NATARAJAShip stability — the upright ship
Learning outcomes & permitted supports
- Read the midship section like an instrument: K, B, M, G — and why GM = KM − KG is the metre that decides everything
- Correct GM for free surface (i·ρ/W) and say why a bulkhead quarters the correction
- Compute list from a transverse shift and trim from a longitudinal one — the same moment on two axes
- Use TPC, FWA and DWA to load to the marks in any dock water
- Sketch the GZ curve and its GM tangent; state what the wall-sided formula assumes
Supports in this lab: Calculator. Hydrostatics here are the exact box-form values; ship's-form hydrostatic tables arrive with Stability II. Engine golden-validated 698/698.
K · B · M · G — and the metre that rules them all
Box-form vessel, 130 m long. KB = draft/2 = 3.50 m; BM = B²/12d = 4.76 m; KM = 8.26 m. Your loading puts G at KG 7.50 m, so GM = KM − KG = 0.76 m. Displacement 18655.0 t. State: STABLE — M above G.
| KB · BM · KM | 3.50 · 4.76 · 8.26 m |
|---|---|
| GM solid | 0.76 m |
| GZ at 6.0° (wall-sided) | 0.08 m |
| Righting moment | 1537.0 t·m |
The GZ curve — righting arm against heel
Wall-sided regime (0–20°): GZ = (GM + ½·BM·tan²θ)·sinθ. At small angles the curve leaves the origin with slope GM — which is why the examiner's construction erects GM as a vertical at 57.3° and draws the tangent. Push KG up and watch the whole curve sag; open the slack tank and the sag is invisible weight — the free surface.
The engine's wall-sided values are golden-verified against a 4000-strip numeric integration of the heeled section — worst disagreement 6.5×10⁻⁸ m.
List and trim — the same moment, two axes
Shift 60 t across the deck by 8 m: GG′ = w·d/W = 0.026 m, and tan(list) = GG′/GM → list 1.2°. The identical logic turned 90° is trim: 120 t moved 35 m aft is a moment of 4200.0 t·m against MCTC 283.7 t·m/cm → change of trim 14.8 cm by the stern, drafts F 6.93 m / A 7.07 m.
| GG′ → list | 0.026 m → 1.2° |
|---|---|
| Moment check (engine closure) | 480.0 ≡ 480.0 t·m |
| MCTC · trim | 283.7 t·m/cm · 14.8 cm |
| Drafts F / A | 6.93 / 7.07 m |