Angle of loll after de-ballasting at anchor
MV Zagros (Handysize, 24,000 t deadweight) has completed cargo operations and is at anchor waiting for a berth. The first officer de-ballasted No. 2 and No. 4 water ballast tanks in preparation, leaving four tanks slack. Within an hour the vessel takes a list of about 5 degrees to starboard; the list then slowly swings to port and back over about twenty minutes. Soundings confirm no cross-connection and no flooding. The loading computer, run on the current soundings, shows displacement 22,400 t, KM 8.72 m, KG corrected for free surface 8.74 m, total free-surface correction 0.31 m, and uncorrected KG 8.43 m; the hydrostatic table gives KB 4.60 m. The chief officer proposes to fill the No. 2 port water ballast tank, on the high side, to bring her upright. The weather is calm with no swell, and the next port requires an alongside arrival in 18 hours.
1. Is this a list or an angle of loll? Justify your answer from the stability data and the observed behaviour, and comment on the chief officer's proposal.
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It is an angle of loll.
From the numbers Fluid GM = KG corrected 8.74 subtracted from KM 8.72 = -0.02 m, i.e. negative. The free-surface correction of 0.31 m is what has turned a sound ship tender: the solid GM is 8.72 - 8.43 = +0.29 m. Negative fluid GM cannot produce a stable list; it produces an angle of loll, where GZ is zero at some small angle either side of upright and the ship is in unstable equilibrium.
From the behaviour A true list caused by an off-centre weight, flooding or a transfer is fixed in direction and magnitude. This ship rolls slowly from one side to the other, which is the signature of a lolled ship sitting on the unstable part of the GZ curve. The soundings rule out flooding and cross-connection, removing the other explanations.
The chief officer's proposal is dangerous At or near the loll angle the righting lever is close to zero. Adding weight on the high side drives GZ negative on that side, so the ship can flop violently through the upright to a larger angle on the other side, or capsize, particularly with the added free surface of a partly filled tank. Weight on the high side is exactly the wrong move for a lolled ship; it is a technique that belongs to correcting a stable list, not an unstable loll.
2. Describe, in order, the actions the master should take to bring the ship upright, explaining the physical reasoning for each.
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1. Make the ship safe first. Stop all cargo and ballast operations, close all watertight and weathertight openings, muster the crew, keep everyone off the deck edges and out of the way of mooring gear, and prohibit hot work and tank entry.
2. Confirm the diagnosis. Re-sound every tank, check for flooding, read the actual list from the inclinometer against the computer, and confirm that no transfer is in progress.
3. Reduce free surface, one tank at a time. Press up the slack tanks, starting with the lowest and most nearly central, for example a double-bottom tank on the centreline. Each tank pressed full removes its own free-surface moment from the 0.31 m correction, and filling low also lowers G. Do one tank at a time, recomputing after each, so the effect is controlled and the ship is never caught with more free surface than she started with.
4. Do not fill the high side and do not shift weight across the deck. No crane or derrick movements to swing weight, and no transfer from the low to the high side.
5. If still lolled, add small weight low down, ideally in a low centreline tank, in small increments.
6. Expect a snap. Once GM becomes positive the ship comes upright quickly and may overshoot; warn everyone on deck.
7. Verify before proceeding. Recompute GM, require at least 0.15 m and a full IS Code check, with no large slack tanks, before weighing anchor. A GM of about 0.29 m is legal but tender; plan all remaining ballast work to avoid returning to this condition.
3. Using the wall-sided approximation, estimate the angle of loll for the present condition, and state the intact stability criteria that must be satisfied before the vessel sails.
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Estimate of the angle of loll BM = KM - KB = 8.72 - 4.60 = 4.12 m. For a wall-sided hull, at the angle of loll GZ = 0, giving tan(theta) = square root of (2 x |GM| / BM). Using the fluid GM of 0.02 m: tan(theta) = square root (0.04 / 4.12) = square root of 0.00971 = 0.0985, so theta = about 5.6 degrees. That matches the 5 degrees observed, which confirms the diagnosis: the ship is lolled because free surface has eaten the whole of a modest solid GM. Press the slack tanks up and the loll disappears, because a solid GM of +0.29 m is reinstated.
Criteria to be met before departure (IS Code 2008, Part A, 2.2)
- Area under the GZ curve up to 30 degrees: not less than 0.055 m.rad.
- Area up to 40 degrees, or to the angle of flooding if that is less: not less than 0.09 m.rad.
- Area between 30 and 40 degrees: not less than 0.03 m.rad.
- GZ not less than 0.20 m at an angle of 30 degrees or more.
- Maximum GZ at an angle of not less than 25 degrees, preferably 30 degrees.
- Initial GM not less than 0.15 m.
In addition the ship must be upright with no residual loll, the free surface minimised by pressing up or emptying tanks, and the cargo secured. The GZ curve should be produced for the final sailing condition, not the computer's raw figure, and filed with the departure stability report.