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SAILING.
THE THIRTEENTH CHESAPEAKE SAILING YACHT SYMPOSIUM
Development of Proposed ISO 12217 Single Stability Index for Mono-Hull
Sailing Craft
Dr. Peter van Oossanen, Van Oossanen & Associates, Wageningen, The Netherlands
ABSTRACT
states, technical standards exist, not backed by
national legislation, thereby not creating obstacles
to trade but, since these are not enforced, no guarantee exists against the production and the sale of
potentially dangerous boats and yachts.
For more than 5 years now, Working Group 22 of
Technical Committee 188 of the International Standards Organization (ISO) has been developing a
standard for the assessment and categorization of
the stability of pleasure craft with a length up to 24
m. This work became necessary when the European
Union decided to issue a Directive on Pleasure
Craft, facilitating the export and import of pleasure
craft to and from the various countries comprising
the European Union. All newly-built pleasure craft
up to 24 m in length, to be marketed in the European Union, must comply with the stability standard
being developed, and some 50 other ISO standards,
covering all aspects of structure, materials, equipment, etc, as of June 1998.
For these reasons, the International Council of
Marine Industry Associations (ICOMIA), in 1988,
decided to propose to the European Commission
that a Directive on Recreational Boats be prepared,
to remove existing barriers to trade and to ensure
that all recreational craft comply with certain technical requirements. This Directive on Recreational
Boats was completed in 1994 and passed by the
European Parliament in 1996. It requires that as of
June 1998, all recreational boats that are to be marketed in the European Union must comply with the
requirements set therein and in the associated technical standards being developed by various working
groups of Technical Committee (TC) 188 of the
International Standards Organization (ISO), or acceptable alternatives thereto. As of June 1996, recreational boats may already be certified in accordance with these requirements.
To support the work of Working Group 22, The
Netherlands carried out a comprehensive study for
Part 2 of ISO 12217, covering the stability of
mono-hull sailing craft. Together with the French,
Swedish and UK delegates, this work finally lead to
the development of a single stability index. Working Group 22, in September 1996, unanimously
agreed to adopt this concept for the assessment and
categorization of the stability of mono-hull sailing
vessels. This paper gives a description of some of
the work that was carried out by the Netherlands in
this regard and gives a description of the single
STability Index (STIX) concept and the way the
STIX value is determined from the various stability
and buoyancy properties of sailing vessels.
1.
Working Group 22 (WG 22) of TC188 is preparing
ISO Standard 12217 on stability and buoyancy.
This Standard is of particular importance among the
50-plus standards presently being developed for use
in conjunction with the European Directive on Recreational Craft as it will, for the first time in many
countries of Europe, indicate specific safety measures that will have to be met with regard to both
stability and flotation. ISO 12217 is divided into 3
parts. Part 1, ready to be issued as a Committee
Draught (CD) at the time of finalizing this paper,
addresses non-sailing vessels of over 6 m in length.
Part 2 addresses sailing vessels of over 6 m in
length, and Part 3 addresses all boats under 6 m in
length.
INTRODUCTION
In Europe, effective barriers to trade exist due to
the fact that some countries impose technical requirements based on national legislation, involving
approval of all recreational craft. Particularly France
and Italy impose such regulations. In other member
97
In ISO 12217-2, sailing vessels are divided into 3
types, viz:
Sailing vessels (mono-hull and multi-hull) reliant on the use of crew weight for capsize
recovery;
Mono-hull sailing vessels;
Multi-hull sailing vessels.
The technical content of this paper covers the work
carried out up to October 1996, the results of which
have all been made available to Working Group 22.
This paper should not be taken as representing the
final content of ISO 12217-2. Further discussions in
the working group during the coming months will
no-doubt lead to changes to some parts of the formulae and requirements as described here.
2.
BASIC CONCEPTS ADOPTED IN THE
WORKING DRAUGHT OF ISO 12217-2
WITH RESPECT TO SAILING CRAFT
various countries in Europe will divide geographical
regions into categories based on wave height and
wind speed. It would not be logical, for example, to
sub-divide geographical regions based on the
highest wave height or highest wind speed ever
recorded in a region. It would be more logical to
calculate the significant wave height and wind
speed over a number of years, based on records
which exclude the highest 2% or 5%. This percentage is arbitrary and must be chosen carefully to
arrive at logical conclusions. After consultation with
the National Meteorological Institute, the authorities
in the Netherlands decided that the lakes, canals
and rivers in the Netherlands constitute Category D
water, while the IJsselmeer and the Scheide estuaries constitute Category C water. Likewise, the
North Sea, IO miles or more from the coast, constitutes category B water. These sub-divisions are
based mainly on recorded wave height, with 5% of
the highest values discarded.
This latter topic will not be considered here in any
further detail as it is mainly the subject of the socalled Notified Bodies responsible for the certification process in the various countries. In the stability (and other) standards, a specific set of design
conditions are associated with a specific set of requirements without further discussion of which
geographical regions are implied.
The requirements set out in the Standard depend on
the so-called Stability Category to be assigned to a
vessel. Stability Category I, intended for vessels
that can sail anywhere in the world, demands that
the highest values are met, while Stability Category
IV, intended for vessels sailing in restricted waters
such as small lakes and rivers, requires that relatively low values are met for the various requirements.
Table 1. Stability categories as defined in the
present draught of ISO Stability Standard 12217.
No specification is given in the Draught Standard
with respect to the geographical areas that pertain to
Stability Category I through IV. Instead, design
criteria are given for values of the significant wave
height and wind speed that vessels in each category
are expected to be able to endure without impairing
the safety of the vessel. These categories are defined in Table 1.
Stability/Design
Category
These stability categories were chosen by Working
Group 22 to coincide with the so-called Design
Categories in the European Directive. Design category A (termed "Ocean" in the Directive), calls for
a design wind force in excess of 8 Beaufort and a
significant wave height in excess of 4 meters (4 to
8 meters in the stability standard). Hence stability
category I in the stability standard coincides with
design category "A" in the Directive. Similarly,
stability category II coincides with design category
"B" in the Directive, III with "C", and IV with "D".
