Five degrees of list after loading: loll or something else
MV Coralie, a 7,800 t displacement general cargo ship with a breadth of 18.0 m, has completed loading at berth. The loading computer gives KM 7.20 m, KG 6.95 m and an upright condition. When the last line is let go she takes a 5 degree list to port, which the chief officer calls a loll. All double-bottom tanks are reported empty and the soundings agree. A rolling-period test alongside, with the ship against the fenders, gives about 26 s; the ship's K value is 0.35B. The tug master reports that when he pushes the ship upright she swings back to about 4.5 degrees to port each time, and does not flop over to starboard.
1. Use the evidence to decide whether this is a list or an angle of loll, showing your working.
Read the worked answer
Start with the two independent estimates of GM.
From the loading computer: KM 7.20 − KG 6.95 = GM 0.25 m, positive.
From the rolling period: with radius of gyration k = 0.35 × 18.0 = 6.30 m, the roll period is T = 2πk / √(g·GM). Rearranging:
√(g·GM) = 2πk / T = (6.283 × 6.30) / 26 = 39.58 / 26 = 1.522
GM = 1.522² / 9.81 = 2.317 / 9.81 = 0.24 m
The two figures agree within 0.01 m, so the ship genuinely has a small positive GM.
That matters because an angle of loll cannot exist with positive GM: a loll is the angle at which a ship with negative GM finds GZ = 0, and by definition it is unstable at the upright. Here the ship is stable at the upright, so the 5 degrees is a list, produced by a real transverse heeling moment - an off-centre weight, or a tank or hold with contents the computer has not been told about.
The tug master's observation confirms it. A ship with negative GM pushed to the upright will fall away to either side, unpredictably, and will not return consistently to the same angle. This ship returns to the same side every time, which is the signature of stable equilibrium displaced by a heeling moment.
The chief officer's label matters, because the treatment for a loll (reduce free surface, lower weights, fill the lowest centre tanks) is not the treatment for a list (find the weight).
2. Quantify the correction and describe how it should be carried out.
Read the worked answer
The heeling moment to be cancelled is W × GM × tanθ.
W = 7,800 t, GM = 0.25 m, tan 5° = 0.0875
Moment = 7,800 × 0.25 × 0.0875 = 170.6 t·m
Using GM = 0.24 m from the roll test gives 163.8 t·m, so plan on about 170 t·m - the answer is sensitive to GM because GM is small, and correcting the list will itself change GM slightly.
If the weight is shifted across a 14 m tank pair in the double bottoms:
w = 170.6 / 14 = 12.2 t
Procedure:
- Do not simply transfer ballast and hope. First find the cause: sound every tank, check the hold for a shifted or badly stowed item, check the deck cargo, and confirm with the terminal what the last few lifts actually weighed against the manifest.
- Transfer in small steps, using low, narrow double-bottom tanks on the starboard side to draw ballast and matching the port side, re-reading the list after each step. A 12.2 t transfer is the target, not a slug to be dumped in one go.
- Keep free surface down. Use one tank pair at a time and press up or empty fully rather than holding several slack tanks, because 12 t of water with a free surface can cost more GM than the list correction is worth at GM 0.25 m.
- Re-check the rolling period after correction; a lengthening period means GM is falling and you are heading toward the condition you do not want.
- Record the cause, the correction and the final GM, and issue a note if cargo was mis-declared.
3. What would change if the roll test had given a period of 45 s and the ship had flopped from side to side when pushed?
Read the worked answer
A 45 s period means √(g·GM) = 39.58 / 45 = 0.8796, so GM = 0.773 / 9.81 = −0.079 m - negative. Combined with the ship flopping to the other side, that is a genuine angle of loll, and the situation is dangerous rather than inconvenient: at the angle of loll GZ is zero, the ship has no righting energy at that angle, and a small heeling moment from wind or a slack tank will capsize her further.
The handling changes completely:
- Do not press up a partly filled tank on the low side. A slack tank on the low side adds free surface at the worst possible moment and can take the ship past the angle of vanishing stability.
- Lower G first. Fill the lowest, most central double-bottom tanks, and press them up completely. Removing the free surface of existing slack tanks may raise GM enough on its own to right the ship.
- Remove deck weights, top-tier containers, heavy derrick or hatch cover gear, anything that can be landed ashore or struck below.
- Never attempt to correct a loll with a high tank on the high side. It may appear to work, but it raises G and can roll the ship straight over.
- Watch for the shift: as GM goes positive the ship will come upright and often overshoot to a list on the other side; correct the remainder gradually with small transverse transfers.
- Inform the office and the port; keep tugs alongside and do not sail until GM is confirmed positive by both the loading computer and a roll test in sheltered water.