Introduction to Draught Survey


Draught surveys – practice

*The master of a vessel should be advised in adequate time that a draught survey will be taking place. If it is an initial light ship survey, he should be requested, subject to the safety of the vessel, to ensure that individual ballast tanks are either fully pressed up or empty – that the vessel is upright, and with a trim which is within the limits of the tank calibration tables.    

*When draught surveys are undertaken by independent surveyors, co-operation of the ship’s officers is essential. 

*Independent surveys should be undertaken together, during the relative survey sections, with the vessel’s chief officer and chief engineer or their appointed respective deputies. 

*Before undertaking the survey, it is recommended that the surveyor makes time to inspect a general arrangement plan in order to confirm the number and position of the various ballast, fresh water and oil bunker tanks on the vessel. 

*Equipment which may be used in the survey:

Strong torch

Patent draught mark indicator or measuring devices (draught tubes, indicators etc)

Calibrated Inclinometer or manometer

Steel tape measure with plumb bob / stainless steel sounding tape with brass plumb bob (preferably calibrated)

Sea water sampling bucket or can of sufficient volume

Calibrated patent draught survey hydrometer

Calibrated salinity refractometer

Ballast water-sampling device

Computer / calculator.

Reading the draught marks 

*At the time of reading the draught marks, the vessel should be upright with a minimum of trim. The trim at survey should never exceed the maximum trim for which corrections may be included in the vessel’s stability book. 

*The vessel should ideally be lying in still, calm water. Otherwise errors, without ease of correction, from reading the draught marks can result. For example:

– Vessels lying at exposed berths or anchorages where wave and swell surface disturbance is almost inevitable; even to the extent that the vessel may be rolling and pitching. In these circumstances it is usual to assess the actual mean water level over a number of readings to be at two-thirds of the distance between the lowest and highest levels of water as seen against the draught marks. Some experts advocate that, after studying wave patterns, a mean of the average highest and lowest draught readings should be used.

– Vessels which are lying at a river berth or in tidal conditions when strong currents are running. Under these conditions the draught marks should ideally be read over periods of slack water (provided that at a low water slack there is sufficient under-keel clearance).

– Currents of appreciable strengths are likely to cause the vessel to change trim or pitch slightly and/or sink bodily into the water from her static draught (‘squat’). This phenomenon becomes more pronounced in shallow waters (shallow water effect).

– Strong currents will result in raised water levels against the leading edge of a stationary vessel lying in flowing water. This is especially true when the flow is in the direction of a vessel’s bulbous bow. 

*Draught marks must be read on both sides of the vessel: forward port and starboard; amidships port and starboard, and; aft port and starboard or, alternatively, if additional marks are displayed on large vessels at all the designated positions.

Should draught marks not be in place amidships, distances from the deck line to the water line on both sides of the vessel must be measured. The amidships draughts can then be calculated from load line and freeboard data extracted from the vessel’s stability booklet. 

*Draught marks should be read with the observer as close to the water line as is safe and reasonably possible, in order to reduce parallax error. 

*Although it is common practice to read the offside draught marks from a rope ladder, a launch or small boat provides a more stable environment and brings the observer to a safer position closer to the water line. 

*A vessel’s remote draught gauge should never be used for surveys, due to lack of the necessary accuracy and the possibility of errors, which may accumulate over the working life of the instrument. 

*When adverse weather conditions are being experienced, access to the offside draught marks may prove difficult or impossible. At these times the draughts on the nearside can be read and the offside draughts calculated using a manometer.

This method should never be used when the offside draughts can be safely observed and accurately read. If, as a final resort, this method cannot be undertaken, the use of a fully calibrated inclinometer, graduated to minutes of arc, is strongly recommended. The type of inclinometer fitted to vessels is not usually of sufficient accuracy to be used.

Density of the water in which the vessel is floating 

*It is prudent to obtain samples of water in which the vessel is floating at, or very close to, the time at which the draught marks are read. This is particularly relevant when the vessel is lying at a estuarial or river berth when density of the water may be changing, due to the ebb or flow of the tide. 

