# Parametric Rolling

#21

I don’t fully understand this but in the case of the pendulum some parameter (center of gravity?) is changing, which is driving the system. In the case of the ship, the changing parameter, is the GM.

GM is the initial slope of the GZ curve.

#22

Physics of Parametric Resonance
When a ship is sailing in head seas, its stability increases when the wave trough is near amidships and decreases on the wave crest. If this stability variation occurs twice during one natural roll period, the rolling motions may build up to quite large angles as a result of parametric resonance.

#23

The changing length of the pendulum seems to be a model of a changing GM, I agree. In a boxy ship, the GM doesn’t vary much from frame to frame down the length. So then, no matter which frames are getting the most weight the GM wont vary much. In a ship with a more variable cross-sectional area, then its GM will vary frame to frame. So then, depending on which frames are getting the most weight at one moment, and which are getting it at the next moment, the GM overall will be changing. That is, the pendulum length will be changing.

Do I understand?

#24

I think that’s very close. my current understanding is that in both cases the GM is changing however with the pendulum the “G” is changing at twice the natural frequency of the system and with the ship it’s the “M” that changing.

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.

From the diagram either GM or GZ can be used as they are related. The G doesn’t change as that’s the center of gravity of the ship.

#25

The pendulum example is a little misleading. In the pendulum model energy is being added to the system. With parametric rolling the restoring forces are changing. With the pendulum the restoring force is gravity.

In order for the swing (pendulum) model to explain parametric rolling the restoring forces would have to change at the right period. So when the child is at the bottom of the swing gravity would be reduced to, say, 1/2 normal, then at the top of the swing increase to 2x normal. Then the analogy works.

GZ is the restoring force which changes with roll period. Restoring force is the parameter which is changing.

#26

I

The m/v APL China lost in 1998 400 containers with 700 or more damaged and a complete hold flooded. The total damage amounted to about 80 million dollar, some say 100 million. The incident was a wake up call for the industry and as a result the phenomenon of parametric resonance is now well understood. A similar incident happened in 2003 with the Maersk Carolina.

Several attempts have been made to develop a signal based automated detection system that will alert when motion signals indicate that a vessel is close to or already in resonance. See also the Arrow system mentioned above.

When experiencing the signs of a resonance occurrence the immediate means to de-tune a resonance is to change the encounter frequency of the waves. This is done by altering the heading and/or changing the ship’s speed. It seems that nautical schools have begun to provide special classes and training on the subject which is very necessary I think.

In the mean time also IMO has issued an updated circular on the subject titled ‘REVISED GUIDANCE TO THE MASTER FOR AVOIDING DANGEROUS SITUATIONS IN ADVERSE WEATHER AND SEA CONDITIONS’

#27

The APL China incident was investigated by William N. France, The story is here Monsterwellen

here is the paper - text below