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1 INTRODUCTION
The actual cargo loaded depends on the ship’s
maximum allowable immersion (deadweight) at the
relevant season, which will include the capacity of
fuel, lubricating oil, provisions, fresh water, crew,
ballast water, and the ship-constant.
Cargo capacity (ton) = deadweight (ton) – balast, fuel,
provisions, etc. (ton)
However, in practice sometimes the discharging
report occurs, which shows a shortage of the cargo
discharged in port of destination. Such claim seemed
rather doubtful and has to be refused when the
amount of cargo loaded was verified by Draft Survey,
as the carrier is under an obligation to verify the
amount of cargo and to verify its condition at the time
the cargo comes into his custody and care.
2 THE ACCURATE CALCULATIONS OF CARGO
CAPACITY
Draft has a direct correlation to the displacement of
the ship and to the deadweight at the same time.
Deadweight (ton) = displacement Δ (ton) – light ship
weight (ton)
It is important that the draft is accurately
determined since each incorrect centimeter in draft
can mean a displacement difference of several tons.
Below, in Table 1 are presented the Hydrostatic data
of the semi-container ship which has been used for the
further calculations. The main particulars of the ship
are as follows:
Gross Capacity GT 11 573
Maximum Displacement 20 767 (ton)
Deadweight 13 593 (ton)
Length Overall 149.15 m
Breadth 22.00 m
High to the main deck 12.00 m
Maximum draught 9.14 m
Table 1. The selected Hydrostatic data of the semi-container
ship.
________________________________________________
T V Δ TPC MJ LCB LCF
[m] [m³] [ton] [ton/cm] [tonm/m] [m] [m]
________________________________________________
5.24 10719 11020 23.4 16686 0.52 0.68
5.28 10810 11113 23.4 16717 0.52 0.66
5.30 10856 11161 23.4 16732 0.52 0.66
5.32 10901 11207 23.4 16747 0.52 0.65
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Draft Survey - The Question of Accuracy
M. Szymoński & Z. Piątek
Polish Naval Academy, Gdynia, Poland
ABSTRACT: Presented paper relates to the influence of the accuracy of calculations on the results of the Draft
Survey method. This method is designed for determine the total weight of cargo a ship is actually loaded, in
tons.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 18
Number 4
December 2024
DOI: 10.12716/1001.18.04.18
916
The density of water ρ, in which the ship floats
must be determined accurately.
The mean draft T (m) is measured at the half
distance mark of the ship’s length between
perpendiculars (1/2 LPP). This mean draft is the same
as the sum of the draft in the fore and aft
perpendiculars, divided by two.
In practice the draft marks are not located on the
perpendiculars nor on the centerline , as it has been
presented in Fig. 1.
Figure 1. The corrections x and y for drafts marks to place
them on perpendiculars.
The value reading from the fore and aft marks has
to be corrected in order to find the value at the
perpendiculars.
It mens, that the corrections x and y are necessary
to have the drafts information on perpendiculars, and
to determine the proper value of the displacement
from the hydrostatic data. The above corrections are
available to be used from ship’s hydrostatic
documentation.
However the drafts can be calculated directly as
the perpendiculars data, by formulas (2) and (3), as
shown in Fig.2.
The ship’s trim ( t ) describes the following
formula (1) :
( )
J
LCG LCB
t
M
−
=
where:
LCG - logitudinal center of gravity,
LCB – longitudinal center of buoyancy
MJ - moment to change the trim per unit
Figure 2. The corrections ΔTA and ΔTF to get a proper mean
draft T.
The longitudinal form data : LCB , LCF and
Moment to change trim per unit MJ are used to
determine:
− the correct displacement at an accepted draft,
− the draft before and after loading.
The correct draft is the vertical distance from the
base line to the waterline at the Center of Flotation -
COF. However the COF in practice does not correlate
to LPP/2 and the above does it means that the ship has
a trim, and special „trim correction” to be adjusted for
the correct displacement determination.
Trim adjustment is determined by formulas (4 – 6).
It should be added that trim adjustment only be
applied if a hydrostatic table with a trim of nil is used.
