Chapter 7

Effect of free surfaceof liquids on stabilityWhen a tank is completely ®lled with a liquid, the liquid cannot movewithin the tank when the ship heels. For this reason, as far as stability isconcerned, the liquid may be considered a static weight having its centre ofgravity at the centre of gravity of the liquid within the tank.Figure 7.1(a) shows a ship with a double-bottom tank ®lled with a liquid

having its centre of gravity at g. The effect when the ship is heeled to asmall angle y is shown in Figure 7.1(b). No weights have been movedwithin the ship, therefore the position of G is not affected. The centre ofbuoyancy will move out to the low side indicated by BB1.

Moment of statical stability � W� GZ� W� GM� sin y

Now consider the same ship ¯oating at the same draft and having thesame KG, but increase the depth of the tank so that the liquid now onlypartially ®lls it as shown in Figures 7.1(c) and 7.1(d).

Fig. 7.1

When the ship heels, as shown in Figure 7.2, the liquid ¯ows to the lowside of the tank such that its centre of gravity shifts from g to g1. This willcause the ship's centre of gravity to shift from G to G1, parallel to gg1.

Moment of statical stability � W� G1Z1

� W� GvZv

� W� GvM� sin y

This indicates that the effect of the free surface is to reduce the effectivemetacentric height from GM to GvM. GGv is therefore the virtual loss ofGM due to the free surface. Any loss in GM is a loss in stability.If free surface be created in a ship with a small initial metacentric height,

the virtual loss of GM due to the free surface may result in a negativemetacentric height. This would cause the ship to take up an angle of lollwhich may be dangerous and in any case is undesirable. This should beborne in mind when considering whether or not to run water ballast intotanks to correct an angle of loll, or to increase the GM. Until the tank is fullthere will be a virtual loss of GM due to the free surface effect of the liquid.It should also be noted from Figure 7.2 that even though the distance GG1

is fairly small it produces a relatively large virtual loss in GM (GGv).

Correcting an angle of lollIf a ship takes up an angle of loll due to a very small negative GM it shouldbe corrected as soon as possible. GM may be, for example ÿ0:05 toÿ0:10m, well below the D.Tp. minimum stipulation of 0.15m.First make sure that the heel is due to a negative GM and not due to

uneven distribution of the weights on board. For example, when bunkersare burned from one side of a divided double bottom tank it will obviouslycause G to move to G1, away from the centre of gravity of the burnedbunkers, and will result in the ship listing as shown in Figure 7.3.

Effect of free surface of liquids on stability 51

Fig. 7.1

Having satis®ed oneself that the weights within the ship are uniformlydistributed, one can assume that the list is probably due to a very smallnegative GM. To correct this it will be necessary to lower the position ofthe effective centre of gravity suf®ciently to bring it below the initialmetacentre. Any slack tanks should be topped up to eliminate the virtualrise of G due to free surface effect. If there are any weights which can belowered within the ship, they should be lowered. For example, derricks maybe lowered if any are topped; oil in deep tanks may be transferred to doublebottom tanks, etc.

52 Ship Stability for Masters and Mates

Fig. 7.2

Fig. 7.3

Assume now that all the above action possible has been taken and thatthe ship is still at an angle of loll. Assume also that there are double bottomtanks which are empty. Should they be ®lled, and if so, which ones ®rst?Before answering these questions consider the effect on stability during

the ®lling operation. Free surfaces will be created as soon as liquid enters anempty tank. This will give a virtual rise of G which in turn will lead to anincreased negative GM and an increased angle of loll. Therefore, if it isdecided that it is safe to use the tanks, those which have the smallest areacan be ®lled ®rst so that the increase in list is cut to a minimum. Tanksshould be ®lled one at a time.Next, assume that it is decided to start by ®lling a tank which is divided

at the centre line. Which side is to be ®lled ®rst? If the high side is ®lled ®rstthe ship will start to right herself but will then roll suddenly over to take upa larger angle of loll on the other side, or perhaps even capsize. Nowconsider ®lling the low side ®rst. Weight will be added low down in thevessel and G will thus be lowered, but the added weight will also cause Gto move out of the centre line to the low side, increasing the list. Freesurface is also being created and this will give a virtual rise in G, thuscausing a loss in GM, which will increase the list still further.

Figure 7.4(a) shows a ship at an angle of loll with the double bottomtanks empty and in Figure 7.4(b) some water has been run into the low side.The shift of the centre of gravity from G to Gv is the virtual rise of G dueto the free surface, and the shift from Gv to G1 is due to the weight of theadded water.It can be seen from the ®gure that the net result is a moment to list the

ship over still further, but the increase in list is a gradual and controlledincrease. When more water is now run into the tank the centre of gravity ofthe ship will gradually move downwards and the list will start to decrease.

Effect of free surface of liquids on stability 53

Fig. 7.4

As the list decreases, water may be run into the other side of the tank. Thewater will then be running in much more quickly, causing G to movedownwards more quickly. The ship cannot roll suddenly over to the otherside as there is more water in the low side than in the high side. If suf®cientweight of water is loaded to bring G on the centre line below M, the shipshould complete the operation upright.To summarize:

(a) Check that the list is due to a very small negative GM, for exampleÿ0:05 to ÿ0:10m.

(b) Top up any slack tanks and lower weights within the ship if possible.(c) If the ship is still listed and it is decided to ®ll double-bottom tanks,

start by ®lling the low side of a tank which is adequately sub-divided.(d) The list is bound to be increased in the initial stages.(e) Never start by ®lling tanks on the high side ®rst.(f) Always calculate the effects ®rst before authorizing action to be taken to

ballast any tanks.

54 Ship Stability for Masters and Mates

Exercise 7

1 With the aid of suitable sketches, show the effect of slack tanks on a ship'sstability.

2 A ship leaves port upright with a full cargo of timber, and with timber ondeck. During the voyage, bunkers, stores and fresh water are consumedevenly from each side. If the ship arrives at her destination with a list,explain the probable cause of the list and how this should be remedied.

3 A ship loaded with timber and with timber on deck, berths with an angle ofloll away from the quay. From which side should the timber on deck bedischarged ®rst and why?