Roll period versus loading computer: which GM governs the sailing decision?
M/V Corrie Star, a 9,000 dwt general cargo ship of 16.0 m breadth, is completing cargo work at a river berth. Displacement on completion is 8,000 t and the loading computer, which has not been updated since the ballast plan was changed, gives KM 8.00 m and a solid GM of 0.95 m for that displacement. No.2 port and No.2 starboard double-bottom ballast tanks will be slack at sailing, with a combined free surface moment of 2,500 t·m at the planned filling; they must stay slack because the ship has to lower her air draught for a bridge on the river transit. In the evening, moored in still water with no tugs alongside, the chief officer times ten complete rolls and records 140 seconds. The approved stability booklet, when checked against the actual tank contents, gives a solid GM of 1.00 m. The forecast for the river and the coastal passage is north-west force 7 with a 2 m swell.
1. Derive the GM from the roll period, apply the free surface correction correctly, and reconcile the three figures.
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From the roll period
Using the standard approximate relation GM = (0.8 × B / T)², with B = 16.0 m and T = 140/10 = 14.0 s:
- 0.8 × 16.0 = 12.8
- GM = (12.8 / 14.0)² = (0.9143)² = 0.84 m
The subtlety: the roll was measured with No.2 tanks slack, so 0.84 m is the effective (fluid) GM - the free surface effect is already inside the measurement. Adding the free surface correction to it would double-count.
- FSC = 2,500 ÷ 8,000 = 0.31 m
- Solid GM implied by the roll test = 0.84 + 0.31 = 1.15 m
Reconciliation
- Roll test: solid GM 1.15 m
- Approved booklet with correct tank contents: solid GM 1.00 m
- Loading computer (stale ballast data): solid GM 0.95 m
So the roll test reads about 0.15 m high relative to the booklet, which is within the normal scatter of the empirical roll formula (the coefficient and the assumed radius of gyration are approximations, and added mass and shallow water bias the period). The governing figure must be the lowest credible one, the booklet value of 1.00 m solid, giving an effective GM in service of 1.00 − 0.31 = 0.69 m. The loading computer must be re-run with the actual tank contents before any decision.
2. Assess the ship against the intact stability criteria and decide whether to sail.
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Criteria check (IS Code 2008, Part A, as applied to this ship type)
- Initial GM ≥ 0.15 m: 0.69 m effective, 1.00 m solid - passes comfortably.
- Area under the GZ curve to 30° ≥ 0.055 m·rad, to 40° ≥ 0.09 m·rad, between 30° and 40° ≥ 0.03 m·rad - cannot be confirmed from GM alone; the approved GZ curve for the actual condition must be checked.
- GZ ≥ 0.20 m at 30°, and maximum GZ occurring at not less than 25° (relaxable to 15° in some cases) - again, the curve, not the GM, decides.
- Severe wind and rolling (weather) criterion: with a shallow-draught general cargo ship and a 2 m swell plus force 7 forecast, the heeling lever from a beam gust must be checked against the righting lever.
Decision
Do not sail until the loading computer has been re-run with the actual ballast distribution and the resulting condition checked against the approved GZ curve and the weather criterion. Every indicator is above the bare minimum, so the statutory criteria are unlikely to fail, but there are two live concerns:
- A stiff ship. GM around 1.0 m on a 16 m beam gives a short, snappy roll, high lateral accelerations and heavy racking loads; with a force 7 beam sea the lashings and any deck cargo will be worked hard. The master should reduce GM where possible (press up the double-bottom tanks after the bridge, or accept a lower GM by ballasting high) and consider a weather routeing or delay decision.
- The stale loading computer. A ship should never sail on a condition computed with the wrong tank contents. The discrepancy between 0.95 and 1.15 m is not itself alarming, but it proves the input data were wrong.
Sailing is acceptable only after the condition is reconciled, the GZ curve checked, lashings verified and the forecast reviewed by the master.
3. After the bridge the double-bottom tanks will be pressed up one at a time. Explain the effect on stability during and after this operation, and the associated hazards.
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During filling
A tank being filled passes through partially filled stages, so the free surface moment rises from zero to a maximum before falling back to zero when the tank is pressed up. If the port tank is filled first, the ship takes a transient list to port and the effective GM dips before recovering. Filling both tanks simultaneously, or in small alternating steps, keeps the list small and the free surface transient short. Always finish one tank completely before starting another where practical, and never leave the operation unattended.
After pressing up
- Free surface from No.2 tanks disappears, so FSC falls by 0.31 m and GM rises by that amount.
- The added weight is low in the ship, which also raises GM because the weight is added below the centre of gravity.
- Net effect: the ship becomes noticeably stiffer, the roll period shortens, lateral accelerations rise sharply and the ride becomes uncomfortable.
Hazards to manage
- The ship becomes stiffer just when the weather is worsening; crew comfort and lashing loads worsen even though the GM number looks better.
- Draught and trim change - check under-keel clearance in the river, and remember that the air-draught benefit is only obtained while the tanks remain full.
- A rapid GM change alters the GZ curve shape; the condition must be re-checked in the loading computer at the start and end of the operation, not assumed.
- Watch for slack tanks left half-full at the end of the transfer, which is the worst of both worlds.
The correct sequence is: pass the bridge, then press up, then re-run the stability condition, verify the lashings for the stiffer ship, and only then enter the coastal passage.