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**2- Definitions, Principal Dimensions, Form Coefficients**

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**Definition 1- Perpendiculars**

Imaginary lines perpendicular to the base line or plane (and the water line) On the ship there is a : - Forward Perpendicular (Fpp or Fp) This is the line crosses the intersection of the water line and the front of the stem -Aft Perpendicular (App or Ap) This line usually aligns the centre line of the rudder stock. This is the imaginary line around which the rudder rotates.

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2. Waterlines The waterline of a ship lying in the water. There are different waterlines (i.e load-lines) for different loading conditions, such as: Light waterline The waterline of a ship carrying only her regular inventory. Fully loaded waterline The waterline of maximum load draft in sea water. Construction (Scantling) waterline (CWL) The waterline used as the limit to which the various structural components are designed.

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**3- Plimsoll Mark (freeboard mark)**

The freeboard mark is a symbol indicating the maximal immersion of the ship in the water, leaving a minimal freeboard for safety. The mark consists of a circle with a diameter of 300 mm, through which a horizontal lines is drawn with its upper edge going through the centre of the circle.

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This level indicates the minimal freeboard in salt water summer conditions. Beside this circle the loadline mark consists of a number of horizontal lines indicating the minimal freeboard required for other than summer conditions. All freeboard lines are 25 mm wide and are connected by a vertical line.

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**The freeboard mark is placed midships on each side of the ship.**

The minimal operating freeboard depends on: Ship’s position at sea The time of year (summer, winter, etc,.._

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**5- Permanent marks on the ship’s hull**

4- Deck Line In general this is the extended line from the upper side of the freeboard deck at the ship’s side. The deck line is placed above the Plimsoll mark so that the freeboard can be easily monitored by the ship’s crew or other interested parties 5- Permanent marks on the ship’s hull It is very important the draft marks can be accurately read as easily as possible.

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**Dimensions FP Forward Perpendicular AP After Perpendicular**

WL Waterline

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WL Waterline CL Centreline

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1- Length over all LOA It is the overall length of the vessel, i.e the horizontal distance over the extremities from stem to stern 2- Length between perpendicular LPP It is the horizontal distance between the FP and AP 3- Length waterline LWL Horizontal distance between the fore and aft when the ship is loaded at the summer mark, less the shell. 4- Breadth over all BOA The maximum breadth of the ship as measured from the outer hull on the starboard to the outer hull on port side, including rubbing bars, permanent fenders.

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4- Breadth or beam BMLD The greatest moulded breadth, measured from side to side at the outside of the frames, but inside the shell 5- Depth D The vertical distance between the base line and the upper continuous deck and is measured at the half Lpp at the side of the ship 6- Draft Forward (TFWD) Vertical distance between the waterline and the underside of the keel, as measured at the forward perpendicular 6- Draft at the stern (TAF) Vertical distance between the waterline and the underside of the keel, as measured at the after perpendicular

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7- Freeboard The distance between the waterline and the top of the deck at the side ( at the deck line). The term summer freeboard means the distance from the top of the summer loadline and the upper edge of the deck line 8- Air draft The vertical distance between the waterline and the highest point of the ship. The air draft is measured from the summer mark. Sheer This is the upward rise of the ship’s deck from mid length towards the bow and stern. The sheer gives the vessel extra buoyancy at the stem and stern Camber The transverse curvature of the weather deck. The curvature helps to ensure sufficient drainage of any water on deck

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**40 Base line Top of the flat keelplace Keel (K)**

Inter section of the base line and the center line plane Beam: B Camber Depth: D Draft: T Freeboard WL K C L 40

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Flare Tumble Home Flare : outward curvature of ship’s hull surface above the waterline Tumble Home : opposite of flare

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Positions of the ship List Heeling to one side about the fore and aft axis Heel to port side

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Trim (t) The difference between the draft at the stern and the draft at the stem i.e the trim fore (tF) + the trim aft (tA) On an even keel, in proper trim The draft of the stern equals the draft of the stem Trim by head TF more than TA

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**Trim by stern TA more than TF**

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Volumes and weights Register ton (RT) To determine the size of a ship the RT is used. It is based on volume where one register ton equals 100 cubic feet or 2.83 m3

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**Gross Register Tonnage**

The Gross Register Tonnage (GRT or GT) usually called Gross Tonnage, is calculated using a formula that takes into account the ship’s volume in cubic meters below the main deck and the enclosed spaces above the main deck Net Register Tonnage The Net Register Tonnage is also a non-dimensional number that describes the volume of the cargo space. The NT is derived from the GT by subtracting the volume of space occupied by: - crew - Navigation equipment -The propulsion equipment - work stations - Ballast

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**Volume of Displacement V m3**

The displacement is the volume of the part of the ship below the waterline including the shell plating, propeller and rudder Displacement Δ ton The displacement is the weight of the volume of water displaced by the ship Lightship weight (ton) This is the weight of the ship including the regular inventory but without any cargo, fuel or crew. The regular inventory includes: anchors. Life-saving equipment, lubricating oil, paint

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Deadweight (ton) This is the weight of the a ship can take on until the maximal allowable immersion is reached. This is a fixed value, unique to each ship. Cargo Capacity (t) This is the total weight of cargo a ship is designed to carry at a given time.

