Eleven chapters of arithmetic, and all of it correct. Every ship in this chapter had the same arithmetic aboard, and in most cases an approved loading instrument to do it with.
12.1 What this chapter is and is not
The casualties named here are matters of public record and of formal investigation. Those investigations were conducted by people with access to the wreck, the survivors, the loading computers and the company files, and this chapter neither adds to their findings nor questions them. Anyone who wants to know what happened to a particular ship should read the report, not this book.
What it does is take the mechanism of each casualty, the piece of physics that actually did the work, and run it on MV Ninja, whose every figure the reader now knows. That turns a paragraph in a report into a number you can feel the size of.
It should be said plainly that people died in most of these casualties, and in two of them in their hundreds. The arithmetic below is an exercise on a fictitious ship, but the mechanisms are not.
12.2 Mechanism one: water on a deck
The loss of the Herald of Free Enterprise off Zeebrugge on 6 March 1987, with 193 dead, was investigated by a formal inquiry under Mr Justice Sheen. The ship sailed with her bow doors open, trimmed by the head, and water came over the bow sill on to the vehicle deck as she gathered speed. The quantity of water that took her stability was, by the standards of a ship of her size, small.
Suppose water ponds on a clear run of MV Ninja’s deck, right across her breadth of 24.20 m, to a depth of only 50 millimetres.
| length of the pond, m | volume m3 | weight t | rise in G, m | free surface correction, m | GM, m | angle of loll |
|---|---|---|---|---|---|---|
| 10 | 12.1 | 12.4 | 0.002 | 0.397 | 1.818 | — |
| 20 | 24.2 | 24.8 | 0.004 | 0.794 | 1.418 | — |
| 30 | 36.3 | 37.2 | 0.007 | 1.191 | 1.020 | — |
| 40 | 48.4 | 49.6 | 0.009 | 1.587 | 0.621 | — |
| 50 | 60.5 | 62.0 | 0.011 | 1.983 | 0.223 | — |
| 60 | 72.6 | 74.4 | 0.013 | 2.379 | -0.175 | 14.4 deg |
| 80 | 96.8 | 99.2 | 0.018 | 3.170 | -0.969 | 31.2 deg |
| 100 | 121.0 | 124.0 | 0.022 | 3.959 | -1.763 | 39.3 deg |
Her metacentric height reaches zero when the pond is 55.6 m long: 67.3 cubic metres of water, 69 tonnes, on a ship of 30 456. Her own cargo weighs about three hundred and sixty times as much.
And now the part that matters most. Make the same pond ten times deeper, half a metre instead of fifty millimetres. The weight goes from 69 tonnes to 690. The free surface correction goes from 2.205 m to 2.161. It has hardly moved.
the moment of inertia of a free
surface does not depend on how deep the water is
depth adds weight; area destroys stability
To lose the same 2.205 m by stowing cargo high instead you would have to move about 11 800 tonnes from the holds to the deck: 171 times the weight of the water. This is why the vehicle deck of a ro ro ship is the most dangerous compartment afloat.
12.3 Mechanism two: a cargo that becomes a liquid
On 2 January 2015 the bulk carrier Bulk Jupiter sank off Vietnam with the loss of eighteen of her nineteen crew. She was carrying bauxite, and the flag State investigation concluded that liquefaction of that cargo was the most probable cause. The casualty led directly to new warnings about bauxite and to a wider re examination of Group A cargoes under the IMSBC Code.
A cargo that liquefies stops being a solid and starts being a liquid with a free surface, and the free surface of a bulk carrier hold is the full breadth of the ship.
| holds liquefied | which ones | free surface correction, m | metacentric height, m |
|---|---|---|---|
| 1 | No.3 | 0.915 | 1.302 |
| 2 | No.3, No.2 | 1.834 | 0.383 |
| 3 | No.3, No.2, No.4 | 2.734 | -0.517 |
| 4 | No.3, No.2, No.4, No.1 | 3.421 | -1.204 |
| 5 | No.3, No.2, No.4, No.1, No.5 | 4.171 | -1.954 |
One hold costs her 0.915 m, which is 41 per cent of her metacentric height (the liquid taken at the density of sea water, 1.025 t per cubic metre, so that the figure can be set beside the water on deck above; at the cargo’s own density of 0.769 it would be 0.687 m). Three holds take her metacentric height negative: she takes up an angle of loll, and the liquid running to the low side adds a heeling moment to it.
And here is the thing that makes it so dangerous
None of those figures depends on how much of the cargo has liquefied. A layer a hundred millimetres deep across the full breadth of the hold produces the same moment of inertia as a layer two metres deep, because the moment of inertia of a free surface depends on the shape of the surface and nothing else. A draught survey would show nothing. The cargo would look exactly as it did when it was loaded. The ship would simply become, over a few hours, a different ship.
