Free Surface Effect During Deballasting in a Low-GM Condition
A 12,000 t displacement general cargo ship has KM 7.20 m and KG (solid) 6.90 m. She is completing discharge at a river berth and the chief engineer is asked to deballast No.2 double bottom centre tank, which is 20 m long and 12 m wide, to lighten ship for the tide. The tank is now slack at 60% and no other tank is partly filled. The ballast pump is rated at 150 m³/h and the tide window closes in three hours. The chief mate reports that the ship feels tender, with a long sluggish roll. The stability booklet sets a minimum GM of 0.15 m for the voyage. The second engineer proposes to run the deballasting during the berthing manoeuvre with the pilot on board, and to correct a small list by transferring ballast from No.2 port to No.2 starboard wing tank.
1. Calculate the fluid GM with the tank slack, and decide whether the ship meets the 0.15 m criterion. Show your working.
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Step 1 - solid GM.
GM(solid) = KM – KG = 7.20 – 6.90 = 0.30 m
Step 2 - free surface moment of the slack tank.
For a rectangular tank the free surface inertia about the centreline is
i = l × b³ / 12 = 20 × 12³ / 12 = 20 × 144 = 2,880 m⁴
(Only the transverse moment matters; the longitudinal moment affects trim, not GM.)
Step 3 - free surface correction.
FSC = ρ × i / Δ = 1.025 × 2,880 / 12,000 = 0.246 m
Step 4 - fluid GM.
GM(fluid) = 0.30 – 0.246 = 0.054 m
Conclusion: the ship does not meet the 0.15 m minimum. She is about 0.10 m short and the margin is gone.
The free surface correction has consumed 82% of the solid GM - this is not a trim detail. Note that the correction depends on the breadth cubed and not on how much liquid the tank contains: a tank at 60% fill has the same free surface as one at 20%, which is why a slack tank is far more dangerous than the sounding suggests. The mate's report of a long sluggish roll is consistent with a very small metacentric height, and if the free surface were any larger the GM would go negative and the ship would loll to one side with no stable upright.
2. What immediate action do you take, and what is the sequence of operations for the next three hours?
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- Do not start the deballasting and do not sail in this condition. With 0.054 m GM the ship is outside her own stability booklet limit. Tell the master and the chief officer in writing, and ask for the ballast plan and the loading computer result before any valve is opened.
- Remove the free surface first. The fastest route is to press No.2 centre tank up to full: a full tank has no free surface, so the correction goes to zero and the GM returns to 0.30 m. Check the load line, hull stress and the tank filling limits before doing it. If pressing up is impossible because of stress or overflow limits, empty the tank completely and quickly instead - full or empty is safe, slack is not.
- Keep only one slack tank at a time. Do not accept the transfer from No.2 port to No.2 starboard to correct the list: that creates two slack tanks simultaneously. Correct the list by filling or emptying one tank at a time, preferring a tank whose free surface is small transversely, and recheck the GM on the loading computer after each step.
- Do it before the manoeuvre, not during it. Finish the ballast work and record the final condition before the tugs are made fast; a 150 m³/h pump leaves ample time inside three hours.
- Verify at every step on the loading computer and record the GM, list and draughts in the ballast record and the deck log. Tell the master when the condition meets the 0.15 m minimum with a sensible margin, not exactly at the limit.
3. Explain the operational risk of this condition and what you would record and report.
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Risk with a GM of about 0.05 m:
- The righting energy is very small and the maximum righting lever occurs at a small angle, so a beam wind, a passing ship's wash or a small load shift can carry her past the angle of vanishing stability or leave her lolled to one side.
- The roll period is long. In a following or beam sea whose encounter period approaches the roll period, the ship can develop synchronous or parametric rolling with large amplitudes, and a small-GM ship has no reserve righting moment to check it.
- Cargo shift and lashing failure risk rises sharply, and any list created by a transverse transfer is harder to correct.
- Free surface changes continuously as the tank is pumped. The GM at the start of the operation is not the GM half an hour later; it is worst at part fill, which is exactly when the pump is running and nobody is recalculating.
Record and report: the calculated GM, the FSC and the i value used, the initial and final soundings of every tank touched, the loading computer printout, the time of each operation, and a note that the operation was stopped until the free surface was removed. Raise an SMS observation that a partly filled double bottom tank was allowed to persist into a low-GM departure condition, and review the ballast plan approval process with the chief officer so that the next plan is checked for free surface before it reaches the engine room.