# Part 2 - Tonnage Measurement of Vessels 24 Metres in Length or More

## 2.1 General

2.1.1  Tonnage measurement of a vessel that is 24 metres in length ( L )* or more shall be carried out in accordance with the provisions of this part.

## 2.2 Definitions

The following definitions apply in this Part:

2.2.1  Amidships is the midpoint of the length ( L ) of a vessel where the forward terminal of that length coincides with the fore side of the stem. Length of a vessel ( L ) is defined in Section 1.1.

2.2.2  Breadth is the maximum breadth of the vessel, measured amidships to the moulded line of the frame in a vessel with a metal shell and to the outer surface of the hull in a vessel with a shell of any other material (see Figure 2.1).

2.2.3  Camber is the vertical distance measured on the centre line plane of the vessel, from the underside of the deck plating to a line athwartships between the points where the underside of the deck plating meets the inner side of the vessel's shell plating (see Figure 2.2).

2.2.4 Cargo Spaces are enclosed spaces included in the calculation of the net tonnage that are appropriated for the transport of cargo which is to be discharged from the vessel, if the spaces have also been included in the calculation of the gross tonnage. These cargo spaces are identified by the readily visible permanent markings CC (cargo compartment). The total volume of cargo spaces as defined above is designated as Vc.

2.2.5 Moulded Depth ( D ) of a vessel is determined by measuring the vertical distance amidships:

• (a) if the vessel has a metal shell, from the moulded line of the upper deck at the side to the point where the line of the hull intersects the side of the keel (see Figure 2.15);
• (b) if the vessel is a wood or composite vessel, from the moulded line of the upper deck at the side to the point at the lower edge of the keel rabbet (see Figure 2.15);
• (c) if the vessel is one in which the form at the lower part of the midship section is of a hollow character or on which thick garboards are fitted, from the moulded line of the upper deck at the side to the point where the moulded line of shell when continued inwards intersects the side of the keel (see Figure 2.15);
• (d) if the vessel has rounded gunwales, from the point of intersection of the moulded lines of the upper deck and side shell plating, the lines extending as though the gunwales were of angular design, to the point referred to in paragraphs (a) to (c), as the case may be (see Figure 2.15);
• (e) if the vessel has a stepped upper deck the raised part of which extends over amidships, from the point at which a line of reference extending along the lower part of the upper deck parallel to the raised part of that deck intersects amidships to the point referred to in paragraphs (a) to (c) as the case may be (see Figure 2.17); and
• (f) if the vessel does not meet the requirements for upper deck as defined in subsection 2.2.10, from the top of the upper strake or gunwale to the point referred to in paragraphs (a) to (c), as the case may be.

2.2.6  Moulded Draught ( d ) referred to in the Net Tonnage formula in Section 2.5 shall be one of the following draughts:

• (a) if the vessel is a Load Lines Convention vessel, the draught corresponding to the summer load line assigned to the vessel in accordance with that Convention. A timber load line must not be used to calculate moulded draught;
• (b) if the vessel is a Safety Convention passenger vessel, the draught corresponding to the deepest subdivision load line assigned in accordance with SOLAS;
• (c) if the vessel is not a Load Lines Convention vessel, but has been assigned a load line in accordance with the laws of the state whose flag the vessel is entitled to fly, the draught corresponding to the summer load line so assigned;
• (d) if the vessel is a vessel to which no load line has been assigned and in respect to which the draught is restricted in accordance with the laws of the state whose flag the vessel is entitled to fly, the maximum permitted draught; and
• (e) in the case of any other vessel, 75% of the moulded depth amidships determined in accordance with the definition for “Moulded Depth” in subsection 2.2.5.

2.2.7  Moulded Line of Hull

• (a) if the vessel has a metal shell, the outer surface of the frame of the hull without the plating (moulded frame line); and
• (b) if the vessel has a shell of a material other than metal, the outer surface of the shell.

2.2.8  Passenger is as defined in Section 2 of the CSA , 2001.

2.2.9  Tonnage Length means the horizontal distance between the extremes of the upper deck (see Figure 2.21a), or in the case of a stepped upper deck, the extremes of the projected line of upper deck (see Figure 2.21b).

