3.2.2.1
Analysis of details relevant to
the casualties
3.2.2.1.1 The evaluation of details relevant to
the casualties is shown in Figures 2
to 7.
3.2.2.1.2 In all 166 casualties reported, the
ships concerned were: 80 cargo ships, 1 cargo and passenger ship,
1 bulk carrier, 4 off-shore supply ships, 7 special service vessels,
and 73 fishing vessels. Distribution of ship’s length is shown
in figure 2. It is seen that
the majority of casualties occurred in ships of less than 60 m in
length.
3.2.2.1.3 A great variety of cargoes were carried
so that no definite conclusions could be drawn. It may be noted, however,
that in 35 cases of the 80 cargo ships reported, deck cargo was present.
3.2.2.1.4 The result of the analysis of the location
of the casualty is shown in Figure
3. It may be seen that the majority of casualties (72% of all
casualties) occurred in restricted water areas, in estuaries and along
the coastline. This is understandable because the majority of ships
lost were small ships of under 60 m in length. From the analysis of
the season when the casualty occurred (Figure 4) it may be seen that the most dangerous season is
autumn (41% of all casualties).
3.2.2.1.5 The result of the analysis of the weather
conditions is shown in Figure 5.
About 75% of all casualties occurred in rough seas at a wind force
of between Beaufort 4 to 10. Ships were sailing most often in beam
seas, less often in quartering and following seas.
3.2.2.1.6 The manner of the casualty was also
analysed (Figure 6). It showed
that the most common casualty was through gradual or sudden capsizing.
In about 30% of casualties, ships survived the casualty and were heeled
only.
3.2.2.1.7 In Figure
7 the results of the analysis of the age of ships are shown.
No definite conclusions could be drawn from this analysis.
3.2.2.1.8 The distributions of stability parameters
for ships’ condition at time of loss are shown in Figures 8 to 14.
3.2.2.2
Analysis of stability parameters
using Rahola method
3.2.2.2.1 The stability parameters for casualty
condition were analysed by plotting in a similar manner, as was done
by Rahola, together with parameters for ships operated safely for
comparison.
3.2.2.2.2 The parameters chosen for analysis were GM0, GZ20, GZ30, GZ40,
GZm, e40, and ϕm
. From
the available data, histograms were prepared, where respective values
of stability parameters for casualty condition were entered by starting
with the highest value at the left of the vertical line (ordinate)
down to the lowest value, and the values of the same parameter for
safe ships were entered on the right side by starting from the lowest
and ending with the highest value. Thus, at the ordinate, the highest
value of the parameter for casualty condition is next to the lowest
value of the parameter for the safe case. In Figure 15 an example
diagram for righting levers comprising all ships analysed is shown.
In the original analysis [IMO 1966, 1966a, 1985] diagrams were prepared
separately for cargo and fishing vessels, but they are not reproduced
here.
3.2.2.2.3 In the diagram (Figure 15), the values for casualty
condition are shaded, only those that have to be specially considered
due to exceptional circumstances were left blank. On the right side
of the ordinate the areas above the steps were shaded in order to
make a distinction between the safe and unsafe cases easier. The limiting
lines or the imaginary static stability lever curves were drawn in
an identical way as in the Rahola diagram. Percentages of ships in
arrival condition, the respective stability parameters which are below
the limiting lines are shown in table
1. The lower percentages mean in general that there is better
discrimination between safe and unsafe conditions.
Table 1 - Percentages of ships
below limiting line
|
Table 1 – Percentages of ships below limiting line
|
|
Stability parameter
|
Percentages
|
|
|
all ships
|
cargo
|
fishing
|
|
GZ20
|
39
|
54
|
26
|
|
GZ30
|
48
|
54
|
42
|
|
GZ40
|
48
|
46
|
48
|
|
e
|
55
|
56
|
53
|
3.2.2.2.4 The type of analysis described above
is not entirely rigorous; it was partly based on intuition and allows
arbitrary judgement. Nevertheless, from the point of view of practical
application, it provided acceptable results and finally was adopted
as a basis for IMO stability criteria.
3.2.2.3
Discrimination Analysis
3.2.2.3.1 When two populations of data, as in
this case, data for capsized ships and for ships considered safe,
are available and the critical values of parameters from these two
sets have to be obtained, the method of discrimination analysis may
be applied.
3.2.2.3.2 The application of the discrimination
analysis in order to estimate critical values of stability parameters
were contained in a joint report by [IMO 1966, 1966a], and constituted
the basis for development of IMO stability criteria along the previously
described Rahola method.
3.2.2.3.3 In this investigation, discrimination
analysis was applied independently to nine stability parameters. Using
data from intact stability casualty records (group 1) and from intact
stability calculations for ships considered safe in operation (group
2) the distribution functions were plotted, where for group 1 the
distribution function F1 and for group 2 function (1 −
F2) were drawn. Practically, on the abscissa axis of the
diagram, values for the respective stability parameter were plotted
and the ordinates represent the number of ships in per cent of the
total number of ships considered having the respective parameter smaller
than the actual value for ships of group 1 and greater than the actual
value for ships of group 2 considered safe.
