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PART 2 — TONNAGE MEASUREMENT OF CANADIAN SHIPS 24 METRES IN LENGTH OR MORE

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

where

V = total volume of all enclosed spaces of the ship in cubic metres; and

K₁ = 0.2 + 0.02 log₁₀V (or as shown in the Table of Coefficients).

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

where:

V_C = total volume of cargo spaces in cubic metres;

K₂ = 0.2 + 0.02 log ₁₀V_c (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 ship’s passenger certificate;

GT = the gross tonnage of the ship as determined in accordance with Section 2.1.

NOTES:

.1 If the sum of N₁ and N₂ is less than 13, N₁ and N₂ are to be taken as zero.

.2 The factor (4d/3D)² is not to be taken as greater than unity.

.3 The term K₂V_c (4d/3D) ² is not to be taken as less than 0.25 GT.

.4 NT is not to be taken as less than 0.30 GT.

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

A ship, 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 2.2, and that tonnage shall be the tonnage applicable to the appropriate assigned Load Line for the trade in which the ship is engaged.

Measurements to calculate the tonnage of a ship are to be taken from:

1.  the ship; and

2.  the scrieve boards, comprising the full or reduced size of the ship; or

3.  the lines plan and scale drawings of the ship; or

4.  computer graphics of the ship.

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 ships constructed of metal, and to the outer surface of the shell and to the inner side of structural boundary surfaces in ships constructed of any other material.

The volume components of gross tonnage are to consist of the sum of the following:

1.  the volume of the ship below the upper deck measured in cubic metres; and

2.  the volume of each enclosed space above the upper deck measured in cubic metres.

The volumes to be measured include the following:

1. the main body;

2. overhangs beyond the upper deck length or breadth;

3. bulbous or similar bows;

4. skegs and keels;

5. shaft bossings;

6. sponsons added for improved buoyancy or stability; and

7. all other permanent volumes except those not included.

The following volumes are not to be included in the tonnage calculation:

1. propellers;

2. rudders;

3. mechanical stabilizers;

4. echo sounders, bilge keels and other non-essential appendages; and

5. spaces within the boundaries of the main volume that open directly to the sea such as bow/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.

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

Volumes within the hulls of ships, such as split-hull barges and dredgers, shall be retained in V and V_c despite the fact that the space within the hull is temporarily opened to the sea when discharging cargo (see Figure 2.1).

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 1.22a).

In a ship 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 1.22b).

Note: It is found that the tonnage length taken on the surface or sheer line of the deck, in ships 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.

Divide the tonnage length determined in Section 2.5.1 into the number of equal parts specified in the following table:

Then subdivide the two foremost and two aftermost parts into two equal parts.

As an example, a ship 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 2.2).

Transverse sections are taken through the points of division determined in Section 2.5.2 and also through the extreme points of the tonnage length at right angles to the centre line, parallel to

the ship’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 2.2).

The depth of each transverse section shall be corrected for camber as follows:

1. by one third of the camber when the deck is rounded athwartships (parabolic curve) (see Figure 2.3);
   

2. by one half of the camber when the deck rises in a straight line from the ship’s sides to the centre line (see Figure 2.4); and
   

3. if the deck athwartship rises in a straight line from the ship’s sides and part of the deck is horizontal, the correction is to be calculated by the following formula (see Figure 2.5):

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.

Measure the depth of the transverse section as follows:

Determine the vertical distance on the centre line, from the moulded line of the upper deck less correction for camber as determined in Section 2.5.4.

Then:

1. for ships built of metal, continue to the moulded line of the keel plate or if a bar keel or duct/box keel is fitted, to the point where the line of the hull intersects the side of the keel (see Figure 2.6);
   

2. for wood or composite ships, continue to the lower edge of the keel rabbet (see Figure 2.6);
   

3. if the form at the lower part of the hull is of a hollow character as in a ship built of glass reinforced plastic or if thick garboards are fitted, the distance is to be measured to the point where the line of the flat of the bottom continued inwards cuts the side of the keel (see Figure 2.6);
   

4. in situations where a point of reference cannot be determined using paragraph (a), (b) or (c), the depth of the transverse section is to be measured to the moulded line of the hull at the centre line (see Figure 2.7).