2.2.10 Upper Deck

• (a) the uppermost complete deck exposed to weather and sea that has permanent means of weathertight closing of all openings in the weather part thereof, and below which all openings in the sides of the vessel are fitted with permanent means of watertight closing (see Figure 2.16); and
• (b) in the case of a vessel that has a stepped upper deck, the lowest line of the exposed deck and the continuation of that line parallel to the upper part of the deck is taken as the upper deck (see Figures 2.16 and 2.17).
• 2.2.10.1  A discontinuity in the upper deck that extends over the full breadth of the vessel and is in excess of 1 metre in length is treated as a step (see Figure 2.18).
• 2.2.10.2  Steps situated outside the length ( L ) (as defined in Section 1.1) are not to be considered.
• 2.2.10.3  A discontinuity in the upper deck that does not extend to the side of the vessel is treated as a recess located below the upper deck level (see Figure 2.19).
• 2.2.10.4  In a vessel that has openings in its side below the uppermost deck, if the openings are not closed but limited inboard by weathertight bulkheads and decks, the deck below the openings is considered the upper deck (see Figure 2.20).
• * Length of a vessel (L) as defined in section 6, Part 2 of the Vessel Registration and Tonnage Regulations (see also section 1.1 of this Standard). (back)

## 2.3 Units of Measurement and Degree of Accuracy

2.3.1  All measurements are to be taken in metres to the nearest centimetre. All lengths are to be measured in a fore and aft direction, breadths athwartships and heights or depths vertically. This order is to be followed on all tonnage calculations.

2.3.2  The volume in relation to any vessel or space in a vessel is to be in cubic metres.

2.3.3  The following calculations are to be carried out to three decimal places, the third figure to be increased by one if the fourth is 5 or more:

• - One-third round of beam;
• - The common interval between the transverse ordinates;
• - The common interval between the breadths in each transverse section;
• - The common interval between the breadths in between deck space and in erections;
• - One-third of the common interval between the transverse ordinate;
• - One-third of the common interval between the breadths in each transverse section;
• - One-third of the common interval between the breadths in the between-deck space and in erections.

2.3.4  The following calculations are to be carried out to two decimal places, the second figure to be increased by one if the third is 5 or more:

• - The area of transverse sections;
• - The mean height of the between-deck space.

## 2.4 Gross Tonnage Formula

2.4.1  The gross tonnage ( GT ) of a vessel is to be calculated using the following formula:

GT = K1V

where

V = total volume of all enclosed spaces of the vessel in cubic metres;
and
K1 = 0.2 + 0.02 log 10V (or as shown in the Table of Coefficients).

## 2.5 Net Tonnage Formula

2.5.1  The net tonnage ( NT ) of a vessel is to be calculated using the following formula:

NT = K2Vc (4d/3D)² + K3 (N1 + N2/10)

where:

• Vc =  total volume of cargo spaces in cubic metres;
• K2 = 0.2 + 0.02 log10Vc (or as shown in the Table of Coefficients);
• K3 = 1.25 x (GT + 10,000)/10,000;
• D = the moulded depth amidships in metres;
• d   = the moulded draught amidships in metres;
• N1 = the number of passengers in cabins containing not more than eight berths;
• N2 = the number of other passengers;
• N1 + N2 = the number of passengers as shown in the vessel’s passenger certificate;
• GT = the gross tonnage of the vessel as determined in accordance with Section 2.4.

NOTES:

• 2.5.1.1 If the sum of N1 and N2 is less than 13, N1 and N2 are to be taken as zero.
• 2.5.1.2 The factor (4d/3D)² is not to be taken as greater than unity.
• 2.5.1.3 The term K2Vc (4d/3D)² is not to be taken as less than 0.25 GT .
• 2.5.1.4 NT is not to be taken as less than 0.30 GT .