Significant
Wave
Height in
meter
Wind
Speed in
m/sec
I/A
0 to 8
25
11/B
0 to 4
21
111/C
0 to 2
17
IV/D
0 to 0.5
13
For sailing vessels reliant on the use of crew weight
for capsize recovery, requirements have to be met
with respect to flotation and stability in the swamped condition. For other sailing craft, a major division is made between vessels that are susceptible to
swamping and vessels that are not susceptible to
swamping. Fully decked vessels having recesses of
These design criteria have been the subject of considerable discussion, since it is not clear how the
98
3.
limited (small) size, or vessels with selfdraining
cockpits/recesses as specified in ISO 11812, are
distinguished from vessels that are not fully decked
or vessels that have moderate to large non-selfdraining cockpits/recesses. The latter type of vessel
cannot be assigned stability category I or II (see
also Paragraph 6.6).
OUTLINE OF STUDY CARRIED OUT BY
THE NETHERLANDS IN SUPPORT OF
THE WORK OF WORKING GROUP 22
To support the work of Working Group 22, the
Netherlands carried out a study of the stability characteristics of mono-hull sailing vessels. This study,
supported by the Government, the National Association of Water Sports Industries (HISWA) and
some 70 individual companies involved in the design and building of recreational craft in the Netherlands, was aimed at analyzing the characteristics of
so-called stability casualties and the characteristics
of craft with a well-proven performance record.
A further general requirement is stipulated with
respect to mono- and multi-hull vessels with a limited range of positive stability (less than 90 degrees).
These vessels can only be assigned stability category I and II when the subject vessel will not sink
after a knock-down or an inversion (from which
such a vessel cannot recover). Such vessels are
required to posses 20% more volume in the hull,
fittings, and equipment than the loaded displacement volume, not including trapped air (apart from
air in air tanks and in watertight compartments).
In the first instance, in 1993 and 1994, stability data
was collected for about 115 sailing vessels of all
types. Particular attention was focussed on vessels
that suffered a knock-down from which they did not
recover, an inversion (usually referred to as a capsize), a sinking, or some other stability-oriented
casualty. Next, the resulting data base was analyzed
with a view to obtaining insight as to the range of
values of various stability parameters associated
with a stability casualty and with a well-behaved
vessel in this respect. It was found that particularly
important parameters are the value of the angle of
vanishing positive stability, the value of the righting
lever at 90 degrees of heel, and the area under the
righting moment curve up to the angle of vanishing
stability. It was also found that the downflooding
angle, i.e. the heel angle at which a critical amount
of water enters the non-selfdraining part of the hull,
is a dominant factor playing a decisive role in the
righting behaviour of a yacht after a knock-down or
an inversion.
Apart from the specific requirements with respect to
the stability characteristics of a vessel, requirements
are also imposed on the minimum freeboard or the
so-called minimum downflooding height. This is the
least height in meter above the waterline to any
point at which water begins to enter the interior or
non-selfdraining part of the vessel (whether cockpit
or bilge) when it is floating upright, fully loaded in
calm water, except for the following which is not to
be considered in this respect:
Selfdraining recesses complying with ISO
11812;
Drains from watertight recesses with a combined volume less than 0.025Lhull· Bhun·FM, in
which Lhull and Bhull are the length and beam of
the hull according to ISO 8666, and FM the
freeboard amidships;
Non-opening appliances which are watertight to
degree 2 of ISO 11812 or ISO 12216;
Openings in the sides of outboard engine wells
in certain cases.
During 1994 and 1995, the Netherlands work was
focussed on defining minimum values of each of
the important parameters, for each of the 4 stability
categories. The results thereof were presented to
WG 22 at various meetings and thoroughly discussed.
Generally, the minimum downflooding height is
Lhuuf 17 with absolute minimum values of 0.5 m for
stability category I, 0.4 m for stability category II,
0.3 m for III and 0.2 m for IV. Alternatively, a
rigorous method may be adopted, explained in an
annex, to calculate the absolute minimum required
downflooding height for a specific vessel.
Late in 1995 and in the beginning of 1996 it became apparent to all members of WG 22 that unanimous agreement on the required minimum values
for each of the important stability parameters was
unattainable. Where one country, for example, wanted to require a moderate minimum value of the
angle of vanishing stability and a high minimum
value of the downflooding angle, another country
wished to impose a relative high minimum value of
the angle of vanishing stability and a moderate
minimum value of the downflooding angle. It was
Finally, specific requirements are also set with
respect to the value of the minimum downflooding
angle.
99
accurate values. Using such refined values of LPS
and RM90, it should be possible to use an IMS
stability calculation as a basis for a first estimate to
determine whether or not the requirements imposed
by ISO Standard 12217-2 are met.
then decided to appoint a small group of experts to
devise a system in which a high value of one parameter could be traded-off against a low value of
another parameter, wherever possible. This group
worked through the summer of 1996, resulting in
the concept of a single stability index presented in
Paragraph 6. At the meeting of WG 22 held in Paris
in September 1996, it was unanimously decided to
adopt this method for the assessment and categorization of stability for mono-hull sailing vessels.
4.
Some of the casualty data was supplied on the basis
that these be used in a statistical sense only, i.e.
that the name or type of yacht, its designer and
builder, not be mentioned in a report or paper. The
information given in this paper in this respect is
therefore only representative. No effort has been
made to provide a full set of pertinent sailing vessel
data.
COLLECTION OF ST ABILITY DAT A
Requests for stability data on mono-hull sailing
vessels of all kind were requested from more than
65 sources world-wide. In particular, information
was requested on sailing craft that had experienced
a serious knockdown, an inversion, a sinking or
some other stability-oriented casualty. Together
with data collected by other members of Working
Group 22, 115 sets of stability data for sailing craft
were collected over a period of about 8 months.