If there is a break in the upper deck, the transverse section of the break is measured on the centre plane from the centre line used to take the vertical distance to the points of reference set out in paragraph (a), (b), (c) or (d) (see Figure 2.8).

For an open ship, measure from an athwartship line extending between the upper edges of the upper strakes to the points of reference set out in paragraph (a), (b), (c) or (d) (see Figure 2.9).

Note: For a ship 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.

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.

Then the lowest common interval is to be further divided into two equal parts (see Figure 2.10).

Breadths are to be measured through each point of division as determined in Section 2.5.6 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 2.5.5 (see Figure 2.10).

In all ships, the bottom breadth will have a value equal to or greater than zero. It will never have a negative value.

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:

1. the uppermost breadth (Breadth No.1) is multiplied by 1;

2. the three last breadths starting with the bottom breadth are multiplied respectively by 0.5, 2 and 1.5;

3. the other even numbered breadths are multiplied by 4, and the odd numbered breadths by 2; and

4. 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.

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 (counted towards the stern) are multiplied respectively by 2,1, 2 and 1.5;

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;

The even numbered transverse ordinates are multiplied by 4 and the odd numbered by 2;

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 2.4.1 and 2.4.2 are taken into account;

In a ship 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 2.6.3 (see Figure 2.11);

The main volume under the upper deck in ships 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 ship 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 2.14 and Section 2.5.10 "Bulbous or similar bows").

The volume of any appendage is measured separately from the main volume below the upper deck as described below.

Overhangs beyond the Upper Deck Length

Overhangs are to be measured by Simpson’s First Rule. The length is divided into two equal parts (three sections) and five ordinates are to be taken at each section (see Figure 2.12).

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

Overhanging Deck

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

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 2.13).

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 2.14).

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 2.15).

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 2.16).

Tunnel Thruster Tubes

The volume may be determined by use of the formula:

V = 0.7854 x diameter² x breadth (mean) or

V = p x radius² x breadth (mean)

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

Anchor Pockets, Sea Chests and Similar Spaces

Any accurate method of measurement is acceptable.

In accordance with Section 2.5.9, 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.

Spaces located within the boundaries of "permanent or movable awnings" are to be treated as excluded spaces.

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:

1.  masts, kingposts, cranes, crane and container support structures;

2.  air trunks having a cross-sectional area not exceeding 1 square metre;

3.  mobile cranes; and

4.   hatchways with volumes less than 1 cubic metre.

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".

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".

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.

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 ships constructed of metal and to the inner side of the structural boundary surfaces in ships constructed of any other material (see Figure 2.17).

All heights for enclosed spaces are to be measured from the top of the deck plate to the underside of the overhead deck plate.

Box-shaped enclosed spaces may be calculated by multiplying the three main dimensions together, i.e., mean length x mean breadth x mean height = V of enclosed space.

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.

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.

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 area is calculated using Simpson’s First Rule, as follows:

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;

The breadths taken at the even numbered points of division are multiplied by 4 and at the odd numbered points of division by 2;

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.

(a) Measure the mean length of the space at the middle of its height and divide the length into the following number of equal parts:

(i) length less than 15 metres - 4 equal parts;

(ii) length 15 metres and above - 6 equal parts;

(iii) 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 2.18);

(iv) 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 2.19).

Division of parts determined in accordance with (i) or (ii) does not apply to spaces such as Break Amidships, Deckhouse, Side House, Trunk and Hatch.

(b) 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.

(i) In spaces such as a Break Forward and a Forecastle, 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.

The breadth taken at the aftermost point of the length is multiplied by 1.

The even numbered breadths are multiplied by 4 and the odd numbered breadths by 2.

(ii) In spaces such as a "Break Aft" and a "Poop", the breadth taken at the foremost point of the length is multiplied by 1.

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.

The even numbered breadths are multiplied by 4 and the odd numbered breadths by 2.

