Trans RINA, Vol 154, Part A2, Intl J Maritime Eng, Apr-Jun 2012
χ (7) where CB = block coefficient
hog 1.55CB χsag 1.44 C0.8 B
1.6
When the coefficients k are calculated, the corresponding MW,h and MW,s can be determined by the equation 33
M χγBL M χγBLW,h hog W,s sag (8)
Where = t/m3 is the specific weight of the sea water B = ship’s width and L = ship’s length.
Available records of the random process
I II III
Selecting the duration of the time windows
Extracting the maximal value and its POE from each time window
Dividing the statistical sample of maximal amplitudes into several
groups using as a criterion the POE of the recorded maximal amplitudes
Replacing each histogram
IV V
containing maximal amplitude with the same POE with theoretical probabilistic distribution
Calculating the probability of exceedance of any given value
Mt,max Figure. 2 Basic steps in the proposed procedure T1
Although Eq. (7) is derived for trochoidal waves, its application here is justified because the real sea wave is closer to trochoidal than to cosine wave. Based on Eq. (7), a new equation was derived to ensure equality of hogging and sagging wave bending moments for CB = 1 and to meet the existing class rules for calculation of the design hogging and sagging wave bending moments:
χ 0.62 2.63CB
M M
W, h W,s
1 (9) MW,s Mt,min T2
Figure. 4 Extraction of MW,s, MW,h and MSW from the filtered quasi-static vertical MW
Step I: Selecting the duration of the time windows
In the examples here, the duration of the time windows was fixed to 20 and 60 minutes over one year and 3.5 years of full scale measurements. Of course, the time window can be of any other duration.
Step II: Extracting the maximal value and its POE from each time window
MW,h
Eq.(9) is illustrated in Figure. 3. The equation was used while subtracted from the records of the total bending moment data for hogging, sagging, and still water bending moments by the formulas:
M;M χM 1 χ
MM M M M sW, t, ma x ht, min W,
W,hh (10) SW
MMt, min t, ma x W, s W, (11)
In almost all published research works, the still water bending moment has been calculated as the mean value of hogging and sagging wave bending moments. However, from the physical point of view, this is incorrect, especially for fast going ships as follows from Eq. (9) and Figure. 3. Thus, MSW is not the mean value of
Mt,max and Mt, min (see Figure. 4) but always above the mean.
1.00 1.05 1.10 1.15 1.20 1.25
0.6 0.7
M2.63C
M
W,s W,h
0.62 1 B
CB [-] 0.8 0.9 1.0 Figure. 3 Ratio between MW,s and MW,h vs. CB
MSW time T
©2012: The Royal Institution of Naval Architects
A-91
Measured B.M. MW,s / MW,h
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