About 30 sets of data involved vessels that had
suffered a stability-oriented casualty of one kind or
another.
Although many sailing craft were identified as
having been knocked down and inverted, the necessary particulars were only actually obtained for
about 30 sailing vessels. Table 2 lists particulars of
some of these casualties.
Table 3 lists the particulars of the 30 category I
sailing craft in the compiled data bank with the
lowest angle of vanishing stability. Stability category I sailing craft (in this study) are those with a
long operational history without any stability-oriented problems. The category I designation was given
by the designer and/or the builder. That is, the respective designer and/or the builder considers these
vessels to be suitable to sail anywhere in the world.
It is explicitly noted here that Table 3 gives a list of
those 30 vessels that have the lowest value of the
angle of vanishing positive stability and/or the
lowest value of the righting lever at 90 degrees of
heel. The data base includes data for 55 other vessels with greater stability values.
All of the stability data collected constituted socalled "rigorous" data, obtained by taking into consideration deck camber, deck houses and structures,
and floodable recesses such as cockpits. During the
course of this study significant discussion ensued
concerning the error involved in considering a flush
deck, without taking into account the effect of deck
camber, deck structures and cockpits. The reason
for this is that the Offshore Racing Council (ORC),
responsible for the International Measurement System (IMS), has on file stability information of thousands of yachts based on inclining experiments,
which could have been made available for this
stability study through the Chief Executive of ORC
(also a member of WG 22). This stability information however does not include the effects of deck
camber, deck structures or cockpits. The outcome of
these deliberations was to request ORC to carry out
a systematic series of stability calculations for a
number of IMS yachts with deck camber, systematically-varied deck structures and cockpits, and sealed
masts. The results of these calculations, discussed in
Paragraph 5.1.3, has allowed the development of
approximate expressions for the effect of deckhouses, cockpits, etc, on the vanishing angle of
positive stability and the righting lever at 90 degrees of heel. With these approximate expressions
the respective IMS stability entities (referred to as
LPS and RM90) can be refined to obtain more
The data collected was for the so-called "minimum
sailing" condition. In this condition all tanks are
considered 10% full with sails hoisted and a minimum crew on-board. For a sailing vessel this is
generally considered to be the condition in which
stability is least.
During the course of collecting this data it became
clear that serious knockdowns and capsizes happen
more frequently than often supposed. Detailed information was obtained from the Royal National
Lifeboat Institution (RNLI) in Dorset, England,
revealing that every year the services by RNLI lifeboats to sailing yachts that have suffered a capsize,
number at least 20. A similar number of capsizes
are reported by the equivalent Netherlands Institution. In all, it was not difficult to pin-point more
than 100 recent stability-oriented casualties. It was
100
extremely difficult, however, to obtain the required
rigorous stability data of most of these vessels to
render them suitable for analysis.
5.
been discerned. The analysis of the 1979 Fastnet race casualties (see the list of references)
has shown that in the same adverse conditions
the smaller boats were generally more vulnerable, as could be expected. It stands to reason
therefore that stability requirements for small
vessels must be relatively harsher than for larger vessels.
ANALYSIS OF STABILITY DAT A
5.1 Minimum Angle of Vanishing Stability
5.1.1
Differentiation Between
"Good" Vessel Data
Casualty
and
In connection with this last observation, it should
be noted that the requirement of a lower value of
the angle of vanishing positive stability for larger
vessels is not because these vessels recover from an
inversion more easily, but rather because a larger
excitation force is required to cause a knockdown in
the first place. If the premise for developing stability criteria were to be such that an inversion has to
be avoided irrespective of the chance of getting
knocked down, the only correct criterion to be applied would be one demanding a specific minimum
vanishing angle of positive stability for all vessels,
irrespective of their size. On the basis of accepting
a specific, small risk in setting safeguard criteria,
the adopted approach of requiring a lower angle of
vanishing stability for larger vessels, in connection
with being able to recover from an inversion, as
adopted here and in the past, can be defended.
A plot of the angle of vanishing positive stability
(<l>v) against overall length L0 ., for all vessels specified in Tables 2 and 3, is shown in Figure I. The
lines shown herein approximately divide the points
for most of the casualties (indicated by pluses) from
those for "good" category I vessels (indicated by
squares).
On the basis of Figure I and Table 2 it is possible
to make a number of important observations, as
follows:
Three casualties are located amongst the socalled "good" category I vessels. A study of the
particulars given in Table 2 for case studies 5,
8 and 14, reveals that these three yachts experienced an inversion in high seas and recovered,
with extensive damage. Although the sailing
craft associated with case studies 2, 4, 6 and 9
also recovered, the sea conditions in these latter
cases were nothing like the extreme conditions
associated with cases 5, 8 and 14.
It is not possible, on the basis of the plot in Figure
1 alone, to define a boundary for the minimum
required angle of vanishing positive stability. The
line drawn provides insufficient latitude between
the so-called casualties and "good" category I vessels. Other presentations of this data was therefore
investigated.
The stability characteristics of the sailing craft
associated with case studies 5, 8 and 14 in
Table 2, are as good as those of the "good"
category I vessels (see Table 3). Accordingly, it
stands to reason that the "good" category I
vessels could also have been knocked down in
conditions experienced by these three vessels. It
also follows that a high value of the vanishing
angle of positive stability will therefore not
prevent a knockdown from occurring but will
ensure that the vessel is capable of righting itself, even after having been totally inverted.
The energy associated with a knockdown is probably more dependent on the mass of the vessel
than on the length of a vessel. Accordingly, a plot
of vanishing angle against displacement mass is
presented in Figure 2. In this figure a significantly
greater latitude is seen to exist between the casualty
data and the data for the "good" category I vessels,
due to the fact that the so-called casualties mostly
constitute sailing craft with a small displacement. A
less arbitrary line can now be defined to distinguish
between the casualties and the "good" boats considered. This line is shown. Accordingly, it was
decided to develop a proposal for the minimum
value of the angle of vanishing positive stability
based on the results of Figure 2. This is further
discussed in Paragraph 5.1.2.
