Chapter 10 spread thousands of tonnes over five holds over some hours. The arithmetic here is the same arithmetic. Only the time scale has changed.
11.1 A weight on a hook
Put a weight on the deck and its centre of gravity is on the deck. Hang the same weight from a derrick and its centre of gravity is at the derrick head, because that is where it is supported from. Nothing else about it has changed. But as far as the ship is concerned that weight is now acting at the top of the mast, and it goes on acting there, wherever the derrick is slewed to, until the weight is landed and the sling goes slack.
Two things follow, and they are the whole of the theory. The moment the sling takes the strain, G rises: for a weight already on board by w d/W, where d is the height of the jib head above wherever the weight was, and for a weight lifted from a barge or the quay by w (h − KG)/(W + w), a loading at the jib head h above the keel, with KM read at the new displacement W + w. That happens before the weight has moved a centimetre. And if the derrick is plumbed over the side there is a heeling moment of w times the outreach, resisted by the displacement times the fluid metacentric height of the lifted condition, free surface included.
GG1 = w × d / W or w (h − KG) / (W + w) tan θ = w × x / (W1 × GM1)
11.2 The lift cycle
She carries 4 deck cranes of 30 tonnes safe working load, jib head 30.00 m above the keel, maximum outreach 20.00 m. Rigged in tandem they lift a 120 tonne item from a barge alongside to port, slew it inboard to 6.00 m from the centreline and land it in No.3 hold, 2.00 m to port. The lift is worked in her part loaded condition (22 668 t at the partial subdivision draught of 7.368 m, solid KG 8.181 m, free surface moments of 815.2 t m from the seven slack consumable tanks, fluid KG 8.217 m, KM 10.632 m, fluid GM 2.415 m) and in her arrival ballast condition (11 668 t, solid KG 5.950 m, fluid KG 6.020 m, KM 14.037 m, fluid GM 8.017 m), where the hold is empty and the item is landed on the tank top at Kg 2.50 m. At her summer marks she could not take 120 t from a barge at all: it would put her over her summer displacement, and a full hold has nowhere to land it.
| stage | W t | fluid KG m | KM m | fluid GM m | heeling moment t m | heel deg |
|---|---|---|---|---|---|---|
| Part loaded | ||||||
| alongside strain not yet taken | 22 668 | 8.217 | 10.632 | 2.415 | 0 | 0.0 |
| lifted clear 20.00 m to port | 22 788 | 8.332 | 10.620 | 2.288 | 2 400 | 2.6 |
| slewed to 6.00 m to port | 22 788 | 8.332 | 10.620 | 2.288 | 720 | 0.8 |
| landed in No.3 hold Kg 8.00 m | 22 788 | 8.216 | 10.620 | 2.404 | 240 | 0.3 |
| Arrival ballast | ||||||
| alongside strain not yet taken | 11 668 | 6.020 | 14.037 | 8.017 | 0 | 0.0 |
| lifted clear 20.00 m to port | 11 788 | 6.264 | 13.957 | 7.693 | 2 400 | 1.5 |
| slewed to 6.00 m to port | 11 788 | 6.264 | 13.957 | 7.693 | 720 | 0.5 |
| landed on the tank top Kg 2.50 m | 11 788 | 5.984 | 13.957 | 7.973 | 240 | 0.1 |
Read the two halves of that table against each other. Part loaded, G rises 0.115 m when the weight lifts. In ballast it rises 0.244 m, more than twice as much, because the displacement is half as great and the jib head stands further above her lower G. And yet the ballast condition heels 1.5 degrees against the part loaded condition’s 2.6. The larger virtual rise produced the smaller list, because she has 8.017 m of fluid metacentric height in ballast against 2.415 part loaded, and with the item at the head 7.693 against 2.288.
11.3 The one quantity that decides it
The heeling moment is w times the outreach. Her resistance to it is W times GM. Their quotient is the tangent of the angle, and nothing else in the ship comes into it.
11.4 What would it actually take?
| condition | to heel her 5 degrees | to heel her 10 degrees | to bring GM to zero |
|---|---|---|---|
| part loaded | 219 t | 406 t | 2 580 t |
| arrival ballast | 370 t | 680 t | 3 929 t |
All at the full 20.00 m outreach, the worst case. Her four cranes together lift 120 tonnes. To heel her five degrees part loaded she would need 1.8 times the whole of her lifting capacity.