In practice an additional, the different one
correction should be taken into consideration. It
means the correction of deflection of the ship’s hull
for hogging or sagging. But in this case the ship is not
deflected and the said correction is not to be
calculated.
The initial data for draft survey calculation has
been presented in Table 2. The conditions are as
follows: As the ship floats in the sea water: ρ = 1.025
t/m², it is not necessary to calculate the correction for
the density of water.
For the ship Displacement ( Δ ) of 11 128.34 t, the
folowing hydrostatic data has to be read:
1. the mean draft T = 5.29 m,
2. the Longitudinal Center of Buoyancy LCB = 0.52 m,
3. the Longitudinal Center of Flotation LCF = 0.66 m,
4. the Moment to change the trim per unit MJ =16 724
tm/m,
5. the length of the ship between the Perpendiculars:
Lpp=140 m.
Calculated trim as per formula (1) equals: t = -
0.2129 m.
Table 2. The initial data for draft survey calculations.
________________________________________________
mass LCG VCG MLCG MVCG Δmh
[t] [m] [m] [tm] [tm] [tm]
________________________________________________
Light ship 9773.00 66.94 8.65 654204.62 84536.45 2439.00
Ship- 300.00 60.00 10.00 18000.00 3000.00 00.00
constant
Cargo in 1055.34 103.30 3.01 109016.62 3176.57 12430.07
hold No. 2
Displace- 11128.34 70.20 8.15 781221.24 90713.02 14869.07
ment
________________________________________________
The drafts fore and aft are, correspondingly :
Tfore = T + (Lpp/2 - LCF) · ( t/Lpp ) = 5.19 m (2)
Taft = T + (-Lpp/2 -LCF) · ( t/Lpp ) = 5.40 m (3)
3 THE INFLUECE OF DRAFT ACCURACY ON A
SHIP–CONSTANT DETERMINATION
The more accurate calculations of fore and aft drafts
are giving the new value of the mean draft
T = (5.19 m + 5.40 m )/2 = 5.295 m,
and the trim t = - 0.21 m.
The hydrostatics data for the more correctly
calculated value of the mean draft are as follows:
The Immersion:
TPC = 23.4 t/cm ; LCF = 0.66 m ; MJ = 16 728 tm/m;
MJ ( T+ 0.5m ) = 17 127 tm/m ; MJ (T- 0.5 m ) = 16 364
tm/m
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The new value of the Displacement1 (Δ1) = 11149 t
The corrections for the Displacement Δ1 due to the
ship’s trim are as follows:
CORR1=100 · LCF · TPC · (t/LPP) = - 2.32 t (4)
CORR2=0,5 · (t
2
/LPP) · [MJ · (T+0.5m) – MJ · (T-0,5
m)]=0.12t (5)
The corrected Displacement is:
Δ1 CORRECTED = Δ1 + CORR1 + CORR2 = 11 146.80 t
(6)
The calculations of the Ship-constant value for the
corrected hydrostatic data has been presented in Table
2.
Table 2. The corrected results of Ship-constant calculations.
________________________________________________
mass LCG VCG MLCG MVCG
[t] [m] [m] [tm] [tm]
________________________________________________
Ship’s 11146.80 70.20 8.15 782505.36 90846.42
Displacement
Light ship -9773.00 66.94 8.65 -654204.62 -84536.45
Cargo in hold -1055.00 103.30 3.01 -108981.50 -3175.55
No.2
Ship-constant 318.80 60.60 9.83 19319.24 3134.42
________________________________________________
The Ship-constant value from Tale 2 is not the
same as the initial. The difference between the initial
and obtained value of the Ship - constant equals
+18.80 t.
The drafts fore and aft, which has been used for
calculations, were defined with the accuracy of 1cm. It
is clear that it is not a satisfactory degree.
When improved the accuracy of the draft
determination to 0.1 cm, the obtained results are as
follows:
TFORE = 5.181 m, TAFT = 5.394 m, trim t = - 0.213 m,
the mean draft T = 5.287 m, and the new value of the
Displacement Δ2 = 11 1330 t.