*Depending upon the length of the vessel under survey, a number of samples, say between one and three, should be taken. In order to overcome the problem of layering, the samples should be obtained using a closed sampling can at a depth of approximately half the existing draught of the vessel. Alternatively, a slowfilling container can be used to obtain an average sample from keel to waterline. 

*When reading the hydrometer floating in the sample of water, the eye of the observer should be as close to the water level as possible, to avoid parallax errors and also to avoid further errors due to the meniscus.

Ballast water tanks 

Ballast water tanks including peaks, even those said to be empty, must be carefully sounded or proven to be full by pressing up and overflowing from all air pipes when local regulations permit. If the ballast hold contains ballast water, this compartment must not be fully pressed up but be carefully sounded and the weights of the water carefully calculated. 

*Spaces such as the duct keel and voids – especially those of the lower stools situated at the base of transverse bulkheads, between cargo holds – must be checked when safe to do so, and proved in same condition at initial and final surveys.

These voids often contain the manhole access covers to the adjacent double-bottom tanks. If these covers are not totally watertight, then the voids will flood, or partially flood, during ballasting or pressing up of the tanks, potentially resulting in huge errors in the lightship or ballast survey. 

*As noted above, the calculation of the weight of ballast water is undoubtedly the most usual source of errors which may result in very large, and unacceptable, inaccuracies of the cargo quantity as calculated by draught survey.

Density of the ballast water 

*It should be established, with the chief officer, where the various ballast tanks were filled. If from a single source, the sea, a few random samples of the water will confirm its density. If from different sources, docks or rivers, etc samples must be taken from the tanks containing water from these various sources and relevant densities of the water in individual tanks established. 

*Do not overflow the tanks substantially to obtain samples unless local regulations permit; instead use sampling equipment suitable for tanks that are only partially filled.

*When small samples are obtained, use a salinity refractometer to establish density (see below). When larger samples have been obtained, a draught survey hydrometer may be used. See details above.

Establishing the correct weights of oils on board 

*This can be established either by sounding or ullaging of the tanks or, in the case of the engine room daily service and settling tanks, by reading the gauges.

*The volumes of oils in each and every tank should be measured and recorded. 

*The relative densities of the most recently delivered oils on board can be obtained from the bunker delivery certificates. However bunkers are almost inevitably mixed with oils already on board, the densities of which are likely to differ.

The relative density of the contents may be calculated using the following formula:

RD of tank contents at survey = ((Old oil volume x Old RD) + (New bunker volume x New RD))/ Total volume of oil in tank 

* After completion of the bunker survey the totals of each oil found must be agreed with the chief engineer and the master.

Calculations & associated corrections of vessel’s displacement from draught readings 

*Before extracting hydrostatic data from the vessel’s stability book, care should be taken by surveyors to familiarise themselves with the format and methods used to display the various particulars, especially the means of depicting positions of Lcf (longtitudinal centre of flotation) etc, relative to amidships or alternatively the after perpendicular. 

*When using a recommended draught survey computer programme or alternatively calculating directly from data extracted from the hydrostatic particulars contained within the vessel’s stability book it is essential that the data is carefully and properly interpolated or, in what should prove to be a rare event, extrapolated. 

*As mentioned below, one of the areas where significant errors often result is from the incorrect application of the sign in respect of the position of the Lcf (in the first trim correction). 

*When undertaking initial and final ‘displacement draught surveys’ to establish weight(s) of cargo loaded, or alternatively unloaded, the difference between the net displacement weights provides the ‘total cargo’ quantity. Nonetheless it is recommended for a cross check that, at the light ship/ballast survey, the vessel’s light ship weight is deducted from net displacement found. The resultant then provides the vessel’s ‘constant’ at that time. These unknown weights might also be termed the vessel’s ‘stores variable’. Although variable, for a number of reasons as later discussed, it should serve as a guide to the accuracy of the light ship/ballast survey.