And the distinction that is easy to miss
All of this applies to the ship’s own gear. If a shore crane or a floating crane holds the weight, the weight is not aboard and the ship feels nothing at all until it lands. The virtual rise of G belongs to whoever is carrying the load, and the moment of truth is the instant it transfers. That is why the critical moment in a shore crane lift is the landing, and in a ship’s gear lift it is the pick up.
So the honest answer for a ship of this size is that the stability limit on a lift is not the limit that bites. The gear is. A thirty tonne crane will part its wire or tear out its seating long before the ship shows any interest. On a coaster the reverse is true, and on a purpose built heavy lift ship the two are deliberately balanced against each other with ballast.
11.5 Anti heeling systems
An anti heeling system is a pair of tanks, one each side, with a means of moving water between them quickly. That is the whole of it. A weight w moved a distance d across the ship produces a heeling moment of w d, and she settles where her righting moment matches it. MV Ninja has three pairs of topside wing tanks, exactly the right shape for the job: high up, well out, and narrow.
| pair | volume each side, m3 | centre off the middle line, m | lever, m | weight moved, t | full transfer moment, t m |
|---|---|---|---|---|---|
| No.1 | 216.9 | 9.82 | 19.64 | 222.3 | 4 366 |
| No.2 | 270.8 | 10.03 | 20.06 | 277.6 | 5 569 |
| No.3 | 256.5 | 10.03 | 20.06 | 262.9 | 5 274 |
| all three | 744.2 | — | — | 762.8 | 15 209 |
The ship is in the prepared condition of the worked examples: the No.2 topside pair half full each side, both tanks slack (part loaded 22 946 t, fluid GM 2.312 m; ballast 11 946 t, 7.633 m). Water beyond the 270.8 m³ of the No.2 pair is taken from the No.3 and then the No.1 pair at their own levers.
Look at which way round these go. With the No.2 pair prepared half full each side, running all 138.8 t one way corrects 3.0 degrees part loaded and only 1.7 in ballast; from one tank full to the other full, the whole 5 569 t m, 6.0 degrees against 3.5. It is more effective on the deeper, tenderer ship, because a given moment produces a larger list on her, so the same moment removes a larger one. An anti heeling system is at its most useful exactly when the ship is at her most vulnerable, which is rare good fortune in this subject.
The free surface price
With both tanks slack the free surface moment is 2 × 295 × 1.025 = 605 t m, which costs 0.026 m of metacentric height in the prepared part loaded condition, 1.1 per cent of what she has, and 0.051 m in ballast, 0.7 per cent. Free surface moment goes as the cube of the breadth, and a topside tank is narrow. Build the same 270.8 m³ as a single tank 10 m long across the full 24.2 m beam and its inertia would be 10 × 24.2³/12 = 11 810 m⁴, forty times that of the topside tank: some 12 100 t m of free surface moment and half a metre of GM gone while it was slack. That is why anti heeling tanks are tall and narrow and out at the sides.
11.6 The pump that cannot keep up
Her transfer pump delivers 200 m³ an hour, so a full transfer takes 81 minutes. A container crane lifts, slews, lands and comes back in about two. The table is for the prepared part loaded condition, W × GM = 22 946 × 2.312 = 53 051 t m.
| to take this much list off her | heeling moment t m | water to move t | in a 2 minute cycle, m3/h | against her pump |
|---|---|---|---|---|
| 0.5 degrees | 463 | 23.1 | 675 | 3.4 times |
| 1.0 degrees | 926 | 46.2 | 1 353 | 6.8 times |
| 2.0 degrees | 1 853 | 92.4 | 2 703 | 13.5 times |
She would need nearly 7 times her pump to take a single degree off within one crane cycle. Her system is not undersized; it is for a different job. It corrects a standing list, not a cyclic one. Ships that must follow a crane use compressed air on large bore ducts and move thousands of cubic metres an hour.
11.7 When the system lies
Chapter 5 worked an example that has been waiting for this chapter. No.2 double bottom tank on the starboard side was bilged. The tank top was below the waterline, so the waterplane never changed and the free surface correction was exactly zero; her metacentric height actually rose, from 2.240 m to 2.382 m. The draught changed by 13 centimetres. The one and only visible symptom was a list of 2.7 degrees to starboard, from a transverse shift of the centre of buoyancy of 0.1135 m.
The heeling moment behind that list is W × BB1 = 30 456 × 0.1135 = 3 457 tonne metres. A full transfer between her No.2 topside tanks produces 5 569. Removing that list would use 62 per cent of the system’s range: 172.3 t, 168.1 m³, about 50 minutes of pumping.
