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SCHRIFTENREIHE SCHIFFBAU Festschrift anlässlich des 100 ...

SCHRIFTENREIHE SCHIFFBAU Festschrift anlässlich des 100 ...

SCHRIFTENREIHE SCHIFFBAU Festschrift anlässlich des 100 ...

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C =<br />

T ⋅ D<br />

⋅<br />

2<br />

B<br />

T<br />

KG<br />

C<br />

⋅<br />

C<br />

Here, T denotes the draft, D a modified depth including hatches, KG is the center of gravity<br />

above base line. CB and CWP denote the block- and the waterline-coefficient, respectively.<br />

The C-factor today is part of the IMO Code on Intact Stability for certain types of vessels<br />

above <strong>100</strong>m in length, but as the overall code, it is not mandatory. Finally the problem still<br />

remains that the C-factor is related to the still water righting lever curve, which is not<br />

sufficiently representative for seakeeping problems.<br />

The Kastner/Roden Criterion for a Minimum GM to Prevent Pure Loss Failures:<br />

Based on model tests carried out on the inland lake Ploen in Germany by Kastner (1962) a<br />

method was developed to determine a minimum GM required to prevent the vessel from<br />

capsizing in rough weather. The author observed the interesting phenomenon that a clear<br />

limiting GM seemed to exist, distinguishing between ships being save or un-save with<br />

respect to capsizing. The criterion is based on the probability density function for the time to<br />

capsize determined during the model tests. The authors then ask for a cumulated probability<br />

of 95% for the event “ship does not capsize” in a certain period of time, which is determined<br />

on the basis of the time until a capsizing event is observed during model test (or numerical<br />

simulations). This time interval Tk is then enlarged by a factor according to the assumed<br />

exponential probability distribution. Assuming that the ship always capsizes in the largest<br />

wave ak occurring during Tk the capsizing probability is linked to the probability of occurrence<br />

of that wave.<br />

Now a maximum wave height ak can be determined which has lead to the capsize in a<br />

specific situation, e.g. during a model test. Now, assuming a probability for a non-capsize, a<br />

related wave height ank the ship needs to survive to be sufficiently safe can be determined in<br />

the same way. The author then conclu<strong>des</strong> that the GM- value of the vessel must be<br />

increased by the ratio which is defined by the these two wave heights:<br />

GM k<br />

GM nk<br />

B<br />

WP<br />

= a k<br />

a nk<br />

This is somewhat doubtful from today’s point of knowledge as the assumptions made, clearly<br />

fail in case the GM gets close to zero.<br />

Soeding’s Concept of Simulating Rare Events by Artificially Amplified Wave Heights:<br />

In principle event probabilities can be determined simply by counting them during model tests<br />

or numerical simulations. But, as extreme events (e.g. capsizing) are rare, it is difficult to<br />

determine significant values for capsizing probabilities during model tests and numerical<br />

simulations due to the limited duration and the resulting small number of occurrences.<br />

Therefore Soeding and Tonguc (1986) suggest the simulations being run in artificially high<br />

waves. Assuming Rayleigh-distributed amplitu<strong>des</strong> the capsizing probability can be<br />

extrapolated to the actual wave height of interest by the following relationship:<br />

2<br />

⋅<br />

<strong>100</strong><br />

L<br />

H sim ln(psim<br />

) + 1.25<br />

=<br />

2<br />

[6]<br />

H ln(p<br />

) + 1.25<br />

act<br />

act<br />

Here H denotes the actual (act) or the simulated (sim) wave height, respectively. P denotes<br />

the capsizing probability, using the same indices. However, the proposed criterion does not<br />

provide a procedure to determine the enlargement factor for the wave height. Additionally the<br />

concept does not include any threshold values for the capsizing probability.<br />

[4]<br />

[5]<br />

35

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