Draft Survey : Full Details with Calculations

Draft Survey : Full Details with Calculations

Table of Contents

What is a draft survey?

A draft survey is a calculation to determine the weight of cargo loaded to or discharged from a ship, derived from changes in the ship’s displacement. 

It is based on Archimedes Principle (a body immersed in a liquid is subjected to an upwards force equal to the weight of the displaced liquid, i.e., a freely floating body shall displace an amount of liquid that is equal to its own weight).

How the draft survey is carried out?

The draft survey is performed by reading the ship’s draft on the draft markings at six standard points on both (port & starboard) sides of the hull: forward, midships & aft. The drafts are corrected by applying corrections factors such as draft, trim, and water density.

The displacement of the ship is determined both before and after loading or discharging and required allowances are made for all known deductibles. The difference between these two displacements, known as net displacement, is the weight of the cargo loaded or discharged.

What are known deductibles?

  1. Lightship displacement of the vessel.
  2. Ballast water or unpumpable ballast water.
  3. Freshwater.
  4. Fuel oil
  5. Diesel oil.
  6. Lubricating oils.
  7. Bilge oily water/sludge.
  8. Other cargo or known weights (dunnage /lashing materials), if any.
  9. Ship’s constant (K).

What is the ship’s constant(K)?

The ship’s constant is the difference between a vessel’s designed lightship and its actual displacement when empty. The ships constant is determined by a draft survey. 

What is the accuracy of the draft survey?

Reading accurate drafts is very important. This mainly depends on the experience of the personnel involved & the weather conditions at the time of reading the drafts such as the height of the swell and the state of the sea. The accuracy of a draft survey that has been properly performed is generally regarded as being up to +/- 0.5 percent of the final figure. 

Draft survey purpose & procedures:


The purpose of Draft Surveys is to determine the weight of cargo on board the vessel using the density of the water in which the vessel is floating. From the total displacement obtained in the calculation from the ship’s loading/stability manual, the weight of the lightship and other known deductibles are subtracted. The difference obtained is the cargo weight. 

Vessel’s condition for a survey

 To have good results during the draft survey, the vessel must meet the following conditions.

  1. Draft marks to be well visible and painted, it should not be obstructed.
  2. Vessels need to be upright; the list should not be more than 0.5 degrees.
  3. The vessel’s trim should be as minimum as possible & to be within the correction covered in the ship’s sounding table.
  4. Good means of access to check draft from seaside to be available (it is preferable to use a small boat)
  5. Availability of approved ship’s hydrostatic and tank sounding tables.
  6. Ballast tanks should be either pressed up or empty. Slack ballast tanks to be kept to a minimum.
  7. All sounding pipes are to be marked and clear of any obstructions.

Reading of Draft

A correct reading of the vessel’s draft is very important. It mostly depends on the experience of the personnel involved in reading drafts. At times it is difficult to read the drafts accurately due to many reasons like:

  1. Draft marks are obstructed by shore fenders or markings are in poor condition.
  2. Drafts cannot be read accurately due to the height of the jetty.
  3. State of sea, swell & presence of strong current.
  4. Movement of the vessel in exposed berth (i.e., rolling/pitching surging).

The step-by-step draft survey calculation is described below:


Observed (Obs) drafts & Apparent trim

Fore mean draft (Fm)= [Obs Fore port draft (FP) + Obs Fore stbd draft (FS)] / 2

Aft mean draft (Am) = [Obs Aft port draft (AP) + Obs Aft stbd draft (AS)] / 2

Mid mean draft (Mm)= [Obs Mid port draft (MP) + Obs Mid stbd draft (MS)] / 2

Apparent trim (AT)= Aft mean draft (Am) – Fore mean draft (Fm)

Length between marks (LBM)= [Length between perpendiculars (LBP)- (Fd+ Ad)]

(Fd is the distance between forward draft mark & forward perpendicular 

& Ad is the distance between Aft draft mark& aft perpendicular).

Draft correction (perpendicular correction)

Fore perpendicular Correction (Fc) = (Fd x AT) / LBM 

Aft perpendicular Correction (Ac) = (Ad x AT) / LBM 

Mid Correction (Mc) = (Md x AT) / LBM

When the vessel is constructed, the draft marks are marked at a convenient position & at times it is offset from the forward & aft perpendiculars or the midship position.

For draft survey calculation the drafts at the perpendiculars & midship are required, hence the observed drafts need to be corrected either by using the above calculation formula or from pre-calculated tables.

To obtain True draft & True trim.

Fore Draft Corrected (Fcd) = Fm + Fc
Mid Draft Corrected (Mcd) = Mm + Mc
Aft Draft Corrected (Acd)  = Am + Ac
True Trim (TT) = Acd – Fcd 

Final Draft Calculation (Quarter mean draft)

Fore and Aft Mean (M2) = (Fcd + Acd) / 2

Mean of Mean Draft (M3) = (Mcd + M2 / 2)

Quarter Mean (M4) draft = (M3 + Mcd) /2

 Or, Quarter mean(M4) is calculated by using below formula

Quarter mean Draft(M4) = {(Fcd x 1) + (Acd x 1) + (Mcd x 6)} / 8

The shape of the ship’s hull leads to an unbalanced distribution of cargo, ballast, lightship weights, and buoyancy of the hull during the different loading conditions, which leads to deformations known as hogging (where the ship’s hull will curve as a beam supported at mid-length and loaded at the ends) and sagging (where the ship’s hull will curve as a beam supported at the ends and loaded at mid-length).

