Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010
The line on the graph represents the simplest formula that provides an effective fit to the data, and might be used as a method of estimating the critical wave height. defined as:
It
Critical Wave Height Range RMmax 10B
=
Because the tests defined the minimum possible wave height
to capsize, this line presents a conservative
estimate of the critical wave height in most cases, although a few of the test results lie slightly below it. It could be adjusted to provide a greater, or indeed lower, level of safety, by the simple subtraction or addition of a constant factor of the length. A lower line was also suggested for consideration as a more conservative option but, for simplicity, has not been included here.
Given a particular critical wave height value, it is
reasonable to suggest that the critical seastate will be somewhat less than that. In research Project 509 it was recommended that the critical seastate can be related to the critical wave height by the factor 0.5. For example, if the critical wave height is predicted to be 2 metres, the critical seastate will be 1 metre, on the basis that one should expect to encounter waves of twice the significant height
every few hours. This gives expression:
Critical Seastate Range RMmax 20B
= 3 INDEPENDENT EVALUATION
The work was submitted to the IMO in 2005, [2], and there seemed to be a view that further validation of the findings was justified. In response to this, in January 2008, the MCA commissioned BVT Surface Fleet to conduct Research Project 583. The aim of the project was to compare the proposed method of estimating the minimum wave height to capsize with other model test results and full scale casualties or service history. The project was completed a year later and the report published on the MCA website, [3].
4
CRITICAL REVIEW OF THE EVALUATION
4.1 SHIP CASUALTIES
For that project the consultants collected well documented reports of capsizes in heavy seas from a number of sources, and compared the proposed formula with the wave heights believed to be present at the time. They identified
only six suitable casualties and
concluded that reliable ship capsize data are scarce. This is partly due to the fact that most ships operate well in excess of the minimum criteria and, unless disabled, actively avoid vulnerable headings to large waves. They
©2010: The Royal Institution of Naval Architects
The EU research project HARDER (Harmonisation of Rules and Design Rationale) was particularly useful in providing a substantial amount of model test data. A number of papers have been published which present selected data or findings, for example [4]. It is interesting to note that one of the findings of that project was that the stability parameter that correlated most closely with wave height to cause capsize was the range of residual stability after damage. The GZmax values also showed reasonable correlation, although they varied with vessel
A - 87 the alternative is
excluded small craft and fishing vessels under 20 metres, and thereby excluded a large number of casualties. They also identified five cases of ships surviving heavy seas. Their data are presented in Figure 3.
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Ship capsize Ship survive
Unsafe zone Safe zone 0.0 0.5 1.0 1.5 2.0
Range(RMmax) LB
2.5 0.5
3.0 3.5
Figure 3 Real ship data gathered in Research Project 583, plotted in relation to the Wolfson formula.
If the formula is reliable in predicting the minimum wave height to capsize, the casualties should lie on or above the line that was derived in Figure 2. Note that the vertical axis in Figure 3 is the significant wave height of the seastate, rather than wave height to capsize, and so the line has been adjusted accordingly. The Research Project 583 consultants stated in their report “While the data conforms to the broad trend, it does not clearly support the positioning of the line defining the safe limit to be applied as a criterion.”
4.2 OTHER MODEL DATA
The consultants also collected results of other model tests where capsizes had been studied, and some data from numerical simulations of capsize. Care must be taken with these data though, because model tests are not usually designed to determine the minimum wave height to capsize. The requirement to test at a range of frequencies at all headings is not normally included in a model test programme because other aspects of the capsize behaviour are being studied. Some data therefore can be expected to lie significantly above the lower boundary of the envelope of Wolfson Unit capsize data, and in that respect are similar to the ship casualty data.
4.2 (a) HARDER Project 4.0
Significant wave height/L
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