That is why the IMSBC Code attacks the problem at the only point where it can be attacked: the moisture content before loading, the transportable moisture limit, and the can test on the quay. By the time it is a stability problem it is no longer a problem that stability can solve.
12.4 Mechanism three: the margin, not the error
On 3 January 2015 the car carrier Höegh Osaka developed a severe starboard list as she turned round the West Bramble buoy after leaving Southampton; with the list beyond 40 degrees she lost steerage and propulsion and drifted aground on the Bramble Bank, which stopped the list increasing. Nobody died. The MAIB (Report 6/2016) found that the ballast quantities assumed on board bore no resemblance to the actual tank levels (a difference of 635 t); that most of the cargo weights supplied to the ship were estimates rather than measured values (265 t); that the loading computer’s facility for entering cargo vertical centres of gravity above the deck had never been used; and, the finding that matters most, that no departure stability calculation had been carried out after loading and before she sailed. The pre-stowage calculation had indicated a GM of 1.46 m against a required 1.34 m; the MAIB could not fix the departure GM exactly, and its modelling of the turn found about 0.7 m plausible.
| believed GM | required GM | margin | the error | |
|---|---|---|---|---|
| the car carrier, as found | 1.46 m | 1.34 m | 0.12 m | 0.76 m |
| MV Ninja, loaded departure | 2.217 m | 0.688 m | 1.529 m | — |
Her margin was 0.12 of a metre and her error was 0.76: 6.3 times the margin. MV Ninja’s margin is 1.529 m. The same error would leave her at 1.457, still +0.769 m clear. To put her on the line would take an error of 1.529 m, 69 per cent of her metacentric height.
| error in KG, m | KG becomes | GM becomes | inside her maximum KG? |
|---|---|---|---|
| 0.250 | 8.363 | 1.967 | yes |
| 0.500 | 8.613 | 1.717 | yes |
| 0.750 | 8.863 | 1.467 | yes |
| 1.000 | 9.113 | 1.217 | yes |
| 1.250 | 9.363 | 0.967 | yes |
| 1.500 | 9.613 | 0.717 | yes |
| 1.529 | 9.642 | 0.688 | on the limit |
| 1.750 | 9.863 | 0.467 | no |
| 2.000 | 10.113 | 0.217 | no |
Which is exactly the wrong lesson to draw
It would be easy to conclude that a bulk carrier is safe from this and a car carrier is not. The right conclusion is narrower: the margin decides, and a ship operating on a margin of a tenth of a metre cannot afford any error at all. Which ship that is depends on the trade, the cargo and the day. MV Ninja with two holds part filled with grain in Chapter 3 had far less margin than MV Ninja carrying a homogeneous bulk cargo, and the seven tier container stow of Chapter 2 had under six centimetres of KG in hand and none at all on the weather criterion.
And the practical finding stands whatever the ship: nobody had calculated the departure condition. The margin cannot decide anything if it has not been worked out.
12.5 Mechanism four: progressive flooding forward
The ore-bulk-oil carrier Derbyshire was lost with all 44 on board on 9 September 1980, in a typhoon south of Japan. The wreck was not found until 1994, and the reopened formal investigation reported in 2000. The sequence it described begins at the bow: water in the forward spaces, the ship trimming by the head, the No.1 hold hatch cover then working in seas it was never designed to meet, and progressive flooding from there.
| flooded | mean m | fwd m | aft m | trim m | GM m | freeboard fwd m |
|---|---|---|---|---|---|---|
| nothing: intact | 9.600 | 9.600 | 9.600 | 0.00 | 2.217 | +3.900 |
| fore peak only, permeability 0.95 (added weight) | 9.850 | 10.652 | 9.096 | +1.56 | 2.233 | +2.848 |
| No.1 hold only, permeability 0.60 (lost buoyancy, Chapter 5) | 10.299 | 12.804 | 8.266 | +4.54 | 2.175 | +0.696 |
| No.1 hold only, permeability 0.90 | 10.699 | 15.551 | 7.086 | +8.46 | 2.172 | -2.051 |
| No.1 and No.2 holds, permeability 0.60 | 11.294 | 17.545 | 6.861 | +10.68 | 2.099 | -4.045 |
Look at the No.1 hold row (the fore peak is worked as an added weight from the Appendix A tank data; the hold cases use the lost buoyancy method and the illustrative hold boxes of Chapter 5, and the last two rows run beyond the hydrostatic table and are indications only). Her metacentric height is 2.175 m against 2.217 intact: for practical purposes, unchanged. She is not unstable, she is not listing, and if you asked the loading instrument whether she was stable it would say yes.