Table 1 — Coefficient K1 and K2 for Sections 2.4 and 2.5

V or Vc = Volume in m³

V or Vc K1 or K2 V or Vc K1 or K2 V or Vc K1 or K2 V or Vc K1 or K2
10 0.2200 45000 0.2931 330000 0.3104 670000 0.3165
20 0.2260 50000 0.2940 340000 0.3106 680000 0.3166
30 0.2295 55000 0.2948 350000 0.3109 690000 0.3168
40 0.2200 60000 0.2956 360000 0.3111 700000 0.3169
50 0.2320 65000 0.2963 370000 0.3114 710000 0.3170
60 0.2356 70000 0.2969 380000 0.3116 720000 0.3171
70 0.2369 75000 0.2975 390000 0.3118 730000 0.3173
80 0.2381 80000 0.2981 400000 0.3120 740000 0.3174
90 0.2391 85000 0.2986 410000 0.3123 750000 0.3175
100 0.2400 90000 0.2991 420000 0.3125 760000 0.3176
200 0.2460 95000 0.2996 430000 0.3127 770000 0.3177
300 0.2495 100000 0.3000 440000 0.3129 780000 0.3178
400 0.2520 110000 0.3008 450000 0.3131 790000 0.3180
500 0.2540 120000 0.3016 460000 0.3133 800000 0.3181
600 0.2556 130000 0.3023 470000 0.3134 810000 0.3182
700 0.2569 140000 0.3029 480000 0.3136 820000 0.3183
800 0.2581 150000 0.3035 490000 0.3138 830000 0.3184
900 0.2591 160000 0.3041 500000 0.3140 840000 0.3185
1000 0.2600 170000 0.3046 510000 0.3142 850000 0.3186
2000 0.2660 180000 0.3051 520000 0.3143 860000 0.3187
3000 0.2695 190000 0.3056 530000 0.3145 870000 0.3188
4000 0.2720 200000 0.3060 540000 0.3146 880000 0.3189
5000 0.2740 210000 0.3064 550000 0.3148 890000 0.3190
6000 0.2756 220000 0.3068 560000 0.3150 900000 0.3191
7000 0.2769 230000 0.3072 570000 0.3151 910000 0.3192
8000 0.2781 240000 0.3076 580000 0.3153 920000 0.3193
9000 0.2791 250000 0.3080 590000 0.3154 930000 0.3194
10000 0.2800 260000 0.3083 600000 0.3156 940000 0.3195
15000 0.2835 270000 0.3086 610000 0.3157 950000 0.3196
20000 0.2860 280000 0.3089 620000 0.3158 960000 0.3196
25000 0.2880 290000 0.3092 630000 0.3160 970000 0.3197
30000 0.2895 300000 0.3095 640000 0.3161 980000 0.3198
35000 0.2909 310000 0.3098 650000 0.3163 990000 0.3199
40000 0.2920 320000 0.3101 660000 0.3164 1000000 0.3200

Note: Coefficients K1 or K2 at intermediate values of V or Vc shall be obtained by linear interpolation.

## 2.6 Change of Net Tonnage

2.6.1 A vessel, to which Load Lines referred to in paragraphs (a) and (b) of the definition “moulded draught” are concurrently assigned, shall be given only one net tonnage as determined in accordance with Section 2.5, and that tonnage shall be the tonnage applicable to the appropriate assigned Load Line for the trade in which the vessel is engaged.

## 2.7 Calculation of Volumes

2.7.1  General

• 2.7.1.1 Measurements to calculate the tonnage of a vessel are to be taken from:
• (a) the vessel; and
• (b) the scrieve boards, comprising the full or reduced size of the vessel; or
• (c) the lines plan and scale drawings of the vessel; or
• (d) computer graphics of the vessel.
• 2.7.1.2 All volumes included in the calculation of gross tonnage and net tonnage are to be measured, irrespective of the fitting of insulation or the like, to the inner side of the shell or structural boundary plating in vessels constructed of metal, and to the outer surface of the shell and to the inner side of structural boundary surfaces in vessels constructed of any other material.
• 2.7.1.3  The volume components of gross tonnage are to consist of the sum of the following:
• (a) the volume of the vessel below the upper deck measured in cubic metres; and
• (b) the volume of each enclosed space above the upper deck measured in cubic metres.

2.7.2 Tonnage Volumes Below Upper Deck

• 2.7.2.1  The volumes to be measured include the following:
• (a) the main body;
• (b) overhangs beyond the upper deck length or breadth;
• (c) bulbous or similar bows;
• (d) skegs and keels;
• (e) shaft bossings;
• (f) sponsons added for improved buoyancy or stability; and
• (g) all other permanent volumes except those not included.

2.7.3  Volumes Not to be Included in the Tonnage Calculation

• 2.7.3.1  The following volumes are not to be included in the tonnage calculation:
• (a) propellers;
• (b) rudders;
• (c) mechanical stabilizers;
• (d) echo sounders, bilge keels and other non-essential appendages; and
• (e) spaces within the boundaries of the main volume that open directly to the sea such as bow or stern thruster tubes, moonpools, hawsepipes, sea valve recesses, stern chutes in fishing vessels, dredging wells in dredges, anchor pockets and sea chests within the boundaries of the main hull volume.

2.7.4 Despite the above, any space with a volume less than 1 cubic metre shall not be taken into account either for inclusion or deduction.

2.7.5 Volumes within the hulls of vessels, such as split-hull barges and dredgers, shall be retained in
V and Vc despite the fact that the space within the hull is temporarily opened to the sea when discharging cargo (see Figure 2.22).

