Three chapters have asked what a ship must survive. This one asks how deep she may be loaded before she is asked to survive anything, and the two questions turn out to have the same answer written from opposite ends.
8.1 What a freeboard is for
The freeboard is the distance from the upper edge of the deck line down to the upper edge of the load line. It is not primarily a stability figure. It is a measure of reserve buoyancy: the volume of intact watertight hull above the waterline, which is what lifts her to a sea instead of letting the sea come aboard, and what she has left to settle into when something floods.
A freeboard may only be assigned once a list of other things are satisfied, and the list shows what the Convention thinks it is protecting: structural strength, reserve buoyancy, the physical means of keeping water out, the safety of the crew on the weather deck, the wetness of that deck, intact stability in the normal loaded condition, and the degree of subdivision and stability after prescribed damage. Only the last is what this volume has been about, and it is the one the assigning authority reaches last.
8.2 Type A and type B
A type A ship carries only liquid cargoes in bulk, has a high integrity of exposed deck with small gasketed steel covers, and a low permeability of loaded cargo compartments. A type B ship is every other ship. Bilge a loaded amidships compartment in each: in the tanker the oil runs out, the displacement falls, the freeboard grows; in the bulk carrier the sea runs in, the displacement rises, the freeboard shrinks. That, plus the close subdivision a tanker needs anyway, is the reason for the smaller table.
8.3 The tabular freeboard and the standard ship
The tabular freeboard is read from Regulation 28 against L. It is what would be assigned to a standard ship: block coefficient 0.68, length to depth ratio 15, no superstructure, a parabolic sheer reaching prescribed heights at the perpendiculars, and a minimum bow height. Every correction that follows says how the actual ship differs from that one.
| L, m | 144 | 145 | 146 | 147 | 148 | 149 | 150 | 151 | 152 |
|---|---|---|---|---|---|---|---|---|---|
| Table A | 1870 | 1886 | 1903 | 1919 | 1935 | 1952 | 1968 | 1984 | 2000 |
| Table B | 2190 | 2209 | 2229 | 2250 | 2271 | 2293 | 2315 | 2334 | 2354 |
At 148 metres the Table B value is 2271 mm and Table A 1935 mm. The difference, 336 mm, is the whole subject of section 8.6.
8.4 The corrections
Four corrections turn the tabular value into an assigned freeboard. The block coefficient factor is (Cb + 0.68)/1.36, and it is a multiplier: a fuller ship has more volume under water, so she needs more freeboard for the reserve buoyancy to stay the same proportion of it. The depth correction adds (D − L/15) × 250 for a ship of 120 m and over: flood an amidships compartment running the full depth of the hull and the deep ship settles further. Superstructures are always a deduction, because the standard ship has none. And a deficiency of sheer is always an addition, because sheer is reserve buoyancy exactly where a ship needs it.
| step | mm | running total, mm |
|---|---|---|
| tabular freeboard, Table B at 148 m | 2271 | 2271 |
| multiplied by the block coefficient factor | × 1.1478 | 2606.7 |
| plus the correction for depth | + 913.3 | 3520.0 |
| less the deduction for superstructures (E/L = 0.2297, 16.08 per cent of 1070 mm) | − 172.1 | 3347.9 |
| plus the correction for sheer (deficiency 445.2 mm × 0.6351) | + 282.8 | 3630.7 |
| minimum summer freeboard | 3631 | |
| the freeboard actually assigned to her | 3920 |
The sheer correction is the deficiency of sheer multiplied by (0.75 − S/2L). The standard profile has seven ordinates, multiples of (L/3 + 10) mm; in each half the four ordinates are multiplied by the factors 1, 3, 3, 1 and the sum of the products is divided by 8 to give the mean sheer of that half (aft 494.7 mm, forward 989.4 mm for 148 m), and the mean sheer of the ship is the arithmetical mean of the two halves, 742.0 mm. At 40 per cent of standard her deficiencies are 296.8 mm aft and 593.6 mm forward, mean 445.2 mm, and with S = 34 m the factor is 0.6351. Dividing the sum of both halves by 8 would double the mean sheer and the correction; that is a common slip.
The calculation gives a minimum summer freeboard of 3631 mm against the 3920 mm on her certificate. The tables give a minimum, and a ship may always be assigned more. A freeboard 289 mm above the geometric minimum usually means that the scantling draught, the draught for which the hull was designed and approved, governs rather than the tables (Regulation 1 makes the assigned freeboard conditional on the strength being adequate for the corresponding draught), and that is how her 3920 mm should be read. Even with no sheer at all the geometry could demand no more than 3819 mm.
