The wind of Chapter 2 pushes the ship over and then stops. Grain pushes her over and stays there. This chapter is about a heeling moment the ship carries in her own holds, and a Code that assumes the worst has already happened.
3.1 Why grain will not stay where it is put
Grain is a granular cargo with an angle of repose of around 20 to 25 degrees, which is low as bulk cargoes go. It is also loaded by pouring, which packs it loosely. Over the first few days of a voyage the vibration of the ship settles it, and the settled surface sits a little lower, some two per cent, than the surface that was loaded. That small void under the deck is the whole of the problem, because it gives the grain somewhere to go.
When the ship rolls, the grain surface does not roll with her. It shifts to leeward, comes to rest on the low side at its angle of repose, and stays there. The ship is left with a permanent list which does not correct itself when the sea moderates, and which reduces the righting lever available for the next roll. The Code does not rely on preventing the shift, although it also requires the cargo to be trimmed and, where necessary, secured. For the stability test it assumes that a shift of a standard and deliberately pessimistic form has already happened, and tests whether the ship remains safe with the result.
3.2 The paperwork, and the three kinds of compartment
A ship carrying grain in bulk must hold a document of authorization issued by or on behalf of her Administration, together with grain loading information approved with it. That information is a specialised extension of the stability book of Chapter 1: the same hydrostatics and the same cross curves, plus a set of grain heeling moment tables and, usually, a table of maximum permissible heeling moments.
The Code recognises three states for a compartment. Filled and trimmed means filled to the maximum extent possible and trimmed to fill the spaces under the deck and hatch covers; the assumed shift is fifteen degrees and for MV Ninja the whole ship comes to 1755 m⁴. Filled, untrimmed means filled in way of the hatch opening but not trimmed outside it, permitted only where the Administration grants a dispensation from trimming, in practice in a compartment approved as specially suitable (two longitudinal grain tight divisions, vertical or sloping at not less than 30 degrees, in line with the hatch side girders); the same five holds then come to 6146 m⁴. Partly filled is anything else: a genuine free surface of grain, a twenty five degree assumed shift, and for No.2 hold at its worst level 13230 m⁴ on its own, 35 times the moment of the same hold filled and trimmed.
A check worth doing once
The assumed shift in a partly filled compartment is twenty five degrees, so the volumetric heeling moment should be close to the transverse moment of inertia of the grain surface multiplied by the tangent of twenty five degrees. For No.3 hold the booklet gives a free surface inertia of 27317 m⁴ when the hold is used for ballast. Multiply by tan 25 degrees and you get 12738, against a tabulated peak of 12532. The two agree to within two per cent.
3.3 Turning the moment into a lever
The tables give a volumetric heeling moment in metres to the fourth power. It is volumetric because it does not yet know what the grain weighs. Divide by the stowage factor and you have a heeling moment in tonne metres; divide that by the displacement and you have a lever in metres, which can be drawn on the same axes as GZ.
lambda 0 = volumetric heeling moment / (stowage factor × displacement)
lambda 40 = 0.8 × lambda 0
A straight line between those two points is the heeling arm curve. It is the grain equivalent of the lw1 line in Chapter 2, and the construction that follows is the same: find where it crosses the GZ curve, and measure what is left above it.
One point of method. The grain heeling moment is not treated as a virtual rise of G. Free surface in the liquid tanks still is, and the GM used in the third criterion is the fluid GM corrected for those tanks in the ordinary way. Mixing the two treatments is the commonest mistake in a grain calculation.
3.4 The three criteria
The angle of heel due to the shift of grain must not be greater than twelve degrees or, in ships built on or after 1 January 1994, the angle at which the deck edge immerses, whichever is the less. The residual area between the two curves, measured from the angle of heel to the angle of maximum difference between the ordinates, or forty degrees, or the angle of flooding, whichever is the least, must not be less than 0.075 metre radians. And the initial metacentric height, corrected for free surface, must not be less than 0.30 metres, which is twice the figure required by the general intact criteria.
