**Draught Survey Book (Canada)
CHAPTER THREE**

**DRAFT SURVEY**

**SURVEY PROCEDURE**

**3.1** 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**

**3.2 **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.
**3.3** 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**

**3.4** 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 vessels 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.
**3.5** 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.

**3.6** 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 ( - )

**3.7** 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

**3.8 ** **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 )**

**3.9** The Quarter Mean ( QM ) or Mean Draft Corrected
for Deformation must be solved next. Use the corrected draft values

**3.10** First calculate the Fwd/Aft Mean
Draft. Add Fwd to Aft, and divide the result by two:

Fwd /Aft Mean = __Fwd + Aft__

2
**3.11** Next, calculate the Mean of Mean Add
the Fwd/Aft Mean (calculated in 3.10.) to the Mid Mean, and divide
the result by two:

Mean of Mean = __Fwd/Aft Mean + Mid Mean__

2

**3.12 **Now calculate the QM Add the Mean of Mean
(calculated in 3.11) 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 given in Figure 12.

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.

(128.0) - represents the length of the vessel between the draft marks

(trim) - the difference between the forward and after drafts.

**3.13** 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

TKM: Transverce
Metacentric Height

**3.14 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.

NOTE: Refer to Figures 13 and 14 for sample Hydrostatic Tables.

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
**3.15 **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.

**3.16 **Before calculating the First Trim Correction,
Corrected Trim (CT) (Ref. 3.3) must be converted from meters to centimetres.
Multiply CT (in) by 100 to get centi-metres.

**3.17 **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

**3.18 **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 )

**3.18.1** VESSEL TRIMMED BY THE STEM
LCF is Forward (Fwd) (+) ADD Trim Correction

LCF is Aft (Aft) (-) SUBTRACT Trim Correction

**3.18.2 **VESSEL TRIMMED BY THE STERN
LCF is Fwd () SUBTRACT Trim Correction

LCF is Aft (+) ADD Trim Correction

**3.19 **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.

**3.20** The second correction is always (+) (additive)
regardless of the trim or other factors.

**3.21 **Before calculating the Second Trim Correction,
MTC differ-ence, sometimes referred to as dM/dZ, must be found.

**3.21.1 **ADD 50 cm to the Quarter Mean Draft
( QM ) to find the corresponding MTC from the vessels

Hydrostatic book.

**3.21.2** SUBTRACT 50 cm from the Quarter Mean Draft
(QM) to find the corresponding MTC from the Vessels Hydrostatic book.
**3.21.3** 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 Ships book)

b) Q M - 50cm = MTC ( Found in Ships 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**

**3.22** 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.
**3.22.1** Sg. is always minus if the measured Sg.
is 1.025 or less.
**3.22.2** Sg. is plus if the measured S9. is 1.026
or more.

**3.23** 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

**VESSELS CONSTANT**

**3.24 ** Subtract-ing the Lightship, weights,
ballast and consumables from the Displacement solves the Constant of an
unladen vessel.

**3.25** Tank tables or graphs should be available
so the tank soundings can be converted from measure to volumes and corrected
for trim.

**3.26** 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.

**3.27** 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.

**3.28 **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.

**3.29 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**

**3.29** The Final Survey follows the same procedure
as the Initial Survey. Total cargo equals DISP. minus Lightship Weight.