Sustained Rolling in Head Seas on a 6,500 TEU Container Ship
A 6,500 TEU container ship (L 300 m, B 42.8 m) is on passage at 14 kn in head seas and is rolling from about 3° up to 28° over roughly eight cycles, then the roll dies away when the master alters speed slightly, only to rebuild. The master reports no slamming and no green water on deck. Loading condition: GM 1.2 m, roll natural period 27 s. From the ship's log and the observed wave period of 17 s the encounter period works out at 13.4 s. The container lashing system is designed for a 25° static-equivalent heel. The forecast keeps the vessel in the same weather area for another 30 hours, with wave periods of 16-18 s and significant wave height 6 m.
1. Identify the phenomenon and show quantitatively why this encounter period matters.
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This is parametric roll, not synchronous roll and not a resonance with beam seas.
The signature is the roll slowly building over many cycles in a head or following sea, with no external forcing at the roll frequency. The mechanism is the periodic variation of the waterplane as the wave crest passes along the hull: in a head sea with wavelength comparable to the ship length, GM is high when a trough is amidships and low when a crest is amidships. That is a stiffness variation at the encounter frequency, and a stiffness (Mathieu-type) excitation at twice the roll natural frequency drives the roll.
Check: T_r = 27 s, so resonance requires T_e ≈ T_r/2 = 13.5 s. The observed T_e is 13.4 s - dead on the condition.
The wave length is λ = 1.56 x 17^2 = 451 m, i.e. 1.5 L: exactly the regime where the midship section is alternately in a crest and a trough. A synchronous beam-sea explanation fails because T_e (13.4 s) is nowhere near T_r (27 s). The intermittent behaviour - dying out on a small speed change, then rebuilding - is typical of parametric roll being just outside or just inside a broad resonance band.
2. Rank the available countermeasures and explain why slowing down is one of the weakest.
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1. Alter course (most effective). Moving 30-60° off the wave direction changes both the encounter period and - more importantly - reduces the longitudinal GM variation that drives the phenomenon. Keep clear of beam seas while doing it, since that introduces synchronous roll and a different set of problems.
2. Alter speed (second, and weaker than masters expect). The encounter frequency is ω_e = ω + ω²U/g. The wave celerity here is c = 1.56 x 17 = 26.5 m/s against a ship speed of 7.2 m/s, so the ship's speed is only about a quarter of the celerity. Dropping from 14 kn to 8 kn moves T_e from roughly 13.4 s to 14.7 s - about a 10% change. That is enough to reduce the build-up but not necessarily to leave the resonance band, which is why the roll keeps returning.
3. Do not use GM as a control. Pressing up double-bottom ballast lowers KG and raises GM, which shortens T_r and shifts T_r/2 away from T_e - but it also stiffens the ship and increases the roll accelerations feeding the lashing loads. It trades one problem for another.
4. Roll damping devices (flume tanks, active fins) are not effective or not fitted for this mode at this speed.
The IMO guidance on avoiding dangerous situations in adverse weather and sea conditions (MSC.1/Circ.1228) explicitly lists parametric roll among the hazards, with the practical advice being course and speed change.
3. What does this mean for the containers and for the passage plan?
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Containers. 28° already exceeds the 25° static-equivalent heel the lashing system is designed for, and parametric roll gives large angles sustained over many cycles - that is the loading case that breaks lashing rods and stacks, even with no green water and no slamming. The absence of impact damage is not reassurance. Actions: reduce stack heights or re-stow the heaviest boxes low if there is any flexibility, confirm the lashing plan matches the actual stack weights, and have the crew check lashings after the event, not during it.
Passage plan. The forecast keeps 16-18 s seas for 30 hours, and 17 s is the worst period for this hull at these speeds. Route around the system or accept a deviation; the ship should not simply press on and repeatedly 'fix' the roll with small speed changes.
Reporting. Log the roll angles, periods and the conditions, and inform the office and charterer - a parametric roll event is a documented operational hazard and may justify a speed/consumption claim or a route deviation.