Page 107 - Practical Ship Design

The Design Equations IS

obtained as a result of the reduction in power which fining the lines achieves. This
is a major exercise but fortunately it is rarely necessary to adopt such an approach,
the more general procedure being the use of an empirical relationship between
block coefficient and the Froude number (F,), which represents the state of the art.

3.4.2 The Alexander formula

One of the oldest such relationships is the Alexander formula. In the 1962 paper
this was expressed as:
C, = K - 0.5 V, /a (3.1 1)

where L, = length in feet. It was suggested that the value of K should vary between
I .03 for high speed ships to 1.12 for slow ships.

3.4.3 The Katsoulis formula

By 1975 it was clear that changes in L/B ratio together with the big increase in the
size of many ships demanded a new approach. A proposal made by Katsoulis was
studied with great interest as it seemed to involve all the right factors. Katsoulis
suggested that C, as well as being a function of F, should also be a function of LIB
and BIT, since both of these affect the resistance of the ship and the flow of water to
the propeller and hence the QPC. He suggested an exponential formula of the form:

(3.12)

and went on to show that this could be transformed into:

(3.13)

Katsoulis deduced values of the constants from regression analysis, but unfort-
unately his values did not appear to give satisfactory agreement with the block
coefficients of a wide variety of ship types for which good data was available.

3.4.4 The Watson and Gilfillan C, /F, relationship

A plot of block coefficient against F, was therefore made using all available data
and it was found that with very few exceptions all the plotted values lay within a
band of k0.025 from a mean line with the majority of the points within much closer
limits.
Whether or not this line represents an optimum depends on whether the large
number of different naval architects whose designs provided the data made wise