Comparison between ‘stores variable’ quantities, or mean thereof, established at previous surveys should be treated with caution unless the variable is a direct comparison that can be made. For example, all surveys include a check and a record of the engine lubricating oil held in storage tank(s), etc. Occasionally, surveyors report a ‘negative’ stores variable which is theoretically impossible unless, in extremely rare instances, the vessel had been subject to modification, and large quantities of structural steel removed, without being subject to a further inclining experiment and commensurate correction of the relevant data contained in the vessel’s stability book.

Charterparties often contain reference to an approximate quantity for the vessel’s ‘constant’, which may well create a discussion between master and surveyor should the constant found by survey to be substantially larger than that quoted by the owners. The surveyor, after relevant checks, should remain confident in the figure obtained, but always record on documents issued to the master and clients, any unusual factors or difficulties experienced during survey. These include any differences between surveyors, should owners, charterers or shippers each appoint separate survey companies to act on their behalf.


*At completion of survey, a ‘survey work sheet’ or computer printout should be placed on board the vessel recording the data and calculations used to obtain the cargo loaded/ unloaded quantity. This document is usually produced by individual survey companies, or by shipping companies for use by their officers. 

*A formal ‘survey report’ should be submitted to clients at a later date. Specific formal documentation has been drawn up, amongst others by IMO, United Nations Economic Commission for Europe and various P&I Clubs.

*The formal report document should not only include details of the survey, but also: Dates and times of surveys.

Vessel particulars.

Ship’s location.

Weather conditions (and whether these were within acceptable limits).

Sea conditions (and whether these were within acceptable limits).

Tidal/current conditions (and whether these were within acceptable limits).

A record of any difficulties or defects in a ship’s documentation or equipment which might cause the calculated weight by draught displacement survey to be outside acceptable limits of normal draught survey measurement error.

Expert opinion

Surveys must be carried out to the very best of the surveyors’ ability, with each part of the survey conducted as accurately as possible in order to minimize procedural and/or measurement errors which could effect the quantity of cargo recorded by survey as being loaded or discharged.

The final report should include details of any defect or circumstance regarding weather, surface water, tides/ currents or on board conditions which the surveyor considers might well influence the result adversely.

Cumulative errors 

*Errors can occur when reading and correcting the draughts. The final fully corrected 3/4 mean draught should be within +/- 10 mm of the true mean draught. 

*Errors of calculation. The main error to be avoided in this section is that of incorrectly positioning the LCF relative to LBP/2 the amidship point. 

*Error of the water density in which the vessel is floating. Always ensure an average sample, or alternatively the average of a number of water samples are obtained and the correct type of certificated hydrometer is used to obtain the density. 

*Sounding of tanks. Leaving aside documented tables which may not be accurate, the way of avoiding the main errors in this section of the survey is by ensuring, as best possible, that all volumes of liquids, especially ballast water, on board are both correctly quantified and attributed with correct densities. These factors, particularly when applied to ballast water, undoubtedly contribute to the largest number and degree of errors likely to be encountered in draught surveying.

Bearing these reservations in mind, a well conducted draught survey under reasonable prevailing conditions is capable of achieving an absolute accuracy of +/- 0.5%




Draught surveys – theory

Draught surveying is a commercially acceptable form of weighing that is based on Archimedes Principle, which states that anything that floats will displace an amount of the liquid it is floating in that is equal to its own weight.

Briefly, the weight of the ship is determined both before and after loading and allowances made for differences in ballast water and other changeable items. The difference between these two weights is the weight of the cargo.

In order to do this the depth that the ship is floating at is assessed from the ‘draught marks’ and the vessels stability book is consulted to obtain the hydrostatic particulars such as the ‘displacement’ and other necessary data.

Several corrections are required and the quantities of ballast and other consumable items need to be assessed so as to obtain the net weights as follows.