The Hogging effect is most common during ballast passage or partial loading condition, The Sagging is most common for loaded vessel. To compensate for the effect of the hull deformations and to determine the average midship draft, above formula for F&A mean(M2), Mean of means(M3) & Quarter mean (M4) are used.

Now from the Hydrostatic table obtain the following data for Quarter mean draft (M4).


a) Displacement

Once the Quarter mean(M4) draft is calculated, the corresponding vessel’s displacement is to be extracted from the vessel’s hydrostatic tables. The vessel’s hydrostatic tables are based on the moulded draft, which is the draft corrected for the keel thickness (some tables contained both moulded and external drafts).

Many times interpolation, between the two closest drafts, is performed to get the required displacement.

b) Ton per centimeter (TPC)

The TPC for any given draught is the weight that must be loaded or discharged to change the ship’s mean draught by one centimeter.

c) Longitudinal Centre of Floatation (LCF)

When the ship floats at a particular draft, any trimming moment acting on the ship would act about a particular point on the water plane. This point is the centroid of the area of the water plane and is called the center of the floatation (CF).LCF (Longitudinal Centre of Floatation) is the longitudinal separation between the After Perpendicular and the Centre of Floatation.

d) Moment to change trim (MCTC)

MCTC is the moment required to change the total trim of the vessel by one centimeter. dMCTC is the difference in Moment to change trim (MCTC) for 1 meter.

dMCTC = MCTC 1 – MTCC 2.
MCTC 1 = M4 + 0.5 (obtain MCTC for quarter mean draft + 0.5m)

MCTC 2 = M4 – 0.5 (obtain MCTC for quarter mean draft – 0.5m)


With all the above data, calculate first trim correction, second trim correction, displacement corrected for trim, density correction & displacement corrected for density.

a) First Trim Correction or Layer correction (FTc)

FTc = (TT x TPC x LCF x 100) / LBP

The reason behind the first trim correction is that the vessel is trimmed over a line passing through the Longitudinal center of floatation (LCF) and not about midship. The previously calculated mean draft is adjusted and corrected for midship, so to determine the true mean draft additional correction for the distance between LCF and midship section must be performed.

Where LCF is the distance between the vessel’s midship and the longitudinal center of floatation. The LCF must be extracted and interpolated from the hydrostatic tables for the calculated draft and assigned “+” if aft from midship and “-” if forward.

b) Second Trim Correction or Nemoto’s correction (STc)

STc = (TT x TT x dMCTC x 50) / LBP

The position of the LCF, as specified in the hydrostatic tables, is for even keel conditions. The longitudinal center of floatation is by nature the geometric center of the waterplane area.

Once the vessel is trimmed, the waterplane area changes due to the non-symmetrical shape of the vessel’s forward and aft parts, which leads to a change in the LCF position. The 2nd trim correction aims to correct the displacement due to the misplacement of the LCF.

The 2nd trim correction is also calculated in tonnes using above formula:

c) Displacement Corrected for Trim (DispTc)

DispTc = Disp + (FTc + STc)

d) Density Correction (Denc) 

Actual Density (ADen) =Sea water Sample density
Denc = DispT x {(ADen – 1.025) / 1.025}

 The final correction, which has to be utilized, is for adjusting the displacement for the water density, in which the vessel floats. The value of 1.025 tm/m3 has been recognized to be the average seawater density and most of the vessel’s hydrostatic tables are calculated for this standard density.

In order to perform an accurate draft survey calculation, a seawater sample has to be taken and actual water density determined using a draft survey hydrometer. After the displacement is corrected for trim, it has to be adjusted for the difference in densities using the above formula:

e) Displacement Corrected for Density (DispDenc)

DispDenc = DispTc + Denc

f) Total Deductible Weight (Deduct)

  1. Ballast water or unpumpable ballast water (BW)
  2. Freshwater (FW)
  3. Fuel oil (FO)
  4. Diesel oil (DO)
  5. Lubricating oils (LO)
  6. Bilge oily water/sludge (BW)
  7. Other cargo or known weights (dunnage /lashing materials), if any (OW)
  8. Ship’s constant (K)
  9. Lightship displacement of the vessel (LS)

*Deductible weight (Deductibles) =BW+FW+FO+DO+LO+BW+OW

**Total Deductible weight (Deduct)=BW+FW+FO+DO+LO+BW+OW+K+LS

g) Estimated cargo quantity on board = DispDenc – Deduct**

Alternatively, the net displacements before and after loading/discharging can be calculated and the difference between them is the cargo loaded/discharged.

Net displacement(initial)= Displacement corrected for density – Deductibles*

Net displacement (Final)= Displacement corrected for density – Deductibles*

Estimated Cargo Quantity= Net displacement(initial) – Net displacement (Final)





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