The minimum required value of the angle of
vanishing positive stability is clearly dependent
on the size of the vessel. For overall length
values in excess of about 22 meters, the minimum value of <Pv would seem to be in the order
of about I 00 degrees. For lengths of I 0 meters
and less, this value would seem to be about 130
degrees. This trend with size has previously
101
Table 2. Particu lars of sailing craft that have suffered stability-orien
ted casualties.
#
LOA
BoA
BwL
Tc
D
4101
GM
GZ 90
cl>v
#1
6.50
2.85
2.15
0.25
1.20
1.50
0.85
0.34
I IO
#2
7.0I
2.70
2.I8
0.35
1.10
1.82
0.88
0.17
103
#3
7.32
2.72
0.30
1.03
1.70
0.1 I
99
#4
7.49
2.74
2.22
0.39
1.23
2.30
0.8I
0.20
II2
#5
8.08
3.20
2.79
0.4I
1.37
4.55
1.35
0.56
133
#6
8.56
2.96
2.44
0.42
1.36
3.1 I·
0.88
0.28
II2
#7
9.I4
3. I4
2.47
0.44
I .4I
3.77
0.85
0.27
II7
#8
10.l
3.40
2.76
0.49
1.50
4.5I
1.33
0.58
132
#9
10.5
3.58
2.85
0.50
1.50
5.30
1.08
0.28
109
#IO
11.1
3.59
3.10
0.70
1.58
12.2
1.15
<O
68
#lI
14.3
3.83
3.22
0.45
1.58
7.92
1.75
0.33
114
#12
17.4
3.60
3.54
0.41
1.45
14.7
1.89
<O
65
#13
18.0
0.26
98
#I4
I9.7
4.96
#15
19.8
#I6
14.3
4.58
1.01
2.41
30.3
1.45
0.59
122
5.94
64.9
1.86
<O
75
26.7
7.01
136
<O
57
#17
27.3
7.0I
#I8
28.0
6.40
Notes
#I
#2, 4, 6 and 9
#3
#5
#7
#8, I4
#10, I2
#I I
#I3
#15,16, 17, 18
6.78
2.2I
3.22
124
1.86
<O
88
I67
0.6I
<O
57
Knocked down/inverted and sank with loss of life (various vessels);
Knocked down in moderate to high seas and recovered with minor
damage (more than
one vessel in each class);
Knocked down/inverted: most vessels recovered with minor damage
: some were
swamped (various vessels);
Rolled 360 degrees in extreme seas: recovered with loss of rig;
Knocked down, inverted and recovered after about 45 minutes: subsequ
ently sank with
loss of life (various vessels of same type were subject of similar casualti
es);
Knocked down and inverted in extreme seas: recovered with extensiv
e damage;
Capsized and sank in shallow water due to wind gust (vessels were
retrieved);
Knocked down & inverted: after one hour righted and swamped, and
subsequently sank
with loss of life;
Capsized and sank;
Capsized and sank with loss of life.
102
Table 3. Particulars of saili11 g craft designated as category I by their designers/builders, with a long
operational history without : my stability-oriented problems.
#
LoA
BoA
BwL
Tc
D
alot
GM
GZ90
<Pv
#1
7.99
2.80
2.28
0.35
1.37
2.50
1.07
0.58
135
#2
9.00
3.20
0.44
128
#3
9.40
3.37
#4
10.5
3.60
#5
10.5
#6
10.7
3.49
#7
11.5
3.81
#8
12.0
3.89
#9
12.7
#10
3.10
2.82
4.32
0.99
0.53
132
6.96
1.20
0.56
131
6.25
1.31
0.54
130
6.21
0.88
0.62
135
8.67
1.39
0.54
129
8.41
1.19
0.44
121
4.07
10.7
1.31
0.65
132
13.l
4.16
12.l
1.44
0.58
129
#11
14.1
4.20
2.50
18.5
0.90
0.55
130
#12
15.5
4.17
2.94
31.8
0.63
0.28
126
#13
16.1
4.80
18.6
1.38
0.65
126
#14
16.9
4.33
27.3
1.00
0.40
124
#15
17.0
4.70
3.25
42.4
0.98
0.32
123
#16
17.5
4.47
3.87
1.23
2.31
21.4
0.86
0.40
118
#17
17.7
5.05
4.30
1.02
2.43
30.6
1.36
0.53
121
#18
18.5
5.25
0.52
119
#19
19.9
4.96
#20
20.5
5.26
4.65
#21
21.1
5.22
4.70
#22
21.5
5.49
#23
21.6
#24
21.7
5.71
5.55
1.69
#25
22.l
5.75
5.14
#26
22.8
5.30
#27
23.l
6.00
#28
24.0
6.07
#29
28.1
6.80
#30
28.2
6.48
2.85
3.28
3.72
0.48
1.43
0.56
1.69
1.73
0.58
0.94
26.7
2.95
77.2
0.87
0.14
107
1.10
2.44
41.1
1.33
0.54
122
1.25
2.17
42.2
1.24
0.23
104
3.03
87.4
1.13
0.10
102
48.7
1.28
0.19
101
3.18
74.9
1.03
0.50
102
1.06
2.51
40.6
1.89
0.65
118
4.42
1.26
2.55
38.1
1.10
0.22
102
4.91
0.91
2.51
45.0
1.53
0.15
97
1.02
2.88
56.6
1.32
0.32
111
6.37
1.46
3.00
98.6
1.75
0.37
106
5.89
1.48
3.00
85.9
1.21
0.25
103
103
5.1.2
On the basis of considerable consultation with
various designers, builders and experts, a proposal
was prepared and forwarded to Working Group 22,
consisting of minimum criteria for vanishing angle
of positive stability, for each of the four stability
categories, as follows:
Proposals for Minimum Value of the
Vanishing Angle
In Paragraph 5. l.l a summary is presented of the
work that was carried out using the 115 sets of
rigorous stability data to derive a meaningful trend
for the value of the vanishing angle of positive
stability with vessel particulars. An account is there
presented of how a sufficiently useful demarkation
between the casualty data and the "good" category I
data can be obtained, using only the mass of the
vessel. This is an important result since the mass of
a sailing vessel is always available or easily determined.