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**Hull Form Coefficients**

Line coefficients define the characteristics of the vessel’s shape at and below the waterline. This makes it possible to get an impression of the shape of the underwater body of a ship without extensive use of any data. 1- Block Coefficient, Coefficient of fineness CB The block coefficient gives the ratio of the volume of the underwater body (V) and the rectangular block bounded by LPP, BMLD and draft (T). The vessel with a small block coefficient is reoffered to as fine.

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**2- Waterline coefficient CW**

The waterline coefficient gives the ratio of the area of the waterline (Aw) and the rectangular plane bounded by LPP, BMLD.

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**Midship Section Coefficient CM**

The midship (main frame) coefficient gives the ratio of the area of the midship section (AM) and the area bounded by BMLD and T.

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**Prismatic Coefficient CP**

The prismatic Coefficient gives the ratio of the volume of the underwater body and the block formed by the area of the Midship Section AM and LPP.

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When the principal dimensions, displacement and hull form coefficients are known, one has an impressive amount of design information, but not yet a clear image of the exact geometrical shape of the shape. The shape is given by the lines plane. The shape of a ship can vary in height, length and breadth. In order to represent this complex shape on paper, transverse sections of the hull are combined with two longitudinal sets of parallel planes, each one perpendicular to the others Since the ship is a 3-dimensional shape, data in x, y and z directions is necessary to represent the ship hull. (Table of Offsets) Lines - body plan (front View) - shear plan (side view) - half breadth plan (top view)

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Example 1 A ship has a length and breadth at the waterline of 40.1 m and 8.6 m respectively. If the water-plane area is 280 m2 calculate the coefficient of fineness of the water-plane area (CW). Solution Example 2 A ship floats at a draught of 3.20 m and has a waterline length and breadth of 46.3 m and 15.5 m respectively. Calculate the block coefficient (CB) if its volume of displacement is 1800 m3. Solution

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Example 3 A ship has length 200 m and breadth 18 m at the waterline. If the ship floats at an even keel draught of 7.56 m in water RD and the block coefficient is calculate the displacement. Solution Example 4 A ship floats at a draught of 4.40 m and has a waterline breadth of m. Calculate the underwater transverse area of the midships section if CM is

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Example 5 A ship has the following details: Draught 3.63 m; Waterline length m; Waterline breadth 9.42 m; Cm 0.946; Cp Calculate the volume of displacement. Solution

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**Tonnes per Centimetre immersion TPC**

The TPC for any given draught is the weight that must be loaded or discharged to change the ship’s mean draught by one centimetre (1cm)

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Where: TPC : tonnes per cm WPA : water plane area m2 ρ : water density t/m3

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Example 6 Calculate the TPC for a ship with a water-plane area of 1500 m2 when it is floating in: (a) fresh water; (b) dock water of RD 1.005; (c) salt water Solution:

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LOAD/DISCHARGE Example 7 M.V. Almar has a displacement of ton at an initial mean draught of 4.40 m in salt water and is required to complete loading with a draught of 6.70 m (displacement will reach ton). Calculate the amount of cargo that must be loaded.

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**Fresh Water Allowance (FWA)**

Fresh Water Allowance (FWA) is the number of millimetres by which the mean draught changes when a ship passes from salt water to fresh water, or vice-versa, when the ship is loaded to the Summer displacement. The FWA is found by the formula: TPCSW is the salt-water TPC value for the summer load draught. Example 8 A ship floats in SW at the Summer displacement of 1680 tonnes. If the TPCSW is 5.18, how much will the draught change by if the ship is towed to a berth where the density of the water is t/m3?

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**3- Classification Societies & Governmental Authorities**

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**Classification Societies**

- Merchant shippers and underwriters provided ship lists and met Edward Lloyd 17th – 18th century - Activities of classification societies (rules, certification, delegation by governments,…)

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**Governmental Authorities (IMO)**

(IMCO) inter governmental maritime consultative organization, 1982 IMO - Committees (maritime safety committee MSC, marine environment protection committee MEPC) Conventions (SOLAS, MARPOL, ILLC, tonnage) - Resolutions

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