3.5 Worked example 3.1: a full cargo of wheat
MV Ninja loads wheat at 1.35 cubic metres per tonne, all five holds filled and trimmed, with the departure consumables of Chapter 1, Worked example 1.1 (509 t of heavy fuel oil at 12.65 m, 35 t of diesel oil at 11.45 m and 165 t of fresh water at 11.86 m, all seven tanks slack, free surface moments 815.2 t m). The grain capacities total 32235 m³, so she takes 23877.8 t. Her displacement is 29536.8 t at a draught of 9.339 m, fluid KG 8.122 m, KM 10.329 m and fluid GM 2.207 m.
The filled and trimmed volumetric heeling moments total 1755 m⁴. Dividing by the stowage factor gives 1300.0 tonne metres, and dividing by the displacement gives lambda 0 = 0.04401 m, with lambda 40 = 0.03521 m. A lever of four centimetres against a GM of 2.207 m produces an angle of heel of 1.13 degrees. The residual area, measured from 1.13 to 40 degrees, is 0.505 metre radians against 0.075, and the GM is 2.207 against 0.30. She complies on all three counts by a factor of several.
3.6 Worked example 3.2: the same ship, two hatches short
Now suppose she is offered a part cargo. Holds No.1, No.3 and No.5 are filled and trimmed. No.2 and No.4 are loaded to about forty five per cent, close to the level at which each gives its largest heeling moment.
The cargo falls to 18264.7 t and the displacement to 23923.7 t. Because the grain in the slack holds sits low, the fluid KG improves from 8.122 to 7.578 m and the GM rises from 2.207 to 2.948 m. Every instinct says this is the better condition.
The volumetric heeling moment says otherwise. It rises from 1755 to 27469 m⁴, a factor of 15.7. lambda 0 rises from 0.04401 to 0.85051 m, and the angle of heel from 1.13 to 14.38 degrees. The limit is twelve. She is refused, and refused on the angle alone: her residual area is 0.383 against 0.075 and her GM 2.948 against 0.30.
3.7 How full is full enough
The obvious remedy is to fill the slack holds. It is worth knowing how much filling is actually needed, because the heeling moment of a partly filled compartment is not a straight line against the level of grain in it. It is nearly zero when the hold is almost empty, because there is little grain to move; it is nearly zero again when the hold is almost full, because there is nowhere for the grain to go; and it peaks somewhere near the middle.
For MV Ninja’s No.2 hold the heeling moment peaks at about 45 per cent of the hold volume, 13230 m⁴. The angle of heel with No.2 and No.4 slack together peaks a little earlier, at about 40 per cent, because a lower level also means less cargo and a smaller displacement to divide the moment by. Filling the two slack holds from that level upward, the angle of heel falls steadily, and she becomes compliant again from about 67 per cent full. Anything between roughly one fifth and two thirds full is refused.
Taking the same picture across the ship, the table below adds one slack hold at a time to an otherwise filled and trimmed cargo. The residual area never comes close to failing, and the GM never comes close either. On a beamy ship with a low grain KG it is nearly always the angle of heel that decides the matter.
| slack holds | moment m4 | moment t m | lambda 0 m | angle of heel | residual m rad | GM m | verdict |
|---|---|---|---|---|---|---|---|
| 0 | 1755 | 1300.0 | 0.0440 | 1.13 | 0.505 | 2.21 | complies |
| 1 | 14612 | 10823.7 | 0.4049 | 8.65 | 0.437 | 2.50 | complies |
| 2 | 27469 | 20347.4 | 0.8505 | 14.38 | 0.383 | 2.95 | FAILS, angle |
| 3 | 39664 | 29380.7 | 1.3824 | 18.55 | 0.337 | 3.58 | FAILS, angle |
| 4 | 49147 | 36405.2 | 1.9172 | 20.79 | 0.310 | 4.38 | FAILS, angle |
| 5 | 59613 | 44157.8 | 2.6409 | 22.96 | 0.265 | 5.49 | FAILS, angle |
3.8 The maximum permissible grain heeling moment
Working the three criteria from scratch for every proposed stow would be slow, so a grain loading manual prints the answer the other way round. For a range of displacements and a range of KG values it tabulates the largest grain heeling moment at which all three criteria are still satisfied. The officer works out his own heeling moment from the tables, enters this one with his displacement and fluid KG, and compares.
