Calculate the reduction in initial GM from a direct total free-surface moment or unrestricted rectangular tank geometry.
Use approved vessel FSM data for irregular, baffled or fill-level-dependent tanks.
Total ΣFSM: — t·m
Initial GM Correction FSC: — m
FSC is equivalent to a virtual rise of G and is subtracted from the uncorrected initial GM.
GMcorrected = GMuncorrected − FSC. This calculator does not contain a GM input, so it does not output corrected GM directly.
A liquid in a partly filled tank can move transversely when a vessel heels. The moving liquid shifts the combined centre of gravity toward the low side and reduces the vessel’s initial restoring tendency. This reduction is represented by the Free Surface Correction (FSC).
FSC is commonly treated as either a virtual rise of the ship’s centre of gravity or an equivalent reduction in initial transverse metacentric height. The numerical correction is the same in both descriptions.
A tank’s free-surface effect is first expressed as a free surface moment. When several relevant tanks are present, their density-adjusted moments are added before division by the vessel displacement.
When ΣFSM is entered in t·m and displacement Δ is entered in tonnes, the resulting FSC is in metres.
These are two equivalent ways of applying the same initial-stability correction. FSC must not be added to GM. It is either subtracted from GM or added to KG.
Direct mode should be used when the total density-adjusted free surface moment is already available from:
Do not multiply a supplied FSM value by density again when that value is already expressed in t·m. Density has already been included in that unit.
For a tank with parallel vertical sides and an unrestricted rectangular free surface, the transverse second moment of free-surface area is:
The breadth is raised to the third power. An error in the transverse free-surface breadth can therefore have a large effect on the calculated moment.
The builder uses one density for all entered rows. For tanks containing different liquids, calculate each liquid group separately or enter the final density-adjusted total through Direct ΣFSM mode.
No generic baffle or swash reduction multiplier is applied. Such a multiplier cannot represent every subdivision, opening arrangement or approved tank correction. Use ship-specific density-adjusted FSM data in Direct mode when unrestricted rectangular geometry does not apply.
| Symbol | Meaning | Unit |
|---|---|---|
| Δ | Vessel displacement mass | t |
| L | Free-surface length | m |
| B | Transverse free-surface breadth | m |
| IT | Transverse second moment of free-surface area | m4 |
| ρ | Liquid density | t/m3 |
| FSM | Density-adjusted free surface moment | t·m |
| ΣFSM | Total free surface moment for relevant tanks | t·m |
| FSC | Initial free surface correction | m |
| GM | Initial transverse metacentric height | m |
| KG | Vertical centre of gravity above keel | m |
A vessel has:
IT,1 = 20 × 83 / 12 = 853.333 m⁴
FSM1 = 1.025 × 853.333 = 874.667 t·m
IT,2 = 15 × 63 / 12 = 270.000 m⁴
FSM2 = 1.025 × 270.000 = 276.750 t·m
IT,3 = 10 × 43 / 12 = 53.333 m⁴
FSM3 = 1.025 × 53.333 = 54.667 t·m
ΣFSM = 874.667 + 276.750 + 54.667 = 1,206.083 t·m
FSC = 1,206.083 / 12,500 = 0.09649 m
If the uncorrected initial GM were 0.800 m:
GMcorrected = 0.800 − 0.09649 = 0.70351 m
The worked-example builder result can be checked in Direct mode by entering:
Both methods should return approximately FSC = 0.09649 m. The Copy ΣFSM button transfers the raw builder total to Direct mode so that the two routes can be compared without retyping a locale-formatted number.
A larger FSC produces a larger reduction in corrected initial GM. The significance of a given correction depends on the vessel’s uncorrected GM and approved stability limits. An FSC of 0.10 m may be a modest proportion of one vessel’s GM but a substantial proportion of another vessel’s GM.
FSC alone does not show whether the vessel satisfies intact-stability criteria. The corrected GM must be considered with the vessel’s approved limits, loading condition, downflooding points and righting-lever characteristics.
Free-surface treatment depends on tank filling level, tank purpose and the stability rules applicable to the vessel. International intact stability guidance distinguishes tanks with fixed filling levels from tanks whose filling levels vary during service or liquid-transfer operations.
Do not replace approved tank FSM tables with a generic empty, slack or full assumption. Nominally full cargo tanks, residual liquid, small tanks and transitory filling stages can require specific treatment under the applicable stability documentation.
For variable consumable tanks, the approved correction may represent the maximum effect expected between operating filling limits rather than the correction at one arbitrarily selected sounding.
Dividing total FSM by displacement gives an initial-stability correction. At larger heel angles, the shape of the liquid surface and the actual transfer of liquid can change. A complete GZ correction may therefore use:
This calculator does not perform those finite-angle calculations.
This calculator is intended for preliminary engineering and educational checks. It does not replace an approved stability booklet, loading computer, tank-capacity plan, Administration requirement or classification review.