6 days, with the forecast swell conditions from numerical wave models. Conditions in which a number of ship handling conditions could occur, including parametric rolling, are calculated using the IMO ‘Revised guidance to the Master for avoiding dangerous situations in adverse weather and sea conditions’ (MSC 1228). Vessels are warned of the possibility of a number of dangerous seakeeping situations including PRM, synchronous rolling, loss of intact stability and surf riding/broaching.

On 26 May 2020 APL England lost 50 containers off Sydney. Photo: AMSA

There are some issues regarding the numerical wave forecasts that need to be considered. There are two wave models in common usage (WaveWatch 3 and the Wave Action Model), both create forecasts of wave spectra. The physics in the models are very good at handling linear affects and with satellite altimetry they have a lot of observations as input data. In short, they produce reliable, accurate forecasts in deep water at a horizontal resolution of 9 to 60 km. However, the energy in the wave spectra is composed of waves at different frequencies, heights and directions and some of this granularity is lost in creating simple outputs such as significant wave height, which is the parameter that is most widely used in ship routing.

For this reason Fleetweather believe it is important to have a router-in-the-loop because phenomena like PRM are non-linear events which are not handled well by route optimisation software and the wave amplitude required to induce PRM in a vessel is not well understood.

An excellent introduction to this topic is provided by the Nautical Institute and there is a very informative video brief by Herbert Engineering Group.

Stay connected and safe.

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