## Monday, April 8, 2013

### Ship’s draft survey calculation

SHIP’S DRAFT SURVEY  ( Draft  Survey Kapal )

Before we explain the following Ship’s draft survey calculation , we provide
the application to calculate the Ship’s draft survey.

There is a simple Ship’s draft survey  display applications ( 55 kb ) that can be

This Survey Procedure is International Standard for any type of ship. The ship is first
surveyed light, to calculate the constant. It is then re-surveyed after loading to determine
the weight of cargo.
APPARENT TRIM
1.       The Forward (Fwd), Aft (Aft), and Midships (Mid) drafts are read at both Port (P) and Starboard (S) marks. The P and S readings are added, and the result divided by two.
2.       The Aft draft is subtracted from the Fwd draft, and the result is Apparent Trim. If Trim is positive, the ship is trimmed By the Head; if Trim is negative, the ship is trimmed By the Stern.
Fwd Draft = Fwd(P) + Fwd(S)
2

Aft Draft = Aft(P) + Aft(s)
2

Mean Mid = Mid(P) + Mid(s)
2

Trim = Fwd – Aft

DRAFT CORRECTIONS TO THE PERPENDICULARS
3.   The After Perpendicular is a right angle line to the keel passing through the rudderpost; it is also the first frame marked «0» on the vessels drawings.
The Forward Perpendicular is a right angle line to the keel cutting the vessel’s Summer waterline at the stern. The vessels stability information is calculated on the drafts measured at the perpendiculars; as the draft marks rarely coincide with these lines, a draft as read must be corrected.
4.
If the marks are not on the perpendiculars, the vessel usually has a tabulated plan in her hydrostatic books. However, some of the older vessels do not have their tabulation and it is therefore necessary to work out the correction to be applied by referring to the vessels capacity plan and measuring the horizontal distance between the draft marks and the perpendiculars of the waterline.
5.  The correction is calculated as follows:
Aft Perpendicular Corr = 7.10 x 1.75(trim)= 0.0971 cm (+)
128.0

Fwd Perpendicular Corr = 1.21 x 1.75(trim)= 0.0165 cm( - )

The rule to apply the correction:
Trimmed by the STERN:   Forward Correction =  MINUS ( - )     After Correction  =   PLUS ( + )
Trimmed by the HEAD :   Forward Correction  =   PLUS (  + )    After Correction   =   MINUS (  -  )

6.  The above corrections are applied to the forward and after  drafts read.
Fwd  2.64 m                                 Aft  4.30 m
— Corr  0.0165                               + Corr 0.0971
Corrected Draft       2.6235           Corrected Draft         4.3971

7.   CORRECTED DRAFT
Aft      5.019  =   Aft - Fwd  =  Corr. Trim
Fwd    2.361
Corrected Trim     2.658

NOTE:  This value is used in Trim Correction Formulas to adjust the displacement

MEAN DRAFT CORRECTION   ( M / M / M )
8.  The Quarter Mean ( QM ) or Mean Draft Corrected for  Deformation must be solved next. Use the corrected draft values
9.   First calculate the Fwd/Aft Mean Draft. Add Fwd to Aft, and divide the result by two:
Fwd /Aft Mean = Fwd + Aft
2
10.
Next, calculate the Mean of Mean Add the Fwd/Aft  Mean (calculated in (No. 9)) to the Mid Mean, and divide the result by two:
Mean of Mean = Fwd/Aft Mean + Mid Mean
2

11.  Now calculate the QM Add the Mean of Mean (calculated in (No.10)) to the Mid Mean, and divide the result by two

NOTE:  The Mid Mean is applied twice, first in calculating   the  Mean of Mean, and second in calculating the QM.
QM =  Mean of Mean +  Mid Mean
2

EXAMPLE :
FWD  P 2.377         AFT P 5.017       MIDSHIP       P 3.59
S 2.377                S  5.017                           S 3.72
4.754                   10.034                              7.31

FWD= 4.754 / 2 = 2.377        AFT= 10.034 / 2 = 5.017        MEAN-MID = 7.31 / 2 = 3.655
TRIM    =   AFT - FWD (vice versa) =   =  5.017 -  2.377 (vice versa) =  -  2.64
Trim by the Stern  ( Apparent )

DRAFT CORRECTION
Corrections for the Fwd and Aft Drafts (Fwd corr. and Aft corr.) and Corrected Trim must be calculated. The correc-tions values are different for each ship, and are found in the Stability Manuals. If required, they can be calculated from the formula ,
EXAMPLE:
Fwd Correction Value =(distance from Fwd Draft to Fwd Perp)
(distance between Fwd and Aft Drafts)

