Page 216 - Practical Ship Design

Powering I 181

It was rather disconcerting to find that the formula for (1 + K) in the third
reference was significantly changed from that given in the second with new
variables being introduced, and even more to find an even greater change in the last
reference involving a new factor Y which modifies (1 + K) to (1 + Y . K) with Y
varying with Froude number.
As this new factor is associated with formulae for C,,, which are not given, most
users continue to use the formulae given in the third reference which seems to have
given reasonably satisfactory results to date.
The simplified formula for (1 + K) mentioned above is as follows:

1+K=
0.93+0.487 . (C),, . (B/L)1.068. (L/L,)o.'22. (L3//v)n.365 . (l-C,)-"."4 (6.43)

factor no. I 2 3 4 5 6 (for reference)

In this formula L is waterline length
C, is the prismatic coefficient on this length
The length of run L, in factor 4 is defined as:

L, = L[ 1 - C, + 0.06 Cp lcb/(4 C, - l)] (6.44)
where lcb is the longitudinal centre of buoyancy forward (+) or aft (-) of 0.5 L as a
% of L.
Factor 1 is defined as C,, = 1 + 0.01 1 C,,,,
C,,,,, = -25 to -20 barge-shaped forms
= -10 after body with V sections
= 0 normal shape of after body
= +IO after body with U sections and Hogner stern

Figure 6.3 abstracted from the 1988 paper may help interpretation of these
values.
Another reason for giving the formula for (1 + K) is because there seems to be
little other data on this factor and designers may wish to use it along with other
powering data (but see later).
Most users of this formula will tend to use it embedded in a computer program
and will thus gain little, if any, knowledge of the relative importance of the various
factors or, indeed, of what (1 + K) value to expect for a particular type of ship.
Values have therefore been calculated in Table 6.2 for a number of ship types.
The first three ships conform to the standard dimensions of 122 x 16.76 x 7.32 m
with two extreme block coefficients and a middle value. The other particulars
required being set at values reasonably appropriate to each of the block
coefficients.