| displacement, t | KG 7.50 m | KG 8.00 m | KG 8.50 m | KG 9.00 m | KG 9.50 m |
|---|---|---|---|---|---|
| 18000 | 16028 (angle) | 14037 (angle) | 12046 (angle) | 10056 (angle) | 8065 (angle) |
| 21000 | 16122 (angle) | 13800 (angle) | 11477 (angle) | 9155 (angle) | 6833 (angle) |
| 24000 | 16749 (angle) | 14095 (angle) | 11440 (angle) | 8786 (angle) | 6132 (angle) |
| 27000 | 17885 (angle) | 14899 (angle) | 11913 (angle) | 8927 (angle) | 5941 (angle) |
| 30000 | 19532 (angle) | 16214 (angle) | 12896 (angle) | 9579 (angle) | 4215 (area) |
Worked example 3.2 asked for 20347 tonne metres at a displacement of 23924 t and a fluid KG of 7.58 m. The table allows about 16700 tonne metres at that displacement even at KG 7.50 m. The proposed loading is not marginal; it is outside the envelope by a wide margin, and the refusal comes before a single tonne is loaded. Note also that at the deepest, highest KG corner the governing criterion changes from the angle of heel to the residual area.
Chapter 3 in seven lines
- Grain settles, leaves a void, and shifts to leeward permanently. The Code assumes the shift has happened and asks whether the ship can live with it.
- A filled and trimmed compartment is assumed to shift fifteen degrees. A partly filled one is assumed to shift twenty five, and its heeling moment can be thirty five times as large.
- lambda 0 = volumetric heeling moment divided by stowage factor and displacement, and lambda 40 = 0.8 lambda 0. A straight line between them is the heeling arm curve.
- The three criteria: angle of heel not more than twelve degrees or the deck edge angle; residual area not less than 0.075 metre radians; fluid GM not less than 0.30 metres.
- The grain moment is a heeling arm, not a virtual rise of G. Free surface in the liquid tanks is still handled as a rise of G in the ordinary way.
- Worked example 3.2: two slack holds raised the volumetric moment from 1755 to 27469 and the angle of heel from 1.13 to 14.38 degrees, while the GM improved. She was refused on the angle.
- A partly filled hold is at its worst about half full. Fill it or leave it empty, but do not leave it in between.
Test yourself
Questions
- Explain, in terms of the angle of repose and of settling, why grain requires a Code of its own when iron ore does not.
- Distinguish between a filled and trimmed compartment, a filled untrimmed compartment and a partly filled compartment, and state the assumed angle of shift for each.
- MV Ninja loads barley at a stowage factor of 1.55 cubic metres per tonne, all five holds filled and trimmed, with the departure consumables of Worked example 3.1. Calculate her displacement, her fluid KG, her grain heeling moment in tonne metres and lambda 0.
- Explain why the grain heeling moment is applied as a heeling arm rather than as a virtual rise of G, and state what would go wrong if a candidate treated it as a rise of G.
- State the three criteria of the Grain Code, and state which of them is stricter than the corresponding requirement of the 2008 Intact Stability Code.
- Using the maximum permissible heeling moment table, state the largest grain heeling moment MV Ninja may carry at a displacement of 24000 t and a fluid KG of 8.50 m, and calculate the largest total volumetric heeling moment this represents for a cargo stowing at 1.35 cubic metres per tonne.
- A hold is to be left partly filled. Explain why filling it to seventy per cent is very much safer than filling it to forty five per cent, and sketch the shape of the heeling moment against filling level.
- In worked example 3.2 the fluid KG improved and the GM rose, yet the ship was refused. Explain this apparent contradiction.
- The residual area is measured to the least of three angles. Name them, and state which one governed in both worked examples of this chapter.
- A ship without a document of authorization is offered a bulk grain cargo. State what the master must establish before he can accept it, and where he would look for the requirements.
Looking ahead
Chapter 2 drew a heeling lever from the wind. This chapter drew one from the cargo. Chapter 4 draws both at once. Timber carried on deck adds windage in the way the weather criterion cares about, absorbs water and gains weight in the way that no other cargo does, and at the same time may be counted as reserve buoyancy, which is the only case in this volume where a deck cargo helps the stability rather than harming it. It also brings its own set of load lines, marked higher on the ship’s side than the ordinary ones, and a separate set of stability criteria to earn them.