Fwd Correction = Fwd Correction Value x Trim ( Apparent )= 0.006037 x 2.64 =  0.016( - )
Aft Correction Value = (distance from Aft Draft to Aft Perp)
(distance between Fwd and Aft Drafts)

Aft Correction   =  0.034716 x 2.64 =  0.91 (+)
Corrected Draft:
Fwd  = 2.377 Aft  =  5.017
Corr = -0.016 Corr = + 0.091
2.361  5.108

Corrected Trim:   Aft Draft - Fwd Draft = Corr Trim (CT)
Aft = 5.108
Fwd =  - 2.361

2.747

Note: this value used in the Trim correction Formulas to adjust the displacement.
EXAMPLE:
Mid Mean = 3.655 M
Fwd + Aft =  2.361 M + 5.019 M = 7.38 M
Fwd and Aft Mean = 7.38  = 3.69 M
2
Fwd and Aft + Mid Mean   =   3.69

+3.655
7.345

Mean Mean of Means  =  7.345  = 3.672 M
2

Mean Mean of Means + Mid Mean = 3.672 + 3.655 = 7.327 M

Quarter Mean = 7.327 = 3.663 M
2

QM = 3.663 M

The value for QM is used throughout the remaining Draft Survey Calculations.
NOTE :  QM is the same as M/M/M

M/M/M = ( Fwd + 6 x Mid + Aft ) / 8 = 3.663 M
7.10 : - represents the distance the draft marks are from the perpendiculars.
128  :- represents the length of the vessel between the draft marks
(trim) - the difference between the forward and after drafts.

12.  Refer to the vessel's Stability & Hydrostatic Manuals
and Tables for the following values:

TPC :  tonnes per Centimetre Immersion
MTC : Moment to change Trim One Centimetre
LcB :  Longitudinal Centre of Buoyancy
LcF :  Longitudinal centre of Flotation
KB : Transverse centre of Buoyancy (Keel of Buoyancy)
TKM :  Transverce Metacentric Height (Keel of  Metacentre)

13.  Interpolation
Calculate the Displacement Correction ( DISP. Corr.)

a) Subtract the nearest smaller Draft from the calculated   QM.
b)Multiply the result by 100 to convert Meters to Centimetres.
c) Multiply this by the TPC for the displacement.
d) This correction is added to the displacement given  for   the nearest smaller draft.
Draft Remainder (cm) = Draft remainder x 100
DISP. Corr. =  TPC x Draft remainder (cm)
Displacement =  DISP. +  Disp. Corr. = Actual Displacement
EXAMPLE:
a)  Draft remaining = 3.6635 - 3.66 = 0.0035 M
b)  Draft remaining =  Draft Remainder(M) x 100 = 0.0035 M =0.35cm
c)  Displacement Correction =   TPC x  Remaining draft (cm)

= 17.66 x 0.35 cm = 6.181 MT
d)  DISPL.CORRECTED = DISPL.(at SMALLER DRAFT ) + correction= 7587.00 + 6.181= 7593.181 MT  (corrected)

TRIM CORRECTION
14.
Trim Correction values for a given Displacement is tabulated in the Ship Stability Manual. Even if these are readily available, the following formulas should be studied in order that the principles governing a Draft Survey are fully understood.
15.  Before calculating the First Trim Correction, Corrected Trim (CT)  must be converted from meters to centimetres. Multiply CT (in) by 100 to get centi-metres.
16.  To calculate the First Trim Correction, multiply TRIM by TPC, then multiply the product by the longitudinal Centre of Flotation (LCF) x 100. Then, divide the final product by the Length Between Perpendiculars (LBP).
CT = CT x 100
First Correction = TRIM x TPC x LCF x 100
LBP

Second Correction = TxT x +/-50 cm x MTC diff.
LBP

17.  The first correction can be either positive (add), or negative (subtract), depending on the location of the LCF  and the trim condition. (It's mean sign of LCF and TRIM )
18.1.  VESSEL TRIMMED BY THE STEM                       LCF is Forward (Fwd) (+) ADD Trim Correction
LCF is Aft (Aft) (-) SUBTRACT Trim Correction

18. 2. VESSEL TRIMMED BY THE STERN                     LCF is Fwd (—) SUBTRACT Trim Correction
LCF is Aft (+) ADD Trim Correction

19.  The second  Trim  Correction is  required when the Trim is greater than the LBP divided by 100. It may be applied without adverse effect at smaller trims.
20.  The second correction is always (+) (additive) regardless of the trim or other factors.
21.  Before calculating the Second Trim Correction, MTC differ-ence, sometimes referred to as dM/dZ, must be found.
21.1 ADD 50 cm to the Quarter Mean Draft ( QM ) to  find the corresponding MTC from the vessel’s
Hydrostatic book.

