Free Surface Effect

Continuing where we left off, and carrying on with tanks and stability, the next topic I would like to address is Free Surface in a Tank.

When a ship heels with a tank partially filled with a liquid, that liquid moves from one side to the other (just like when you walk with a washbasin half filled with water). As a result, the metacentric height (GM) reduces, while the height of ship’s Vertical Centre of Gravity (KG) increases.

It can be very dangerous to have to much Free Surface. So much that many companies actually request that none is permitted, unless when strictly necessary, and even then, with care.

So, to increase GM and eliminate the Free Surface Effect:

• Empty the tank -> g higher than G
• Fill up -> g lower than G

Inside Brown’s Nautical Almanac, is goes to give you how to calculate the Free Surface Moment for a tank. But since all ships has a Stability Book, where it states it. I’ve decided to go where it actually matters: the effects.

Due to the Free Surface in the tank, G will move to G1 and the metacentric height will decrease in:

G1M = GM-[(i*ẟ):D]

Where:

i = Free Surface Moment, found in the Stability Book of the vessel

ẟ = Density of the liquid inside the tank

D = Displacement of the Ship

The Free Surface Effect also shifts the centre of gravity from G1 to G2 when the liquid starts to move due to heel, as shown in the picture on the right.

G1G2 = (w*b*0.5):D

Where:

w = Weight of the liquid in the tank

b = tank’s breadth

D = Displacement of the Ship

And finally, the angle of heel due to the Free Surface effect, is represented by:

tanθ = G1G2:G1M

One way to reduce the Free Surface Effect is the Longitudinal Bulkheads, even with openings (think, instead of a washbasin, an ice tray, filled with water)

To end this article, the Brown’s Nautical Almanac warn us about the Free Surface a ship can face inside the Fresh Water, Fuel and Ballast Tanks. And the dangers (and benefits, in some cases) of getting Salty Water inside the Cargo Holds.