8.5 The seasonal freeboards
The summer freeboard fixes everything else. Winter is summer plus one forty eighth of the summer draught, tropical is summer minus the same: 200 mm. The fresh water allowance is the displacement divided by four times the TPC, 216 mm, and the tropical fresh water freeboard takes both.
| mark | freeboard, mm | draught, m | |
|---|---|---|---|
| Tropical Fresh Water | 3504 | 10.016 | TF |
| Fresh Water | 3704 | 9.816 | F |
| Tropical | 3720.0 | 9.800 | T |
| Summer | 3920.0 | 9.600 | S |
| Winter | 4120.0 | 9.400 | W |
| Summer Timber | 3620 | 9.900 | LS, from Chapter 4 |
The fresh water allowance computed here is the 216 mm printed in her booklet, which is a satisfying independent check on both. And she is over 100 metres, so no separate Winter North Atlantic line is marked: for a ship of her size the winter line serves.
8.6 Buying freeboard with damage stability
A type B ship of over 100 metres may have part of the difference between the tables back if she can earn it: adequate crew protection, adequate freeing arrangements, steel hatch covers in positions 1 and 2, and the prescribed flooding survived. B-60 returns 60 per cent of the difference, B-100 the whole of it, which is the Table A figure exactly.
| tabular freeboard | what must be survived | |
|---|---|---|
| type B | 2271 mm | nothing is required |
| B-60 | 2069 mm | flooding of any one compartment, permeability 0.95 |
| B-100 | 1935 mm | flooding of any two adjacent fore and aft compartments, machinery excluded |
| type A | 1935 mm | liquids in bulk, and the type A conditions |
The damage assumptions are those of Regulation 27: transverse extent B/5 or 11.5 m whichever is less, vertical from the base line upwards without limit, and the flooding confined to a single compartment between adjacent transverse bulkheads. That last point is the difference from Chapter 7: here the damage is a compartment, not a box.
8.7 Could MV Ninja claim B-60?
She is 148 metres, so her machinery space is not treated as a floodable compartment at all: Regulation 27 treats it so, at a permeability of 0.85, only in a ship over 150 metres. The test is on her holds, each at a permeability of 0.95. Her booklet carries no compartment geometry, so the holds used here are the illustrative box holds of Chapter 5 (a flat floor 2.20 m above the keel, bulkheads at 20.80, 44.90, 68.70, 92.90, 117.20 and 139.60 m from the after perpendicular), and every draught after flooding lies above the last row of her hydrostatic table, 10.40 m, which is carried on in a straight line. The initial condition is her summer departure condition, solid KG 8.09 m, standing in for the homogeneous loading the Regulation prescribes.
| hold flooded | draught m | trim cm (+ by the head) | forward m | aft m | GM m | verdict |
|---|---|---|---|---|---|---|
| No.5 hold | 10.880 | -580 | 8.143 | 13.943 | 2.188 | the deck goes under aft |
| No.4 hold | 10.961 | -206 | 9.934 | 11.994 | 2.083 | survives |
| No.3 hold | 10.988 | +131 | 11.683 | 10.369 | 2.081 | survives |
| No.2 hold | 10.995 | +537 | 14.001 | 8.626 | 2.081 | the deck goes under forward |
| No.1 hold | 10.769 | +929 | 16.131 | 6.837 | 2.194 | the deck goes under forward |
Three of her five holds put the freeboard deck under water. Her residual metacentric height never falls below 2.08 metres in any of them. She does not qualify for B-60, and stability has nothing to do with it: it is the trim that decides the result. The residual lever curve, range and area of Regulation 27(13)(e) need cross curves for the damaged hull, which her booklet does not carry, so they are not settled here.
The holds are the illustrative box holds of Chapter 5, not in her booklet, and the hydrostatic table is carried on in a straight line above 10.40 m. The deck edge angle and area are a wall sided estimate on the mean draught, shown for interest only when the deck is clear; the range and area criteria of Regulation 27(13)(e) need the damaged cross curves and are not settled here.
