Ship Stability and Trim
Stability questions move quickly from definitions to numbers. You must be able to compute GM, apply free surface correction, take a GZ value off a curve, check the IMO intact stability criteria and work out a list or a trim change. The examiner also expects you to recognise angle of loll and to know when damage stability requires a different booklet.
Definitions and formulae
- KB + BM = KM, where BM = I / V.
- GM = KM − KG; GM fluid = GM solid − FSC, where FSC = FSM / displacement.
- GZ = GM x sin(theta) for small angles only; beyond about 10° to 15° use the GZ curve.
- Trim change = (w x d) / MCTC, with the trimming moment taken about the LCF.
IMO intact stability criteria (2008 IS Code)
- Area under GZ curve 0°–30°: at least 0.055 m·rad.
- Area 0°–40°: at least 0.090 m·rad; area 30°–40°: at least 0.030 m·rad.
- GZ at 30°: at least 0.20 m; angle of maximum GZ at least 25°.
- Initial GM: at least 0.15 m.
- Weather criterion must also be satisfied.
Worked example - list from a transverse shift
80 t shifted 6 m to starboard. Displacement 9,000 t, GM fluid 0.45 m. Heeling moment = 80 x 6 = 480 t·m. Righting moment per degree of heel = displacement x GM = 9,000 x 0.45 = 4,050 t·m per radian. tan(theta) = 480 / 4,050 = 0.1185, so theta = 6.8° to starboard. Check that the deck edge is not immersed at 6.8° and that the residual freeboard is acceptable; if the GM were smaller, the same shift would produce a much larger heel.
Loll and free surface
Angle of loll occurs with negative initial GM: the ship lies at an angle either side of upright. Correct it by lowering weights, filling low centre tanks, and removing free surfaces - never by a large shift that could flop the ship to the other side.
Traps that cost marks
- Quoting GM solid where GM fluid is required; FSC is in metres, FSM in tonne-metres.
- Using GZ = GM sin(theta) at 40°.
- Forgetting that KM changes with draft when ballast is taken.
- Confusing list (G off centreline) with loll (negative GM).