Page 232 - Practical Ship Design

194 Chapter 7

7.1.3 Calculating (I + K)

There are two possible approaches to obtaining a (1 + K) value to use in a C,,( '78)
calculation. The first of these is, of course, the Holtrop and Mennen formula given
in $6.9 - or any update of this which becomes available.
A second method is to calculate a (1 + K) value using the tank test data. The
simplest approximate way is to assume that C, = 0 at the lowest available Froude
number (provided this is less than 0.18) and therefore at this point (1 + K) = C,, /Cf,.
A value established in this way will be higher than that given by the more accurate
Prohaska method described below as there is likely to be a small residual C,.
The Prohaska method assumes that C, is a function of F," .

C,, = Cf,(l + K) + k, F," (7.9)

The value of K can be obtained at Fn = 0, by plotting

(7.10)

as ordinate against F,"/Cfm as abscissa and finding the intercept at F, = 0.
An approximate formula which avoids plotting uses two data points and the
following formula:

(7.11)

The data points should be at low Fn values (< 0.18), where Prohaska's line should
be straight. Whilst the method is theoretically correct, the absence of the smoothing
which plotting provides can introduce error and to minimise this it is wise to make
two calculations with two adjacent sets of data. The results will show if the points
are out of line and taking an average of two values should increase the accuracy.
A spread sheet for calculating (I + K) in this way is shown in Table 7.2. The data
used in this table relate to the warship powering data presented in Fig. 7.10.
A comparison of the figures calculated in Table 7.2 with the Holtrop and
Mennen figures shown in Fig. 6.4 shows very good agreement. It had been
intended to make similar calculations for the single screw data plotted in Figs. 7.6
to 7.8 and the twin screw merchant ship data in Fig. 7.9, but on examination this
data was found to be unsatisfactory at the low Froude numbers required for this
calculation (see also 57.2.2).
Although trying to establish (1 + K) values from some data may be unsuccessful,
designers with suitable tank test results, and especially where these relate to
specialist ship types, are recommended to try to establish their own (1 + K) values.