# How to Calculate the Draft of a Ship

All around the globe, draft surveys have been accepted as a reliable means of cargo measurement in the maritime sector. In this article, we’ll be discussing the processes involved in calculating the draft of a ship in Nigeria and also provide some additional information we think might be useful concerning the subject matter. Read on. How to calculate the draft of a ship in Nigeria would be discussed below:

• ## Why is the Calculation of the Draft of a Ship Carried Out?

The draft survey, or calculating the draft of a ship, has to do with the calculation involved to know what the weight of the cargo aboard a ship is at any given time, derived from the changes in the ship’s displacement. This calculation is usually performed when cargo is loaded onto or discharged from a ship.

The principle that guides the calculation of draft survey is the Archimedes Principle which states that “a body immersed in a liquid is subjected to an upward force equal to the weight of the displaced liquid”. What this means in a layman’s understanding is that a freely floating object shall displace an amount of liquid that is equal to its own weight.

• ## How is the Draft Survey of a Ship Carried Out and How Accurate is it?

As earlier mentioned, the purpose of calculating the draft of a ship is to determine the weight of the cargo on board the vessel using the density of water in which the vessel is floating. To perform a draft survey of a vessel, the draft markings at six standard points on both (port and starboard) sides of the hull would have to be read, as well as the draft at forward and aft perpendiculars and at midship of these two. Thereafter, the drafts are corrected by applying corrections factors such as draft, trim and water density.

The displacement of the ship would have to be determined both before and after loading while making allowance for required deductibles such as diesel oil, fuel oil, freshwater, and ballast water, to name a few (more on deductibles later). It is the difference between the displacement before and after the ship is loaded or discharged that translates to the weight of the cargo loaded or discharged.

Concerning the accuracy of a draft survey in determining the weight of cargo loaded or discharged from a ship, we need to point out it is dependent on the experience of the seaman reading the draft and the weather conditions at the time of reading the draft. When the draft survey of a ship is accurately performed, the accuracy is +/- 0.5% of the final figure.

To ensure that good results are obtained during the draft survey of a ship, certain conditions have to be met. One is, draft marks on the vessel must be well-painted to enhance visibility. Another condition that will help a draft survey of a vessel achieve good results is that the ship must be upright, with the list not being more than 0.5 degrees. In addition to the vessel conditions that help promote good results during a draft survey, ballast tanks should be either pressed up or empty. Slack tanks must be kept to a minimum.

Some more vessel conditions to have good results during the draft survey include the availability of approved ship’s hydrostatic and tank-sounding tables, the availability of good means of access to check draft from the seaside (preferably a small boat), and sounding pipes should be marked and clear of any obstructions. Another important suggestion is that the vessel’s trim should be as minimum as possible and be within the correction covered in the ship’s sounding table.

• ## Step-by-Step Procedure of How to Calculate Draft of a Ship

This section of this article gets to the main crux of the article title – how to calculate the draft of a ship. The step-by-step procedure involved in the draft survey includes six distinct stages which we would handle one after another. In each of the stages of the calculation process that would be discussed below, you’d be provided with the relevant formula to help you solve that stage.

Before we proceed with the explanation of the six steps involved in the calculation of the draft of a ship, let’s outline the six steps involved. Here they are:

• Observed (Obs) Drafts and Apparent Trim
• Draft Correction (perpendicular correction)
• Obtaining True Draft & True Trim
• Final Draft calculation (Quarter Mean Draft)
• Obtaining relevant data for Quarter Mean Draft from the Hydrostatic table
• Calculation of First Trim Correction, Second Trim Correction, Displacement Corrected for Trim, Density Correction, and Displacement Corrected for Density

Now that we’ve outlined the procedures involved in calculating the draft of a ship, let’s dive right into providing explanations of the calculations involved in each of the procedures.

• ## Step 1: Observed (Obs) Drafts and Apparent Trim

The first stage of every draft survey calculation is obtaining the observed drafts and apparent trim. Remember there are two drafts for a ship, that is the draft at actual draft marks painted on the sides of the vessel (also known as Apparent Trim) and the draft at forward and aft perpendicular and at midship of these two (this type of draft is listed in the ship’s Trim and Stability booklet).

Below is the formula required:

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 visual draft marks (LBM)= [Length between perpendiculars (LBP) – (Fd+ Ad)]

N/B: “Fd” in the formula for LBM is the distance between the forward draft mark & forward perpendicular, while “Ad” is the distance between the Aft draft mark and aft perpendicular.

• ## Step 2: Draft Correction (perpendicular correction)

When ships are built, draft marks are typically marked at a convenient position and at times it is offset from the forward and aft perpendiculars or the midship position. That is why the Draft Correction formulae (which would be provided below) is needed to correct the observed drafts.

Draft Correction = [Distance from perpendicular × Apparent Trim] / Length between visual draft marks (LBM)

The distances from the perpendicular can be found in the Trim and Stability booklet of the ship.