## 2.8 Calculation of Enclosed Spaces Below the Upper Deck

2.8.1 Measurement

• 2.8.1.1 Measure the tonnage length in a straight line along the upper side of the upper deck from the moulded line of the hull at the stem to the moulded line of the hull at the stern (see Figure 2.21a).
• 2.8.1.2 In a vessel having a stepped upper deck, such as a break forward, a break amidships or a break aft, the lowest line of exposed deck and the continuation of that line parallel to the upper part of the deck are to be measured as described in the preceding paragraph (see Figure 2.21b).
• Note: It is found that the tonnage length taken on the surface or sheer line of the deck, in vessels of standard sheer, is sufficiently accurate for the practical purpose of tonnage. In all cases of unusual sheer, such as trawlers, the length for calculation shall be taken by means of a tape or line stretched tightly from end to end of the deck.

2.8.2 Division of Tonnage Length

• 2.8.2.1 Divide the tonnage length determined in Section 2.8.1 into the number of equal parts specified in the following table:
• Table 2 – Division of Tonnage Length

 Tonnage length less than 30 m 6 parts Tonnage length 30 m or more but less than 45 m 8 parts Tonnage length 45 m or more but less than 60 m 10 parts Tonnage length 60 m or more but less than 75 m 12 parts Tonnage length 75 m or more but less than 90 m 14 parts Tonnage length 90 m or more but less than 105 m 16 parts Tonnage length 105 m or more but less than 120 m 18 parts Tonnage length 120 m and more 20 parts
• 2.8.2.2  Subdivide the two foremost and two aftermost parts into two equal parts.
• 2.8.2.3  As an example, a vessel with a tonnage length of 50 metres would be divided into 10 equal parts and the two foremost and aftermost parts would be further divided into two equal parts each making a total of 14 parts (15 sections) (see Figure 2.23).

2.8.3  Transverse Sections

• 2.8.3.1  Transverse sections are taken through the points of division determined in Section 2.8.2 and also through the extreme points of the tonnage length at right angles to the centre line, parallel to the vessel’s main transverse bulkheads. These transverse sections are numbered from stem to stern, the terminal point at the fore end of the tonnage length being No. 1 (see Figure 2.23).

2.8.4  Depth Correction for Camber

• 2.8.4.1  The depth of each transverse section shall be corrected for camber as follows:
• (a) by one third of the camber when the deck is rounded athwartships (parabolic curve) (see Figure 2.24);
• (b) by one half of the camber when the deck rises in a straight line from the vessel’s sides to the centre line (see Figure 2.25); and
• (c) if the deck athwartship rises in a straight line from the vessel’s sides and part of the deck is horizontal, the correction is to be calculated by the following formula (see Figure 2.26):

Correction = x(B - b)/ 2B

where
x = camber in metres;
B = the uppermost breadth of the transverse section; and
b = breadth of the horizontal part of the deck.

2.8.5  Depth of Transverse Section ( DS )

• 2.8.5.1  Depth of transverse Section is measured as the vertical distance on the centre line between the upper and lower termini as described in subsections (a) and (b) below:
• (a) upper terminus:
• (i) if the upper deck has no break, the moulded line of the upper deck less correction for camber as determined in Section 2.8.4. (see Figure 2.27);
• (ii) if there is a break in the upper deck, the molded line of the lowest part of exposed deck and the continuation of that line parallel to the upper part of the deck less correction for camber as determined in Section 2.8.4. (see Figure 2.29);
• (iii) if the vessel does not meet the requirements for upper deck as defined in subsection 2.2.10, the athwartship line extending between the upper edges of the upper strakes /gunwales (see Figure 2.30).
• (b) lower terminus:
• (i) for vessels built of metal, the moulded line of the keel plate or, if a bar keel or duct/box keel is fitted, the point where the moulded line of the hull intersects the side of the keel (see Figure 2.27);
• (ii) for wood or composite vessels, the lower edge of the keel rabbet (see Figure 2.27);
• (iii) if the form at the lower part of the hull is of a hollow character as in a vessel built of glass reinforced plastic or if thick garboards are fitted, the point where the moulded line of the flat of the bottom continued inwards cuts the side of the keel (see Figure 2.27);
• (iv) in situations where a lower terminus cannot be determined using paragraph (i), (ii) or (iii), the moulded line of the hull at the centre line (see Figure 2.28).
• 2.8.5.2  For a vessel with decks and tanks below the upper deck, the depth of the transverse section is taken at each level and the various deck and tank plate thicknesses are added.

