SCHRIFTENREIHE SCHIFFBAU Festschrift anlässlich des 100 ...

C =
T ⋅ D
⋅
2
B
T
KG
C
⋅
C
Here, T denotes the draft, D a modified depth including hatches, KG is the center of gravity
above base line. CB and CWP denote the block- and the waterline-coefficient, respectively.
The C-factor today is part of the IMO Code on Intact Stability for certain types of vessels
above 100m in length, but as the overall code, it is not mandatory. Finally the problem still
remains that the C-factor is related to the still water righting lever curve, which is not
sufficiently representative for seakeeping problems.
The Kastner/Roden Criterion for a Minimum GM to Prevent Pure Loss Failures:
Based on model tests carried out on the inland lake Ploen in Germany by Kastner (1962) a
method was developed to determine a minimum GM required to prevent the vessel from
capsizing in rough weather. The author observed the interesting phenomenon that a clear
limiting GM seemed to exist, distinguishing between ships being save or un-save with
respect to capsizing. The criterion is based on the probability density function for the time to
capsize determined during the model tests. The authors then ask for a cumulated probability
of 95% for the event “ship does not capsize” in a certain period of time, which is determined
on the basis of the time until a capsizing event is observed during model test (or numerical
simulations). This time interval Tk is then enlarged by a factor according to the assumed
exponential probability distribution. Assuming that the ship always capsizes in the largest
wave ak occurring during Tk the capsizing probability is linked to the probability of occurrence
of that wave.
Now a maximum wave height ak can be determined which has lead to the capsize in a
specific situation, e.g. during a model test. Now, assuming a probability for a non-capsize, a
related wave height ank the ship needs to survive to be sufficiently safe can be determined in
the same way. The author then concludes that the GM- value of the vessel must be
increased by the ratio which is defined by the these two wave heights:
GM k
GM nk
B
WP
= a k
a nk
This is somewhat doubtful from today’s point of knowledge as the assumptions made, clearly
fail in case the GM gets close to zero.
Soeding’s Concept of Simulating Rare Events by Artificially Amplified Wave Heights:
In principle event probabilities can be determined simply by counting them during model tests
or numerical simulations. But, as extreme events (e.g. capsizing) are rare, it is difficult to
determine significant values for capsizing probabilities during model tests and numerical
simulations due to the limited duration and the resulting small number of occurrences.
Therefore Soeding and Tonguc (1986) suggest the simulations being run in artificially high
waves. Assuming Rayleigh-distributed amplitudes the capsizing probability can be
extrapolated to the actual wave height of interest by the following relationship:
2
⋅
100
L
H sim ln(psim
) + 1.25
=
2
[6]
H ln(p
) + 1.25
act
act
Here H denotes the actual (act) or the simulated (sim) wave height, respectively. P denotes
the capsizing probability, using the same indices. However, the proposed criterion does not
provide a procedure to determine the enlargement factor for the wave height. Additionally the
concept does not include any threshold values for the capsizing probability.
[4]
[5]
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