(iii) In the case of a Break Amidships, a Deckhouse, a Sidehouse, a Trunk and a Hatch, the breadths at the foremost and aftermost points of the length are multiplied by 1.

The even numbered breadths are multiplied by 4 and the odd numbered breadths by 2.

The sum of the product determined in subparagraph (i), (ii) or (iii) 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.

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.

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.

Division of the Length

The length of each cargo space [l] taken in a straight line at the uppermost point of the depth of the space is divided into the following number of equal parts:

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.

(a) A total of four (4) equally spaced parts [l /4] using five (5) transverse ordinates is taken

through the points of division specified in Section 2.7.1 which includes the two extreme enclosing bulkheads of the cargo space, in a similar manner as explained in Section 2.5.3. 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 2.2 for an example of 10 parts, 15 ordinates).

(b) The depth of each transverse section is divided as indicated in Section 2.5.6.

(c) The breadths are measured as indicated in Section 2.5.7.

(d) The area of the transverse sections is calculated in accordance with Section 2.5.8.

(e) 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.

(f) The sum of the products determined in (e) is multiplied by one-third of the common interval (i.e. 1/3 x l /4) between the transverse ordinates, and the product obtained is the volume of the cargo space below the upper deck.

2.7.3 — VOLUME OF CARGO SPACE BELOW UPPER DECK (6 OR 1

(a) A total of six [or ten] equally spaced parts (l /6 or l /10) using seven or eleven transverse ordinates is taken through the points of division specified in Section 2.7.1 which includes the two extreme enclosing bulkheads of the cargo space, in a similar manner as explained in Section 2.5.3. 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:

(i) for a cargo space of 6 parts - 11 ordinates;

(ii) for a cargo space of 10 parts - 15 ordinates;

(See Figure 2.2 for an example of 10 parts, 15 ordinates).

(b) The depth of each transverse section is divided as indicated in Section 2.5.6.

(c) The breadths are measured as indicated in Section 2.5.7.

(d) The area of the transverse sections is calculated in accordance with Section 2.5.8.

(e)  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.

 (f) The sum of the products determined in clause (e) is multiplied by one third of the common interval [i.e.1/3 x l /6 or l /10] between the transverse ordinates, and the product obtained is the volume of the cargo space below the upper deck.

2.7.4 — Cargo Spaces above the Upper Deck ^

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.

2.7.5 — Interpretations of Compartment Volumes for Cargo Spaces ^

The following are interpretations of compartment volumes for cargo spaces:

The volumes of segregated ballast tanks are not to be included in cargo volume (V_C) provided they are not to be used for cargo;

The volumes of clean ballast tanks in oil tankers are included in V_C if the ship is fitted with a crude oil washing system which would permit dual purpose cargo/clean ballast tank use of these tanks;

The volumes of dedicated clean ballast tanks are not to be included in V_C provided that:

1.  the tanks are not used for cargo;
   

2.  the ship 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.

Tanks, permanently located on the upper deck, provided with removeable pipe connections to the cargo system or the vent (de-airing) lines of the ship, are to be included in V_C;

The volume of weathertight steel pontoon covers on hatchway coamings are included in the calculations of the total volume (V) of the ship. If covers are open on the underside, their volume is also included in V_C;

Multipurpose ships that have the facility to trade with cargo hatches open or closed are always measured with the hatch covers considered to be closed;

The volumes of slop tanks for cargo residues are included in V_C;

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 V_C. Fishing gear stores are not included in V_C;

The volume of refrigerating machinery used for refrigerating cargoes and situated within the boundaries of the cargo spaces is included in V_c;

The volumes of mail rooms, baggage compartments separate from passenger accommodation, and bonded stores for passengers are included in V_C. The volume of provision rooms for crew or passengers and bonded stores for crew are not included in V_C;

Dual purpose oil/ballast tanks on combination carriers that have been converted to ballast tanks are to be excluded from V_c 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;

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 ships that have permanent independent cargo tanks constructed within the ship, e.g. gas tankers, the volume to be included in V_C 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;

The volumes of dual-purpose spaces such as those used for both ballast and cargo are included in V_C;

Spaces allocated to passenger automobiles are included in V_C.

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