2.8.6  Division of Depth of Transverse Section

• 2.8.6.1  The depth of each transverse section is to be divided into:
• (a) five equal parts, where the depth at the middle of the tonnage length does not exceed 6 metres; or
• (b) seven equal parts where the depth at the middle of the tonnage length exceeds 6 metres.
• 2.8.6.2  Then the lowest common interval is to be further divided into two equal parts (see Figure 2.31).

• 2.8.7.1  Breadths are to be measured through each point of division as determined in Section 2.8.6 and at the extreme points of the depth. The breadths will be numbered from above, the No. 1 breadth being taken at the upper point of the depth determined in Section 2.8.5 (see Figure 2.31).
• 2.8.7.2  In all vessels, the bottom breadth will have a value equal to or greater than zero. It will never have a negative value.

2.8.8  Calculation of Transverse Section

• 2.8.8.1  If the area of a transverse section of the under deck can be calculated by a direct method, such as depth and breadth, without loss of accuracy, such a method may be used. Otherwise, the area is calculated using Simpson's First Rule, as follows:
• (a) the uppermost breadth (Breadth No. 1) is multiplied by 1;
• (b) the three last breadths starting with the bottom breadth are multiplied respectively by 0.5, 2 and 1.5;
• (c) the other even numbered breadths are multiplied by 4, and the odd numbered breadths by 2; and
• (d) the sum of these products is then multiplied by one third of the common interval between breadths. The product obtained is the area of the transverse section.

2.8.9  Calculation of Volume below Upper Deck

• 2.8.9.1  Once the areas of the transverse sections have been ascertained, the volume below the upper deck is calculated using Simpson’s First Rule, as follows:
• (a) The area of the foremost transverse section is multiplied by 0.5 and the following four (counted towards the stern) are multiplied respectively by 2,1, 2 and 1.5;
• (b) The areas of the five aftermost transverse ordinates starting at the aftermost section are multiplied respectively by 0.5, 2, 1, 2 and 1.5;
• (c) The even numbered transverse ordinates are multiplied by 4 and the odd numbered by 2;
• (d) The sum of these products is multiplied by one-third of the common interval between the transverse ordinates, and the product obtained is the volume of the space below the upper deck, after the included and excluded spaces detailed in Section 2.7.2 and 2.7.3 are taken into account;
• 2.8.9.2  In a vessel having a stepped upper deck such as breaks situated forward, aft, or amidships, the under deck volume is the sum of the volume below the upper deck and its line of continuation and the volume between the line of continuation and the deck above. For the method of calculating a break, refer to Section 2.9.4 (see Figure 2.32);
• 2.8.9.3  The main volume under the upper deck in vessels with a bulbous bow or similar shape bow is to be calculated assuming there is no bulbous bow or similar bow volume; i.e. normal vessel shape bow. Calculate the additional volume that is present due to the bulbous bow or similar shape bow and add as an appendage (see Figure 2.35 and Section 2.8.10.4 “Bulbous or similar bows”).

2.8.10  Additional Volumes of Enclosed Spaces below the Upper Deck

• 2.8.10.1  The volume of any appendage is measured separately from the main volume below the upper deck as described below.
• 2.8.10.2  Overhangs beyond the Upper Deck Length. Overhangs are to be measured by Simpson’s First Rule. The length is to be divided into two equal parts (three sections) and five ordinates are to be taken at each section (see Figure 2.33). An equivalent method of measurement without loss of accuracy may be used.
• 2.8.10.3  Overhanging Deck.
• (a) A closed in space beneath an overhanging deck supported by deck beams, brackets or by other means is measured by: mean length x mean breadth x mean depth
• (b) If the space beneath the overhanging deck is not enclosed because the bottom is open or the external side is open, it is to be ignored. If the space beneath the overhanging deck is not enclosed because the internal side is open, it is to be measured (see Figure 2.34).
• 2.8.10.4  Bulbous and Similar Bows. Such bows are measured by Simpson’s First Rule. The length is divided into four equal parts (5 sections) and five ordinates are taken at each section (see Figure 2.35).
• 2.8.10.5  Skegs and Keels. Volume displacement type skegs and keels, whether separate from or open to the hull, are measured using Simpson’s First Rule. The length of the space is divided into four equal parts (five sections) and three ordinates are taken at each section. An equivalent method of measurement, without loss of accuracy, may be used.
• Note: Some of the measurements may have already been included in the measurement of the main volume below the upper deck (see Figure 2.36).
• 2.8.10.6  Shaft Bossings. Shaft Bossings are measured by Simpson's First Rule. The length is divided into four equal parts (five sections) and five ordinates are taken at each section (see Figure 2.37).