The weight of an empty ship consists of three elements

1. Empty ship – FIXED ITEM


3. Ballast oil and fresh water – CHANGEABLE

Empty net weight = Empty ship + Stores The weight of a loaded ship consists of four elements

1. Empty ship – FIXED ITEM


3. Ballast oil and fresh water – CHANGEABLE

4. Cargo – FIXED ITEM

Loaded net weight = Empty ship + Stores + Cargo

Therefore the cargo weight is the difference in the net weights.


Density is mass per unit volume at a given temperature. As already stated weight can be considered the same as mass as far as draught surveying is concerned. Therefore the weight of the block above is its underwater volume multiplied by the density of the liquid in which it is floating.

Weight in vacuum

The density of a substance can be determined by weighing a unit volume, which in the case of the metric system is a cubic metre. If a quantity of liquid – for example, fresh water or sea water – is weighed on a balance or on a weighbridge against the equivalent of brass weights then the atmosphere will exercise an upward thrust upon the water much greater than the upward thrust exercised on the smaller volume of brass weights. This ‘air buoyancy’ effect is in fact the same as the buoyancy force for a body immersed in a fluid, as explained in the Archimedes’ Principle. However, this time the fluid is air, which has a density of 0.00125 t/m3 (the density of dry sea air at sea level is about 1/800th of the density of fresh water, ie 1.25 kg/m3). If the weight of the unit volume is corrected for this ‘air buoyancy’ effect, the result is weight in vacuum which is equivalent to mass. For all practical purposes it is accepted that the density of fresh water is 1000 kg/m3 and that of sea water 1025 kg/m3.

Apparent density

It is commercial practice to make no allowance for air buoyancy so that commercial weights are normally weights in air. Weight in air per unit volume is known as apparent density and this should be the criteria used for all draught surveys as, after all, the ship is in air not in a vacuum.

The Zeal Draught Survey Hydrometer reads ‘apparent density in air kg/Lt @150 C’ and is an industry standard accepted worldwide.

Reading the draughts

Draught marks (the depth at which the ship is floating) are so constructed as to make the reading of them simple. Metric marks are 10 cm high and are placed 10 cm apart. The steel plate they are made from is 2 cm wide. There are still a few ships using the ‘Imperial’ system but they are now few and far between. However for the sake of reference, the Imperial system has numbers that are six inches high and located six inches apart with the numbers constructed from one inch wide steel plate.

Metric marks


The photo shows some draught marks in the metric system. The picture shows depths from 8.49 metres to 9.64 metres. The water level is at 8.49 metres as half the width of the top of the ‘4’ is visible above the water level (the number is made from 2 cm wide steel plate). Some numbers are easier to assess than others. For example, in the diagram each pair of lines is 2 cm apart and it can be seen that the assessment of the depth is easy when the water level is across the ‘8’. The ‘6’ and the ‘9M’ in the picture would also have the same easy to read features.

Some small coasters are often only marked at the midships point with a designated line (again 2cm wide) called the deck line. The upper edge of this is at a known distance from the keel (’K’) which is the summation of the vessels official summer freeboard and summer draught. Draughts are then calculated by measuring the actual freeboard (distance of the upper edge of the deck line from the water level) with a measuring tape and deducting it from the ‘K’.

The stability book

All ships are provided with a stability book, which includes a section of hydrostatic particulars giving data for different draughts. Included in these are Displacement, Tpc, Lcf and Mctc. Each of these is required in order to calculate the survey and they are tabulated for any given draught. Taking each in turn:


Displacement is the weight of the ship. It is the underwater volume multiplied by a density. In the majority of cases the standard density used is 1.025 although there are many other in use such as 1.027, 1.000, 1.02522 etc. In order to obtain the volume the displacement is divided by whichever density has been used to compile the data.


Represents ‘tonnes per centimetre’ of immersion. It is the weight that must be loaded or discharged in order to change the ships mean draught by one centimetre.