In line with the Draft Correction formulae  above, let’s provide the relevant Draft Correction formula for the perpendiculars and midship drafts below:

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

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

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

• ## Step 3: Obtaining True Draft & True Trim

The third step of calculating the draft of a ship is to obtain the true draft and true trim of a vessel. Below is the formula for obtaining the true draft and true trim:

Fore Draft Corrected (Fcd) = Fm + Fc

Aft Draft Corrected (Acd) = Am + Ac

Mid Draft Corrected (Mcd) = Mm + Mc

True Trim (TT) = Acd – Fcd

• ## Step 4: Final Draft calculation (Quarter Mean Draft)

The fourth step of the procedure of calculating the draft of a ship is the final draft calculation (also referred to as Quarter Mean Draft) using the formula below:

Fore and Aft Mean Draft (M2)

= (Fcd + Acd)

2

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

2

Quarter Mean Draft (M4) = (M3 + Mcd)

2

Alternatively, Quarter Mean can be calculated using the formula below:

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

• ## Step 5: Obtaining relevant data for Quarter Mean Draft from the Hydrostatic Table

After the Quarter Mean Draft (M4) figure has been gotten using the formula in Step 4 above, the next step of the draft survey procedure is to obtain certain data from the ship’s hydrostatic tables. For the sake of the calculation of draft for a ship, the following data are to be obtained from the hydrostatic tables:

1. ## Displacement

Using the ship’s hydrostatic tables, the vessel’s displacement that corresponds to the value of the Quarter Mean (M4) draft should be extracted. The hydrostatic tables of vessels are typically based on the moulded draft (i.e. the draft corrected for the keel thickness), however, some tables also contain external drafts. To get the required displacement for the vessel, there might be a need to interpolate between the two closest drafts.

1. ## Ton Per Centimeter (TPC)

TPC, short for Ton Per Centimeter, connotes the weight that must be loaded or discharged from any given draught to change the ship’s main draught by one centimeter.

1. ## Longitudinal Center of Floatation (LCF)

Longitudinal Center of Floatation (LCF) refers to the longitudinal separation between the After perpendicular and the center of the floatation. In other words, LCF is the point on the water plane that acts on a ship whenever there is a  trimming movement as the ship floats at a particular draft.

1. ## Moment to Change Trim (MCTC)

Moment to Change Trim (MCTC refers to the moment that is required to change the total trim of the ship by a centimeter. dMCTC connotes the difference in moment for the trim of the vessel to change by 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)

• ## Step 6: Calculation of First Trim Correction, Second Trim Correction, Displacement Corrected for Trim, Density Correction, and Displacement Corrected for Density

To calculate First Trim Correction (also known as Layer Correction) (FTc), use the formula below:

FTC =

(TT×TPC×LCF×100)

LBP

N/B: LBP is the length between virtual draft marks

To calculate Second Trim Correction (also known as Nemoto’s correction), use the formula below:

STC =

(TT×TT×dMCTC×50)

LBP

To calculate Displacement Corrected for Trim (DispTC), use the formula below:

DispTC = Disp + (FTC + STC)

To calculate Density Correction (DenC), use the formula below:

DenC = DispT × {(ADen – 1.025)/1.025}

The calculation for calculating density correction contains 1.025 tm/m3, a value recognized to be the average seawater density. For this reason, most ships’ hydrostatic tables are calculated for this standard density. To accurately calculate the adjustment of the displacement for water density, a seawater sample must be taken to determine the actual water density using a draft survey hydrometer. When this value (i.e. ADen) is obtained, the displacement for the water density is corrected accordingly using the above formula.

Displacement Corrected for Density (DispDenc) is calculated thus:

DispDenc = DispTc + Denc

To be able to get what truly the measurement of a vessel’s cargo is, certain deductible weights have to be subtracted. Before we go ahead to provide the formula for the Total Deductible Weight (Deduct), see the list below:

• Ballast water or unpumpable ballast water (BW)
• Freshwater (FW)
• Fuel oil (FO)
• Diesel oil (DO)
• Lubricating oils (LO)
• Bilge oily water/sludge (BW)
• Other cargo or known weights (dunnage /lashing materials), if any (OW)
• Ship’s constant (K): This is the difference between a vessel’s designed lightship and its actual displacement when empty.
• 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

With the value obtained from *Deductible weight (Deductibles) and *Total Deductible weight (Deduct), the weight of the cargo loaded or discharged from a vessel can be determined. To do this, use the formula below:

Estimated cargo quantity on board = DispDenc – Deduct

Or, use this:

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)

We hope that we’ve been able to explain how the draft of a ship can be calculated. The more a seafarer gains attempts to conduct draft surveys, the more experience such personnel builds, thereby enhancing the individual’s ability to accurately calculate the draft of a ship. Aside from the human factor, the vessel must meet the conditions stated in this article for good results to be obtained during a draft survey.