Have you seen a truck weighing bridge ? Do you know how it works ?
It weighs the empty weight of the truck and then the loaded weight. The difference is the weight of the cargo on that truck.
Well draft survey uses a similar principle to measure the cargo loaded on board ships.
With draft survey we measures the initial weight (displacement) of the ship and it measures the final weight (displacement) of the ship after loading. The difference plus all the weights that were taken out (like ballast) will be the cargo loaded.
The only difference between weight measurement in case of truck and ship is that for later the calculation is not that simple.
So in this post I will discuss about how to go about measuring the cargo quantity with draft survey.
1. Why Draft survey ?
On tankers, the measurement of cargo quantity loaded is simple. We know the density of the cargo and we know the volume. It is easier to know the weight of the cargo loaded.
But with cargoes like coal, we cannot measure the weight by just measuring the the height of the hold to which cargo is loaded.
This is because unlike liquids, solid cargoes would not take the shape of the hold.
Calculating the cargo loaded with draft survey is the most appropriate way.
But it isn’t only with solid cargoes. Sometimes we have to measure the cargo quantity of liquids by draft survey. One such cargo is Mollasses loaded on chemical tankers.
This cargo has air in it and thus the density of this cargo is not uniform. Calculating the way we calculate the weights for other liquids will give wrong quantity. Draft survey is the answer in this case too.
So let us see how we need to go about draft survey.
2. Basics of Draft survey
With draft survey calculations, all we want to know is the difference in ship’s arrival weight (Displacement) and departure weight (displacement).
Let us say we have these figures
Displacement: 20000 T
Ballast: 6000 T
Other weights : 1000 T
Displacement: 50000 T
Ballast: 500 T
Other weights : 1000 T
The difference in displacement is 30000 T. Out of this 5500 T of ballast was removed and some cargo was loaded at the port.
It is simple calculation to know the quantity of the cargo loaded which is 35500 T.
In this simple calculation, it is not difficult to know the ballast and fuel on board. What we need to know is the displacement of the ship on arrival and after completion of loading.
Once we know that, we can know the cargo quantity. The easiest way to calculate the ship’s displacement is by noting down the draft of the vessel and looking for the displacement for that draft in the trim and stability booklet.
That is the simplest way of saying it but then there are few corrections to this which we will discuss.
3. Draft of the vessel
There are two drafts for a vessel.
- Draft at forward and aft perpendiculars and at midship of these two. This is the draft that is listed in the ship’s trim and stability booklet.
- Drafts at actual draft marks painted on ship side.
So to get the displacement from the trim and stability booklet, we must get the drafts at the perpendiculars.
What we will get from the visual drafts will not be the drafts at perpendiculars in most of the cases.
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Let us say we have the visual draft as follows. In draft survey calculation we call the visual drafts as “Apparent drafts”.
So let us say that the mean of both side of the apparent drafts is
Forward = 6.43 m
Aft = 8.53 m
Midship = 7.42 m
Apparent Trim = 2.1 m
As I said we need to bring these drafts to the perpendiculars.
The formula for correction to the visuals drafts to bring it to the perpendiculars is
You will find this distances in the Trim and stability book of the ship. Have a look at these corrections for one of the ship.
As we can see that the distance from forward perpendicular to the forward draft mark is 9.95 meters.
So the correction to the forward draft would be 9.95 x 2.10 / 155. This will be equal to 0.135 meters. As the forward perpendiculr is forward of the draft marks and we have stern trim, this correction will be negative.
Same way for apparent trim of 2.10 meters, the corrections to the apparent drafts are
Ideally we should now take the midship draft (7.451 m in this case) and look for the displacement from the trim and stability booklet.
But there can be errors in this drafts and we have to make sure that draft is correct. These error could be
- Errors in reading few of the visual drafts
- Errors due to Hog or Sag of the vessel
To minimise these errors we finalise the draft of the vessel by having mean of means draft. This is also called Quarter mean draft.
Below is the mean of means draft for our example.
4. Calculating displacement of the ship
Now that we know the draft of the ship, we can open the trim and stability booklet and check the displacement for this draft.
We may have to interpolate to get the exact displacement.
Here is the relevant page of Trim and stability booklet for this ship.
We have now got the displacement for the actual draft of th vessel. But there will be few corrections to this displacement. Let us see what these are.
5. 1st Trim correction
The draft and displacement we got so far is at the mean of aft and forward perpendicular.
As per Archimedes principle, a floating ship displaces the amount of water equal to its own weight. And the ship floats at the center of floatation. So the correct displacement is the displacement corresponding to the draft at the center of floatation and not at the mean draft.
The correction applied to the displacement at mean draft to bring it to the displacement at center of floatation is called the “1st Trim correction”.
The formula for 1st trim correction is
If you wish to know how this formula arrived, watch this video
As we need the values of TPC and LCF for calculating 1st trim correction, open the Trim & stability booklet and find these values for the vessel’s draft. Again we have to do the interpolation to get the exact values.
Now let us calculate the 1st Trim correction for our example.
In this case it comes out to be 65 T but it can have larger value in other situations. This 1st trim correction we need to add to the displacement we got earlier.
Sign of 1st trim correction
This is not so difficult to find. We have the draft at the Midship and we are applying the correction for change in draft because LCF is not at the midship.
Now let us say vessel has stern trim and LCF is aft of midship. Which draft will be more ? The one read at the LCG or at the midship ?
