Continuing
with our talk on the basic ship terminologies (read Part 1 here), we come to one of the most
crucial issues namely, the hull form for the vessel.

The hull, as
we know is a complex three-dimensional structure extending lengthwise from fore
to aft, beam wise arthwartships and also along the depth. For the construction
and detailed study of the hull, we as naval architects need to develop a set of
lines or curvatures to define the hull form.

So, we have
developed three discrete plans or drawings for the ship in congruence with
three views, namely the aerial or the plan
view, the side or the profile view
and the front or the sectional view.

Fig. 1: An impression of the concept behind the development of ship stations (Copyright: Learn Ship Design) |

Fig. 2: A typical body plan (Copyright: Learn Ship Design) |

Now, again
if we imagine the loaf of bread to be cut, now longitudinally or lengthwise, we
get a congregation of vertical sections which vary in thickness, curvature but
remain the same in length. Thus, for a ship these intersections showing the
intersections of the fore and aft planes with the hull are grouped together in the sheer
profile. The imaginary line running directly from the bow to the stern parallel
to its side along the center is called the centreline of the ship denoted by CL.

Fig. 3: Impression of the concept behind the development of a sheer plan (Copyright: Learn Ship Design) |

A series of planes parallel to one side of the centreline plane are imagined at regular intervals from the centreline. Each plane will intersect the ship's hull and form a curved line at the points of intersection. These lines are called buttocks at the aft end or buttock lines and similarly breast lines at the fore end .These are projected onto a single plane called the Sheer Plan.

Fig. 4: A typical sheer plan (Copyright: Learn Ship Design) |

Each buttock line shows the true shape of the hull from the side view for some distance from the centreline of the ship. The centreline plane gives a special buttock line called the profile of the ship. This is essentially termed as the sheer plan because in the particular profile, the sheer of the ship (Remember Sheer?) The inclination or the departure of the upper deck from the horizontal line coinciding with the parallel middle body, fore and aft) is a crucial parameter defined in the view.

Fig. 5: Impression of the concept behind the development of half breadth plan containing waterplanes (Copyright: Learn Ship Design) |

Now, let our bread loaf be sliced again, this time depth wise (horizontally), where each slice is parallel to the base. In the case of a ship, the base plane is usually level with the keel. A series of planes parallel and above the base plan are imagined at regular intervals, usually at every meter or subdivisions of it. Each plane will intersect the ship's hull and form a line at the points of intersection. These lines are called waterlines and are all projected onto a single plane called the Half-Breadth Plan. This view is typically defined for the plan, where each line coinciding with the respective waterline depth wise along the hull symmetrical with the centreline on both the port and starboard. However on the account of symmetry, we omit any one of the halves and hence the name, half-breadth plan!

Fig. 6: A typical half breadth plan (Copyright: Learn Ship Design) |

Each waterlines shows the true shape of the hull from the top view for some elevation above the base plane.

For each of these lines drawings, the distances of the
various intersection points from the middle line plane is called offsets.

Clearly,
the three sets of curves making up the lines plan are interrelated as they
represent the same three dimensional body. This inter dependency is used in
manually fairing the hull from, each set being faired in turn and the changes
in the other two noted. At the end of an iterative process, the three sets will
be eventually compatible. Fairing is now achieved by computer using
mathematical fairing techniques, such as the use of curved surface patches, to
define the hull. Manual fairing process
was done first done in design office on a reduced scale drawing. To aid
production, the lines were then laid off full scale on the floor of a building
known as

*mould loft.*Then they were re-faired. Some shipyards used a reduced scale, say one-tenth, for use in building process. Nowadays, the data are passed to a shipyard in digital form where it is fed to a computer-aided manufacturing system.

**Hull characteristics**

The hull of
any ship plays a vital role in deciding a range of characteristics like the
speed, manoeuvrability, sea keeping and performance, stability, capacity and
storage, fullness, safety and so on. Thus, the first and foremost focus should
be on on the hull characteristics depending on his requirements of designing
the type of vessel.

Some
mathematical interpretations are introduced for the purpose of defining the
nature of hull for a particular make of a ship. Take the example of CB:

Block Coefficient: It is abbreviated as CB. Suppose you see a
bulk carrier and a frigate

coming at the same time. How will you decide or
assess whose Block Coefficient is more?

Thus, it is a parameter in deciding the
fullness of the hull. It is represented as:

###

### Block Coefficient (CB)

The
block coefficient of a ship at any particular draft is the ratio of the volume
of displacement at that draft to the volume of a rectangular block having the
same overall length, breadth and depth.

The Figure here represents the volume of the ship's displacement at the
draft concerned, enclosed
in a rectangular block having the same overall length, breadth and depth.

###

Fig. 7: Impression of the concept behind the ship's block coefficient (Copyright: Learn Ship Design) |

###
**Coefficient
of fineness of water plane (Cwp****)**

It is a measure of the free-surface
area or the span occupied by a ship. It is the ratio of the Water plane area
(Aw) to the area bounded by the rectangle formed by
the length between perpendiculars and the beam. So, it is easily understandable that for the
same given length, a battle cruiser will have a smaller water plane coefficient
than a mighty oil tanker. The water plane coefficient expresses the fullness of the water
plane, or the ratio of the water plane area to a rectangle of the same length
and width. A low C

Mathematically:

_{w }figure indicates fine ends and a high C_{w}figure indicates fuller ends. High C_{w}improves stability as well as handling behaviour in rough sea conditions. This is also known as the coefficient of fineness.Fig. 8: Graphical Representation of the coefficient of fineness of waterplane (Courtesy: Ship Hydrostatics and Stability by Adrian Biran ) |

Mathematically:

*C**wp=**Area of Waterplane(A**w**)/Length between Perpendiculars(LBP) *Beam(B)***Prismatic Coefficient (CP)**

The term prismatic alludes to a state of continuum in the terms of dimensions and physicals constants of the particular body. Here, essentially, prismatic coefficient gives a ratio of the volume of the hull immersed to the product of its own length and the maximum cross-sectional area present in the ship namely, the midship section. This is used to evaluate the distribution of the volume of the underlying body. A low or fine C

_{p}indicates a full mid-section and fine ends, a high or full C

_{p}indicates a boat with fuller ends. Planning hulls and other high speed hulls tend towards a higher C

_{p}. Efficient displacement hulls travelling at a low

*Froude number*will tend to have a low C

_{p}.

Fig. 9: Graphical Representation of the prismatic coefficient of hullform (Courtesy: Ship Hydrostatics and Stability by Adrian Biran ) |

So,
coming again to the Mathematics involved:

*Cp=Volume of hull immersed (V*

*immersed*

*)/Area of Midship-Section * Length*

**And so**

And now as technology surges forward, we have to do more and more innovative improvisations on the hull for better speed, manoueuvrability, sea keeping, sea-keeping, performance, capacity, structural strength, stability and most importantly, SAFETY.

Every Ship Maker and Naval Architect takes immense care of the aspects of the hull like the above discussed hullform characteristics and it's coefficients before laying out it's final plan for the ship. Manipulating with these parameters depending upon requirements, (now mainly by computational techniques) the final designs of any vessel are laid out before she sets sail.

**LSD**

__Article By:__**Subhodeep Ghosh**