3.2.2.3.4 The point of intersection of both curves
in the diagram provides the critical value of the parameter in question.
This value is dividing the parameters of group 1 and of group 2. In
an ideal case, both distribution functions should not intersect and
the critical value of the respective parameter is then at the point
between two curves (see Figure 16).
3.2.2.3.5 In reality, both curves always intersect
and the critical value of the parameter is taken at the point of intersection.
At this point, the percentage of ships capsized having the value of
the respective parameter higher than the critical value is equal to
the percentage of safe ships having the value of this parameter lower
than the critical value.
3.2.2.3.6 The set of diagrams was prepared in
this way for various stability parameters based on IMO statistics
for cargo and passenger ships and for fishing vessels. One of the
diagrams is reproduced in Figure 17.
It means that the probability of capsizing of a ship with the considered
parameter higher than the critical value is the same as the probability
of survival of a ship with this parameter lower than the critical
value.
3.2.2.3.7 In order to increase the probability
of survival, the value of the parameter should be increased, say up
to x* (Figure 16),
at which the probability of survival (based on the population investigated)
would be 100%. However, this would mean excessive severity of the
criterion, which usually is not possible to adopt in practice because
of unrealistic values of parameters obtained in this way curves do
intersect could be explained in two ways. It is possible that ships
of group 2 having values of the parameter in question x <
x
crit
are unsafe, but they were lucky
not to meet excessive environmental conditions which might cause capsizing.
On the other hand, the conclusion could also be drawn that consideration
of only one stability parameter is not sufficient to judge the stability
of a ship.
3.2.2.3.8 The last consideration led to an attempt
to utilize the IMO data bank for a discrimination analysis where a
set of stability parameters was investigated [Krappinger and Sharma
1974]. The results of this analysis were, however, available after
the SLF Sub-Committee had adopted criteria included in resolutions A.167(ES.IV) and A.168(ES.IV) and were
not taken into consideration.
3.2.2.3.9 As can be seen from Figure 17, the accurate estimation
of the critical values of the respective parameters is difficult because
those values are very sensitive to the running of the curves in the
vicinity of the intersection point, especially if the population of
ships is small.
3.2.2.4
Adoption of the final criteria and
checking the criteria against a certain number of ships
3.2.2.4.1 The final criteria, as they were evaluated
on the basis of the diagrams, are prepared in the form as shown in
Figures 15 and 17. The main set of diagrams did show righting lever
curves (Figure 15), but diagrams
showing distribution of dynamic stability levers were also included.
Diagrams were prepared jointly for cargo and passenger vessels and
for fishing vessels, except vessels carrying timber deck cargo. Sets
of diagrams were also separately prepared for cargo ships and fishing
vessels. Diagrams in the form as shown in Figure 17 were prepared separately for each stability parameter
and separately for cargo and passenger ships and for fishing vessels.
3.2.2.4.2 After discussion by the Working Group
on Intact Stability and the SLF Sub-Committee, the stability criteria
were rounded off and finally adopted in the form as they appear in
the resolutions A.167(ES.IV) and
A.168(ES.IV).
3.2.2.4.3 In the original analysis the angle of
vanishing stability was also included. However, due to the wide scatter
of values of this parameter, it was not included in the final proposal.
3.2.2.4.4 As each criterion or system of criteria
has to be checked against a sample of the population of existing ships,
it was necessary to find the common basis for comparison results achieved
with the application of different criteria. The most convenient basis
for the comparison was the value of KG
crit that
is the highest admissible value of KG satisfying the
criterion or system of criteria, and the higher the value of KG
crit, the less severe the criterion.
3.2.2.4.5 As an example, criteria related to the
righting lever curves could be written as:
3.2.2.4.6 If for GZ and φ , values of respective
criterion are inserted, values of KG
crit for
respective displacement are obtained. Then the curve KGcrit
= f (Δ) could be drawn. KG
crit could
also be obtained graphically as shown in Figure
18. It is possible to calculate values KG
crit also
for dynamic criteria, although the method is more complicated.
3.2.2.4.7
Figure
19 shows the results of calculations of KG
crit for
a fishing vessel ([IMO 1966]). Curves KG
crit
= f (Δ) for 11 different criteria are plotted in the Figure. By
having such curves for each individual criterion, it is easy to determine
critical KG curve for a system of criteria by drawing
envelope.
3.2.2.4.8 Curves for KG
crit,
as shown in Figure 19, also
allow conclusions to be drawn regarding the relative severity of various
criteria or systems of criteria and to single out the governing one.
If, in addition, actual values of KG for the particular
ship are available, then it is possible to estimate whether the ship
satisfies the criteria and which criterion leads to the condition
most close to the actual condition. If it is assumed that ships in
service are safe from the point of view of stability, it could be
concluded which criterion or system of criteria fits in the best way
without excessive reserve of stability.
a histogram of distribution of k is shown for
the group of ships analysed (Figure
20).