(a) Block Coefficient, This is defined as the ratio of the volume of displacement of the molded form up to any waterline to the volume of a rectangular prism with length, breadth and depth equal to the length, breadth and mean draft of the ship, at that waterline. Thus,

where L is length, B is breadth and T is mean molded draft to the prevailing waterline. Practice varies regarding Land B. Some authorities take L as LBP, some as LWL, and some as an effective length. B may be taken as the molded breadth at the design waterline and at amidships, the maximum molded breadth at a selected waterline (not necessarily at amidships), or according to another standard. Most merchant ships have vertical sides amidships, with upper waterlines parallel to the centerline, thereby removing possible ambiguity in B.

Values of at design displacement may vary from about 0.36 for a fine high-speed vessel to about 0.92 for a slow and full Great Lakes bulk carrier.

(b) Midship Coefficient, The midship section coefficient, , sometimes called simply midship coefficient, at any draft is the ratio of the immersed area of the midship station to that of a rectangle of breadth equal to molded breadth and depth equal to the molded draft amidships. Thus,

Values of may range from about 0.75 to 0.995 for normal ships, while for vessels of extreme form with a slack bilge and a hollow garboard area (immediately outboard of the keel) amidships, might be as low as 0.62. In some cases vessels have been built with bulges or blisters below the design waterline. Assuming B is taken at the prevailing waterline, then may be greater than unity on such vessels.

(c) Prismatic Coefficient, The prismatic coefficient, sometimes called longitudinal prismatic coefficient, or simply longitudinal coefficient, gives the ratio between the volume of displacement and a prism whose length equals the length of the ship and whose cross section equals the midship section area. Thus,

The term longitudinal coefficient was originated and used by Adm. D. W. Taylor (1943) for the reason that this coefficient is a measure of the longitudinal distribution of a ship's buoyancy. If two ships with equal length and displacement have different prismatic coefficients, the one with the smaller value of will have the larger midship sectional area ( ) and hence a larger concentration of the volume of displacement amidships. This is clearly shown by Figure below,

which compares the sectional area curves for two different vessels. The ship with the smaller is also characterized by a protruding bulbous bow, which causes the swelling in the sectional area curve right at the bow, and its extension forward of Station O.

Prismatic coefficient is a frequently used parameter in studies of speed and power. Usual range of values is from about 0.50 to about 0.90. A vessel with a low value of (or ) is said to have a fine hull form, while one with a high value of has a full hull form.

(d) Waterplane Coefficient, . The waterplane coefficient is defined as the ratio between the area of the waterplane and the area of a circumscribing rectangle. Thus,

As with the other coefficients, the length and breadth are not always taken in a standard way. The coefficient may be evaluated at any draft. The values of at the DWL range from about 0.65 to 0.95, depending upon type of ship, speed, and other factors.

(e) Vertical Prismatic Coefficient, . This coefficient is the ratio of the volume of a vessel's displacement to the volume of a cylindrical solid with a depth equal to the vessel's molded mean draft and with a uniform horizontal cross section equal to the area of the vessel's waterplane at that draft. This ratio is analogous to the prismatic or longitudinal coefficient, except that the draft and area of waterplane have been substituted for the vessel's length and area of midship section. The vertical prismatic coefficient of fineness is designated as and written as nofollows:

(f) Volumetric Coefficient, . This coefficient (or fatness ratio) is defined as the volume of displacement divided by the cube of one tenth of the vessel's length, or

In essence, it is the dimensionless equivalent of displacement-length ratio, frequently used in the past, where . is ship displacement in long tons in salt water, and L is ship length in feet. These coefficients express the displacement of a vessel in terms of its length. Ships with low volumetric coefficients might be said to be "thin", while those with a high coefficient are "fat." Values of the volumetric coefficient range from about 1.0 for light, long ships like destroyers, to 15 for short heavy ships like trawlers.

(g) Ratios ofDimensions. The three principal dimensions of the underwater body are sometimes referred to in ratio form. These are noted below, with approximate ranges for each:

In view of the confusion which can arise when different definitions of dimensions-especially lengthare used by different designers in forming the above coefficients and ratios, it is suggested that length between perpendiculars-on single-screw ships-and molded breadth at the design waterline and at amidships be used in forming these ratios. The length on the DWL is preferred for twin-screw ships. The definitions adopted should always be specified.

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