Practical Ship Hydrodynamics
Practical Ship Hydrodynamics
Practical Ship Hydrodynamics
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204 <strong>Practical</strong> <strong>Ship</strong> <strong>Hydrodynamics</strong><br />
The tanker performs a soft stop manoeuvre. The engine is reducing linearly<br />
the torque Q within one minute to zero. The next three minutes are used to<br />
brake the shaft and to prepare the engine for reverse operation. During the<br />
following two minutes the engine is started and accelerated again linearly<br />
to full reverse torque.<br />
How long will be the stopping distance for the tanker if it sails exactly<br />
straight ahead? Quantities not given are to be estimated!<br />
Hints:<br />
(a) During the short periods of acceleration and deceleration of the engine,<br />
the ship speed is virtually constant.<br />
(b) The linear deceleration and acceleration shall be approximated by step<br />
functions covering the same ‘area’ of Q Ð t, wheret is the time:<br />
Q<br />
1' 2' 3' 4' 5' 6'<br />
(c) The added mass in longitudinal motion may be approximated by<br />
m 00<br />
m D<br />
1<br />
�<br />
⊲L 3 /r⊳ 14<br />
where L is the length, r the displacement of the ship.<br />
(d) In reverse propeller operation the ratio of thrust to resistance shall be<br />
jT/Rj D0.945.<br />
3. (a) A ship lays rudder according to sine function over time alternating<br />
between port and starboard with amplitude 10° and 2 minutes period.<br />
The ship performs course changes of š20°. The maximum course deviation<br />
to port occurs 45 seconds after the maximum rudder angle to<br />
port has been reached. Determine from these data the parameters of the<br />
Nomoto equation:<br />
T R C P D Kυ<br />
The ship is yaw stable for K>0. Is the ship yaw stable?<br />
(b) The ship speed is reduced to 50% of the value in (a). The rudder action<br />
is the same as in (a). How large is the amplitude of course changes<br />
and what is the delay between maximum rudder angle and maximum<br />
course deviation?<br />
(c) The rudder height is kept constant at 6 m. The rudder area is increased<br />
from 18 m 2 in (a) to 24 m 2 . The speed is kept as in (a). How large now<br />
is the course amplitude and the delay between maximum rudder angle<br />
and maximum course deviation?<br />
Hint: For constant rudder angle, the Nomoto equation has the solution:<br />
P D ae ˛t C b.<br />
4. A ship follows the ‘Norrbin’ equation:<br />
T R C P C ˛ P 3 D Kυ<br />
t
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