Question 1

Your 280 GT near-coastal coaster has four cargo holds partially filled with liquid cargo, and the fuel oil service tank is at 60% capacity. Explain free surface effect and how it affects your GM.

Accepted Answer

FREE SURFACE EFFECT (FSE): when a tank is partially filled with liquid, as the vessel heels, the liquid shifts toward the low side. This transfer of weight adds a heeling moment and effectively reduces the metacentric height. The free surface correction formula: FSE = (ρ_liquid × i) / (ρ_seawater × V), where: i = second moment of area of the tank's free surface about the tank's longitudinal centre line (a function of the tank's SHAPE, not the amount of liquid in it); V = vessel's displacement volume; ρ = density. CRITICAL POINT: FSE depends on the TANK DIMENSIONS (breadth cubed), NOT the amount of liquid in the tank. A wide tank at 5% full has the SAME FSE as at 95% full (the free surface area is approximately the same). In this scenario: four partially-filled cargo holds + 60% fuel service tank = significant combined FSE. EFFECT: GM_effective = GM_solid − Σ(FSE per tank). If total FSE exceeds the calculated solid GM, the vessel has NEGATIVE effective GM. MITIGATION: (1) Fill or empty tanks to eliminate the free surface (a full or empty tank has zero FSE); (2) Use baffles or tight fuel consumption strategy (keep service tanks full or empty); (3) Avoid multiple tanks at partial fill simultaneously; (4) Use the stability booklet FSE data for the actual loading condition. Free surface effect is one of the most misunderstood stability concepts at the OOW and Master oral level. The critical teaching point: FSE depends on the SHAPE of the free surface (breadth cubed), NOT the amount of liquid. This is counter-intuitive — most candidates assume an almost-empty tank (a small depth of liquid) has less FSE than a half-full tank. In fact, a wide shallow free surface gives the same FSE as a wide deep free surface of the same plan area shape. Option C is exactly wrong — this is a classic examiner trap. The practical consequence: a vessel with multiple partially-filled tanks may have a severely reduced effective GM even though the solid GM calculation looks acceptable. The stability booklet must account for FSE using the tabulated correction values for each tank at each stage of fill. Ballast tanks and FSE: it is good practice to either fill ballast tanks completely or pump them out — never leave them at a partial fill without accounting for the FSE in the stability calculation. The breadth cubed relationship: doubling the breadth of a tank quadruples the FSE (because i = L×B³/12 for a rectangular free surface). Wide beam tanks (beam tanks, cross-bunker tanks) are particularly significant — their FSE can be enormous. Some vessels have longitudinal divisions in wide tanks specifically to reduce FSE by halving the effective breadth (reducing i by a factor of 8).

Question 2

Your small coastal vessel (45m LOA) is on passage in moderate seas. You notice she is listing to starboard, doesn't return upright, and appears to "hang" at about 8° to starboard. The list was not present on departure. What do you suspect and what are your immediate actions?

