Page 233 - Practical Ship Design

Pouwing II I95

Table 7.2
Twin-screw warship.
Calculation of (I + K) based on (I + K) = ctml -Ctm2(Fn1 lFn2 (Cf,” values based on ITTC.57)

CI”,, -Ctmz(Fd 1 F“? )J

_ _ ~ ~- -
0.391 0.144 0.003794 0.003497 0.192 0.003764 0.0033 16 0.750 0.316 1.063
0.420 0.146 0.003821 0.003489 0.195 0.003792 0.003308 0.749 0.314 1.073
0.451 0.148 0.003849 0.00348 1 0. I97 0.003820 0.003301 0.75 1 0.319 1.083
0.486 0.150 0.003878 0.003473 0.199 0.003850 0.003294 0.754 0.323 1.094
0.525 0.152 0.003908 0.003465 0.202 0.003881 0.003286 0.752 0.321 1.105
0367 0.153 0.003940 0.003457 0.205 0.003913 0.003278 0.746 0.310 1.117
0.614 0.156 0.003973 0.003448 0.207 0.003946 0.003271 0.754 0.323 1.128
~~ ~ ~~

Having established (1 + K) at a low Froude number, the same value is assumed
to apply at higher Froude numbers.
It is worth noting that a C,, value calculated to ITTC’78 will always be less than
a C,, based on ITTC’57 with the difference increasing both at the higher values of
K that apply to fuller block coefficients and with the reduced values of C,
applicable to longer ships. Both of these are clearly shown in eq. (7.12) (see also
57.2.2).

(7.12)

7.1.4 The Grigson friction line
Another alternative to both ITTC’S7 and ITTC’78 involves the use of the Grigson
friction line which has already had a brief mention in 56.2.4. This line was presented
in 1993 in an R.I.N.A. paper “An accurate smooth friction line for use in perform-
ance prediction”. Grigson plotted a mass of experimental data on friction coeffi-
cients and found that the ITTC’57 line did not provide an accurate representation
of this data. To improve the accuracy required a change from the simple formula
used for ITTC’S7 and the use of two separate formulae for respectively the
Reynold’s number ranges of tank test models and ships. Both of the formulae
proposed are somewhat complex but can be readily built into a spreadsheet where
they will do their job without any problems. In considering the merits of Grigson’s
line it is perhaps worth remembering that ITTC’S7 was never claimed to be an
accurate friction line but was introduced to improve ship/model correlation. The
Grigson formulae are: