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Hull forms are defined as follows


Hull forms are defined as follows:
  • Length overall (LOA) is the extreme length from one end to the other.
  • Length at the waterline (LWL) is the length from the forwardmost point of the waterline measured in profile to the stern-most point of the waterline.
  • Length between perpendiculars (LBP or LPP) is the length of the summer load waterline from the stern post to the point where it crosses the stem. (see also p/p)
  • Beam or breadth (B) is the width of the hull. (ex: BWL is the maximum beam at the waterline)
  • Depth or moulded depth (D) is the vertical distance measured from the top of the keel to the underside of the upper deck at side.[2]
  • Draft (d) or (T) is the vertical distance from the bottom of the keel to the waterline.
  • Freeboard (FB) is Depth plus the height of the keel structure minus draft.
  • Form Derivatives that are calculated from the shape and the Block Measures. They are:
  • Volume (V or ) is the volume of water displaced by the hull.
  • Displacement (Δ) is the weight of water equivalent to the immersed volume of the hull.
  • Longitudinal Centre of Buoyancy (LCB) is the longitudinal distance from a point of reference (often Midships) to the centre of the displaced volume of water when the hull is not moving. Note that the Longitudinal Centre of Gravity or centre of the weight of the vessel must align with the LCB when the hull is in equilibrium.
  • Vertical Centre of Buoyancy (VCB) is the vertical distance from a point of reference (often the Baseline) to the centre of the displaced volume of water when the hull is not moving.
  • Longitudinal Centre of Floatation (LCF) is the longitudinal distance from a point of reference (often Midships) to the centre of the area of waterplane when the hull is not moving. This can be visualized as being the area defined by the water's surface and the hull.

Parallel midbody In many modern ships, the form of the hulls transverse section in the midships region extends without change for some distance fore and aft. This is called parallel midbody and may be described as extensive or short, or expressed as a fraction of the ships length.
Forebody The portion of the hull forward of the midship section.
After body The portion of the hull abaft the midship section.
Entrance The immersed portion of the hull forward of the section of greatest immersed area (not necessarily amidships) or forward of the parallel midbody.
Run The immersed portion of the hull aft of the section of greatest immersed area or aft of the parallel midbody.
Deadrise The departure of the bottom from a transverse horizontal line measured from the baseline at the molded breadth line. Deadrise is also called rise of floor or rise of bottom. Deadrise is an indicator of the ships form; fullbodied ships, such as cargo ships and tankers, have little or no deadrise, while fine-lined ships have much greater deadrise along with a large bilge radius. Where there is rise of floor, the line of the bottom commonly intersects the baseline some distance from the centerline, producing a small horizontal portion of the bottom on each side of the keel. The horizontal region of the bottom is called flat of keel, or flat of bottom. While any section of the ship can have deadrise, tabulated deadrise is normally taken at the midships section.
Knuckle An abrupt change in the direction of plating or other structure.
Chine The line or knuckle formed by the intersection of two relatively flat hull surfaces, continuous over a significant length of the hull. In hard chines, the intersection forms a sharp angle; in soft chines, the connection is rounded.
Bilge radius The outline of the midships section of very full ships is very nearly a rectangle with its lower corners rounded. The lower corners are called the bilges and the shape is often circular. The radius of the circular arc is called the bilge radius or turn of the bilge. The turn of the bilge may be described as hard or easy depending on the radius of curvature. If the shape of the bilge follows some curve other than a circle, the radius of curvature of the bilge will increase as it approaches the straight plating of the side and bottom. Small, high-speed or planing hulls often do not have a rounded bilge. In these craft, the side and bottom are joined in a chine.
Tumblehome The inward fall of side plating from the vertical as it extends upward towards the deck edge. Tumblehome is measured horizontally from the molded breadth line at the deck edge. Tumblehome was a usual feature in sailing ships and many ships built before 1940. Because it is more expensive to construct a hull with tumblehome, this feature is not usually incorporated in modern merchant ship design, unless required by operating conditions or service (tugs and icebreaking vessels, for example). Destroyers and other high-speed combatants are often built with some tumblehome in their mid and after sections to save topside weight.
Flare The outward curvature of the hull surface above the waterline, i.e., the opposite of tumblehome. Flared sections cause a commensurately larger increase in local buoyancy than unflared sections when immersed. Flaring bows are often fitted to help keep the forward decks dry and to prevent "nose-diving" in head seas.
Camber The convex upwards curve of a deck. Also called round up, round down, or round of beam. In section, the camber shape may be parabolic or consist of several straight line segments. Camber is usually given as the height of the deck on the centerline amidships above a horizontal line connecting port and starboard deck edges. Standard camber is about one-fiftieth of the beam. Camber diminishes towards the ends of the ship as the beam decreases. The principal use of camber is to ensure good drainage in calm seas or in port, although camber does slightly increase righting arms at large angles of inclination (after the deck edge is immersed). Not all ships have cambered decks; ships with cambered weather decks and flat internal decks are not uncommon.
Sheer The rise of a deck above the horizontal measured as the height of the deck above a line parallel to the baseline tangent to the deck at its lowest point. In older ships, the deck side line often followed a parabolic profile and sheer was given as its value at the forward and after perpendiculars. Standard sheer was given by: where sheer is measured in inches and L is the length between perpendiculars in feet. Actual sheer often varied considerably from
sheer forward = 0.2L + 20
sheer aft = 0.1L + 10
these standard values; the deck side profile was not always parabolic, the lowest point of the upper deck was usually at about 0.6L, and the values of sheer forward and aft were varied to suit the particular design. Many modern ships are built without sheer; in some, the decks are flat for some distance fore and aft of midships and then rise in a straight line towards the ends. Sheer increases the height of the weather decks above water, particularly at the bow, and helps keep the vessel from shipping water as she moves through rough seas as well as improving sea keeping by adding bouyancy Ford and Aft.
Rake A departure from the vertical or horizontal of any conspicuous line in profile, defined by a rake angle or by the distance between the profile line and a reference line at a convenient point. Rake of stem, for example, can be expressed as the angle between the stem bar and a vertical line for ships with straight stems. For curved stems, a number of ordinates measured from the forward perpendicular are required to define the stem shape. Ships designed so that the keel is not parallel to the baseline and DWL when floating at their designed drafts are said to have raked keels, or to have drag by the keel.
Cut-up When a keel departs from a straight line at a sharp bend, or knuckle, the sloping portion is called a cut-up. This is seen on some high speed craft and on Ice breakers allowing them to ride up on to the ice
Deadwood Portions of the immersed hull with significant longitudinal and vertical dimensions, but without appreciable transverse dimensions. Deadwood is included in a hull design principally to increase lateral resistance or enhance directional stability without significantly increasing drag when moving ahead. Sailing craft require deadwood to be able to work to windward efficiently.
Skegs or fins are fitted on barges to give directional stability. Deadwood aft is detrimental to speed and quick maneuverability and is minimized by use of cut-up sterns and by arched keels or sluice keels (with athwartships apertures) in tugs and workboats.
Appendages Portions of the vessel that extend beyond the main hull outline or molded surface. Positive appendages, such as rudders, shafts, bosses, bilge keels, sonar domes, etc., increase the underwater volume, while negative appendages, such as bow thruster tunnels and other recesses, decrease the underwater volume. Shell plating, lying outside the molded surface, is normally the largest single appendage, and often accounts for one-half to two-thirds of the total appendage volume. Appendages generally account for 0.2 to 2 percent of total immersed hull volume, depending on ship size, service, and configuration.
Hull Surfaces Hull surfaces are either warped, consisting of smoothly faired, complex three-dimensional curves, developed, consisting of portions of cylinders or cones, or flat. Hydroconic hulls are built up of connected flat plates rather than plates rolled to complex curves. Hydroconic construction lowers production costs and may simplify fitting patches to a casualty.
The part of the hull which effects the speed and fuel consumed is the area under the water. Thus Length Overall (LOA) is not relevant. Instead the length between perpendiculars (LPP and Length at waterline (LWL) are used. For LPP the aftermost perpendicular is usually taken as passing through the rudder stock. An accepted method of calculation is
LPP = 0.97 x LWL
The draught is taken as the design draught. This draught depends on the trading of the vessel and may be between the summer loadline draught and ballast draught.
1) Block Coefficient (Cb) is the volume (V) divided by the LWL x BWL x T. If you draw a box around the submerged part of the ship, it is the ratio of the box volume occupied by the ship. It gives a sense of how much of the block defined by the LWL, beam (B) & draft (T) is filled by the hull. Full forms such as oil tankers will have a high Cb where fine shapes such as sailboats will have a low Cb.