21.2  SUBTRACT 50 cm from the Quarter Mean Draft (QM) to find the corresponding MTC from the Vessels Hydrostatic book.
21.3
The difference between 3.21.1 and 3.21.2 is the MTC difference, or dM/dZ.
EXAMPLE:
(1)First correction: Trim = 2.74 M ( By STERN "+" )  TRIM x LCF x TPC x 100
LBP

(+)2.74 x (—)4.53 x 17.65 x 100 = 159.909 (-) MT= 159.91(-)
137.00

2) Second Correction: TxT x  +/-50 x MTC diff
LBP

MTC diff.: a)  Q M + 50cm = MTC ( Found in  Ship’s book)
b)  Q M - 50cm = MTC ( Found in Ship’s book)
MTC diff = ( a) — ( b)   a)     QM = 3.675
+ 0.50
4.175         MTC = 169.4

b)    QM = 3.675
- 0.50
3.175        MTC =160.7

(a)  =    169.4
(b) = - 160.7
MTC diff  =        8.7

7.5 x 50 x 8.7 = 23.81 + MT
137

(3) DISP Corrected for TRIM:
1st correction:   a) 7587.00
b)- 159.91
=c) 7427.09 (-)

2nd Correction:    c)  7427.09
d) +  23.81
= e)  7450.90 (+) = Displ. Corr.for Trim

NOTES for TRIM FORMULAS FOR IMPERIAL CALCULATIONS:

TPI = Tons Per Inch   (12 converts all to inches)

6» = +/-6» of the QM draft to obtain the two MTI differences.
1st Correction = TRIM x LCF x TPI  x 12
LBP

2nd Correction = T? x +/-6» x MTI diff
LBP

SPECIFIC GRAVITY CORRECTION
22.  A Specific Gravity (Sg) of 1.025  is generally assumed
for SeaWater in calculating Displacement (DISP). Because the Sg. is almost never exactly 1.025, Sg. correction
must be calculated.
22.1
Sg. is always minus if the measured Sg. is 1.025 or less.
22.2
Sg. is plus if the measured S9. is 1.026 or more.
23.  Calculate the Sg. correction by subtracting the measured density from 1.025, divide this by 1.025 and then multi-ply that answer by the DISP.
Sg. corr. = 1.025 - Measured Density x DISP.
1.025
EXAMPLE:
Measured Density = l.020.4

1.025 — 1.0204 x 7450.9 = 32.71
1.025

DISP. corr. for Trim      7450.90
Density Corr. (Sg.) —      32.71
DISP. Corr. for Density    7418.19

VESSEL’S CONSTANT
24.   Subtract-ing the Lightship, weights, ballast and consumables from the Displacement solves the Constant of an unladen vessel.
25.  Tank tables or graphs should be available so the tank soundings can be converted from measure to volumes and corrected for trim.
26.  Figure 16 is a typical tank graph. In addition to volume against sounding information, it provides KG and Inertia data for trim and stability calculations. Figure 17 is a tank trim correction table and Figure 18 is a typi-cal tank table.
27.  Volume multiplied by Sg. equals weight. A Sg. of 1.000 is used for Fresh Water, and for Salt Water Ballast a Sg. of 1.025 is used. Therefore, one cubic meter of Fresh Water equals one Metric Tonne and one cubic Meter of SeaWater equals 1.025 Metric Tonnes.

28.
The Chief Engineer is obliged to supply the Sg. of the various fuel oils on board. It is good practice, if possible, to measure the Sg. at the same time the tanks is being sounded.

29.      DEDUCTABLE WEIGHTS

FUEL OIL                    545.86 MT
DIESEL OIL                 100.70 MT
LUBE OIL                      21.00 MT
FRESH WATER           401.00 MT
DRINK WATER               NIL
BOILER WATER             NIL
BALLAST WATER      1870.84 MT
SLUDGE (BILGE)            5.50 MT
STORES, etc.                  NIL
CONSTANT                 200.42 MT
= TOTAL WEIGHT:     3145.32 MT

NETT DISP.                                7418.19 MT
-TOTAL  WEIGHT                     - 3145.32 MT
NETT DISP LIGHTSHIP               4272.87 MT

FINAL SURVEY
30.  The Final Survey follows the same procedure as the Initial Survey. Total cargo equals DISP. minus Lightship Weight.