NATARAJABilging & the damaged ship
Learning outcomes & permitted supports
- Apply the lost-buoyancy method: displacement and KG unchanged, buoyancy and waterplane lost
- Find the new draft after bilging, with permeability, from volume conservation rather than a first guess
- Show why BM (and usually GM) falls when the waterplane loses a slice
- Work the drafts fore and aft after an end compartment floods, about the new centre of flotation
- Find the list after side damage from BB′ and the damaged GM — and state where that small-angle step stops being safe
- Reason about counter-flooding as a trade, not a reflex
Supports in this lab: Calculator. Lost-buoyancy method on box-form geometry; every figure produced twice by independent routes. Damage-stability regulations and the ship's damage-control plan govern aboard. Engine golden-validated 840/840.
Where is the hole?
The same hole in three different places gives three completely different casualties. Pick one, then push the permeability up and watch how much of the answer it owns.
| Lost waterplane | 144 m² of 2000 m² — intact 1856 m² |
|---|---|
| Draft before → after | 7.00 m → 7.543 m (sinkage 0.543 m) |
| KB · BM · KM after | 3.77 · 4.42 · 8.19 m |
| GM before → after | 2.262 m → 2.191 m |
| Displacement | 14350 t — unchanged, and so is KG |
Notice what did NOT change: her weight and her KG. Nothing was loaded — she simply lost the buoyancy that compartment used to provide, so she sinks until the intact volume makes it up. BM falls because the waterplane lost its middle; that, not the sinkage, is what usually bites.
Permeability — the number that decides how bad it is
Permeability μ is the share of the compartment the sea can actually occupy. An empty tank is nearly all sea; a hold packed with cargo is much less. It scales the lost waterplane and the lost buoyancy together, which is why the same hole in a full hold and an empty one are different casualties.
| space | μ (typical) | draft after this hole |
|---|---|---|
| Store room | 60% | 7.543 m |
| General cargo hold | 60% | 7.543 m |
| Machinery space | 85% | 7.795 m |
| Accommodation | 95% | 7.901 m |
| Empty tank / void | 95% | 7.901 m |