You are right !!! The draft at the LCF will be more. So in this case the correction need to be added to the midship displacement we have got.
So for sign of 1st trim correction, all we have to see is the location of LCF with respect to Midship.
So for sign of 1st trim correction, all we have to see is the location of LCF with respect to Midship. Then by pure logic, we can find out if we need to add that correction or subtract.
6. 2nd Trim correction
Now there is this another correction. First trim correction was because LCF was not at the midship. If the LCF was at the midship, there would not be any 1st trim correction.
The distance of LCF from the midship is given in the trim and stability booklet. For hydrostatic ship particulars for some ships, the value of LCF is at zero trim condition. For example see below
Now if the vessel is trimmed, the position of LCF will change slightly because of change in water plane of the ship.
2nd Trim correction takes care of this change of position of LCF because of trim of the vessel.
The formula for 2nd trim correction is
To get the value of Dm-Dz, get the value of MCTC for (mean draft +50 cms) and for (mean draft-50 cms). The difference between these two values of MCTC will be the value for Dm-Dz.
With this value of Dm-Dz, we will get 2nd Trim correction as 35 T.
The 2nd trim correction is always positive.
But see the hydrosatic particulars of the vessel that I took the data from. LCF values are given for different trims.
We can interpolate to get the LCF for actual trim of the vessel. In this case 2nd trim correction will not be applicable.
7. Final Displacement
Once we have 1st trim correction and 2nd trim correction, we need to apply these to the ship’s displacement.
So the actual displacement with respect to the draft at LCF will be
Displacement at Midship + 1st Trim correction + 2nd Trim correction
In our example this would be 30702.28 + 65 +0 = 30802.28 T
8. Density correction
We have now got the displacement for quarter mean draft. To this displacement we have applied 1st trim correction and 2nd trim correction.
We now have vessel’s actual displacement. But this displacement is in salt water density of 1.025 as most of the hydrostatic tables have the data for that density.
Now if the water density around the vessel is different than 1.025, the displacement of the vessel will change.
Why ? As per archimedes principle the ship displaces water equal to its own weight. If the density of the water is more, ship would displace less volume of water (less draft). And if density of the water is lesser, it would need to displace more volume of water (more draft) to have same weight as of the ship itself.
For draft survey, we need to measure the density of dock water just before or after reading the visual drafts. The density is measured by draft survey hydrometer with a sample of dock water drawn from around the vessel.
The density of dock water changes with depth. So it is important to know at what depth the sample is drawn. Many take the sample from a depth that is half the draft of the vessel. Others prefer to take the sample by running the emergency fire pump.
Now say we have measured the density and we have the dock water density as 1.01
So how to correct the displacement we calculated so far for density ?
So in our example it will be 30802.28 x 1.01/1.025. That will be equal to 30351.51.
9. Cargo quantity from initial and final displacement
Apart from calculating the displacement, we need to to know the existing weights on vessel.
For example we need to know the exact weight of ballast, Fuel oil, Lube oil, fresh water etc on board on arrival. That is not a difficult thing to know. But there are some best practices.
First it is easier to measure the quantity if a tank is either completely full or completely empty. This also removes the ambiguity and measurement error.
Second, the vessel must not be down by head (negative trim). This is because it brings ambiguity to the actual quantity of ballast in a tank.
Third, since we need to know the weight of the ballast, we must know the density of the water in the ballast. We will know the volume from the sounding table and multiplying with the density will give the weight in each ballast tank.
Fourth, we need to measure and sound each space on ship and not assume that it is empty. For example if there is any void spaces, we must sound these spaces as well.
So now we will know what contributes to the the arrival displacement of the ship.
Arrival displacement = Lightweight of ship + Ballast + Fuel + Fresh water + Lube oil + Constants
And among these things we know the quantity of ballast, fuel, lube oil, and fresh water.
We need to repeat this calculation and measurement of all spaces after completion of loading.
Departure Displacement = Cargo + Lightweight of ship + Ballast + Fuel + Fresh water + Lube oil + Constants
Lightweight of the ship and constants will remain same and so these does not matter. We would know the arrival and departure displacement from draft survey. All other weights we know by sounding and measurement. The only known is the cargo loaded. It is simple mathematics then to know the cargo quantity.
10. Calculating constants on arrival
Calculating constants is not really required if our aim is only to know the weight of the cargo loaded. This is because the the quantity of constants will not change.
But calculating the constants on arrival is a good practice. This gives a fair idea of the correctness of calculation. For example, let us say we know that constants will be in the range of 200 to 300 tons.
If initial calculations give too high or too low constants, we know something is wrong somewhere.
We can sometimes get negative constants. This would mean that we have done some mistake and we must find it and correct it. It may be that we have wrong drafts, wrong soundings etc. Whatever it is, we must correct it before loading starts.
Draft survey is widely used for cargo measurement. It is acceptable way of measuring the cargo quantity.
The calculation however requires practice. It may sometimes be confusing to seafarers using the draft survey for the first time. This can lead to the errors in calculations and cargo claims.
We must know the basics of the draft survey. Once we know that draft survey would not look that difficult.
About Capt Rajeev Jassal
Capt. Rajeev Jassal has sailed for over 19 years mainly on crude oil, product and chemical tankers. He holds MBA in shipping & Logistics degree from London. He has done extensive research on quantitatively measuring Safety culture onboard and safety climate ashore which he believes is the most important element for safer shipping.