$v > 130 - 0.750A.,,, for A.,, < 40 (category I)
$v > 120 - 0.625A.,,, for A.,, < 40 (category II)
$v > 110 - 0.500A.,,, for A.,, < 30 (category III)
Here, the results of Paragraph 5 .1.1 are further
elaborated to derive a set of proposed criteria for
vanishing angle of positive stability for the different
stability categories.
$v > 95, for all A.,,
(category IV)
$v > 100, for 11m > 40
(category I)
$v > 95, for 11m > 40
(category II)
$v > 95, for 11m > 30
(category III)
• "goc>cP: calegory I ......
- .....- - .......-- -·' -- - - - --- -~ -- .... -- .... -*-~~ -~:-
.....
140
"":.
I
I
......
100
I
I
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-.. ---.. . _: _-.. . ---.. . ~ -.+. . --~ :- -~-. . . . ._.. ._. ---.. -_:_ . --·- ---*.~ -.. --.. . -..:.. --.. --.. . -~' ---..
I
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.
-. -... -_: _-. --+ ±:.+ .. ±· - ~. - - - .. - .-::::--....... - .. - ; . - - - .... -~- - . - - .. - . ~ - - . .:•
. . .:'........ . .:
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.:
.: +.:
:
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......
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110
--.. --._:_. ---.-.-~ --..
:
:
:
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;. . . . . -l- • :
--.. . --.. _: . -.. -~ _. . _ . . -'" -.. ~ +1 . -~ -~ --.-.. --:. . -.. . ----:-.. --.. . -.. .:-.. . ------:--.......
130
120
'
I
I
I
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I
I
I
I
......
.....
......
•
IO
. --.. . --·: ·. ---.. . -·:· . ---.. . --·: . ---.. . --·:· --.. --.. . . . . . -.. . --.. .:. -.. -.. . ·+: --.. -
IO
- - - - • - - -, • • - - - • - - - r - - - • • - - - ... - - - ... - - - - - ,- - • - ... - • - -
70
-.. . -.. --·:.. . . --.. . -.. . .. . . --..+ .. . . -.. . ---:.- -.+. . . --.. . :.-.. -.. -.. ---:.- --------' . --
I
I
I
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T - - - • - - - .... , - .. - - "' .. - • ..
r "' • "' -
I
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eo
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f
I
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++
L iA(m)'
_~~
..._~...._~_._~_._~___.~~---~...._~~~__.
IO.__~...._~~~__._~__.~~..._~.
0
4
8
12
18
20
28
Figure 1. Plot of the angle of vanishing positive stability against overall length for stability-oriented
casualties (pluses) and "good" category I vessels (squares) - (93-020-1.chJ/hpp).
104
In which:
cl>v
~
5.1.1, was used as the boundary between stability
category I and II. This is a well-defined boundary.
The boundaries between categories II and III, and
between Ill and IV, are less well-defined. These
boundaries are based, in part, on information provided by designers, builders and other experts concerning the category of various well-known yachts of
which the stability particulars were available. For
example, different experts considered that the J24,
at best, is a category III yacht.
Angle of vanishing I ositive stability in degrees;
Mass of sailing vess1 :I in tons of I 000 kg,
in the minimum saili1 tg condition.
The minimum angle of vanist ing stability according
to this proposal is shown in Figure 3.
It should be noted that the v 1lue of cl>v is the rigo-
rous value, including deck c< mber, cockpits, masts
and deck houses. Extruded, i.e. non-solid masts are
not to be considered as wate1 tight as this is hardly
ever the case. The specific ( ffect of deck camber,
cockpits, masts and deck hou ;es on cl>v is discussed
in Paragraph 5 .1.3.
During the meetings of Working Group 22 in which
the above proposal was discussed, a suggestion was
made to reduce these minimum criteria to account
for the case that a vessel possesses a relatively low
stability in the inverted position. It was proposed to
adopt an expression based on the value for the
vanishing angle as given in the above formulae but
corrected for the value of GM in the inverted position, in the form:
The demarkation between "gc od" category I sailing
craft and casualty data, as p1 esented in Paragraph
140 . - - - - - - - - - - - - - - - . . . . . - - - - - - - - - - - - - - - - - - - -....
• "aoocr cataaory I Wlllall
+
130
~lly~
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'.
+" . . - ---: •-t
120
''
:rl"
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:
:
:
:
~~. i - - . - -~ . . . . - - - ~. - - - - .. ~ . . . . . - . -:- - - - - - - - ~ - - . - - - - ~ - - - - - - - -:- . - '
'
'
'
'
'
'
'
+.. - ..'". - ..... ,. - . - . - ..... - - - . - . - . - - - ...,... - ....•... - ....... - - - - ., - - -
110
'I
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- . - ......
- . - .'. ""·:...... - - ...
- .... -:- - - . - - - . ' - .. - . - . - '..... - - . -' - . - - - . - ....
-
100
+:
:
:
:
:
:
"1>v(degr.):
- . - ... , - . - . - . - -·- .... - . - • - - ..... , .. - - .. - -·-. - - . - . - ·- .. - - - - - , . - - - - - - -·- - :+
I
IO
I
~.
:~---~----~----~----~----~----~-I
I
I
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80
- - - - - - - - ...... -·· - - - - - - - ...... - - - - - - - - . - -·- . - - . - . - .... - - - ... - - . - - - .. - - - -
70
. -+· . ;- . -.. -.. . ":" . --.. ---;:+----.. . . . -.. --.. -·:· --.. -.. . . ;. . . . -.. . .............. ·:· . . .
