SCHRIFTENREIHE SCHIFFBAU Festschrift anlässlich des 100 ...

leads to the final capsizing of a ship, including water on deck, water ingress through nonweathertight
openings and cargo shift. Thus, from our point of view, the it is more reasonable
not to ask how often a ship fails in a given situation, which naturally inherits large
uncertainties, but to ask whether a certain situation is dangerous for a ship with a set of
operational parameters. That is the reason why we replace the failure probability
pfail(H1/3,T1,µ,vs) by the failure coefficient Cfail, a saltus function which takes the value 0 for all
situations considered to be safe and 1 for all un-safe situations. It is determined from the time
series of the numerical simulation by applying the Blume-criterion which is described
separately in The Blume Criterion at page 36.
In some cases where the Blume-criterion does not deliver suitable results, typically due to
large angles of vanishing stability, the occurrence of a certain maximum roll angle may be
taken into account simultaneously. The more conservative value is taken for the decision
between “safe” and “unsafe”. The results may be plotted in form of polar diagrams as
presented in Fig. 1. Each polardiagram presents the limiting wave heights for a specific
significant period (or the related significant deep water wave length), giving an overview
about critical situations (see Cramer and Krueger (2005) and Krueger (2002)).
All situations where the failure criterion is set to 1 contribute to the overall index with the
overall probability of occurrence of the individual operational cells. A operational cell in this
context always is defined by loading condition, speed, heading, wave length and wave
height.
From the experience with a lot of model tests and more than hundred ships tested in
numerical simulations we expect only a very small contribution from beam sea situations.
Larger ships in general can be considered as being not endangered by waves encountering
from abeam. Therefore we restrict the contributing courses to a 45-degree sector of
encounter angles, port and starboard in head and following seas. Consequently, it is then
useful to split the ISEI in a head sea and a following sea index. A further step is to discretise
Equation [1] as the probability of occurrence of a specific sea state as well as the failure
coefficient Cfail are available as discrete values for the individual operational cells. The
insufficient stability event index ISEI then can be written as follows:
( j ( ) ( i)
C ) ( j)
( i ( ) ( k ) ( l
ISEI =
)
∑∑∑∑ δPsea
H , T1
⋅δPrisk
H , T1
, µ , vs
)
[3]
Here, the δP denote the cumulated probability for the individual discrete range of values.
The index C expresses that Prisk is calculated with the failure coefficient Cfail. The encounter
angles run from µ=-π/4 to µ=+π/4 for the following sea cases and from µ=3/4 π to µ=5/4 π for
head seas. The speed summation runs from the minimum speed possible in that condition to
the maximum speed possible. The indices h and f indicate head and following seas,
respectively.
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