After perpendicular (AP)

A line which is perpendicular to the intersection of the after edge of the rudder-post with the designed load water-line. This is the case for both single- and twin-screw merchant ships. For some classes of warships, and for merchant ships having no rudder-post, the after perpendicular is taken as the centre-line of the rudder stock.


This is the point midway between the forward and after perpendiculars.

Breadth moulded (B).

This is the maximum beam, or breadth, of the ship measured inside the inner shell strakes of plating, and usually occurs amidships.

Breadth extreme (BE).

This is the maximum breadth including all side plating, straps, etc.


This is the rounded plating at the lower corners between the vertical shell plating and the outer bottom plating.

Block coefficient (CB).

This is a measure of the fullness of the form of the ship and is the ratio of the volume of displacement to a given water-line, and the volume of the circumscribing solid of constant rectangular cross-section having the same length, breadth and draught as the ship.

ie: CB = (L x B x T)

The LPP is normally used in calculating the value of CB which varies with the type of ship.

Fast ships

0.50-0.65 (fine form)

Ordinary ships

0.65-0.75 (moderate form)

Slow ships

0.75-0.85 (full form)

Camber or round of beam.

This is the transverse curvature given to the decks, and is measured by the difference between the heights of the deck at side and centre. The amount of camber amidships is often one-fiftieth of the beam of the ship.

Coefficients of form.

Form is used as a general term to describe the shape of the ship's hull; and when comparing one ship's form with another, the naval architect makes use of a number of coefficients. These coefficients are of great use in power, stability, strength and design calculations.

Centre of flotation (F).

This is the centre of gravity of the area, or centroid, of the water-plane of a ship. For small angles of trim consecutive water-lines pass through F.

Centre of buoyancy (B).

This is the centroid of the underwater form of a ship, and is the point through which the total force of buoyancy may be assumed to act. Its position is defined by:

  • (a) KB the vertical distance above the base
  • (b) FB the longitudinal distance from the forward perpendicular.
  • (c) LCB the longitudinal distance from amidships.

Centre of gravity (G).

This is the point through which the total weight of the ship may be assumed to act. It also is defined by:

  • (a) KG the vertical distance above the base
  • (b) FG the longitudinal distance from the forward perpendicular.
  • (c) LCC the longitudinal distance from amidships.

Depth moulded (D).

This is the vertical distance between the moulded base line and the top of the beams of the uppermost continuous deck measured at the side amidships.

Draught moulded (T).

This is the draught measured to any water-line, either forward or aft, using the moulded base line as a datum.

Draught extreme (TE).

This is obtained by adding to the draught moulded the distance between the moulded base line and a line touching the lowest point of the underside of the keel. This line is continued to the FP and AP, where it is used as the datum for the sets of draught marks.


This equals the volume ( ) , weight ( ), or mass of water displaced by the hull.

Displacement as a volume. ( )

This is the size of the hole in the water occupied by the ship measured in cubic metres. There is no density correction.

Displacement as a weight. ( )

This is the weight of water displaced by the ship and equals the volume displaced multiplied by a constant representing the density of water, ie:

In fresh water = x 1000 kg/m
In sea water = x 1025 kg/m

The displacement weight of a ship can vary according to circumstances and position in the world, although displacement weight and ship weight are equal when the ship is at rest in equilibrium in still water.

Displacement as a mass.

This equals the quantity of water displaced and as the kilogram is the unit of mass and 1000 kg = 1 tonne this is the unit which is used when referring to the size of a ship.

Displacement moulded.

This is the mass of water which would be displaced by the moulded lines of the ship when floating at the designed loadwater-line.

Displacement extreme. ( E)

This equals the moulded displacement, plus the displacement of the shell plating, bossings, cruiser stern and all other appendages.


This is the difference between the extreme displacement at any draught and the lightship displacement, and is sometimes known as the burden.

Displacement tonnage.

This represents the amount of water displaced by a ship, expressed in tonnes. (1 tonne = 1000 kg). The size of warships is always given in terms of displacement tonnage.

Deadweight tonnage.

This is the measure of a ship's capacity to carry cargo, fuel, passengers, stores, etc, expressed in tonnes. It is the difference in displacement in tonnes between the light and loaded conditions.

The size of tankers is often given in terms of deadweight tonnage. Ships are usually chartered on the deadweight tonnage.

Entrance and run.

These are the shaped underwater portions of the ship forward and aft of the parallel middle body.

Forward perpendicular (FP)

This is represented by a line which is perpendicular to the intersection of the designed load water-line with the forward side of the stem.

Flat of keel.

This is the amount of flat bottom plating on each side of the centre girder.


This is the outward curvature of the hull surface above the water-line and is the opposite of tumble-home.


This may be considered to be the height amidships, of the freeboard deck at side above the normal summer load water-line.

Freeboard length (L)

The length is taken as 96% of the total length on a water-line situated at 85 % of the least moulded depth or, if greater, as the length from the fore side of the stem to the axis of the rudder stock on that water-line.

