Page 538 - Practical Design Ships and Floating Structures

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4 RESISTANCE PREDICTION
Considering the special feature of the model resistance as a unit function of the effective speed, the
conventional prediction of the ship resistance by means of the common form-factor method can be
demonstrated as follows:
Estimating the model wave resistanceR, (Vm) as a function of the effective speed vEM
Rw (Vm) = R, (Vm 1- R, YE,) = Rm (V. )-(I + k)ECFom ,%P, .SA.+ .V,& (4)
with the ITTC friction line C,,, = O.O75/(log R,,,-2)2 for a Reynolds number corresponding
to the effective speed at model scale R,, = VEM . L, /v, ;
Evaluating the ship speed V, = V, fi as well as the effective speed VEs = Vm fi ;
Predicting the ship resistance at the corresponding water-depth tested
R, (vs) = R, WE,> + ~ws (vEs) = [(I + k)ECFoEs + C, IXPSV,A + ~/~uRwnra~ (5)
with the ITTC friction line CF0, = O.O75/(log R,,-2)2 and for the effective Reynolds number at
the full scale R,, = VEs L,/vs ;
Predicting the ship resistance at the water-depth h/T=Prediction from the available model test
h/T=Test:
-
[~m (G )lm=Prediction - IR, (v, )lhm=PWiction + RWSh/T=Tesl ('ESJm=predldon
. (6)
= [(l+ k)E ' cFO€S ' ,% P ' ' V,$]M=Prediction + P'PM [RW ]M=Test '
According to the prediction mentioned above, the measured resistance at h/T=3.0, 2.0 and 1.5, see the
full-filled symbols in Fig. 6, was directly converted to its full scale value via equation (5) and then
compared with those predicted by means of the model test at the water depth h/T=3.0 via equation (6),
where the measured sinkage at h/T=2.0 and 1.5 was used to determine the corresponding effective
speed. As shown in Fig. 6, the agreement is generally acceptable. Similar agreement was also found at
different scales for the same inland ship, see Lochte-Holtgreven et al.(2001). However, it was shown
in their work, there is a disagreement for the extremely shallow water at h/T=l.2. Generally speaking,
the proposed method is only valid for a subcritical speed Fnh 50.7 and in a not too extremely shallow
water.
150
120
- 90 -e- h17'-2 0 Prediction
5 60
8"
30
0
I ' 1 I , 1 ( 1 ( 1 , 1 ( 1 , 1 1 1 , 1 , 1 , ~
0 2 4 6 8 10 12 14 16 18 20 22
V,[km/h]
Figure 6: Comparison of the predicted ship-resistance via equation (5) with those from the direct
conversion via equation (6) for the subject inland ship

The excellent agreement for h/T=1.5 in Fig. 6 demonstrates the quality of the proposed method for
predicting the ship resistance in shallow water. More importantly, it implies that the model tests at
h/T=l.5 could be entirely saved if the corresponding sinkage is realistically approximated, for instance
by empirical formulae for ships moving at a narrow channel and by numerical calculations based on
the potential theory. Fig. 7. compares the predictions based on the measured sinkages and the
empirical estimations by Emerson (1959). Fig. 8 compares the predictions based on the measured