Page 276 - Introduction to Naval Architecture

MANOEUVRING 261

The pull-out manoeuvre
1
This manoeuvre is also related to the directional stability of the ship.
The rudder is put over to a certain angle and held until the ship is
turning at a steady rate. The rudder is returned to amidships and the
change in the turn rate with time is noted. For a stable ship the turn
rate will reduce to zero and the ship takes up a new steady straight line
course. A plot of the log of the rate of turn against time is a straight line
after a short transition period. If the ship is unstable the turn rate will
riot reduce to zero but there will remain some steady rate of turn. The
area under the plot of turn rate against time gives the total heading
change after the rudder angle is taken off. The smaller this is the more
stable the ship.
If the ship is conducting turning trials it will be in a state of steady
turning at the end of the run. If the rudder is centred the pull-out
manoeuvre can be carried out immediately for that speed and rudder
angle.

MANOEUVRING DEVICES
Rudder forces and torques
Rudder forces
Rudders are streamlined to produce high lift with minimum drag. They
are symmetrical to produce the same lift characteristics whichever way
they are turned. The force on the rudder, F, depends upon the cross-
sectional shape, area A, the velocity Vthrough the water and the angle
of attack a.

The constant depends upon the cross section and the rudder profile, in
particular the ratio of the rudder depth to its chord length and the
degree of rounding off on the lower corners. The lift is also sensitive to
the clearance between the upper rudder surface and the hull. If this is
very small the lift is augmented by the mirror image of the rudder in
the hull. f(a) increases roughly linearly with a up to the stall angle
which is typically about 35°. f(a) will then decrease.
Various approximate formulae have been proposed for calculating F.
An early one was:

In this an allowance was made for the effect of the propeller race by
multiplying Fby 1.3 for a rudder immediately behind a propeller and