Accepted Answer

ANGLE OF LOLL: this is the classic presentation of negative GM (unstable equilibrium). Cause: the vessel's metacentric height (GM) has become negative — the metacentre (M) is now BELOW the centre of gravity (G). At 0° upright, the vessel has no restoring moment — but as she heels, the waterplane area shifts, moving B outward until a point of neutral equilibrium is found: this is the angle of loll (typically 5°-20°). The vessel "rests" here rather than returning upright. Common causes on a small coastal vessel: (1) Free surface effect from flooded compartments, slack tanks, or water in bilges; (2) Topside icing (raised G); (3) Cargo shift or absorption of water by deck cargo (timber); (4) Consumption of fuel and water from the bottom of tanks without compensating. IDENTIFICATION test: if you push the vessel toward the loll (to starboard) she returns to the loll angle; if you force her past the loll, the GZ curve at higher angles may generate restoring force — she "snaps" back to the loll. EMERGENCY ACTIONS: (1) DO NOT immediately ballast the high side (port) — if she rolls through the loll onto the other side, she may capsize; (2) Check and pump out bilges; (3) Fill double bottom ballast tanks SLOWLY starting with those on the LOW side (starboard) to raise M; (4) Reduce topweight; (5) Call master (if OOW); (6) Alert crew and consider reducing speed. Angle of loll is one of the most dangerous and counter-intuitive stability phenomena — and one of the most commonly tested at MCA orals at all levels. The critical danger: the GZ curve for a vessel with negative GM shows negative righting levers at small angles of heel (between 0° and the loll angle) but may show positive GZ at larger angles. This means the vessel is stable at the loll but would capsize if forced past the angle of loll to the opposite side. If you ballast the PORT side first (trying to push her upright), you are making her roll toward upright through the "negative GZ" zone — and she may not stop there, continuing to roll to port and capsizing. The correct corrective procedure: increase the rise of floor and shift the metacentre upward by ballasting low in the vessel (double bottom tanks), starting on the LOLL SIDE, then distributing the ballast. Simultaneously reduce free surface (pump out bilges, fill slack tanks). Free surface: a partially-filled tank creates a free surface effect that reduces the effective GM. The formula: GM_effective = GM_solid − Σ(i/V) where i = second moment of area of the tank's free surface and V = vessel displacement. At small vessel level, free surfaces in bilges and slack fuel tanks are a significant hazard. On a 45m coastal vessel, water accumulating in the bilges after a period at sea is a genuine risk factor for reduced stability.

Question 3

As master of a 300 GT near-coastal cargo vessel you are about to load. Your stability booklet shows the calculated GM at the proposed loading condition is 0.22m. Your examiner asks whether this is acceptable.

Accepted Answer

IS CODE 2008 (International Code on Intact Stability) — criteria for cargo ships: the IS Code provides mandatory stability criteria for vessels under the 2008 International Code on Intact Stability (made mandatory under SOLAS II-1 and Load Lines). Minimum criteria: (1) AREA under GZ curve from 0° to 30° must be not less than 0.055 metre-radians; (2) Area from 0° to 40° (or flooding angle, whichever is less) not less than 0.09 metre-radians; (3) Area between 30° and 40° (or flooding angle) not less than 0.03 metre-radians; (4) GZ at 30° or greater must be not less than 0.20m; (5) Maximum GZ must occur at an angle of heel not less than 25°; (6) Initial GM (GM_0) must not be less than 0.15m. In this scenario: GM of 0.22m exceeds the minimum 0.15m — it satisfies this criterion. HOWEVER: GM alone does not determine acceptability — you must check ALL the criteria listed above (particularly the GZ curve at 30° and the area criteria). A vessel can have a positive GM but still fail the area criteria if the GZ curve drops too early. The stability booklet must be consulted to verify the full GZ curve for the proposed loading condition. IS Code 2008 stability criteria are mandatory for cargo ships under SOLAS. The criteria are multi-parameter — no single value determines acceptability. The initial metacentric height (GM) minimum of 0.15m is the threshold but the GZ curve criteria are equally important. A vessel with GM 0.22m but a rapidly declining GZ curve that drops below 0.20m before 30° would fail criterion 4 even though GM exceeds the minimum. The stability booklet: every vessel must carry an approved stability booklet that contains: lightship stability data (from the inclining experiment or sister ship data); loading condition calculations; stability criteria verification for the standard conditions. The master must use the booklet to calculate stability at each departure condition. The inclining experiment: establishes the vessel's lightship KG and displacement. Class approves the booklet. The master's responsibility: the IS Code and SOLAS II-1 place the obligation on the master to verify stability before departure. Signing the stability calculation and loading condition form is a legal act. A master who departs knowing the vessel fails stability criteria is criminally negligent. The question's intent: GM of 0.22m tests whether candidates know the minimum (0.15m) AND that they must check further — not just the GM alone.