Page 198 - Practical Ship Design

164 Chapter 6

It should be noted that the two knots are not quite identical, and neither are the
metriclimperial conversion figures; this can cause problems in complex equations.
Although great care has been taken with the calculation of the various constants
quoted in this section the accuracy of many of these figures depend on several
conversion figures and exactness cannot be guaranteed, but any error should be less
than 1%.
Some figures quoted in this section are intended only to give a “feel” and their
use should be limited to approximate calculations.
Because the change from the Froude method to the ITTC’57 method of extra-
polation from model to ship results in markedly different P, and @ values, it has
been necessary in recent years when these treatments have been in use in parallel to
annotate each of these items as “Froude” or “ITTC” to ensure that the correct ship
model correlation factor is used.
From eqs. (6.13) and (6.15) the relationship between and C, can be shown to be

= 40.46 C, ’ SlA2/3 (6.16)
= 39.80 C, . 8

As eq. (6.15) requires the use of the wetted surface, it may be appropriate to give
some approximate formulae for S at this point.
The following formulae, based on metric dimensions, give the value of S in m2:

Mumford’s formula
S = 1.7 L . T+ C, L . B (6.17)

It may be noted that Guldhammer and Harvald in the paper discussed in $6.8
suggest increasing the Mumford value by adding a factor of 1.025.

Taylor’s formulu
s =CJM (6.18)
This was originally based on A in tons and L in feet but has been metricated in Fig
6.1. For merchant ships of normal proportions C = 2.55 can be used as a quick
approximation.
Holtrop and Mennen, whose powering method is examined in $6.7, suggest the
following formula which, although too complex for use in hand calculations, can
be readily incorporated in a computer program.

S = L(2T + B) (Cm)’/2(0.453 + 0.4425 C, - 0.2862 C, - 0.003467 BIT
+ 0.3696 C,,) + 2.38 Ab&, (6.19)
where A,, = transverse sectional area of the bulb at the fore perpendicular.