Free Surface Effect (FSE) Stability Loss Calculator
Calculate free surface correction, loss of GM, corrected GM, and virtual rise of G caused by slack liquid tanks. Use either a known free surface moment or rectangular tank dimensions.
Free Surface Effect Result
What is free surface effect?
Free surface effect occurs when liquid in a partially filled, or slack, tank moves as the vessel heels. The shifting liquid produces a virtual rise in the vessel's center of gravity and reduces effective GM. :contentReference[oaicite:0]{index=0}
Free Surface Effect Formula
When the free surface moment is already known from tank tables:
$$FSC = \frac{\sum FSM}{\Delta}$$
$$GM_{corrected} = GM - FSC$$
The correction is in meters when FSM is in tonne-meters and displacement is in tonnes. :contentReference[oaicite:1]{index=1}
How do you calculate free surface moment for a rectangular tank?
For a simple rectangular free surface:
$$I = \frac{L B^3}{12}$$
$$FSM = \rho I$$
$$FSM = \rho \frac{L B^3}{12}$$
L is the length of the free surface, B is its breadth, and ρ is liquid density in tonnes per cubic meter. The breadth is cubed, so tank breadth has a particularly strong effect on free surface moment. :contentReference[oaicite:2]{index=2}
Free Surface Effect Example
Suppose a vessel has a free surface moment of 1,250 t·m, displacement of 25,000 tonnes, and an original GM of 1.10 m.
$$FSC = \frac{1250}{25000} = 0.05\ m$$
$$GM_{corrected} = 1.10 - 0.05 = 1.05\ m$$
The free surface therefore reduces GM by 0.05 m, leaving a corrected GM of 1.05 m. :contentReference[oaicite:3]{index=3}
How do multiple slack tanks affect stability?
The free surface moments of the relevant slack tanks are added:
$$FSM_{total} = FSM_1 + FSM_2 + FSM_3 + \cdots$$
$$FSC = \frac{FSM_{total}}{\Delta}$$
This is why ballast, fuel, freshwater, and other partially filled tanks need to be considered in the relevant loading condition. :contentReference[oaicite:4]{index=4}
How does free surface effect change KG?
The correction can also be represented as a virtual rise in the vessel's center of gravity:
$$KG_{corrected} = KG + FSC$$
The corrected KG then produces the same reduction in GM:
$$GM_{corrected} = KM - KG_{corrected}$$
Why are wide tanks more affected by free surface effect?
For a rectangular tank, FSM contains B³. This means that increasing tank breadth has a much larger effect than making the tank slightly longer. Longitudinal subdivisions can substantially reduce the free-surface moment because they reduce the breadth of each individual free surface. :contentReference[oaicite:5]{index=5}
Does a full tank have free surface effect?
A tank that is completely pressed up and has no free surface normally does not receive the same free-surface correction. The important condition is a liquid surface that can shift as the vessel heels. :contentReference[oaicite:6]{index=6}
FSE Stability Loss Chart
For a vessel with 25,000 tonnes displacement, the table below shows how different total FSM values change GM.
| Total FSM | GM Loss | Original GM 1.50 m | Corrected GM |
|---|---|---|---|
| 500 t·m | 0.020 m | 1.500 m | 1.480 m |
| 1,000 t·m | 0.040 m | 1.500 m | 1.460 m |
| 1,500 t·m | 0.060 m | 1.500 m | 1.440 m |
| 2,000 t·m | 0.080 m | 1.500 m | 1.420 m |
| 2,500 t·m | 0.100 m | 1.500 m | 1.400 m |
| 5,000 t·m | 0.200 m | 1.500 m | 1.300 m |
What is free surface correction?
Free surface correction (FSC) is the amount that must be deducted from uncorrected GM to account for the stability loss caused by free liquid surfaces.
$$FSC = \frac{\sum FSM}{\Delta}$$
What happens if corrected GM becomes very small?
As free surface correction increases, effective GM decreases. A sufficiently large correction can materially reduce the vessel's stability margin. Stability limits should therefore be assessed using the vessel's approved stability information and applicable requirements rather than a generic calculator alone. :contentReference[oaicite:7]{index=7}
Free Surface Effect FAQ
The usual correction is FSC = ΣFSM ÷ displacement, and corrected GM = original GM − FSC.
FSM is free surface moment. It represents the moment generated by the transverse movement of liquid on a slack tank's free surface.
Yes. The free surface correction is subtracted from the uncorrected GM.
It can be represented as a virtual rise of KG by the amount of the free surface correction.
Slack liquid tanks with a movable free surface are the primary concern. Relevant fuel, ballast, freshwater, and service tanks should be considered for the loading condition being assessed.
For a rectangular free surface, FSM = ρLB³/12. For actual vessel tanks, FSM is normally obtained from tank tables or hydrostatic stability data.