16 Waterplane area coefficient

The waterplane area coefficient CWP influences resistance and stability considerably. It is geometrically closely related to the shape of cross-sections. So before making even a temporary determination of the coefficient, we should consider the sectional shapes fore and aft.

The usual procedure is to find a value for CWP in the preliminary design and retain it in the lines design. There is a common tendency to use a high CWP to attain a desirable degree of stability. This frequently causes unwanted distortions in lines. It is better to choose a CWP at the lower limit which matches the other values, and then to design the lines independently of this. Lines which are not bound to one definite CWP are not only easier to design, they generally also have lower resistance.

In the early design stages, CWP is uncertain. Many approximate formulae for the stability, especially the exacter ones, contain CWP. If these formulae are not to be disregarded, CWP has to be estimated. The value of CWP is largely a function of CB and the sectional shape. Ships with high L/B ratio may have either U or V sections. Ships with low L/B usually have extreme V forms. Although not essential geometrically, these relationships are conventionally recognized in statistical work.

The following are some approximate formulae for CWP of ships with cruiser sterns and 'cut-away cruiser sterns'. As these formulae are not applicable to vessels with submerged transom sterns, they should be tested on a 'similar ship' and the most appropriate ones adopted.

U section form, no projecting stern form: CWP = 0.95CP + 0.17^1 - CP

V section form, possibly as projecting stern form: CVp = \/Cb ~ 0.025

32 Ship Design for Efficiency and Economy

Table 1.8 shows examples of CWP obtained by these formulae.

Table 1.8 Waterplane area coefficient values

0.95CP

Table 1.8 Waterplane area coefficient values

0.95CP

CB

Cm

(l + 2Cs)/3

+0.17^1 -Cp

c2/3

yc^- 0.025

(1 + 2Cs/VCi)/3

0.50

0.78

0.666

0.722

0.745

0.682

0.710

0.50

0.94

0.666

0.637

0.658

0.682

0.677

0.60

0.98

0.733

0.706

0.722

0.749

0.740

0.70

0.99

0.800

0.785

0.793

0.812

0.802

0.80

0.99

0.866

0.866

0.868

0.869

0.870

A further influence is that of the aft overhang if the values CB and CP relate as usual to the perpendiculars. The above formulae for a pronounced overhang can be corrected by a correction factor F:

The point where the line of a small stern is faired into the centre-line can be regarded as the aft endpoint of an idealized waterplane length. A length 2.5% greater than Lpp is 'normal'.

Where the lines have been developed from a basis ship using affine distortion, CWP at the corresponding draught remains unchanged. Affine distortion applies also when length, width and draught are each multiplied by different coefficients.

For 'adding or removing' a parallel middle body, CWP is easily derived from the basis design.

where:

Lv = Lpp of the basis design;

aL = the absolute length of the parallel middle body to be added. The index p refers to the project ship, the index v to the basis ship.

In the affine line distortion, the KM values, obtained using Cwr, can be derived directly from the basis design:

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