Freeboard depth (D)

This is the moulded depth, as measured amidships, from the top of the keel to the top of the freeboard deck beams at side, plus the thickness of the stringer plate if no wooden deck is fitted. If a wooden deck is fitted:

D = Moulded depth + (T(L - S)) L


  • T = the mean thickness of the exposed deck clear of deck openings
  • L = the freeboard length
  • S = total length of superstructures.

Freight tonnage.

This represents the total cubic capacity of a ship available for the carriage of cargo. When expressed as a weight, 1.13 m are taken as 1 ton.

Gross tonnage.

This is a measure of the under-deck tonnage with the addition of 'tween-deck spaces and enclosed spaces above the upper deck. Certain spaces are exempted from measurement. The size of most ordinary merchant ships is quoted in terms of gross tonnage.

If no other information is available, the following formula will give an approximation to the gross tonnage of an ordinary passenger or cargo ship with medium erections.

Gross tonnage = (L x B x D) 3.5 tons

  • L = LPP in metres
  • B = Breadth moulded, m
  • D = Depth moulded to upper deck, m


This is the amount of inclination of the ship in the transverse direction, and is usually measured in degrees.

Length between perpendiculars (LPP).

This is the horizontal distance between the forward and after perpendiculars.

Length on the designed load water-line (LWL).

This is the length, as measured on the water-line of the ship when floating in still water in the loaded, or designed, condition.

Length overall (LOA).

This is the length measured from the extreme point forward to the extreme point aft.

Lightship displacement.

This equals the extreme displacement of the ship when fully equipped and ready to proceed to sea, but with no crew, passengers, stores, fuel, water, or cargo on board. The boiler or boilers, however, are filled with water to their working level.

Midship section.

This is the transverse section of the ship amidships. For a warship, amidships may be midway between the ends of the LWL.

Moulded base line.

This represents the lowest extremity of the moulded surface of the ship. At the point where this line cuts the midship section a horizontal line is drawn, and it is this line which acts as the datum, or base line, for all hydrostatic calculations. This line may, or may not, be parallel to the LWL depending on the type of ship.

Midship section area coefficient(CM).

This is the ratio of the immersed area of the midship section to the area of the circumscribing rectangle having a breadth equal to the breadth of the ship and a depth equal to the draught.

ie: CM = AM (B x T)

CM values range from about 0.85 for fast ships to 0.99 for slow ships.

Net or register tonnage.

This represents the gross tonnage of a ship after certain approved deductions, ie nonfreight earning spaces, have been made. A register ton represents 100 cubic feet of volume.

Parallel middle body (LP).

This is the length over which the midship section remains unchanged.

Prismatic coefficient (CP).

This is the ratio of the volume of displacement of the ship to the volume of the circumscribing solid having a constant section equal to the immersed midship section area AM, and a length equal to the LPP

ie CP = (AM x L)

The Cp is a measure of the longitudinal distribution of displacement of the ship, and its value ranges from about 0.55 for fine ships to 0.85 for full ships.

Rise of floor.

This is the amount by which the line of the outer bottom plating amidships rises above the base line, when continued to the moulded breadth lines at each side.


This is the curvature given to the decks in the longitudinal direction, and is measured at any point by the difference between the height at side at that point and the height at side amidships. The amount of sheer forward is often twice the sheer aft.


The thickness and dimensions of rolled sections and plates which are used to define and build the ship.


These are detached decked structures on the freeboard deck extending transversely to at least within 0.04B from the ship's side. The length of a superstructure (S) is the mean length of the part of the superstructure which lies within the length (L).


This is the difference between the draughts forward and aft. If the draught forward is greater than the draught aft it is called trim by the head, or bow. If the draught aft is greater, it is called trim by the stern.


This is the amount by which the midship section falls in from the half-breadth line at any particular depth.

Tonnes per centimetre (TPC).

This is the mass which must be added to, or deducted from, a ship in order to change its mean draught by 1 cm. If the ship changes its mean draught by 1 cm and if AW m is the area of the water- plane at which it is floating, then:

Change of volume = AW x 0.01 m
Change of displacement = AW x 0.01 x 1.025 tonnes in salt water
TPC = AW x 0.01025
= AW 97.5
or TPC = AW x 0.01 tonnes fresh water
        = AW 100

Under-deck tonnage.

This is the total internal capacity of a ship measured in register tons from the top of the floors to the tonnage deck. This includes all spaces above the floors. The tonnage deck is the upper deck in all ships with less than three decks, and the second deck from below in all other ships. Only complete decks are counted.

Water-plane area coefficient(CWP).

This is the ratio of the area of the water-plane to the area of the circumscribing rectangle having a length equal to the LPP and a breadth equal to B.

ie: CWP = AW (L x B)

The range of values is from about 0.70 for a fine ship to 0.90 for a full ship.