Represents ‘longitudinal centre of flotation’. It is the position about which the ship will trim when weights are loaded or discharged. It is the geometric centre of the water-plane, and will move as the shape of the water-plane changes when weights are loaded or discharged.

The water-plane is the area of the ships hull that would be visible if the ship was cut off at the waterline.


This stands for ’moment to change trim 1 centimetre’. It is the moment required to change the trim of the vessel by one centimetre (a ‘moment’ is weight x distance). Mctc is used in the second trim correction.

Other necessary data provided within the stability book are the following:

Light ship

The weight of the ship complete in all respects when empty, but with full equipment, engine spares, water in the boiler and lubricating oil in the engine.


The weight a ship can carry. Deadweight includes any fuel, water, ballast, passengers, crew and stores. It is the difference between light ship and displacement at any draught. ‘Cargo carrying capacity’, therefore, depends on the amount of fuel water and ballast remaining on completion of loading, and any additions which will be required by the ship on passage to its final port of discharge.


Represents ‘length between perpendiculars’. A ship is built to plans and the plans are drawn around two perpendicular lines that represent the forward (FP) and aft (AP) extremities of the section of the ship from which the volume is calculated. The remaining two sections of the ship, the small part of the bow and stern sections, called the appendages, are added in afterward.

The forward perpendicular is considered to be where the load water line (summer load line) cuts the line of the foreside of the bow. The aft perpendicular is where it cuts the aft edge of the rudder post, or in the case of most modern vessels where no rudder post is fitted, the centre line of the rudder stock.

Calculating a ship’s draught

The mean draught at which the ship is floating cannot be calculated by simple average because ships are not rectangular, or box like, in shape and because they bend due to the distribution of weight on board. The draughts themselves also need to be corrected before they can be used.

Perpendicular corrections

As mentioned above, ships volumes are calculated around the section of the vessel that lies between the forward and aft perpendiculars (FP and AP). When a ship is built the draught marks are located at convenient positions on the hull and these will not always be at the perpendiculars. For calculation purposes, the draughts at the perpendiculars are required and this is done with the use of similar triangles. The actual trim of the vessel, in relation to the length of the vessel between the draught marks, is one of a pair of similar triangles. The other is the correction in relation to the distance the draught marks are displaced from the relevant perpendicular. Therefore these two triangles can be used to correct the draught mark readings to what they would be at the perpendiculars. For example:

Forward Corr’n = Apparent Trim x Fd / LBM


Apparent trim = trim at the draught marks.

Fd = distance of forward draught marks from Perpendicular

LBM = length between draught marks

The calculation of the aft and, sometimes, a midships correction uses the same formula but substitutes the distances of the midships or aft draught marks from the relevant perpendicular (the midships perpendicular is located at LBP/2).

Each of these corrections is applied according to the following rule: If the direction of the displacement of the draught marks from the relevant perpendicular is the same as the direction of the trim, then the correction applied to the observed draught is negative, otherwise it is positive.

3/4 mean draught

Ships bend (hog or sag) due to the distribution of the weights in the various holds and tanks on board. The ship is assumed to bend as a parabola and the area below a parabola, in a circumscribing rectangle, is equal to twice the area above the parabola, or in other words the area under the parabola is two-thirds the total area. The mathematics of this fact is not important from the point of view of draught surveying. What is important, is to understand the effect it has on a ship that is hogged or sagged (hogged is when the vessel is deflected upwards in its central section, and sagged is the opposite).


e.g. If a box-shaped barge’s draught readings produce an arithmetical mean of the forward and aft draughts that is more than the middle draught then this indicates that the barge is hogged. Utilising the maths of the parabola, the lost section of volume (yellow area in the diagram) is 2/3 of the box that encloses it. To calculate the effect of this the following formula would be used:

Mean adjusted draught = ((4 x Middle) + Forward + Aft) / 6

(4/6 of the middle draught is 2/3 or 66.67%)

The resulting draught calculated is the mean draught adjusted to compensate for the deflection in the barge structure. This is known as the two-thirds mean correction, and was derived directly from ‘Simpson’s First Rule’ for finding an area under a curve. This is fine for a box shape, but ships are very rarely box shaped.