I
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+
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~ ... - - - - - - JI ............ - - -·- - - - - - - ·- - - - - - - ~ - - - - - - - .. • .. - .. I
I
+:·
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:+
,
I0,__.._.._.._..__..__..__..._.__1.__.__.__.__1.__.__.__.__1.__.__.__.__1.__.__ .__.__1.__.__.__.__1.__..__..__..__1___.
0
20
40
IO
80
100
120
140
180
Figure 2. Plot of the angle of vanishing positive stability against displacement mass. Here, a welldefined demarkation exist 1 between the casualties and the "good" category I vessels (93-0202.ch3/hpp).
105
~v > ~vrarmula
A study of this concept revealed that for most vessels, the numerical value of GM 180 is difficult to determine from existing GZ curves because of the
rapid rate of change of GZ near a heel angle of 180
degrees. Also, when the inverted vessel is rolling
through a heel angle of up to 30 degrees or so in
waves, the use of the minimum value of GZ, i.e.
the minimum lever in the negative stability part of
the GZ curve, is often more meaningful than the
use of GM 180. The value of GZmin is easily determined from a GZ curve based on calculations at,
say, 5 degree intervals, whereas the determination
of GM 180 requires calculations at 1 degree intervals
from, say, 17 5 to 180 degrees of heel.
c/GM1so
-
In which:
Angle of vanishing positive stability;
Required value of the angle of
vanishing positive stability according to the initial proposal;
A constant to be determined;
Metacentric height of the intact
hull in the inverted position (at a
heel angle of 180 degrees).
~Vformula
This proposal is based on the fact that recovery
from an inversion (which is the hazard that is addressed here), is dependent on the degree of stability in the inverted position, for example, as depicted by the value of GM 180 •
130
I
•
... •
-
-
- •
J I
-
-
-
-
- J ... -
.......
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- - .. -
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.......... J - .... - - - J - - - ... - - -· ... - - - - .. -· - - .. - - .. -· - -
- ...... - • - - - - - - I
•
I
•
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I
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I.
- - .!! - 1
• •gobd" cat8g'ary I V8IMll
+ 81alt111ty cuUnlee
:
:
.-t-~ :
GZmin nearly always varies from 0 to -1 meter. The
following table lists some typical values for some
well-known yachts:
'
120
'
'
'
'
••••
_!_
- - - ..... i - ........ - - -. - - - - - .. -. - - - - - - -. - - ... - .. - -.- - - - - .. -.- - - - - -
110
..
.I
-
........
-
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'
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Stabll.,~1
:
:"
:
:•
. ..
-
-
-
..
-
... -
-
-
-
.........
-
..
. ..
•
'!! - .......... - .. - -· - - - .. - ......... - - - - -•- - ...........
'
'
100
'
"'1"'
:
:
•:
•
•
'
IO
IO
-
-
.... - 1 .. I
-
-
-
-
.I I
-
-
-
-
- J I
- - - - -
-· .. - - - - - -· .. - - .... - -· - - - - - - -· - ........... -·- I
I
I
I
I
- - - .... • ........... - I
+
-----:+·---:------:--.. . . . :·. . . . . ·: ·-----·:- -.. -.. . ·: ·. ----·:· . . . . . ·:· -----
70
..............._.........
I
I
I +
,
,
I
I
I
I
I
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I
I
I
I
I
I
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,
,
.
·(IDnne) ,
,
,
...................._._........._,__........._,__..........................................................................................................._._......._._...._._._...._.~
100
IO
IO
IO
IO
70
40
....._~...........~...........~
o
10
2G
Figure 3. Initial proposal forwarded to Working Group 22 for the minimum value of the angle of
vanishing positive stability as a function of displacement mass, for stability categories I through IV
(93-020-4.ch3/hpp).
106
Yacht name
Swan 55
Oyster 68
Auklet 9
Trekker 42
Contessa 32
Moody 346
Moody 44
CNB 23
Dufour 48
Taka
124
Sigma 33 OOD
Oyster 55
Fastnet 1/2 ton
Jongert 2200
Jongert 21S
of this type.
GZminJm.l
-0.22
-0.39
-0.34
-0.08
-0.12
-0.25
-0.32
-0.81
-0.50
-0.30
-0.50
-0.40
-0.37
-0.87
-0.65
-0.44
5.1.3
Effect of Deck Camber, Cockpit and
Deck Houses on the Angle of Vanishing
Stability
The work carried out to investigate the effect of
deck camber, cockpit and deck houses on the righting moment reveals that it is essential to include
these effects in the calculation of GZ. The impact
thereof is significant. The value of the angle of
vanishing positive stability generally increases when
these factors are taken into account. Together with
ORC and US Sailing, a systematic study was carried out comprising the calculation of the righting
moment curves for the following cases:
Case A: Comprised a calculation of the righting
moment curve for 4 different types of mono-hull
sailing yachts with a flat deck (similar to the calculations carried out to determine LPS as given on
IMS rating certificates). For each of these 4 types
of yachts the following additional variations were
studied;
It is important to note that "1 'aka" (one of the con-
sidered casualties) has a GZm" of -0.3 meter. Since
this yacht remained inverted for about 1 hour in
high waves, It is appropriate to not adopt a credit
for values of GZmin less thar about -0.3, but only
for values greater than -0.3, i.e. closer to 0. Accordingly, a proposal was fc rwarded to Working
Group 22 to only modify the original formulae
when GZmin > -0.3. The form1 la proposed was:
Case B: Deck camber equal to 7.5% of local beam.
This was found to increase <l>v by between 3 and 8
degrees, depending on the type of vessel;
<l>v > <l>vronnula - 4 / [O.l+i'.BS(GZmin)] + 10
Case C: Deck camber equal to 15% of local beam.
This was found to increase <l>v by between 7 and 21
degrees, depending on the type of vessel;
which is only to be applied w lien GZmin > -0.3.
In this formula, ABS indic: 1tes that the absolute
value of the relative expres. :ion (GZm;n) is to be
taken.
