Page 277 - Introduction to Naval Architecture

262 MANOEUVRING

by 1.2 for a centreline rudder behind twin screws. Other formulations
based on the true speed of the ship are:

The first two were proposed for twin rudders behind twin screws and
the third for a centreline rudder behind a single screw.
If wind or water tunnel data is available for the rudder cross section
this should be used to calculate the lift and the centre of pressure
position.
Typically the rudder area in merchant ships is between ^ and ^ of the
product of length and draught.

Rudder torques
To establish the torque needed to turn a rudder it is necessary to find
the position on the rudder at which the rudder force acts. That
position is the centre of pressure. For a rectangular flat plate of breadth B
at angle of attack a, this can be taken as (0.195 + 0.305 sin a) B aft of
the leading edge. For a typical rudder section it has been suggested 2
that the centre of pressure for a rectangular rudder can be taken at
K X (chord length) aft of the leading edge, where:

The open water figure is used for both configurations for a ship going
astern.
For a non-rectangular rudder an approximation to the centre of
pressure position can be obtained by dividing the rudder into a
number of rectangular sections and integrating the individual forces
and moments over the total area. This method can also be used to
estimate the vertical location of the centre of pressure, which dictates
the bending moment on the rudder stock or forces on the supporting
pintles.

Example 10.1
2
A rudder with an area of 20 m when turned to 35° has the centre
of pressure 1.2m from the stock centreline. If the ship speed is 15
knots, and the rudder is located aft of the single propeller,
calculate the diameter of the stock able to take this torque,
2
assuming an allowable stress of 70 MN/m .