Calculations have shown that the most likely amount of correction required for hog or sag on a conventionally shaped ship is threequarters or 75 %. The formula for this is called the 3/4 mean draught and is as follows:

3/4 mean draught = ((6 x Middle) + Forward + Aft)) / 8

(6/8 of the middle draught is 3/4 or 75%)

This is the draught used to enter the ships hydrostatic tables and obtain the displacement of the ship. However, the displacement scale in the ships stability book is calculated for the ship on an even keel and in an upright condition; that is without any trim or list. Ships rarely appear in that state, although it has been known. Therefore, two corrections are now required to give the true displacement.

First trim correction, (layer correction) Sometimes called the ‘A’ correction

A ship trims about the longitudinal centre of flotation (Lcf). This is the geometric centre of the water plane at any time. The water plane is the area of the ship shape if it were cut off at the water line. It obviously changes as draught increases as the shape becomes more rounded aft while remaining more pointed at the bow. A diagram will explain this better.

dr acorr1

The position of Lcf is crucial to the calculation of the draught survey. The ‘true mean draught’ is the draught at the Lcf and not the draught amidships; unless, of course, Lcf is positioned at amidships.

Consider the following diagrams. dr acorr2

In the above diagram the ship is on an even keel and the draught at the Lcf is the same as the draught at amidships. However, if a weight within the ship is moved further aft, the ship will trim about the Lcf so that she is deeper aft and not so deep forward; as in the next diagram. The displacement will not have changed, as the trim is achieved by moving a weight already on board and the draught at the Lcf remains the same. dr acorr3

In the above diagram the change to the forward draught is greater than the change to the aft draught because the ship is trimming about the Lcf and the draught at the Lcf is greater than the draught amidships, which is the mean of the forward and aft draughts. In order to obtain the true mean draught (the draught at the Lcf) a correction needs to be applied to the adjusted mean draught (the 3/4 mean draught). This correction is called the layer correction and is easily calculated using similar triangles as follows.

The green trim triangle is similar to the red layer triangle as both have two of their sides in the same proportion and their included angles are equal.


Layer correction = (Trim x Distance of Lcf from amidships) / LBP

In this case the true mean draught is the draught amidships plus the layer correction. Had the Lcf been forward of amidships the correction would have been negative.

The above corrections are in metres and can be applied to the 3/4 mean draughts to give the true mean draught. However, the normal method used is to calculate the correction in tonnes. The displacement is taken out of the tables for the 3/4 mean draught and the layer correction applied as a negative or positive correction in tonnes by using the Tpc at that draught (Tpc is the number of tonnes required to sink the ship one centimetre).

This is the first trim correction, and is calculated using the following formula:

First trim correction = Trim (in centimetres) x Lcf x Tpc / LBP

Where Lcf is measured in metres from amidships.

The correction is applied according to the following rule:

If the Lcf and trim are in the same direction the correction is positive and alternatively when they are in opposite directions the correction is negative.


Position of Lcf The understanding of how Lcf moves is crucial. In the above formula it is measured from amidships and it is absolutely essential that it is understood which side of amidships it is. There have been more incorrect draught survey results obtained due to getting this detail wrong than anything else.

The position of Lcf, in the hydrostatic particulars, is indicated by three main methods. These are:

1.Either with a minus (-) sign or a plus (+) sign, indicating a direction from amidships (see below).

2.Or labelled with the letters ‘a’ or ‘f’ (sometimes ‘aft’ or ‘ford’) indicating aft or forward of amidships.

3.Or as a distance from the aft perpendicular (in which case the distance and direction from amidships can be easily calculated by use of the LBP/2).

The latter is the clearest method.

