Practical Ship Hydrodynamics

186 Practical Ship Hydrodynamics
angles concerned), the centre of effort moves up a little, but never more than
7.5% of b, the value for a rudder without a gap at its upper edge.
Air ventilation may occur on the suction side of the rudder if the rudder
pierces or comes close to the water surface. The extent of the ventilation may
cover a large part of the rudder (even the whole rudder height) decreasing the
rudder effectiveness drastically. This is important for manoeuvres at ballast
draft for full speed, e.g. at ship trials.
The dynamic pressure along the profile of a rudder depends on the local
velocity v according to Bernoulli’s law:
� �
pdyn D 2 Ð ⊲V 2
v 2 ⊳ D q Ð
1
v 2
V 2
For the usual straight profiles v/V is decomposed into two components:
1. Component vt/V due to the profile thickness t. This component is equal on
both sides of the profile. vt/V may be taken from Table 5.6. For different
profile thickness t, the velocity ratio vt/V must be corrected by
�� �
vt
V
actual
�
1 D
�� �
vt
V
table
�
1
Ð tactual
ttable
Table 5.6 vt =V ; flow speed vt along the profile over inflow velocity V as a function of
the profile abscissa x, a = 0 ◦
NACA NACA HSVA HSVA IFS58 IFS61 IFS62
x/c (%) 643-018 0020 MP73-20 MP71-20 TR15 TR25 TR25
0 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.75 0.77 0.69 0.69 0.57 0.79 0.67 0.68
1.25 0.96 0.91 0.91 0.88 1.06 0.95 0.94
2.5 1.05 1.03 1.08 1.00 1.20 1.09 1.18
5.0 1.11 1.17 1.22 1.10 1.29 1.47 1.48
7.5 1.15 1.25 1.27 1.12 1.30 1.52 1.53
10 1.17 1.27 1.29 1.14 1.28 1.50 1.52
15 1.20 1.30 1.31 1.18 1.26 1.47 1.48
20 1.22 1.29 1.30 1.20 1.23 1.43 1.44
30 1.25 1.26 1.27 1.24 1.20 1.31 1.33
40 1.26 1.21 1.24 1.28 1.16 1.18 1.21
50 1.20 1.17 1.17 1.30 1.08 1.06 1.08
60 1.13 1.13 1.07 1.14 1.00 0.96 0.97
70 1.06 1.08 1.01 1.04 0.94 0.90 0.90
80 0.98 1.03 0.95 0.96 0.93 0.90 0.87
90 0.89 0.96 0.88 0.87 0.96 0.94 0.90
95 0.87 0.91 0.89 0.87 0.97 0.95 0.93
Information on other profiles may be found in Abbott and Doenhoff (1959)
or computed by CFD (e.g. boundary element method).
2. Component va/V due to the angle of attack ˛. This component has opposite
sign on both sides of the profile. It is practically independent from the profile
shape. Only in the front part does it depend on the profile nose radius.
Figure 5.16 illustrates this for a lift coefficient CLl ³ 1. The values given