2.8.11  Excluded Volumes of Enclosed Spaces below the Upper Deck

• 2.8.11.1  Tunnel Thruster Tubes. The volume shall be determined by use of the formula:

V = 0.7854 x diameter² x breadth (mean)

or An equivalent method of measurement without loss of accuracy may be used.

• 2.8.11.2  Anchor Pockets, Sea Chests and Similar Spaces. Any accurate method of measurement may be used.

## 2.9 Calculations of the Volume of Enclosed Spaces Above the Upper Deck

2.9.1  General

• 2.9.1.1  In accordance with Section 2.8.9.2, the volume of a “break” is to be included as part of the volume below the upper deck. However, for calculation purposes, "breaks" have been grouped in with enclosed spaces above the upper deck.
• 2.9.1.2  Spaces located within the boundaries of “permanent or movable awnings” are to be treated as excluded spaces.
• 2.9.1.3  The following are not included in the total volume of enclosed spaces, if they are completely inaccessible and above the upper deck and separated on all their sides from other enclosed spaces:
• (a) masts, kingposts, cranes, crane and container support structures;
• (b) air trunks having a cross-sectional area not exceeding 1 square metre;
• (c) mobile cranes; and
• (d) hatchways with volumes less than 1 cubic metre.
• 2.9.1.4  The space between the side longitudinal bulkhead of a deckhouse and the bulwark below a deck extending from side to side supported by stanchions or vertical plates connected to the bulwarks is treated as an “excluded space”.
• 2.9.1.5  In the case of a ro-ro ship, for example, if the space at the end of an erection is fitted with means for securing cargo, the space is included in volume (V) in accordance with the first condition contained in the definition “excluded spaces.”

2.9.2  Applying Simpson’s First Rule to Enclosed Spaces above the Upper Deck

• 2.9.2.1  Enclosed spaces above the upper deck, including breaks, are measured using Simpson’s First Rule. However due to the shape and location of these spaces, variations in the application of Simpson’s First Rule, as explained in the following paragraphs, must be observed.
• 2.9.2.2  In applying this rule, the breadths taken are numbered consecutively starting at the foremost point of the length. All lengths and breadths of enclosed spaces above the upper deck are measured, irrespective of the fitting of insulation or the like, to the inner side of the structural boundary plating in vessels constructed of metal and to the inner side of the structural boundary surfaces in vessels constructed of any other material (see Figure 2.38).
• 2.9.2.3  All heights for enclosed spaces are to be measured from the top of the deck plate to the underside of the overhead deck plate.
• 2.9.2.4  Box-shaped enclosed spaces shall be calculated by multiplying the three main dimensions together, i.e. ,

mean length x mean breadth x mean height = V of enclosed space.
• 2.9.2.5  If spaces have an irregular shape and cannot be measured by the foregoing methods, they may be divided into parts, which may be calculated separately.

2.9.3  Between Deck Space

• 2.9.3.1  Measure the mean length of the space at the middle of its height and divide this length into the same number of parts determined for the tonnage length of the space below the upper deck.
• 2.9.3.2  Breadths taken at half the height of the space are measured through each point of division and also through the extreme points of the length.
• 2.9.3.3  The area is calculated using Simpson’s First Rule, as follows:
• (a) The breadth taken at the foremost point of the length is multiplied by 0.5. The following four breadths are multiplied respectively by 2, 1, 2 and 1.5. The breadths taken at the five aftermost points of division starting at the aftermost point of the length are multiplied respectively by 0.5, 2, 1, 2 and 1.5;
• (b) The breadths taken at the even numbered points of division are multiplied by 4 and at the odd numbered points of division by 2;
• 2.9.3.4  The sum of the products determined above is multiplied by one-third the common interval between breadths, and the result obtained is multiplied by the mean height of the space to determine the volume of this space.