Case E: A small deck house with a width equal to
40% of local beam, with a horizontal roof, a height
of 15% of maximum beam at the location of lowest
freeboard on the sheerline. and a length equal to
50% of hull length. This was found to increase <l>v
by between 2 and 9 degrees depending on the type
of vessel;
The result of this formula is t iat when GZmin = -0.3,
the required value of the angl ~ of vanishing positive
stability remains unchanged. When GZmin = -0.2,
the required value of the angl ~ of vanishing positive
stability is decreased by 3. l degrees, and when
GZmin = -0.1, the decrease is 0 degrees.
Case F: A moderate deck house with a width equal
to 70% of local beam, with a horizontal roof. a
height of 15% of maximum beam at the location of
lowest freeboard on the sheerline. and a length
equal to 50% of hull length. This was found to
increase <l>v by between 6 and 13 degrees depending
on the type of vessel;
It should be noted that if sm :h a proposal is adop-
ted, the GZ requirement at 9) degrees of heel (see
Paragraph 5.2) becomes even more important than it
already is. This is because i vessel with a small
negative GZmin value will si 1metimes also have a
small value of GZmax and, h~ nee, a small value for
GZ 90 • In such a case, consic .erable credit is given
for good recoverability from an inversion (in terms
of allowing the vessel to have a smaller value of
the angle of vanishing positive stability) while the
ability to withstand a knock-c own in the first place,
is extremely low. Yacht D, h Figure 4, is a vessel
Case G: A large deck house with a width equal to
100% of local beam. with a horizontal roof. a
height of 15% of maximum beam at the location of
lowest freeboard on the sheerline, and a length
equal to 50% of hull length. This was found to
increase <l>v by between 8 and 15 degrees depending
107
(lowest) freeboard, and a length of 20% of hull
length. This was found to reduce ~v by between I
and 3 degrees depending on the type of vessel;
on the type of vessel;
Case K: A large cockpit with a width equal to
87.5% of local beam, a depth equal to 62.5% of the
(lowest) freeboard, and a length of 20% of hull
length. This was found to reduce ~v by between 2
and 5 degrees depending on the type of vessel;
Case J: A small cockpit with a width equal to
52.5% of local beam, a depth equal to 37.5% of the
(lowest) freeboard, and a length of 20% of hull
length. This was found to reduce ~v by between 0
and 2 degrees depending on the type of vessel.
Case I: A moderate cockpit with a width equal to
70% of local beam, a depth equal to 50% of the
.
.
:
~7--:for
.~--SO·
.....- .
••
L
A
'
• • • • • • • 1• • • • • • • • 1 •
.,
•
., . . . . . .
-' . . . . . . . . . . . . ..
A
- - .... - -
- - - - ·- - - - .... - -·- - - - - - - J ...... - - - -
;B_ - .... -- .. ------ .. --- ........... ------- .. ----I
I
I
I
I
I
.
.
I
I
c
: GZmlnfor
·:·: - .... - - .. ---- .. -
~
Vanls~ing p~sltlve ~Hity tor·c -· ~ -··· · -·:
·0.5
;:·:·
·
•1'----'---''---'---'~-'----'-~...L......:::....J....-=--.i......=--'---=..&~-'---'-~.....__--........F----'-----'
0
20
40
100
120
140
180
180
Figure 4. Righting arm (GZ) curves for 4 yachts. Curve A is for the Contessa 32, while curves B, C
and D are for hypothetical sailing craft. Yacht A is an ideal yacht from a transverse stability point
of view. It possesses a high resistance against knock-down (i.e. a high value for GZ 90) and low stability in the inverted condition (a small negative value for GZmin and a high value for the angle of
vanishing positive stability). Yacht B has a high resistance against knock-down (a high value for
GZ90 ) and high stability in the inverted condition (i.e. a large negative value for GZmin and a
moderate value for the angle of vanishing positive stability). Yacht C is a bad yacht from a stability
point of view. It possesses a low resistance against knock-down (a low value for GZ90) and high
stability in the inverted condition (a large negative value for GZmin and a low value for the angle of
vanishing positive stability). Yacht D also possesses undesirable stability characteristics. Although it
possesses low stability in the inverted condition (a low negative value for GZmin and a moderate
value for the angle of vanishing positive stability), it will be easily knocked down - (93-0206.hpp/ch3).
108
5.2 Minimum Value of the Righting Moment at
90 Degrees of Heel
5.2.1
Differentiation Bel ween
"Good" Vessel Dab.
Casualty
defined line can be drawn to distinguish between
the casualties and the "good" category I sailing
craft. Accordingly, it was decided to develop a
proposal for the minimum value of the righting
moment at 90 degrees of heel based on the results
of Figure 5.
and
The value of the righting levc r at 90 degrees of heel
(GZ90 ) was studied in a sh 1ilar way as was the
angle of vanishing stability. Here, a plot of the
righting lever against length or displacement was
found not to provide a mear ingful relationship, as
only a "cloud" of points ei ·olved. A plot of the
actual righting moment at 90 degrees of heel however is seen to result in a ' ery meaningful trend.
Figure 5 gives this plot of the value of the righting
moment against overall Ieng th. This righting moment is calculated from ~.C iZ90 , where ~ is the
mass of displacement in the minimum sailing condition, in tons of 1000 kg. J. .gain a relatively well-
5.2.2
Proposals for the Righting Moment at 90
Degrees of Heel
In Paragraph 5.2.1 a summary is presented of the
work that was carried out using the 115 sets of
rigorous stability data to derive a meaningful trend
for the righting moment at 90 degrees of heel with
vessel particulars. An account is there presented of
how it was possible to define a sufficiently useful
demarkation between the casualty data and the
"good" category I data, using only the overall
length of the vessel.
• "goacP catego y I vaaell:
_______
+ 8t8blllly ~-
___,
•
.... -- - .. --- - ~ - .... - .... --- .... ·- -- -- ..... -.... --·- .. -.... -. -- ...... •............... -----·- ............ -... --
21
I
I
I
I
I
••
IO
- ............ - ......
p
...
-
................ -
p
-
........... -
-
......