The use of (-) and (+) signs can be very confusing depending on what the compiler of the tables meant by their use. In Russian and in Korean shipyards (-) means aft of amidships but they also refer to aft trim as (-). The European convention is to use (+) to mean aft of amidships and aft trim. The main reason for errors in applying the Lcf in the first trim correction are an obsession with the (+) or (-) signs as being mathematical. They are in fact only an indicator of which side of amidships Lcf is located and that depends on the shipbuilder’s logic.

Usually the convention used is indicated at the beginning of the tables or somewhere on the pages listing the data.

Lcf is the centre of the of the vessel’s waterplane area and as such is a function of the shape of the vessel on the waterline at any given draught and nothing else. Because the water plane changes shape to get rounder at the aft part, as the ship gets deeper, the Lcf moves aft as displacement increases and forward as displacement decreases but does not necessarily move through amidships.

This means that from light to loaded condition Lcf will move either from: 

*Forward to less forward.  *Forward to aft.  *Aft to more aft.

In the absence of reliable information as to the convention used in the hydrostatic tables, these facts should help to determine which side of amidships Lcf lies. Therefore, when displacement is increasing, if the actual number (indicating the position of Lcf from midships) is decreasing, then it is forward of amidships (it is getting closer to zero, which is when it is at amidships) and if it is increasing it is aft of amidships (it has already passed zero at amidships and is moving further aft).

Note: A recent anomaly to this rule was found with a ship that was completely box shaped except for the bow area. In this rare case the movement of Lcf was dictated by the shape of the bow alone,and Lcf initially moved aft and then forward as the vessels draught increased.

Under normal circumstances, when loading a ship the Lcf can be expected to be further aft at the final survey than at the initial survey. In some cases (Russian river ships in particular) the Lcf is always aft of amidships. The opposite situation will exist when discharging cargo. Normal circumstances mean that the draught is greater after loading or, conversely, less after discharge. This may not always be the case, as a ship could load a small parcel of cargo and at the same time discharge a greater amount of ballast, thus being less deep than before loading due to the extra ballast discharged.

When Lcf is shown, in the vessels hydrostatics tables, as measured from the aft perpendicular, then a simple calculation will give its position in relation to amidships.

Lcf from amidships = LBP/2 – distance from aft perpendicular.


Second trim correction, (Nemoto’s correction) Sometimes called the ‘B’ correction The recorded data for Lcf is for an even keel condition, but as the ship trims the waterplane will change shape. This change of shape involves the waterplane increasing in size aft and decreasing forward, and in this situation the position of Lcf will change by moving further aft to maintain its geometric position in the centre.

The new position is not tabulated in the normal hydrostatic tables and a second trim correction is required to compensate for this. It is known as Nemoto’s correction, after the Japanese naval architect. The correction is a compromise but is reasonably accurate up to trims of about 1% of the vessels length.

Second trim correction = Trim2 x 50 x (dm~dz) / LBP

This correction is always positive.

(dm~dz) is the rate of change of Mctc per unit of draught (1 metre). It is the difference in Mctc for 50 cm above and below the mean draught. The derivation of this formula and the evaluation of the expression dm~dz is not important. Mctc, known as the trimming moment, is the moment required to change the vessels trim by one centimetre.

Heel correction In situations where a substantial heel exists, a correction should be applied. The effect of heel (or list) is to increase the waterplane area and thus lift the ship out of the water.

This correction is always positive.

Correction (in tonnes) = 6 x (TPC1 ~ TPC2) x (Draught1 ~ Draught2)

Where 1 is port side and 2 is starboard.


Summary Once both trim corrections, and if required the heel correction, have been applied to the displacement for the 3/4 mean draught, we then have the weight of the ship if it were in salt water of the same density as the ship’s tables.


Density correction Once the displacement – obtained from the 3/4mean draught and the ‘A’, ‘B’ and, if required, heel corrections – has been found it needs to be corrected for the density of the water in which the ship is floating.

