## Free Surface Effect & Sloshing

Q. Can the water on freeboard deck cause virtual loss of GM?
Ans.Yes, the free surface of liquid on the main deck or any deck will cause free surface effect and hence virtual loss of GM. In fact any movable weight even free moving drums can cause virtual loss of GM.

Q. Will it cause the virtual loss in case of an open floating drydock where the DB or tank top deck is submerged?
Ans.No, it is like vessel rolling through the liquid rather than liquid changing its location athwart-ship on board, in rolling conditions. The liquid on deck of floating dry dock belongs to sea rather than the vessel. The liquid does not exert any weight or has its existence on ship and hence, does not cause any athwartship movement of COG in rolling conditions. For the FSE to be caused, the COG of ship must go to & fro when the ship rolls.

Q. Why the ship’s COG is said to virtually move in upward direction?
Ans. The free surface effect causes virtual rise of COG. Actually, the shift of COG of ship is parallel to the shift of wedge of liquid which travels transversely during rolling of the vessel. The shift is more or less horizontal in athwart ship direction. Still, the shift is considered vertically upwards. COG’s movement parallel to the shift of ‘g’ of the liquid reduces the righting lever (GZ) of the ship at all angles of heel. In the figure the reduced righting lever is G1Z1. Instead if COG had moved vertically upwards to G2, the righting lever would be G2Z2, same as G1Z1. The COG therefore, in spite of shifting athwartships, in effect, is considered to shift upwards. Thus, we may say that net effect of free surface is to reduce the righting lever or reduce the righting capability of the ship.

Q. What is the free surface moment for a tank of rectangular surface area?
Ans. Let there be a tank of length l, breadth b with free surface of liquid. The moment of inertia of the liquid surface about its fore and aft axis passing through centroid of surface is given by; $\dfrac {lb^{3}}{12}$ m3. The free surface moment (FSM) is equal to the product of moment of inertia and density

FSM = $\dfrac {lb^{3}}{12}$ x δtm.

FSC is given by $\dfrac {\dfrac {lb^{3}}{12}\times \delta _{i}}{displacement}$ m.

Q. Is the FSC dependent on the total quantity of liquid within a tank?
Ans. The free surface effect depends upon:

1. The dimensions of the free (moving) surface.

2. The displacement of the vessel.

3. The specific gravity of the movable liquid / material in the compartment. The free surface effect does not depend upon the total amount of liquid in tank.

Q. Why sloshing is dangerous?
Ans.The ballasting / deballasting must be planned carefully. Sloshing in a rolling vessel can cause damage to anything within the tank that causes obstruction to this sloshing mass. Rather than the vertical height of the tank it is the dynamic mass on top that moves athwartships.

In a tank that is 30 m wide & 30 m long may have a wedge weighing about 600 tonnes. On a rolling ship this quantity attaining a speed of 20mps will get a momentum big enough to badly damage, say a tween deck if it comes in the way.

Q. In what way a fore and aft division can reduce the free surface effect?
Ans. The fore and aft division helps reducing the FSE with much higher degree than the number of divisions employed. Thus, if there is a tank of length 10m and width 12m containing fresh water. It will cause an FSM equal to $\dfrac {10\times 12^{3}}{12}=1440tm$.  If two fore and aft subdivisions divide the tank in three segments, the total FSM will be equal to $3\times \dfrac {10\times 4^{3}}{12}=160$, the total FSM reduces 9 times.  Thus, if the breadth of free surface is divided in three segments, the FSM caused will reduce 32 times.

(You may also visit my youtube videos @captsschaudhari.com)