B-100 does not need testing after that, but it is worth seeing where two adjacent holds take her. On the same model the amidships pair, Nos. 3 and 4 together, puts her at a mean draught of about 13 metres, 2.6 m beyond the hydrostatic table, with the deck at side still clear aft by about 9 cm and a metacentric height near 1.9 m; every other pair puts an end of the freeboard deck deep under water. A ship whose deck is clear by only nine centimetres has very little residual stability: the residual righting lever curve would have to reach 20 degrees beyond equilibrium and enclose 0.0175 m rad, and a deck edge a few centimetres above the water is immersed within a degree or two of heel. That criterion exists for exactly this case.
Qualifying for B-60 would have cut the tabular freeboard by 202 mm, which carried through the same corrections is 231 millimetres of extra draught, worth about 816 tonnes of cargo on every loaded voyage for the life of the ship. That is the gain an owner sets against the cost of the additional subdivision. To MV Ninja as her booklet describes her it would be worth nothing: her assigned freeboard of 3920 mm already exceeds her geometric minimum of 3631 mm by 289 mm, so a smaller tabular figure would not move her marks unless her structure were approved for the deeper draught.
Why Chapter 6 and Chapter 8 disagree, and why both are right
Chapter 6 found her compliant with the probabilistic requirement, her attained index above the required one. Chapter 8 finds her failing the deterministic test in three holds out of five. There is no contradiction. The probabilistic method asks what fraction of all damages, weighted by their likelihood, she survives. Regulation 27 asks whether she survives every one of a named set of damages, and a single failure refuses the reduced freeboard. She is a lawful ship with the freeboard she has; she simply may not have a smaller one.
Chapter 8 in seven lines
- Freeboard is reserve buoyancy, measured from the deck line to the load line.
- The tabular freeboard comes from Regulation 28 against L. At 148 m, Table A gives 1935 mm and Table B 2271 mm.
- Four corrections follow: block coefficient, depth, superstructures and sheer. For her the depth correction alone is 913 mm.
- Her calculated minimum summer freeboard is 3631 mm; the 3920 mm assigned is 289 mm more, the scantling draught governing.
- Winter and tropical are the summer freeboard plus and minus one forty eighth of the summer draught, 200 mm. The fresh water allowance is displacement over four TPC, 216 mm.
- B-60 and B-100 return 60 and 100 per cent of the difference between the tables, for surviving one compartment or two adjacent ones at a permeability of 0.95.
- She fails the B-60 test in three of her five holds. A B-60 freeboard would be worth about 816 tonnes a voyage to a ship assigned the geometric minimum; to her, as her booklet describes her, nothing.
Test yourself
Questions
- Define freeboard, and state the matters that must be satisfied before a freeboard may be assigned to a ship.
- State the Convention definitions of length L, depth for freeboard D and block coefficient Cb, and explain how each differs from the corresponding figure used elsewhere in a stability book.
- Distinguish a type A ship from a type B ship, and explain by reference to a bilged amidships compartment why the type A tabular freeboard is the smaller.
- List the five characteristics of the standard ship on which the tabular freeboards are based, and state for each whether a departure from it increases or decreases the freeboard.
- A type B ship of 148 m has a depth for freeboard of 13.520 m and a block coefficient of 0.881. Calculate the correction for block coefficient and the correction for depth, and explain the reasoning behind each.
- Describe the standard sheer profile and the method by which a deficiency of sheer is converted into a correction to the freeboard. Explain why the forward ordinates are the larger.
- From a summer freeboard of 3920 mm, a summer draught of 9.600 m, a displacement of 30456 t and a TPC of 35.28, calculate the winter, tropical, fresh water and tropical fresh water freeboards.
- State the conditions a type B ship must satisfy to be assigned a B-60 freeboard, and the additional condition for B-100.
- State the damage assumptions and the condition of equilibrium required by Regulation 27, and identify which of the criteria can and cannot be settled without the damaged cross curves.
- A ship passes the SOLAS probabilistic requirement comfortably but fails the Regulation 27 test for a B-60 freeboard. Explain why there is no contradiction.
Looking ahead
Chapter 8 has fixed the deepest draught she may have, and every mark on her side follows from it. What none of those marks records is what the hull felt while the cargo was going in. A bulk carrier can be inside every load line she carries, upright, with a good metacentric height and a lawful trim, and be sustaining bending moments and shear forces that her class approval never contemplated, because the terminal put six thousand tonnes into one hold in forty minutes. Chapter 9 takes up the loading sequence, the BLU Code and the ship to shore checklist. Chapter 10 takes up the longitudinal strength calculation itself, and the two curves the loading instrument is really there to draw.