The displacement of the vessel, from the ship’s hydrostatic tables, is calculated at the density used to compile the tables. When divided by this density, it gives the volume of the ship. This volume is then multiplied by the density of the water the ship is floating in to obtain the true weight of the ship.


True displacement = Displacement in salt water x Density of the dock water / Density used to compile the ships tables

The reason for saying ‘density of the ships tables’ is that some vessels are built in shipyards where 1.020 mt/m3, 1.027 mt/m3 or some other figure may be used for the hydrostatic particulars. However the norm in 99% of cases is to calculate tables at a density of 1.025 mt/m3.


Alternative hydrostatic information There are some vessels that do not have a tabulated value for Lcf. Generally these are small coasters.

There are two types of table in use. One requires the calculation of Lcf from trim factors. The other uses a set of tables, which give a displacement with inclusive trim and density corrections. In this case the calculation of the actual true displacement involves a simple, if long-winded, interpolation.


Trim factors Trim factors are derived from the position of Lcf. They are a quick way for the vessel’s chief mate to calculate his final trim when loading the ship.

Because Lcf is not listed in the tables its position has to be calculated from the trim factors, which are tabulated as ‘ford’ and ‘aft’. A formula to calculate the position of Lcf is:

Lcf from aft perpendicular = aft factor x LBP / (ford factor + aft factor)

Final net weight Regardless of the method used to obtain the true displacement of the ship, the weight of the variable items mentioned at the beginning of this section must be deducted to produce the net weight. This net weight of the ship is the total weight (true displacement) minus the ballast fuel and fresh water quantities. This should also include any other items that have been identified and measured such as dirty oil (slops), swimming pool quantities and shore machinery on board for example payloders, bobcats and bulldozers etc. These latter items sometimes remain on board whilst the survey is taking place and must be allowed for in the calculation.

The net weight, in the case of an empty ship survey, will be the weight of the ship including the ‘constant’. In the case of a loaded ship, it will be the weight of the ship, the ‘constant’ and the cargo. Clearly the weight of the cargo is the difference between these two weights.


Constant Under the heading ‘stability book’, light ship was stated tobe the weight of the empty ship in operational condition.

This is: The ship, its full equipment, engine room spares, water in the boilers to working level and lubricating oil in the engine.

It does not include: Personnel, cargo, fuel oils, ballast water, fresh water or stores.

The weights of ballast water, fresh water and fuel are calculated and are known collectively as the ‘deductibles’ or ‘total variables’. Once this total weight is subtracted from the true displacement, a net weight is left that is either the ship and stores, or the ship, stores and cargo depending on whether it is an empty or loaded ship survey.

This stores quantity – the difference between the light ship weight and the empty ship survey – is often referred to as the ‘constant’. Constant is a misnomer and it should really be referred to as a ‘stores variable’.

A ship’s constant’ may be affected by a variety of changes, such as under or over stated fuel figures, slops, mud in ballast tanks, incorrect ballast calibration tables, crew and stores changes, etc. and it should not be considered a fixed amount. Also a vessels light ship weight can change over the years due to a variety of additions and removals from the structure. These could be due to a variety of factors such as rebuilding, repairs, additions and modifications. As a consequence the vessels constant will include these changes unless a new light ship survey is carried out after each instance. From experience, this usually only happens after a rebuild or major additions.

The reason for a survey when the vessel is empty is to determine this variable quantity (constant). The vessel’s previous experience of this constant may be the result of unreliable and badly carried out surveys. Many surveys include the lube oil in the constant and others do not. The constant can also be affected by understated fuel figures from the chief engineer, who may be keeping a quantity of oil ‘up his sleeve’ for a rainy day!

However, within reason this stores variable quantity (constant) can be considered to remain fixed for the duration of the ships stay in port. This is assuming that the surveyor takes note of any major changes that take place to the stores between the initial and final surveys. In other words it can be considered as a reliable measurement of the ships stores etc for that reasonably short period of time.

(Source: UK P&I CLUB)

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