NATARAJATankers, grain & timber — cargoes with laws of their own
Learning outcomes & permitted supports
- Run the tanker's custody chain: ullage → observed volume → VCF to 15 °C → tonnes, and say which step the cargo claim usually hides in
- Apply the 98% rule as physics: thermal expansion needs headspace, and 2% is what a 25 °C warming would take
- Estimate loading time from parcel and rate — and say why topping off breaks the estimate honestly
- Work the grain shift: GG′ = w·d/W, list from tan(list) = GG′/GM, the Grain Code's 12° test, and what shifting boards buy
- Explain the timber load line: why lashed deck timber EARNS deeper loading, and what absorbed water does to KG on passage
Supports in this lab: Calculator. VCF is the stated linear teaching model (1 − α(T−15)) — aboard, the printed ASTM/API tables govern; the grain list is the shifted-tonnage physics beneath the volumetric tables. Golden 878/878 (tanker chain closes to machine precision).
Glossary: ullage · VCF · angle of repose · timber load line · stowage factor · free surface
The tanker's chain: ullage → volume → 15 °C → tonnes
Oil is bought by the tonne but measured by the metre. The tape drops from the deck to the surface — the ullage — and everything else is arithmetic: volume from the tank tables (here an honest rectangle), then the volume correction factor shrinks warm cubic metres to the standard 15 °C before the density can turn them into tonnes. VCF = 1 − α(T − 15) is the physics the printed ASTM 54B tables encode; aboard, the tables govern.
| Observed volume V = l·b·(depth − ullage) | 10152.0 m³ |
|---|---|
| VCF to 15 °C = 1 − α(T − 15) | 0.9864 |
| Cargo = V · VCF · ρ₁₅ | 8612.0 t |
| Loading time at the rate | 5.6 h |
The 98% rule drawn on the tank: minimum ullage 0.40 m for this 20 m tank. The last metres slow to a crawl anyway — topping off is done with the valves half-shut and the tape in your hand, so the 5.6 h above is the pump's promise, not the mate's.
Grain — the cargo that flows uphill when you roll
A full, trimmed hold leaves grain nowhere to go. Leave a slack surface and a roll can shift it; the pile does not come back. The regulation's currency is volumetric heeling moments from the grain booklet; underneath sits exactly this: shifted tonnage w at lever d moves G by GG′ = w·d/W, and the list follows tan(list) = GG′/GM. The angle of repose (~23° for wheat) is how steep the pile stands before it slides; shifting boards cut the lever d in half — watch what that alone does to the list.
| GG′ = w·d/W | 0.113 m |
|---|---|
| List = atan(GG′/GM) | 10.6° |
| With shifting boards (lever d/2) | 5.4° |
The Grain Code's shape in these sliders: list under the assumed shift ≤ 12° (and residual dynamic stability besides). This one passes the 12° test as loaded.
Timber — the load line that lets her sink deeper
The timber marks (L-prefixed: LS, LW, LT…) permit less freeboard than the plain marks — the one load line that says "load her deeper". The bargain: a properly stowed, properly lashed timber deck cargo is itself reserve buoyancy, sealing the deck like a raft. The price is paid aloft: timber soaks up water on passage — weight added high, KG creeping up, GM quietly going.
| Absorbed water, carried up high | 80 t at Kg 11.5 m |
|---|---|
| KG after loading + absorption | 7.58 m |
| GM remaining at arrival | 0.52 m |
Ship: W 9000 t, KG 7.20 m, KM 8.10 m; deck cargo at Kg 11.5 m. Rule-of-thumb aboard: allow up to ~15% of the timber's weight in absorbed water when proving departure GM will still serve at arrival — the code asks the arrival condition, not the hopeful one.