Ranger Hope © 2008, contains edited material courtesy of A.N.T.A publication’s.

Principle of Flotation -Archimedes’ Principle     

Relationship between Weight and Buoyancy







Fresh Water Allowance(FWA)                   

Tonnes per Centimetre Immersion (TPC)


Reserve Buoyancy

Principle of Flotation- Archimedes’ Principle

“Archimedes” Principle states that when a body is wholly or partially immersed in a fluid it appears to suffer a loss in mass equal to the mass of the fluid it displaces.

Relative Density

The relationship between weight and volume is called density.  It is defined as ‘mass per unit volume’.  One metric tonne of fresh water has a volume of one cubic metre. Therefore it has a density of 1.000 tonnes/m3. Salt water on the other hand, is heavier.  One cubic metre of salt water weighs 1.025 tonnes, and so salt water has a density of 1.025 tonnes/m3.

The relative density (or specific gravity) of a substance is defined as the ratio of the weight of the substance to the weight of an equal volume of fresh water. In other words, it is simply a comparison of the density of a substance with the density of fresh water.

                             Density of Substance

          R.D.  =    Density of Fresh Water

This is a pure number and has no units.  The R.D. of sea water is therefore 1.025.

Relationship Between Weight and Buoyancy

Suppose we have a body or block that measures 1 cubic metre and weighs 4000 kg.  If we now lower the block into fresh water, it will displace 1 cubic metre of fresh water - which, as we now know, weighs 1000 kg.  In other words, there is a force acting upwards of 1000 kg and a force acting downwards of 4000 kg: the resultant force has to be 3000 kg downwards.  That is, the block will sink.

If we take the same 4000kg block and mould it into a hollow box with a volume of 5 cubic metres, and then place it in fresh water, it has sufficient volume to displace 5 cubic metres of fresh water.  If the box were now completely submerged, it would experience an upward force of 5000 kg.

However, the downward force of the box is still only 4000 kg, thus the resultant force will be 1000 kg upwards.  In this case the box will rise out of the water to a level where the forces are equal and opposite, that is, with 4 cubic metres under water, and 1 cubic metre still outside water.

Thus for a body to (just) float in water, its weight must be exactly balanced by the force of buoyancy.  If the volume of the body is further increased, it will float with a certain amount outside the water.



When a vessel is floating in water, the whole of the weight of the vessel is supported by the buoyancy of the water.  In order to provide that buoyancy the vessel sinks in the water, until the portion of the hull which is below the water surface pushes aside, i.e. 'displaces' a weight of water equal to the weight of the vessel.

This is the law of flotation; namely, a floating vessel displaces its own weight in water.



When a vessel is floating in water the distance from the underside of the hull to the water surface is called the draft.  Numbers are painted at the forward and after ends of a vessel, so that the draught can be read off at any time.  These numbers are referred to as draft marks.

When a vessel is fully loaded with fuel, fresh water, cargo, gear, crew, etc., it will float more deeply in the water than when it has less weight on board.

In this situation the vessel is said to float at load draft and is therefore at load displacement.

When a vessel has no weights on board, that is when it consists of only the hull, superstructure, accom­modation and machinery it is said to float at light draft and to be at light displacement.


The difference between load displacement and light displacement is called deadweightThings such as fuel, fresh water, crew, gear, cargo, fish, etc., are all items of deadweight


At any draft the distance from the waterline to the deck is called the freeboard.

Figure 5.1 Lightship

Figure 5.2 Loaded


Most trading vessels are required by law to have marks on the sides, at amidships, which indicate the draft to which the vessel can be loaded.  Section 7 of the USL Code deals with loadlines.  Loadlines are not required to be marked on vessels of less than 24 metres in length but note that the definition of length (as given in Section 7 of the USL Code, for loadline purposes) is not the same as measured length.  For most vessels the loadline looks like the one shown in Fig 5.3.

Figure 5.3  Loadlines

Figure 5.3 shows the typical loadlines for a vessel trading solely in Australia.  The abbreviations are as follows:

TF     Tropical Fresh Water Mark

F       Fresh Water Mark

T       Tropical Mark

S       Summer (Plimsoll) Mark

W      Winter Mark

The tropical, summer and winter are the marks which must not be submerged when the vessel is trading in a designated tropic zone, summer zone or winter zone.

The names of the zones are only loosely related to the seasons of the year.  It is possible to have summer zones in winter and vice versa.

Bad sea and weather conditions are associated with winter zones; better weather with summer zones, and good conditions with tropical zones.  As a result, a greater freeboard is required for the bad weather zones than for the good weather zones.

A seasonal zone is one which changes its name according to different times of the year.  (See Fig 5.4).