What has changed is that her forward freeboard has gone from 3.900 m to 0.696. The deck at the forward end of the No.2 hatch, which was 3.9 m above the sea, is now 1.6 m above it, and the hatch cover is taking the weight of every sea that comes aboard. Once it goes, the last rows of that table apply, and the classical trim calculation has stopped describing anything real.
That is the whole argument for SOLAS chapter XII regulation 12. There is no stability symptom to notice. There is no list. Water level detectors exist because nothing else in the ship will tell anybody in time.
12.6 Mechanism five: compliant is not the same as safe
This one needs no casualty at all. Chapter 2 stacked seven tiers of empty containers on the hatch covers and found a condition that was inside the maximum KG table and passed the general criteria, but failed the severe wind and rolling criterion on the steady angle of heel, 17.25 degrees against a limit of 16; pressing up the No.1 double bottom pair, 792 tonnes, brought it back to 13.43 degrees. Chapter 3 found two holds part filled with grain whose heeling angle came out at 14.38 degrees against a limit of 12.00.
Both were refused, and rightly. But consider the ship that comes out at fifteen point nine degrees instead of seventeen point two five. She sails. She is compliant. She is not, in any physical sense, safer than the one that was refused: the difference between them is smaller than the error in anybody’s estimate of the wind: a ten per cent error in the wind lever moves the steady angle of the seven tier condition by nearly a degree either way, to 16.36 or 18.09 degrees. She is simply on the other side of a line that had to be drawn somewhere.
A criterion is a floor below which a ship may not go. It is not a level at which she is safe. Every ship in this chapter had been approved to the stability criteria of her day, and the criteria were not what failed.
12.7 What they have in common
| mechanism | what the calculation would have said | what actually failed |
|---|---|---|
| water on a deck | nothing: it was not asked | a door, and the assumption that it was shut |
| a cargo that liquefies | the departure condition was correct | the moisture content, tested on the quay or not at all |
| the departure condition | it was never worked out | the weights and the soundings that go into it |
| progressive flooding | stability is fine, and it was | a freeboard, and a hatch cover meeting seas it was not built for |
| compliant but not safe | the ship meets the criteria | the belief that meeting them was the question |
Not one of those rows is a failure of stability theory. Four of the five are failures of input, and the fifth is a failure of interpretation. That is not a comforting conclusion, because input and interpretation are precisely the parts no software will ever do for you.
12.8 The four questions
Before she sails
- Do I know the weights, or was I told them? A tally is not a weighing. A sounding is not an estimate. A declared stowage factor is a document, not a measurement.
- Do I know where the free surfaces are? Including the ones that are not in any tank: water on a deck, water in a hold, a cargo that has become a liquid.
- How much margin have I got, and over what? Not the metacentric height. The distance between it and the least the criteria allow her, and between her forward freeboard and the sea.
- If she lists, do I know why? And will I find out before I correct it.
None of the four is a calculation. All four are things that have to be true before the calculation is worth doing, and all four are the responsibility of somebody standing on the ship rather than sitting in front of a screen.
Test yourself
Questions
- Explain why the free surface effect of water on a deck does not depend on the depth of the water, and state what it does depend on.
- Water lies 50 mm deep across the full 24.20 m breadth of a deck over a length of 50 m on a ship of 30 456 t displacement. Calculate the free surface correction and comment on the weight of water involved.
- Explain, in terms of free surface, what happens to a bulk carrier when a Group A cargo liquefies, and why a draught survey would not reveal it.
- Explain why the IMSBC Code attacks cargo liquefaction through moisture content rather than through stability criteria.
- Distinguish between an error in a ship’s departure condition and her margin of stability, and explain which of the two decides whether the error matters.
- A ship’s pre departure estimate gives a metacentric height of 1.46 m against a requirement of 1.34 m. State what margin that represents and what error would be needed to make her non compliant.
- Describe the progressive flooding sequence that begins with water in the forward spaces of a bulk carrier, and explain why the ship’s stability gives no warning of it.
- Explain the purpose of SOLAS chapter XII regulation 12 by reference to the flooding of a forward hold, and state why a clinometer would not serve instead.
- Explain the difference between a ship that is compliant and a ship that is safe, with reference to a criterion of your choice.
- State the four questions of section 12.8 and explain, for each, why it cannot be answered by a loading instrument.
Looking ahead
Twelve chapters have computed everything by hand, and every figure has been checked against a second route to the same answer. Chapter 13 does the obvious next thing: it writes the software. The hydrostatics, the cross curves, the intact criteria, the damage cases and the longitudinal strength, in code, for MV Ninja. And then, which is the part that matters, it tries to break it, because a stability instrument that nobody has tried to break is one nobody should trust. Every ship in this chapter had software that worked perfectly on the numbers it was given.