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COMPIT 2004 in Siguenza/ Spain - Institut für Entwerfen von ...

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2<br />

172.8 ⋅H<br />

1<br />

⎪⎧<br />

⎪⎫<br />

−5<br />

− 691.2<br />

3<br />

−4<br />

S<br />

ζ<br />

( ω)<br />

=<br />

⋅ω ⋅ exp ⎨ ⋅ ω<br />

4<br />

4 ⎬<br />

(1)<br />

T1<br />

⎪⎩ T1<br />

⎪⎭<br />

ω<br />

p<br />

(2001).<br />

2 π<br />

= , the modal frequency, T1 = 0. 772 ⋅Tp<br />

, transformation from mean to peak period, Journée<br />

T<br />

p<br />

3. Ship responses <strong>in</strong> waves<br />

Response amplitude operators (RAOs) and response functions for the added resistance due to waves<br />

(RFs) were employed for the evaluation of the ship performance <strong>in</strong> waves. Both have been calculated<br />

prior to the optimization by means of the strip theory code SEAWAY, Journée (2001), based on<br />

potential theory. Besides RAOs for the center of gravity motions for all six degrees of freedom and<br />

RAOs for the motions of selected po<strong>in</strong>ts also relative to the free surface, two different methods are<br />

available to determ<strong>in</strong>e the added resistance due to waves: The radiated energy method of Gerritsma<br />

and Beukelman and the <strong>in</strong>tegrated pressure method of Boese, Journée (2001).The numerical results<br />

used with<strong>in</strong> the optimization procedure are:<br />

• The RAOs of the translatory motions on the bridge (calculation of the load<strong>in</strong>g on the crew by<br />

means of accelerations).<br />

• The RAOs of the motion relative to the free surface (calculation of the slamm<strong>in</strong>g probability).<br />

• The RFs for the added resistance due to waves (preferably accord<strong>in</strong>g to the <strong>in</strong>tegrated<br />

pressure method which displays a smoother distribution over the wave frequency ω than its<br />

radiated energy counterpart).<br />

Fig.1 shows the RAOs of motion on the bridge, relative motion at the bow and the RFs of the added<br />

resistance due to waves as computed with SEAWAY. The plots serve to illustrate the <strong>in</strong>put to the<br />

response simulations with<strong>in</strong> the route optimization.<br />

3.1. Ship motions<br />

Fig.1: RAOs of motion on the bridge, relative motion at the bow<br />

and the RFs of the added resistance due to waves<br />

The product of the wave spectrum S ζ and a squared RAO of the considered motion yields the response<br />

spectrum of the ship motion S s :<br />

( ω) = RAO ⋅S<br />

( ω)<br />

S s<br />

2<br />

ζ<br />

(2)<br />

Tak<strong>in</strong>g <strong>in</strong>to account the ship velocity, this operation has to be performed with all <strong>in</strong>volved terms<br />

28

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