A Contradicted GM: Rolling Period Against the Loading Computer
MV Cape Meridian, a 1,800 TEU container ship of 25,000 t displacement, is 36 hours out of Ningbo for Fremantle when the master notices heavy, easy rolling. Beam is 30.2 m. The officer of the watch times 10 complete rolls at 260 s, giving a roll period of 26 s. The stability booklet gives the rolling-factor constant C as 0.78 for this condition. The loading computer, last updated on sailing, shows GM 1.42 m and the ship inside all limits, with the 9-high stack of 20 ft containers on bay 14 lashed per the CSS Code and the Cargo Securing Manual. Since sailing, 380 t of heavy fuel oil has been consumed from double-bottom tanks and 90 t of fresh water used; no ballast has been adjusted. A 3.5 m swell at 9 s is forecast to build to 5 m at 11 s. Two containers in bay 14 have already shifted, distorting the lashing rods. The next port of refuge with a container crane is Colombo, three days away; Fremantle is eight days away.
1. Derive GM from the observed rolling period, compare it with the loading computer, and state the limits of the method.
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Using GM = (C x B / T)^2, where T is the full roll period in seconds: GM = (0.78 x 30.2 / 26)^2 = (23.56/26)^2 = (0.906)^2, giving about 0.82 m.
The computer says 1.42 m. A 0.6 m gap is not noise; it changes the ship from comfortably stiff to tender, and tender in a container ship means slow, large-amplitude roll that loads lashings and can walk a stack over the side. The observed behaviour - easy rolling - is consistent with the lower figure.
Limits of the method: the formula is empirical, C depends on hull form and loading and is only an average for the block coefficient in question; the period measured must be a free roll, and in a 3.5 m swell at 9 s you are measuring a forced roll that is being partly driven by the sea. Amplitude matters too, because the period lengthens at large angles. So 0.82 m is an indicator, not a computed GM, and it should not replace the loading computer. But when the two disagree by this much the burden shifts: you act on the conservative number until the discrepancy is explained, and you must explain it before the deeper forecast arrives.
2. What could explain the discrepancy, and what do you check before accepting the computer output?
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First test the arithmetic of the change since sailing. Burning 380 t of HFO from double bottoms and 90 t of fresh water raises KG by roughly (380 x 7 + 90 x 3) / (25,000 - 470), about 0.12 m, so GM should have fallen from 1.42 to about 1.30 m - that explains only 0.12 m of the 0.6 m gap. Something else is wrong.
Check, in this order: tank soundings against the computer for every ballast, fuel and fresh-water tank, including any transfer or ballast taken without a note; free surface in partly filled tanks, which can easily cost 0.1-0.3 m and is the most common omission; verified container weights against the manifest and VGM declarations, especially the heavy boxes low in the 9-high stack, and whether the computer KG includes the stack weights and the lashing gear; water or cargo ingress - sound the bilges and void spaces, check hatch covers and hold ventilation for condensation on a long ocean leg; the departure condition itself - recalculated or copied forward from the last voyage, and whether the C constant matches this loaded trim and beam; and the GZ curve at the actual displacement against the IS Code 2008 Part A criteria: area to 30 deg at least 0.055 m.rad, to 40 deg at least 0.09, between 30 and 40 deg at least 0.03, GZmax at least 0.20 m at 30 deg or more, and initial GM at least 0.15 m, plus the weather criterion. GM alone proves nothing about the GZ area.
3. Given the shifted containers and the forecast, what do you do now, and would you divert?
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Treat the ship as tender and act before the sea builds. (1) Rig for the sea state: alter course and speed to take the sea off the beam and to break the synchronism - with a natural roll near 26 s, an 11 s swell gives an encounter period close to 13 s, roughly half the roll period, which is the parametric-rolling condition; a modest change of heading or speed moves the encounter period out of that window. (2) Restore stability: fill low double-bottom ballast to bring GM up towards 1.0-1.2 m and press up slack tanks to kill free surface - but do not overdo it, because an over-stiff ship shortens the period and increases lashing accelerations. (3) Secure bay 14: no one on deck in the affected area unless the roll and sea make it safe, then inspect and re-secure with supplementary lashings, and examine the adjacent bays for the same failure mode; record the inspection. (4) Report: master to company and DPA, charterers advised of possible diversion, and the reason stated. (5) Divert to Colombo if the lashings cannot be restored, or if any further stack shows distress. One day of schedule against a stack loss, cargo damage, a flooding container in a hold and a possible structural fire is not a close call. Keep timing the roll: a shortening period means GM is rising, a lengthening period means it is falling further and the diversion decision should be made immediately.