The corrections Corr 1 and Corr 2 due to the trim
of the ship are giving the value
Corr Δ2 = Corr1 + Corr2 = - 2.20 t
The results of ship-constant calculations has been
presented in Table 3. These results are very close to
the initial.
The value of corrected Displacement equals:
Δ2 CORRECTED = 11 127.80 t
Table 3. The more accurate results of Ship-constant calculations.
________________________________________________
mass LCG VCG MLCG MVCG
[t] [m] [m] [tm] [tm]
________________________________________________
Ship’s 11127.80 70.20 8.15 78117.56 90691.57
Displacement
Light Ship -9773.00 66.94 8.65 -654204.62 -84536.45
Cargo in Hold -1055.00 103.30 3.01 -108981.50 -3175.55
No. 2
Ship-constant 299.80 59.99 9.94 17985.44 2979.57
________________________________________________
When again improved the accuracy of the draft
determination to 0.01 cm, the results of the draft
survey calculations are as follows:
TFORE = 5.1810 m; TAFT = 5.3939 m; trim t = - 0.231 m;
the mean draft T = 5.2875 m, Displacement Δ3 = 11 130
t .
The hydrostatic data for the above parametrs are
presented below:
Immersion TPC = 23.4 t/cm; LCF = 0.66m; the Moment
to change trim per unit
MJ = 16 722.626 tm/m;
The corrections to the Displacement due to the
trim of the ship has been calculated as:
CORR 1 = - 2.3486 t; CORR 2 = 0.1234 t.
The final results of corrected Displacement is:
Δ3 CORRECTED = Δ3 + CORR1 + CORR2 = 11 130 t – 2.2 t =
11 127.80 t
The results of the Ship–constant determination for
the accuracy of 0.01 cm in draft calculations, has been
presented in Table 4.
The obtained parameters of the Ship-constant are
very close to the initial value.
Table 4. The results of high accuracy of Ship-constant
determination
________________________________________________
mass LCG VCG MLCG MVCG
[t] [m] [m] [tm] [tm]
________________________________________________
Ship’s 11127.80 70.2011 8.1515 781171.56 90708.26
Displacement
Light Ship -9773.00 66.94 8.65 -654204.62 -84536.45
Cargo in Hold -1055.00 103.30 3.01 -108981.50 -3175.55
No. 2
Ship-constant 299.80 59.99 9.99 17985.44 2996.26
________________________________________________
4 CONCLUSIONS
In a general, the amount of cargo loaded on the ship
depends on, among other things:
− the capacity of space reserved for cargo,
− the maximum cargo capacity (tonnage) of the trade
route,
− the duration of voyage relative to the amount of
fuel which reduces the cargo capacity,
− the maximal permissable draft during the voyage.
Table 5. The comparison of obtained results of Draft Survey
calculations.
________________________________________________
Ship-constant LCG (X) VCG (Z)
[t] [m] [m]
________________________________________________
Initial Data 300.00 60.00 10.00
Accuracy of draft 318.80 60.95 9.83
calculations 1 cm
Accuracy of draft 299.80 59.99 9.94
calculations 0.1 cm
Accuracy of draft 299.80 59.99 9.99
calculations 0.01 cm
________________________________________________
However, on the begining of the voyage the
captain should be familiar with the actual weight of
cargo loaded. The total weight of cargo is calculating
918
by Draft Survey method. How accurate the result can
be obtained - it has been presented in the above
analyse and compared in Table 5.
REFERENCES
[1] Z. Piątek, „ The influence of accuracy calculations on
Draft Survey results”, unpublished review, Department
of ship’s exploitation, Naval Academy of Gdynia,
Poland, 2019;
[2] Dibble W.J.,Mitchell P., Draugh Surveys: A guide to
good practice., North of England P&I Association, 2009.;
[3] UNECE – United Nations Economic Commission for
Europe, Code of uniform Economic and Social council,
Commitee on Energy, United Nations, 1992;
[4] Wolfram I., A note of correction for hog and sag., The
Naval Architect, July 1980.
