NATARAJATrim, loading & the marks
Learning outcomes & permitted supports
- Keep the loading table honestly: every weight changes W, KG and the trim moment at once
- Find final drafts F and A after any sequence of loads, discharges and shifts (moments about the centre of flotation)
- Run the inclining experiment: pendulum reading → tanθ → GM → light-ship KG
- Load to the marks in any dock water with FWA and DWA
- State when a loading makes the ship unstable before the water does
Supports in this lab: Calculator. Box-form hydrostatics (exact); ship's-form tables arrive with Stability III. Engine golden-validated 840/840.
The loading table — every weight is three moments
Ship 140 × 21 m, sailing condition 19588 t at KG 7.8 m, even keel 6.50 m. Each weight you load changes W (drafts), KG (stability) and the trim moment (attitude) — the exam's loading problems are just this table kept honestly.
| Operation | w (t) | Kg (m) | lcg from ⊗ (m, +fwd) | |
|---|---|---|---|---|
| Bunker (No.3 DB) | 250 | 0.9 | -12 | |
| Cargo, tween deck | 400 | 9.2 | 18 |
| Final W · mean draft | 20238 t · 6.72 m |
|---|---|
| Final KG (moments about keel) | 7.742 m |
| GM at the new draft | 1.09 m |
| Trim moment · MCTC | 4200 t·m fwd± · 345.2 t·m/cm |
| Change of trim | 12.2 cm by the head |
| Drafts F / A | 6.78 / 6.65 m |
The inclining experiment — weighing GM itself
Move a known weight a known distance across the deck of the light ship; read the heel on a long pendulum. GM = w·d / (W·tanθ) — with tanθ = deflection / plumb length. Here the true GM is 0.85 m; the pendulum deflects 11.9 cm on 8 m, and the formula hands back 0.850 m — the closure the golden suite holds to 10⁻¹² m. From GM and the known KM the yard reads off the light-ship KG, the number every later loading sum stands on.
| tan θ · heel | 0.01486 · 0.85° |
|---|---|
| Pendulum deflection | 11.9 cm on 8 m |
| GM recovered | 0.850 m ≡ 0.850 m |
Loading to the marks — FWA and the dock water
At W 20238 t the FWA is 168 mm; in dock water of 1012 kg/m³ you may submerge the load line by DWA 87 mm — the ship rises exactly that much reaching salt water. (Engine-proved exact, not an approximation.)
| FWA · DWA | 168 · 87 mm |
|---|