Practical Ship Hydrodynamics

72 Practical Ship Hydrodynamics
S is the wetted surface in calm water, Vs the ship speed. The resistance coefficient
of the ship is then determined as:
cTs D cFs C cR C cA D cFs C ⊲cTm cFm⊳ C cA
The index s again denotes values for the full-scale ship, the index m values
for the model. cR is assumed to be independent of model scale, i.e. cR is the
same for model and full scale. The model test serves primarily to determine
cR. The procedure is as follows:
1. Determine the total resistance coefficient in the model test:
cTm D
RTm
1
2 m Ð V 2 m Ð Sm
2. Determine the residual resistance, same for model and ship:
cR D cTm cFm
3. Determine the total resistance coefficient for the ship:
cTs D cR C cFs C cA
4. Determine the total resistance for the ship:
RTs D cTs Ð 1
2 sV 2 s Ss
The frictional coefficients cF are determined by the ITTC 1957 formula:
cF D
0.075
⊲log 10 Rn 2⊳ 2
This formula already contains a global form effect increasing the value of cF
by 12% compared to the value for flat plates (Hughes formula).
Historically cA was a roughness allowance coefficient which considered
that the model was smooth while the full-scale ship was rough, especially
when ship hulls where still riveted. However, with the advent of welded ships
cA sometimes became negative for fast and big ships. Therefore, cA is more
appropriately termed the correlation coefficient. cA encompasses collectively
all corrections, including roughness allowance, but also particularities of the
measuring device of the model basin, errors in the model–ship correlation line
and the method. Model basins use cA not as a constant, but as a function of the
ship size, based on experience. The correlation coefficient makes predictions
from various model basins difficult to compare and may in fact be abused to
derive overly optimistic speed prediction to please customers.
Formulae for cA differ between various model basins and shipyards. Examples
are Table 3.1 and:
cA D 0.35 Ð 10 3
cA D 0.11 Ð ⊲Rn Ð 10 9
2 Ð Lpp Ð 10 6
2.1 a⊳ 2
a D max⊲0.6, min⊲CB, 0.8⊳⊳
a C 0.62 with