Ship Stability and Ship Construction
What the stability paper tests
This paper tests hydrostatics you can apply under time pressure: GM from KM and KG, free surface correction, interpretation of the GZ curve against the IMO intact stability criteria, and the structural members that keep those figures meaningful.
Core rules
- GM = KM - KG. Positive GM means the ship returns upright. The righting lever GZ = GM x sin(theta) holds only at small angles; beyond that you must read GZ from the curve.
- Free surface correction FSC = total free surface moment / displacement. It always reduces effective GM, no matter where the tank sits vertically.
- IMO intact stability criteria (2008 IS Code): area under the GZ curve to 30 degrees at least 0.055 m.rad; to 40 degrees at least 0.09 m.rad; between 30 and 40 degrees at least 0.03 m.rad; maximum GZ at least 0.20 m occurring at not less than 30 degrees; initial GM at least 0.15 m.
- Construction: transverse frames with longitudinal stiffeners suit tankers and bulkers; the collision bulkhead is placed at least 0.05L or 10 m from the forward perpendicular, whichever is less, and not closer than 0.05L.
Worked example
Displacement 8,000 t, KM 8.00 m, KG 6.50 m. Solid GM = 1.50 m. A slack tank has free surface moment 4,000 t.m: FSC = 4,000 / 8,000 = 0.50 m. Fluid GM = 1.00 m. Still legal, but the GZ curve flattens and maximum GZ drops, so the margin to the criteria is smaller than the solid figure suggests.
Traps that cost marks
- Mixing KM, the height of the metacentre above the keel, with GM.
- Assuming a low tank has no free surface effect: the moment depends on the tank waterplane, not its height.
- Confusing list (off-centre weight, zero GZ upright) with loll (negative GM, unstable equilibrium).
- Quoting maximum GZ without the angle at which it occurs.