block coefficient

Hull (watercraft)

A hull is the body of a ship or boat. It is a central concept in floating vessels as it provides the buoyancy that keeps the vessel from sinking.

General features

Nearly all watercraft, from small boats to the largest ships, adhere to a general form that serves the needs of stability and efficient propulsion, featuring:

  • horizontal cross-sections that have narrow, usually pointed, fronts (at the bow),
  • smooth widening from the bow until roughly the middle of the length (midships), and often narrowing smoothly but usually significantly to the extreme end (the stern), whose width may range from a large to an insignificant fraction of the beam.

Hull shapes

Hulls come in many varieties and can have composite shape, (e.g., a fine entry forward and inverted bell shape aft), but are grouped primarily as follows:
* Moulded, round bilged or soft-chined. Examples are the round bilge, semi-round bilge and s-bottom hull.
defined as smooth curves
* Chined and Hard-chined. Examples are the flat-bottom (chined), v-bottom and multi-bottom hull (hard chined).
have at least one pronounced knuckle throughout all or most of their length


After this they can be categorized as:
* Displacement
the hull is supported exclusively or predominantly by the pressure of water displaced by the hull. These hulls have a shape which does not promote planing. They travel through the water at a limited rate which is defined by the waterline length. They are often heavier than planing types, though not always.
* Semi-displacement, or semi-planing
the hull form is capable of developing a moderate amount of dynamic lift, however, most of the vessel's weight is still supported through displacement
* Planing
the planing hull form is configured to develop positive dynamic pressure so that its draft decreases with increasing speed. These hulls have a shape that promotes the boat to rise higher and higher out of the water as the speed increases. They are sometimes flat-bottomed, sometimes V-bottomed and sometimes round-bilged. The most common form is to have at least one chine to allow for stability when cornering and for a supportive surface on which to ride while planing. Planing hulls allow higher speeds to be achieved, and are not limited by the waterline length the way displacement hulls are. They do require more energy to achieve these speeds. (see: Planing (sailing)).

Most used hull forms

At present, the most widely used form is the round bilge hull.

The inverted bell shape of the hull, with smaller payload the waterline cross-section is less, hence the resisitance is less and the speed is higher. With higher payload the outward bend provides smoother performance in waves. As such, the inverted bell shape is a popular form used with planing hulls.

Hull forms

Smooth curve hulls

Smooth curve hulls are hulls which use, just like the curved hulls, a sword or a attached keel.

Semi round bilge hulls are somewhat less round. The advantage of the semi-round is that it is a nice middle between the S-bottom and chined hull. Typical examples of a semi-round bilge hull can be found in the Centaur and Laser cruising dinghies.

S-bottom hulls are hulls shaped like an s.In the s-bottom, the hull runs smooth to the keel. As there are no sharp corners in the fuselage. Boats with this hull have a fixed keel, or a kielmidzwaard. This is a short keel which still sticks a sword. Examples of cruising dinghies that use this s-shape are the yngling and Randmeer.

Chined and hard-chined hulls

A chined hull consists of straight plates, which are set at an angle to each other. The chined hull is the most simple hull shape because it worked only with straight planks. These boards are often bent lengthwise. Most home-made constructed boats are chined hull boats. Benefits of this type of boating activity is the low production cost and the (usually) fairly flat bottom, making the boat faster at planing. Chined hulls can also make use of a sword or attached keel.

Chined hulls can be divised up into 3 shapes:

  • V-bottom chined hulls
  • flat-bott chined hulls
  • and multi-chined hulls.


* A protrusion below the waterline forward is called a bulbous bow and is fitted on some hulls to reduce the wave making resistance drag and thus increase fuel efficiency. Bulbs fitted at the stern are less common but accomplish a similar task. (see also : Naval architecture)

* A keel may be fitted on a hull to increase the transverse stability, directional stability or to create lift.

* Control devices such as a rudder, trim tabs or stabilizing fins may be fitted.


Bow is the frontmost part of the hull

Stern is the rear-most part of the hull

Port is the left side of the boat when facing the Bow

Starboard is the right side of the boat when facing the Bow

Waterline is an imaginary line circumscribing the hull that matches the surface of the water when the hull is not moving.

Midships is the midpoint of the LWL (see below). It is half-way from the forwardmost point on the waterline to the rear-most point on the waterline.

Baseline an imaginary reference line used to measure vertical distances from. It is usually located at the bottom of the hull.


Hull forms are defined as follows:

* Block Measures that define the principal dimensions. They are:
* Length Overall (LOA) is the extreme length from one end to the other.
* Length on 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.
* Draft (d) or (T) is the vertical distance from the bottom of the hull to the waterline.
* Freeboard (FB) is the difference between Depth and 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.

* Coefficients help compare hull forms as well:

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, Bwl & 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_{wl} cdot T}

2) Midship Coefficient (Cm or Cx) is the Bwl x draft divided by the cross-sectional area (Ax) of the slice at Midships (or at the largest section for Cx). 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_{wl} cdot T}

3) Prismatic Coefficient (Cp) is the volume (V) divided by Lwl x Ax. It displays the ratio of the underwater volume of the hull to a rectangular block of the same overall length as the underbody and with cross-sectional area equal to the largest underwater section of the hull. This is used to evaluate the distribution of the volume of the underbody. A low Cp indicates a full mid-section and fine ends, a high 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_{wl} cdot A_m}

4) Waterplane Coefficient (Cw) is the waterplane area divided by Lwl x Bwl. 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_{wl} cdot B_{wl}}

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


Rafts have a hull of sorts, however, hulls of the earliest design are thought to have each consisted of a hollowed out tree bole: in effect the first canoes. Hull form then proceeded to the Coracle shape and on to more sophisticated forms as the science of Naval architecture advanced.



  • Hayler, William B.; Keever, John M. (2003). American Merchant Seaman's Manual. Cornell Maritime Pr.
  • Turpin, Edward A.; McEwen, William A. (1980). Merchant Marine Officers' Handbook. 4th, Centreville, MD: Cornell Maritime Press.

See also

External links

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