Fishing Craft Technology

Unit 3 - Design procedure

3.1. Properties of Irregular shapes

a) Properties of irregular shapes:
The Geometry of the ship has been defined, it is necessary to anticipate what properties of these shapes are going to be useful and find out how to calculate them.

(i) Plane shapes (Two dimensional shapes)
Water planes, transverse sections, flat decks, bulk heads, the curve of areas and expansion of curved surfaces are some of the plane shapes whose properties are of interest. The area of a plane surface shape in the plane OXY defined in Cartesian co-ordinates is

In which all strips of length y and width /x are summed over the total extent of x. Because y is rarely, with ship shapes a precise mathematical function of x the integration must be carried out by an approximate method.

There are first moments of area about each axis (x1 and y1 are lengths and x and y are co-ordinates)

Dividing each expression by the area gives the co-ordinates of the centre of area (x, y)

For a plane figure placed symmetrically about the x- axis such as a water plane Mxx = x1 y dy = o and the distance of the centre of area called in the particular case of water plane, the centre of Floatation (CF) from the y axis is given by

(ii) Three dimensional shapes:
The ships under water form can be represented by three–dimensional shape. The volume of displacement is given by

It is the sum of all such slices of cross-sectional area A over the total extent of “x”.

The shape of the ship can be equally represented by a curve of water plane areas on a vertical axis, the breadth of the curve at any height, Z above the keel representing the area of the water plane at that draught. The volume of displacement is again sum of all slices of cross – sectional area Aw over the total extent of Z from zero to draught.

The first moments of volume in the longitudinal direction about OZ and in the vertical direction about the keel is given by ML =  A X dx and Mv = 0d Aw Z dz
Dividing by the volume in each case gives the co-ordinates of the centre of volume. The centre of volume of fluid displaced by a ship is known as the centre of buoyancy. Its projection in the plan and in sections is known as the Longitudinal Centre of Buoyancy (L.C.B.) and the Vertical Centre of Buoyancy (V.C.B.)

Should the ship not be symmetrical below the water line, the centre of buoyancy will not lie in the middle line plane. The centre of buoyancy of a floating body is the centre of volume of the displaced fluid in which the body is floating. The first moment of volume about the centre of volume is zero.
The weight of a body is the total of the weights of all of its constituent parts. First moment of the weights about particular axes divided by the total weight, define the co-ordinates of the centre of weight or centre of gravity (C.G) relative to those axes.

Projections of the centre of gravity of a ship in plan and in section are known as the Longitudinal Centre of Gravity (L.C.G.) and Vertical Centre of Gravity (V.C.G.)

Defining it formally, the centre of gravity of a body is that point through which, for statistical consideration, the whole weight of the body may be assumed to act.