2.9.4  Break, Forecastle, Poop, Deck House, Side House, Trunk, Hatchway

• 2.9.4.1  Measure the mean length of the space at the middle of its height and divide the length into the following number of equal parts:
• (a) length less than 15 metres – 4 equal parts;
• (b) length 15 metres and above – 6 equal parts;
• (c) in spaces such as a Break Forward and a Forecastle, the two foremost parts determined in accordance with (a) or (b) are each divided into two equal parts (see Figure 2.39);
• (d) in spaces such as a Break Aft and a Poop, the two aftermost parts determined in accordance with (a) or (b) are each divided into two equal parts (see Figure 2.40).
• Note: Division of parts determined in accordance with (a) or (b) does not apply to spaces such as Break Amidships, Deckhouse, Side House, Trunk and Hatch.
• 2.9.4.2  Breadths taken at half the height of the space are measured through each point of division and also through the extreme points of the length. The breadths are numbered consecutively starting with breadth No. 1 at the foremost point of the length.
• 2.9.4.3  The area is calculated using Simpson’s First Rule, as follows:
• (a) In spaces such as a Break Forward and a Forecastle:
• (i) the breadth taken at the foremost point of the length is multiplied by 0.5 and the following four breadths are multiplied respectively by 2, 1, 2 and 1.5;
• (ii) the breadth taken at the aftermost point of the length is multiplied by 1;
• (iii) the even numbered breadths are multiplied by 4 and the odd numbered breadths by 2.
• (b) In spaces such as a “Break Aft” and a “Poop,”
• (i) the breadth taken at the foremost point of the length is multiplied by 1;
• (ii) the breadths taken at the five aftermost points of division starting at the aftermost point of the length are multiplied respectively by 0.5, 2, 1, 2 and 1.5;
• (iii) the even numbered breadths are multiplied by 4 and the odd numbered breadths by 2.
• (c) In the case of a Break Amidships, a Deckhouse, a Sidehouse, a Trunk and a Hatch,
• (i) the breadths at the foremost and aftermost points of the length are multiplied by 1;
• (ii) the even numbered breadths are multiplied by 4 and the odd numbered breadths by 2.
• 2.9.4.4  The sum of the products determined in subparagraph 2.9.4.3 (a), (b) or (c) must be multiplied by one-third of the common interval between breadths and the result obtained is multiplied by the mean height of the space to determine its volume.

## 2.10 Calculation of the Volume of Cargo Spaces

2.10.1  General

• 2.10.1.1  If any cargo space is of a shape that the volume may be calculated by a direct method without loss of accuracy, such a method may be used. Otherwise, it must be measured using Simpson’s First Rule. Lengths, breadths, depths, and heights are to be measured irrespective of the fitting of insulation or the like, to the inner side of the boundary of the space.
• 2.10.1.2  For the purposes of measurement, “cargo space” can be taken as a longitudinal series of cargo holds or tanks, if they are not separated by machinery or accommodation spaces and do not have discontinuities.

2.10.2  Division of Length of Cargo Spaces Below the Upper Deck

• 2.10.2.1  The length of each cargo space taken in a straight line at the uppermost point of the depth of the space is divided into the following number of equal parts:
• (a) length of cargo space less than 20 metres – 4 parts;
• (b) length of cargo space 20 metres or more but not more than 40 metres – 6 parts;
• (c) length of cargo space more than 40 metres – 10 parts.

2.10.3  Volume of Cargo Space Below Upper Deck (4 Parts)

• 2.10.3.1  A total of four (4) equally spaced parts using five (5) transverse ordinates is taken through the points of division specified in Section 2.10.2 which includes the two extreme enclosing bulkheads of the cargo space, in a similar manner as explained in Section 2.8.3. The transverse ordinates are numbered forward to aft with the terminal point at the forward bulkhead position being No. 1, and the aftermost bulkhead being No. 5. In addition, the foremost and aftermost parts are further divided into two equal parts making a total of seven (7) ordinates (see Figure 2.23 for an example of 10 parts, 15 ordinates).
• 2.10.3.2  The depth of each transverse section is divided as indicated in Section 2.8.6.
• 2.10.3.3  The breadths are measured as indicated in Section 2.8.7.
• 2.10.3.4  The area of the transverse sections is calculated in accordance with Section 2.8.8.
• 2.10.3.5  Once the areas of the transverse ordinates have been ascertained, the volume below the upper deck is calculated using Simpson’s First Rule, as follows: the area of the foremost transverse section is multiplied by 0.5 and the following six sections (counted towards the stern) are multiplied respectively by 2, 1.5, 4, 1.5, 2 and 0.5.
• 2.10.3.6  The sum of the products determined in 2.10.3.5 is multiplied by one-third of the common interval between the transverse ordinates, and the product obtained is the volume of the cargo space below the upper deck.

