## Parametric Roll

Q. What is the effect of resting of ship on a wave traveling in fore and aft direction?
Ans. The GZ values available on ship are provided for static sea conditions. When vessel rests on a longitudinal wave of about the ship length, with the crest amidships, the GZ values decrease in size for all the angles of heel. The reverse happens when the trough is amidships.

Q. What happens when a wave in longitudinal direction has crest amidships?
Ans. With crest amidships, the ship is lifted up with the virtual displacement reducing. The ship, in a way experiences a pinnacle grounding effect, causing a virtual loss of GM. Also, the beam and the length of water plane will be less than what would be in still water. BMT = $\dfrac {b^{2}}{12d}$for a box vessel. Generally, in case of any vessel, it may be said that the transverse BM varies as the square of beam or BMT α breadth2. Thus, the effect is overall shrinking of the GZ curve.

Q. What happens when a wave in longitudinal direction has trough amidships?
Ans. With trough amidships, the ship is sunk in the sea with increase of virtual displacement. The ship experiences a virtual rise of GM. The beam and the length of water plane will be more than what would be in still water. For the same reason stated earlier, it can be said that GM would increase. Thus, the effect is overall amplification of the GZ curve.

Q. What is periodic variation of righting moment? What is result of this?

Ans. Liquid displaced and GZ are important stability “parameters”. In a situation where waves encounter the ship longitudinally, both these parameters fluctuate cyclically. This causes a periodic variation of righting moment. This can trigger off roll, if it occurs with an appropriate period. Weight (virtually displaced) varies only within a limited range but the righting lever can undergo periodic variations to a large extent. This is the predominant cause of possible roll excitation. The excitation is originated due to cyclic fluctuation of stability parameters hence the name “parametric excitation” or “parametric roll“.

Q. What happens when a wave moving in the same direction as ship encounters the ship in following seas?
Ans.Periodical fluctuation of GZ and hence righting moment is likely in such conditions. In the forward trimming & stern trimming postures the sizes of righting levers are different owing to the different underwater forms causing cyclic fluctuation of GZ.

In addition to this the crest & trough cyclically positioning amidships, would also cause the cyclic fluctuation of stability parameters. The causes of cyclic change may or may not match or cause a modified cycle of change. If the ship’s beam is considerable, the basic GMT to start with, is likely to be high, making the ship stiff with a generally large righting levers. All above put together may cause the ship to violently roll.

Q. What are the conditions favourable for a parametric roll?
Ans.With the merchant ships, a periodic variation of the righting lever in case of longitudinal wave system can happen in one of the following situations:

1. Periodic positioning of crest and trough amidships making the ship alternately tender and stiff.
2. Periodic changes of righting lever due to the ship periodically pitching forward and aft.

The periodic variation of righting moment can trigger off the roll. In particular the following are the favourable conditions for large parametric amplitudes:

1. Ship type to be of New generation container vessel or similar ship type.
2. Waves traveling along the ship’s length or at a fine angle to the ship’s length, from forward or from aft.
3. Wave length approximately equal to the ship’s length.
4. Pitching period = ½ roll period.
5. Wave encounter period = pitching period.

Q. What is the effect of wave encounter period being half of rolling period?
Ans. The effect of this is that, as the ship rolls from port to starboard (half of the roll), a full pitching oscillation is completed. Thus, the crest passes a given point on the ship twice. This is because in one cycle of wave encounter the vessel experiences two crests and two troughs. With synchronism having duly established, it may be said that at the time of extreme roll on starboard side, the trough is amidships and as the ship goes to extreme port, the trough is again amidships. This means, if the ship has rolled to say 5o starboard, the GMT is very high and therefore the righting moment is large. Thus, vessel becomes stiff at extremity of a roll and alternately tender in the middle of oscillation. The heavy momentum caused at one extreme causes the vessel to roll violently through the upright point, when the vessel has crest amidships and has become tender and would therefore allow a higher amplitude of roll on the opposite side. The amplitudes will keep increasing owing to the vessel cyclically becoming tender and stiff.

Q. What action must be taken if a parametric rolling is feared?
Ans. An avoiding action, is very important without any delay. A reference to and identifying such a situation, is generally also given in loading and stability manual’. It is important to alter the course and get the direction of wave propagation between 4 to 6 points on bow. Reduction of speed along with the alteration will help changing the encounter period. Sometimes, increase of speed rather than decreasing it for a high powered vessel may help.

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