Practical Ship Hydrodynamics

Resistance and propulsion 79
t is the maximum blade thickness, c the maximum chord length. The Reynolds
number Rnco D Vcocm/ m at 0.7Dm, i.e.Vco D
�
CDs D 2
1 C 2 ts
cs
��
� 2.5
cs
1.89 C 1.62 log10 kp
�
V 2 Am C ⊲0.7 nmDm⊳ 2 .
kp is the propeller blade roughness, taken as 3 Ð 10 5 if not otherwise known.
The evaluation of the propulsion test requires the resistance and open-water
characteristics. The open-water characteristics are denoted here by the index
fv. The results of the propulsion test are denoted by pv:
KTm,pv D
KQm,pv D
Tm
m Ð D 4 m Ð n2 m
Qm
m Ð D 5 m Ð n2 m
Thrust identity is assumed, i.e. KTm,pv D KTm,fv. Then the open-water diagram
can be used to determine the advance number Jm. This in turn yields the wake
fraction of the model:
wm D 1
JmDmnm
Vm
The thrust deduction fraction is:
t D 1 C FD RTm
Tm
FD is the force compensating for the difference in resistance similarity between
model and full-scale ship:
FD D 1
2 Ð V 2 m Ð S Ð ⊲⊲1 C k⊳⊲cFm cFs⊳ cA cAA⊳
With known Jm the torque coefficient KQm,fv can also be determined. The
propeller efficiency behind the ship is then:
bm D KTm,pv
Ð
KQm,pv
Jm
2
The open-water efficiency is:
0m D KTm,fv
Ð
KQm,fv
Jm
2
This determines the relative rotative efficiency:
R D bm
0m
D KQm,fv
KQm,pv
While t and R are assumed to be the same for ship and model, the wake
fraction w has to be corrected:
� �
cFs
cFs
C ⊲t C 0.04⊳ 1
ws D wm
cFm
cFm