2.10.4  Volume of Cargo Space Below Upper Deck (6 or 10 parts)

• 2.10.4.1  A total of six or ten equally spaced parts using seven or eleven transverse ordinates is taken through the points of division specified in Section 2.10.2 which includes the two extreme enclosing bulkheads of the cargo space, in a similar manner as explained in Section 2.8.3. The transverse ordinates are numbered forward to aft with the terminal point at the forward bulkhead position being No. 1, and the aftermost bulkhead being No. 7 (or 11). In addition, the two foremost and two aftermost parts are further divided into two equal parts making a total of 11 ordinates for a cargo space of 6 parts or 15 ordinates for a cargo space of 10 parts (See Figure 2.23 for an example of 10 parts, 15 ordinates).
• 2.10.4.2  The depth of each transverse section is divided as indicated in Section 2.8.6.
• 2.10.4.3  The breadths are measured as indicated in Section 2.8.7.
• 2.10.4.4  The area of the transverse sections is calculated in accordance with Section 2.8.8.
• 2.10.4.5  Once the areas of the transverse sections have been ascertained, the volume below the upper deck is calculated using Simpson’s First Rule as follows: the area of the foremost transverse section is multiplied by 0.5 and the following four sections (counted towards the stern) are multiplied respectively by 2, 1, 2, 1.5; the areas of the five aftermost transverse sections are multiplied (starting at the aftermost section) respectively by 0.5, 2, 1, 2 and 1.5; the even numbered transverse sections are multiplied by 4 and the odd numbered by 2.
• 2.10.4.6  The sum of the products determined in clause 2.10.4.5 is multiplied by one third of the common interval between the transverse ordinates, and the product obtained is the volume of the cargo space below the upper deck.

2.10.5  Cargo Spaces above the Upper Deck

• 2.10.5.1  If any cargo space is of such a shape that the volume can be calculated by a direct method without loss of accuracy, that method may be used. Otherwise the cargo space must be measured using Simpson’s First Rule.

2.10.6  Interpretations of Compartment Volumes for Cargo Spaces

• 2.10.6.1  The volumes of segregated ballast tanks are not to be included in cargo volume ( Vc) provided they are not to be used for cargo.
• 2.10.6.2  The volumes of clean ballast tanks in oil tankers are included in Vc if the vessel is fitted with a crude oil washing system which would permit dual purpose cargo/clean ballast tank use of these tanks.
• 2.10.6.3  The volumes of dedicated clean ballast tanks are not to be included in Vc provided that:
• (a) the tanks are not used for cargo;
• (b) the vessel carries a single International Oil Pollution Prevention Certificate which indicates it is operating with dedicated clean ballast tanks in accordance with regulation 13A, Annex I, MARPOL.
• 2.10.6.4  Tanks, permanently located on the upper deck, provided with removable pipe connections to the cargo system or the vent (de-airing) lines of the vessel, are to be included in Vc;
• 2.10.6.5  The volume of weathertight steel pontoon covers on hatchway coamings are included
in the calculations of the total volume ( V ) of the vessel. If covers are open on the underside, their volume is also included in Vc;
• 2.10.6.6  Multipurpose vessels that have the facility to trade with cargo hatches open or closed are always measured with the hatch covers considered to be closed;
• 2.10.6.7  The volumes of slop tanks for cargo residues are included in Vc;
• 2.10.6.8  In fishing vessels, the volumes of fish processing space for fishmeal, liver oil and canning, tanks for re-cooling fish, wet fish bunkers, stores for salt, spices, oil and tare are included in Vc. Fishing gear stores are not included in Vc;
• 2.10.6.9  The volume of refrigerating machinery used for refrigerating cargoes and situated within the boundaries of the cargo spaces is included in Vc;
• 2.10.6.10  The volumes of mail rooms, baggage compartments separate from passenger accommodation, and bonded stores for passengers are included in Vc. The volume of provision rooms for crew or passengers and bonded stores for crew are not included in  Vc;
• 2.10.6.11  Dual purpose oil/ballast tanks on combination carriers that have been converted to ballast tanks are to be excluded from Vc if they are solely allocated to carry ballast, permanently disconnected from the oil cargo system and connected to an independent ballast system and not used for the carriage of cargo;
• 2.10.6.12  When determining the volumes of cargo spaces, no account shall be taken of insulation, sparring or ceiling that is fitted within the boundaries of the space concerned. For vessels that have permanent independent cargo tanks constructed within the vessel, e.g. gas tankers, the volume to be included in Vc is calculated to the structural boundary of such tanks, irrespective of insulation which may be fitted on the inside or outside of the tank boundary;
• 2.10.6.13  The volumes of dual-purpose spaces such as those used for both ballast and cargo are included in Vc;
• 2.10.6.14  Spaces allocated to passenger automobiles are included in Vc.