C_b = \frac {V}{L_{WL} \cdot B \cdot T}
2) Midship Coefficient (Cm or Cx) is the cross-sectional area (Ax) of the slice at Midships (or at the largest section for Cx) divided by beam x draft. It displays the ratio of the largest underwater section of the hull to a rectangle of the same overall width and depth as the underwater section of the hull. This defines the fullness of the underbody. A low Cm indicates a cut-away mid-section and a high Cm indicates a boxy section shape. Sailboats have a cut-away mid-section with low Cx whereas cargo vessels have a boxy section with high Cx to help increase the Cb.

C_m = \frac {A_m}{B \cdot T}
3) Prismatic Coefficient (Cp) is the volume (V) divided by Lpp x Ax. It displays the ratio of the immersed volume of the hull to a volume of a prism with equal length to the ship and cross-sectional area equal to the largest underwater section of the hull (midship section). This is used to evaluate the distribution of the volume of the underbody. A low or fine Cp indicates a full mid-section and fine ends, a high or full Cp indicates a boat with fuller ends. Planing hulls and other highspeed hulls tend towards a higher Cp. Efficient displacement hulls travelling at a low Froude number will tend to have a low Cp.

C_p = \frac {V}{L_{pp} \cdot A_m}

4) Waterplane Coefficient (Cw) is the waterplane area divided by Lpp x B. The waterplane coefficient expresses the fullness of the waterplane, or the ratio of the waterplane area to a rectangle of the same length and width. A low Cw figure indicates fine ends and a high Cw figure indicates fuller ends. High Cw improves stability as well as handling behavior in rough conditions.

C_w = \frac {A_w}{L_{pp} \cdot B}


C_b = {C_{p} \cdot C_{m} }
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