Practical Ship Hydrodynamics

Ship manoeuvring 177
also performed in towing tanks with an adjacent round basin at one end. The
manoeuvre is then initiated in the towing tank and ends in the round basin.
Spiral tests and pull-out manoeuvres require more space than usually available
in towing tanks. However, towing tanks are well suited for zigzag manoeuvres.
If the ship’s track is precisely measured in these tests, all necessary body force
coefficients can be determined and the other manoeuvres can be numerically
simulated with sufficient accuracy.
Model tests with captured models determine the body force coefficients
by measuring the forces and moments for prescribed motions. The captured
models are also equipped with rudders, propellers, and electric motors for
propulsion.
ž Oblique towing tests can be performed in a regular towing tank. For various
yaw and rudder angles, resistance, transverse force, and yaw moment are
measured, sometimes also the heel moment.
ž Rotating arm tests are performed in a circular basin. The carriage is then
typically supported by an island in the centre of the basin and at the basin
edge. The carriage then rotates around the centre of the circular basin. The
procedure is otherwise similar to oblique towing tests. Due to the disturbance
of the water by the moving ship, only the first revolution should be
used to measure the desired coefficients. Large non-dimensional radii of
the turning circle are only achieved for small models (inaccurate) or large
basins (expensive). The technology is today largely obsolete and replaced
by planar motion mechanisms which can also generate accelerations, not
just velocities.
ž Planar motion mechanisms (PMMs) are installed on a towing carriage. They
superimpose sinusoidal transverse or yawing motions (sometimes also sinusoidal
longitudinal motions) to the constant longitudinal speed of the towing
carriage. The periodic motion may be produced mechanically from a circular
motion via a crankshaft or by computer-controlled electric motors (computerized
planar motion carriage (CPMC)). The CPMC is far more expensive
and complicated, but allows the extension of model motions over the full
width of the towing tank, arbitrary motions and a precise measuring of the
track of a free-running model.
5.4 Rudders
5.4.1 General remarks and definitions
Rudders are hydrofoils pivoting on a vertical or nearly vertical axis. They
are normally placed at the ship’s stern behind the propeller(s) to produce a
transverse force and a steering moment about the ship’s centre of gravity by
deflecting the water flow to a direction of the foil plane. Table 5.4 gives offsets
of several profiles used for rudders depicted in Fig. 5.11. Other profile shapes
and hydrodynamic properties are available from Abbott and Doenhoff (1959),
and Whicker and Fehlner (1958).
Rudders are placed at the ship’s stern for the following reasons:
ž The rudder moment turning the ship is created by the transverse force on
the rudder and an oppositely acting transverse force on the ship hull acting
near the bow. This moment increases with distance between the rudder force
and the hull force.