Question 1

Your examiner asks: "What is the free surface effect and how does it affect GM?" Explain the formula and identify which tanks are most critical.

Accepted Answer

Free surface effect (FSE) is the virtual rise of the centre of gravity caused by liquid moving in a slack tank when the ship heels. The correction to GM is: GG1 = (i x rho_l) / (V x rho_s) where i = second moment of area of the free surface, rho_l = density of liquid in tank, V = volume of displacement, rho_s = density of salt water. Tanks with large surface areas (wide tanks) and tanks containing heavy liquids (fuel oil > fresh water > ballast) have the greatest FSE. Filling a tank to 100% or emptying it to 0% eliminates FSE. FSE reduces the effective GM by a virtual rise in G. The key formula variable is the second moment of area (i) of the free surface — this varies as the CUBE of the breadth of the tank, so wide tanks have a disproportionately large FSE. Density of the liquid matters: fuel oil (RD ~0.85) has a smaller FSE correction than ballast water (RD 1.025) of the same tank dimensions (because rho_l/rho_s is smaller for fuel). Examiners often ask: "which has more FSE — a tank 90% full or 50% full?" Answer: both have FSE determined by the free surface area. A 50% tank may have the same breadth of free surface as a 90% tank, so FSE may be similar. Only 100% or 0% full eliminates FSE entirely.

Question 2

Your examiner asks: "What is GM, what does a positive GM indicate, and what are the dangers of a very high or very low GM?" Give a complete OOW answer.

Accepted Answer

GM (metacentric height) is the distance between the centre of gravity (G) and the metacentre (M). A positive GM (M above G) indicates stable equilibrium — the vessel will right itself when heeled. A very low GM risks loll, slow period of roll, and potential capsize. A very high GM (stiff ship) causes a rapid, violent rolling motion that can create excessive dynamic loads on cargo, structures, and crew — which can be as dangerous as low stability. GM = KM - KG (metacentric height = height of metacentre above keel minus height of centre of gravity above keel). Positive GM: G below M — vessel returns to upright after heeling (initial stability). Zero GM: neutral equilibrium. Negative GM: G above M — vessel is in loll. The "stiff vs tender" concept is critical at OOW orals: a stiff ship (very high GM) has a very short rolling period, creates high accelerations, and can cause cargo shift and structural damage. A tender ship (low positive GM) rolls slowly and may approach the limits of the GZ curve. Examiners often ask "why is a very stiff ship dangerous?" to test this understanding.

Question 3

Your examiner shows you a GZ curve and asks you to name the key features and state the IMO IS Code 2008 minimum stability criteria for a cargo vessel.

Accepted Answer

Key GZ curve features: range of stability (angle at which GZ returns to zero); maximum GZ and angle of maximum GZ; area under the curve (dynamical stability). IMO IS Code 2008 criteria: area 0-30 degrees minimum 0.055 metre-radians; area 0-40 degrees (or to flooding angle if less than 40) minimum 0.090 metre-radians; area 30-40 degrees minimum 0.030 metre-radians; maximum GZ at least 0.200 metres at 30 degrees or greater; initial GM not less than 0.150 metres. IMO Resolution MSC.267(85) (IS Code 2008, Chapter 2.2): the five weather criterion and five area/GZ criteria must all be satisfied simultaneously. The five criteria frequently examined: (1) area 0-30: 0.055 m.rad; (2) area 0-40: 0.090 m.rad; (3) area 30-40: 0.030 m.rad; (4) max GZ at 30 degrees or more, at least 0.200m; (5) GM0 not less than 0.15m. Candidates should know all five values precisely as examiners ask them directly. The weather criterion (criterion 6 in the IS Code) relates to the ability to withstand a beam wind and rolling — assessed separately. The IS Code 2008 replaced the earlier 1985 IMO guidance and applies to new vessels; flag states have transition arrangements for existing vessels.