Reproduced with the permission of the Australian Government Publishing Service.

Seasonal Zones

In all cases measurements are made to the tops of the lines.  For example a vessel loaded to full draft in a Winter Zone will have a waterline as shown in Fig 5.5.

Figure 5.5

The letters on either side of the disc indicate the marine authority which is responsible for the survey of the vessel.  In the Fig 5.3 CA is used, this means Commonwealth of Australia.  A full list of Australian marine authority designations is:

CA    Commonwealth of Australia

QA    Queensland

VA    Victoria

TA     Tasmania

SA    South Australia

WA   Western Australia

NTA  Northern Territory

NA    New South Wales



Fresh Water Allowance (FWA)

When a vessel is floating in water, the underwater part of the hull displaces a quantity of water which is equal to the weight of the vessel.  The hull actually displaces a volume of water measured in cubic metres, which is equal to the underwater volume of the hull.  Each cubic metre of water has a weight, 1 000 tonne in the case of fresh water; 1.025 tonnes in the case of salt water.  The hull must displace sufficient cubic metres of water to balance the weight of the vessel exactly.  One cubic metre of sea water will balance 1.025 tonnes of weight therefore 1.00 cubic metre of sea water will balance 1.025 x 100 = 102.5 tonnes of weight.

Imagine a vessel, floating first in sea water and then in fresh water.  It will need to displace more cubic metres of fresh water to balance its weight, than it would in sea water, because each cubic metre of sea water balances more weight than each cubic metre of fresh water.  The number of cubic metres displaced determines the size of the underwater portion of the hull.

In sea water, the underwater portion of the hull will be smaller, that is the vessel will not sink as far as it will in fresh water, and the draft in sea water will be less than the draught in fresh water.

The difference between the two drafts is called the fresh water allowance (FWA).

FWA is measured as the distance between the top of the Summer (S) line and the top of the Fresh (F) line.

When loading a vessel which has a loadline, the appropriate loadline must not be submerged.  For example, if a vessel is in a Summer Zone, the waterline will look as shown in Fig 5.6.

Figure 5.6

If this vessel is loading in a river then it will be allowed to load as shown in Fig 5.7.

Figure 5.7

When the vessel reaches sea water it will rise to the summer load line level.  It is important to take advantage of the FWA because there will be a loss of cargo carried, and therefore a loss of revenue, if the vessel only loads up to the summer loadline level in freshwater.

When a vessel loads in a brackish waters harbour, the specific gravity of the dock water must be tested with a hydrometer. The amount that the summer load line can be immersed is then calculated as a percentage of the FWA. The example below shows a vessel with a FWA of 50cms loading in dockwater of SG 1005. This water is only four fifths fresh so the vessel can only use 40 cms of its 50cms FWA if it must float at the summer loadline out at sea.




1025 –1005 

1025 –1000











Tonnes per Centimetre Immersion (TPC)

As weights are loaded on board a vessel, it will gradually sink lower in the water.  The amount of weight which will sink the vessel 1 cm deeper in the water, that is, the weight which will increase the draft by 1 cm is called the tonnes per centimetre immersion (TPC).




As weights are loaded on board a vessel, the draft will increase, as the vessel sinks deeper in the water. If the weights are loaded towards the ends of the vessel, it will not sink evenly.  If a weight is loaded forward, then the draft at the bow will increase more than the draft at the stern.  Of course the overall draft will still increase.  At any given time therefore, a vessel may have different drafts at the bow and stern.

The difference between the draft aft and the draft forward, is called the trim.

Trim = Draft Aft - Draft Forward

If the draft aft is greater than the draft forward, as shown in Fig 5.8 the vessel is said to be trimmed by the stern.  If the reverse is true the vessel is said to be trimmed by the head.  This is shown in Fig 5.9.

Figure 5.8  Trim = Draught Forward - Draft Aft

Figure 5.9

It is usually desirable to have your vessel trimmed by the stern.  This gives you increased reserve buoyancy forward, and the vessel will ride more comfortably over head seas.  The rudder will be more responsive and gen­erally the vessel will handle better.  Excessive trim by the stern is not good.  The vessel becomes over responsive and considerably less stable.  It should be remembered that the stability calculation for the safe operation of all vessels are based on the assumption that the vessel is on an even keel (equal drafts fore and aft).

Reserve Buoyancy

The amount of freeboard which a vessel has is a measure of the amount of buoyancy which is left above the water line, to support the vessel in case of bad weather or damage, etc.  This buoyancy is referred to as reserve buoyancy.  Every vessel is designed to operate with a certain freeboard which provides for safety of vessel and crew.  See Figs 5.6 and 5.7