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Geometry Of The Ship


A ship is a three-dimensional object that can be defined accurately by comparing it with two- and three-dimensional figures. Standard reference lines and planes provide the means of locating points in ships. The standard reference lines and planes are:

  • Forward Perpendicular (FP) - A vertical line through the intersection of the design waterline with the stem. Points in the ship are measured fore and aft from the FP.

  • After Perpendicular (AP) - A vertical line passing through the rudder post or through the intersection of the design waterline with the stern. The AP is an alternative to the FP for locating points fore and aft.

  • Midships Section: - A vertical athwartships plane halfway between the forward and after perpendiculars.

  • Centerline: - A vertical fore and aft plane passing down the center of the ship.

  • Baseline: - A horizontal plate passing through the lowest point in the ship.

The position of any point in the ship is described by locating its height above the baseline, position to either side of the centerline, and distance fore and aft from one of the perpendiculars or the midships section.

The principal dimensions of a ship are:

  • Length between Perpendiculars (LBP): - The distance between the forward and after perpendiculars measured in feet or meters.

  • Beam (B): - The maximum breadth of the ship measured in feet or meters.

  • Draft (T): - The distance, measured in feet or meters, between the keel and waterline at any point along the length. When the point at which the draft is taken is not specified, it is assumed to be the midships or mean draft.

  • Depth (D): - The distance between the keel and the uppermost watertight deck measured in feet or meters.

Other quantities used in describing ships include:

  • Length Overall (LOA): The extreme length of the ship measured along the centerline in feet or meters.

  • Displacement Volume (V): The underwater volume of the ship measured in cubic feet or meters.

  • Displacement (W): The weight of the ship and all the material on board measured in long tons (2,240 pounds) or metric tons (1,000 kgs or 2,204 lbs.). Displacement is directly related to displacement volume. In salt water one ton of displacement equals 35 cubic feet of volume; in fresh water one ton equals 36 cubic feet. In SI units in salt water one ton is equivalent to one cubic meter, in fresh water 1.025 cubic meters.

  • Lightship: The weight of the structure, machinery, and permanent outfit of the ship.

  • Deadweight (dwt): The total weight of cargo, passengers, crew, stores, and water carried by the ship. A deadweight scale relating deadweight to draft, displacement, and other quantities normally appears on the ship's Capacity Plan. In the absence of a deadweight scale, maximum displacement can be estimated for ships of 100,000 tons dwt or less by multiplying maximum deadweight by 1.3. Above this point the multiplier decreases to 1.15 at 150,000 and 1.05 at and above 200,000 tons. (These dwt calculations are for Salvors.)

  • Gross Registered Tonnage (grt): A measure of the earning capacity or the cubic capacity of the ship and a basis for charges levied against the ship. One ton is equal to 100 cubic feet or 3 cubic meters. Gross registered tonnage is a volume, not a weight, and has no meaning in salvage calculations.

  • Net Tonnage: A figure derived from gross registered tonnage by deducting the volume of spaces not contributing to the earning capacity of the ship.

  • Load Line: The maximum draft to which a ship may be loaded and still maintain a statutory amount of reserve buoyancy.

  • Freeboard (F): The distance between the waterline and the uppermost watertight deck measured in feet or meters.

  • Reserve Buoyancy: The volume of the hull between the waterline and the uppermost watertight deck.

  • Trim: Fore and aft inclination measured as the difference between the drafts at the forward and after perpendiculars. Ships designed with drag have zero trim when floating at their design drafts. Excessive trim is defined as more than one percent of the ship's length.

  • List: Athwartships inclination, usually measured in degrees.

  • Tons Per Inch Immersion (TPI): The weight in tons added or removed that increases or decreases the draft one inch. Tons per inch immersion is equivalent to the displacement of a one-inch thick slice of the waterplane. (Also Tonnes Per Centimeter Immersion (TPC))

  • Moment to Change Trim One Inch (MT1): The moment required to cause one-inch change in trim. Calculation of MT1 is neither as simple nor as straightforward as that of TPI.

  • Center of Gravity (G): is the center of mass of the vessel and the point through which the weight of the vessel and all cargo and other material on board acts vertically downward. The position of the center of gravity varies in three dimensions with the amount and placement of weights in the ship. The vertical position of the center of gravity is a critical factor in transverse stability. The height of the center of gravity above the keel (KG) for specific conditions of loading may be found in the Report of Inclining Experiment or the Trim and Stability Booklet. The depth of the hull multiplied by 0.60 gives an initial estimate of KG that is accurate enough in most ships for initial salvage calculations.

  • Center of Buoyancy (B): is the center of mass of the underwater body of the ship and the point through which the force of buoyancy equal to the weight acts vertically upward. The longitudinal position of B (LCB) is import because, when the ship is afloat, B and G are in the same longitudinal position. If they are displaced form one another, the ship trims until the two centers are in the same longitudinal position. When the ship is aground it may be unable to trim, so there is a considerable longitudinal distance between B and G.

    In most ships, the height of the center of buoyancy above the keel (KB) lies between 0.53 and 0.58 of the ship's mean draft, depending upon the shape of the ship's bottom. A reasonable quick first estimate of the height of KB is 0.55 times the mean draft.

  • Center of Flotation (F): is the center of mass of the ship's waterplane and is the point about which the ship trims.

    Normally the center of flotation lies abaft amidships within 2 percent of the length. The longitudinal position of the center of flotation can be estimated as a function of length and speed for various ship types by standard equations.

  • Metacenter (M): is the intersection of a vertical through the center of buoyancy of an inclined ship and the vertical through the center of buoyancy when the inclination approaches zero as a limit. The same principle applies to both the transverse and longitudinal metacenters. The metacenter and the relative positions of the metacenter and the center of gravity are prime factors in establishing the initial stability of a ship.
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