Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010
type, and they concluded that the most useful measure of survivability is a criterion based on the product of the two. This finding correlates very well with the outcome of Research Project 509. Their recommended formula for a survivability factor was submitted to IMO and has been adopted as a basis for the probabilistic damage stability regulations; SOLAS 2009 (MSC.216(82) – Annex 2):
s K GZmax 0.12
= ⎡
⎢ ⎣
×
Range⎤ 16
⎥ ⎦
Where K is a constant, depending on ship type.
Reference 4 does not report whether the HARDER researchers considered the inclusion of displacement or other ship dimensions to relate ship size to wave height, and thereby make their formula truly non-dimensional. The project concentrated on large ships, and their aim was to develop a method of assessment for certain types of ship, not a method that might be applied to vessels of any size. Notwithstanding that, the authors of that paper apparently believed the formula to be non-dimensional as they state “…
..since all factors in the equation are already non-dimensionalized.”
The values 0.12 and 16 in their formula were empirically derived values of GZ and range, and the formula therefore appears non-dimensional. The use of a constant value to replace GZ in this way, however, returns the formula to a dimensional form. In practice, for a limited range of vessel sizes and types, GZ curve characteristics tend to be similar because of regulatory or practical design constraints. The
formula may be effective,
therefore, in the same way as conventional criteria that apply constant minima for all vessels, but it is no more non-dimensional than they are. If very small vessels had been considered it is likely that different constants, or perhaps a different formula might have been required to fit their test results. Indeed, different values have been recommended to replace the constant 0.12 for ships of different types, such as Ro-Pax ships, where the value 0.25 is more appropriate.
This aspect is discussed with particular reference to the 2009 Solas regulations in [5], where it is noted that these new “harmonized” probabilistic regulations
require
different formulae for different ship types. It is common for regulations to have different approaches or formulae for different sizes or types of ships, but it presents problems if design trends take new vessels outside the range of those used in the rule development. It would be preferable for
truly harmonised standards to be non-
dimensional and capable of assessing all vessels with a common formula.
Models of six ships were tested in the HARDER project, and the results of four of these were used in Research Project 583. Figure 4 presents these selected HARDER model test data in a similar way to [3], and again using
A - 88
4 1
significant wave height as the vertical scale. The
conclusion drawn in Research Project 583 was that “These model test plots do not convincingly support the Wolfson Criterion.” because some capsizes fall below the line, and “Many survive cases are well above the line and in general the data do not exhibit a trend that follows the Wolfson line even vaguely.” It is the case that the capsize cases appear widely distributed on this graph, and the suggested combination of stability parameters has not collapsed the data into a convincing narrow envelope. It should be appreciated that for each model configuration tested by the Wolfson Unit in project 509 there were many capsizes at higher wave heights than those plotted in Figure 2. If all of those were presented together they would not fall into a narrow envelope. It is only by plotting the minimum wave heights at which capsize occurred for each case that this trend may be found.
0.00 0.01 0.02 0.03 0.04
model capsize no capsize
0.0
0.1
0.2
0.3
0.4
Range(RMmax) LB
0.5
Figure 4 Results of tests on 4 models in the HARDER project, plotted in relation to the Wolfson formula.
The use of seastates rather than regular waves may introduce greater scatter into model test results because the models encounter waves of varying height, and may be capsized by a particularly large wave. Conversely, in regular waves, some capsizes may be influenced by the resonant nature of the roll motion, which will only occur in a seastate if a group of relatively regular waves is encountered. These different test methods should be borne in mind when comparing data.
It appears that
several of the HARDER models capsized in the same seastate, with a significant height/L of just over 0.01on the graph, and some of these are the cases that fall on the “safe” side of the line. The actual waves that caused the capsizes may have been of different heights and, if recorded, might have been plotted in different locations relative to each other using critical wave height as an axis, as in Figure 2. Whilst this horizontal stratification on the graph may have given rise to the perception that the data do not follow the trend of the line, it is unlikely to account for the fact that one of the models capsized in a significant wave height about half that predicted by the Wolfson line. There are a number of other factors that might account for this.
0.5
0.6
0.7
©2010: The Royal Institution of Naval Architect
Sig. wave height to capsize/L
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