SCHRIFTENREIHE SCHIFFBAU Festschrift anlässlich des 100 ...

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C1 -4.257E-01
C2 9.311E-01
C3 -1.807E-01
C4 1.511E+00
C5 4.578E-01
C6 1.912E+00
C7 7.773E-01
C8 -6.200E-02
C9 2.318E-02
C10 1.1308
C11 0.9251
Table 3: Correlation Coefficients
The determination of the resonance conditions requires the natural roll frequency of the
ships. The common way to estimate the natural roll frequency by using the initial metacentric
height in still water conditions as measure for the uprighting moments is not suitable here, as
the stability changes significantly in waves and, moreover, as the lever arm characteristics of
modern ship types are highly non-linear. Usually the estimates obtained from this procedure
are rather pure. Due to this reason a mean effective stability is used here for the calculation
of the natural roll frequency. For this concept an average mean righting lever curve is
calculated from the the two extreme lever arm curves in wave trough and wave crest
conditions. We then define an effective linear stability coefficient, denoted as GMeff, which is
determined such that the value of the linearized stability, integrated over the heeling angle up
to 40 degrees, equals the area under the mean lever arm curve up to 40 degrees. Fig. 11
illustrates the concept.
Fig. 11: Effective linearized stability
The correlation between the simplified criterion and the simulated index values has been
tested for all 176 ships in our database. Each ship is investigated in three generic loading
conditions, of which the first one equals the intact stability limit according to the IMO
regulations in the IMO Res. A.749. The second and third loadcase have GM values
increased by 0.5 and 1.0 meters with respect to the intact limit.