Practical Ship Hydrodynamics

Table 3.1 Recommended values
for CA
Lpp (m) cA
50–150 0.00035–0.0004
150–210 0.0002
210–260 0.0001
260–300 0
300–350 0.0001
350–4000 0.00025
Resistance and propulsion 73
3.2.4 Method of Hughes–Prohaska
This approach decomposes the total resistance (coefficient) as follows:
cT D ⊲1 C k⊳ Ð cF0 C cw
Both form factor ⊲1 C k⊳ and wave resistance coefficient cw are assumed to
be the same for model and full scale, i.e. independent of Rn. The model test
serves primarily to determine the wave resistance coefficient. The procedure
is as follows:
1. Determine the total resistance coefficient in the model test as for the ITTC
1957 method:
cTm D
RTm
1
2 m Ð V 2 m Ð Sm
2. Determine the wave resistance coefficient, same for model and ship:
cw D cTm cF0m Ð ⊲1 C k⊳
3. Determine the total resistance coefficient for the ship:
cTs D cw C cF0s Ð ⊲1 C k⊳ C cA
4. Determine the total resistance for the ship:
RTs D cTs Ð 1
2 sV 2 s Ss
The frictional coefficients cF0 for flat plates are determined by Hughes’
formula:
cF0 D
0.067
⊲log 10 Rn 2⊳ 2
The correlation coefficient cA differs fundamentally from the correlation coefficient
for the ITTC 1957 method. Here cA does not have to compensate for
scaling errors of the viscous pressure resistance. ITTC recommends universally
cA D 0.0004.
The Hughes–Prohaska method is a form factor method. The form factor
⊲1 C k⊳ is assumed to be independent of Fn and Rn and the same for model
and ship. The form factor is determined by assuming:
cT
cF0
D ⊲1 C k⊳ C ˛ F4 n
cF0