And then she is upright
Her stability is better than it was. Her draught is almost unchanged. She is standing straight up, and the sea is still coming in.
An anti heeling system is designed to remove a symptom, and it does not know or care what caused it. A list has two kinds of cause. One is a weight somebody put somewhere, and correcting that is what the system is for. The other is water nobody put anywhere, and correcting that is the single most dangerous thing the system can do.
The rule is short. Before you correct a list, find out why there is one. If the cargo plan does not explain it and the ballast log does not explain it, do not touch the system until something does. This is precisely why SOLAS chapter XII requires water level detectors in every hold rather than trusting anybody to notice a list.
11.8 The other special operations
Ship to ship transfer
Two ships moored together, each changing draught and freeboard continuously and in opposite directions. Neither stability calculation is unusual; what is unusual is that the fenders, the manifold and the mooring geometry all depend on the difference between the two, and that difference changes faster than either ship does. The stability arithmetic is ordinary. The seamanship is not.
Grab discharge and lightering
A grab takes a few tonnes at a time from wherever the driver happens to be working, and over an afternoon that is thousands of tonnes leaving from one part of the ship. Chapters 9 and 10 apply in reverse and less predictably, because nobody agreed a discharge sequence with the care they agreed a loading one. And the list the anti heeling system is quietly correcting may be telling you the driver has taken more out of the port side than the starboard.
The tandem lift
Two cranes on one load share it in whatever proportion the geometry dictates, not the proportion the plan assumed. The stability calculation is unaffected, since the total weight and its position are what matter. The crane that is overloaded is not.
Chapter 11 in seven lines
- A suspended weight acts at the point of suspension. G rises by w d/W the instant the sling takes the strain, and stays risen until the weight is landed.
- The list from a lift is tanθ = w x/(W GM). Nothing else in the ship comes into it.
- MV Ninja part loaded has W times GM of 52 139 with the 120 t item at the head. Her whole lifting capacity at full outreach lists her 2.6 degrees; it would take about 219 t to reach five.
- A shore crane lift puts nothing aboard until the weight lands.
- Her No.2 anti heeling pair, prepared half full each side, moves up to 138.8 t either way across 20.06 m, correcting 3.0 degrees part loaded and 1.7 in ballast; from one tank full to the other, 6.0 and 3.5.
- A full transfer takes 81 minutes. It corrects a standing list, not a cyclic one.
- The system removes a symptom without asking what caused it. Find out why she is listing before you take the list off her.
Test yourself
Questions
- Explain why the centre of gravity of a suspended weight is at the point of suspension, and state the expression for the resulting rise in the ship’s centre of gravity.
- A ship of 30 000 t displacement and 2.2 m metacentric height lifts 120 t at an outreach of 20 m from the centreline, the jib head being 22 m above the weight’s original position. Calculate the virtual rise of G, the new metacentric height and the angle of heel.
- Explain why a ship in ballast may suffer a larger virtual rise of G than the same ship loaded, and yet heel less.
- Explain the difference, from the ship’s point of view, between a lift made with her own gear and a lift made by a shore crane, and state at which moment in each the stability changes.
- State the two limits on the weight a ship may lift, and explain which of the two normally governs on a ship of 30 000 t displacement and which on a coaster.
- Describe an anti heeling system, state the expression for the heeling moment it produces, and explain why the tanks are made tall and narrow rather than wide.
- A pair of anti heeling tanks holds 270 m3 a side with centres 10.0 m either side of the centreline. Calculate the maximum heeling moment available and the list it would correct on a ship of 30 000 t with a metacentric height of 2.25 m.
- Explain why an anti heeling system corrects a larger angle of list when the ship is loaded than when she is in ballast.
- Explain why an anti heeling system of modest pump capacity cannot follow a container crane through its cycle, and what is used instead on ships that must.
- A ship develops a list of two and a half degrees alongside which is not explained by the cargo plan or the ballast log. State what the officer of the watch should and should not do, and give your reasons by reference to the behaviour of a bilged double bottom tank.
Looking ahead
Eleven chapters of arithmetic, and all of it correct. Every ship in the next chapter had the same arithmetic aboard: a stability booklet, an approved loading instrument, a set of criteria she satisfied on paper, and officers who could work the sums. Chapter 12 takes the casualties one at a time, not to apportion blame, which is for others, but to work out in the terms of this volume exactly what was happening to each of those ships in the hours before she was lost. A number you have calculated yourself is a number you will recognise when you meet it at sea.