~
...... -
.... -
.
................
...
-
............. , ................
•
+
•
11
•
-
-
-
-
•
.. - - ........ - - - ~ ...... - - - .......... :- - - ........ - - ...... :- ...... - .... - ...... -:- .......... - - ...... -:- ................ - -
:
I
10
I
I
I
••
•
. ••
•
~
...... - - - ........ ~ - ........ - - ........ ~ - - .................. ~ .............. - .... -:- ... -.- .......... - .. :· .................. ..
•
I
•
••
I
f
::- •
..:---+
+ .+ ----+:
..!--f+'
" :-=F°
.
..... I
_
__.
!-- ·
I
......... - - ........ i ....... - - ...........- - .. -.- ...... - - .... .......... - : ·..:;.
I
•
:
·-
-~ ... .........
-
- - - - - - ... I,.. - .......... - - - -
LQA(m)
oi.--.....:=-_.___,__.___._" "'Ffs::..i...--'-_..__.__,.__, __..__.__.....__.__.__.__._ __,___.__,.__,__..__.__... __..___._.....
0
I
10
11
20
21
•
Figure 5. A plot of the r ghting moment (in ton.m) against overall length for the same vessels
considered in Figures 1, 2 and 3. Here, also, a well-defined line can be drawn, differentiating between the casualties and
th,~
"good" category I vessels (93-020-3.ch3/hpp).
109
On the basis of considerable consultation with
various designers, builders and experts, a proposal
was prepared and forwarded to Working Group 22
for the righting moment at 90 degrees of heel, for
each of the four stability categories. The required
demarkation between category I and II was again
deduced from the boundary between the casualty
data and the category I vessels. The demarkation
between categories II and III, and between III and
IV was again based on the opinion of various designers and builders about the category of specific
vessels.
RM90
=
gi\i.GZ90 > 3.50+1.5(Lhun-7) (category III)
(category IV)
When Lhun is less than 7 meter:
(category I)
(category II)
(category III)
(category IV)
In analytical form it was proposed that when Lhull is
greater than 7 meter:
RM90
=
gi\i.GZ90 > 10.5+4.5(Lhun-7) (category I)
RM90
=
gi\i.GZ90 > 7.00+3.0(Lhun-7) (category II)
In these expressions:
Righting moment in kNewton.m at
90 degrees of heel;
Acceleration due to gravity;
g
• "good• oatagory I vwel.:
lltablllly ~
+
•
•
.......... .- ........... .- ........... .- ....... ... .- ..
I
11
I
I
I
~
.
.GZ90 ~m)
.
I
~
~-
i ... .
.•
.
"!
•
.••
.
-- - .............. " -- -- .......... -- --- .... -.... _._ ..... --- ................. ._ .......... -.. - ...... .·- ---
10
.
\.
••
.
I
.................... r .....................
0
I
.
-~
•
••
.
....................
10
..
"'t"'
11
ID
21
Figure 6. Initial proposal forwarded to Working Group 22 for the minimum value of the righting
moment at 90 degrees of heel as a function of over-all length, for stability categories I through IV
(93-020-S.ch3/h pp).
110
Lhun
Displacement mass of vessel in
minimum sailing condition, m
tons;
Length of h 111 as defined in ISO
8666.
(category IV)
5.3 Minimum Value of the Area Under the Righting Moment Curve
5.3.1
Graphs according to these ex11ressions are shown in
Fig. 6, in which the rightin~ moment is given in
ton.m, not in kNewton.m. 1'"ote again that the 3
casualties referred to in Paragraph 5.1.1 (number 5,
8 and 14 of Table 2) are again situated above the
lines depicting the boundary >etween stability categories I and II.
Some mono-hull sailing craft have little or no ballast in the keel or in the hull. These vessels depend
almost entirely on hull form for stability. Accordingly, they usually posses an insufficient range of
positive stability. When knocked down by wind or
waves to an angle of heel near 90 degrees, they are
usually unable to recover. In this respect, this class
of vessel is similar to multi-hulls, which also have a
restricted range of positive stability. In order for
these vessels to attain stability categories I and II,
ISO 12217-2 will require that such vessels have
sufficient buoyancy when swamped or inverted, so
that they do not sink.
Subsequent validation studies carried out in Japan
and England revealed that f< 1r small boats with a
length of hull less than 7 m, the required righting
moment at 90 degrees of bet I, as specified by the
above formulae, is too harsh For a typical MiniTransat design with Lhun = 6.0 J meter, at a displacement mass of 1.5 ton, . these: formulae lead to a
required GZ 90 value of 0.61 ! meter (for stability
category I), where actual values are closer to 0.3
meter. (It can be argued hm fever that such small
boats should not be crossing oceans at all.) Further
study revealed that, if an ab! olute minimum value
of the righting moment is to be imposed, this
should be done for lengths of 6 m and less, not for
7 m and less.
During early discussions in Working Group 22, a
majority of the members were of the opinion that
the only requirement these vessels need to adhere
to, in addition to the buoyancy requirement mentioned above and the general requirements mentioned in Paragraph 2, is a specific area under the
righting moment curve up to the heel angle at
which the maximum righting moment occurs, to
ensure that these vessels have sufficient stability to
withstand a sufficiently high wind strength. Such a
criterium is often referred to as the "heeling energy
required to capsize". Since many traditional Dutch
sailing barges (in Dutch referred to as "rond- en
platbodem jachten) fall into tpis category, the stability study in the Netherlands also included a study
of this minimum area under the righting moment
curve for this class of sailirig vessel.
At the same time, an indept ndent working group
consisting of Netherlands-base l naval architects and
yacht designers carried out i 1 validation study revealed similar results. On rn :onsidering all of the
available data it was decided to prepare a new proposal, utilizing a quadratic fr nction of hull length.
This led to the following final proposal:
For Lhull greater than 6 meter:
RM9o=gA,,,.GZ90 > 0.3125(Lhun>2
-
7.25 (category I)
RM90=gA,,,.GZ90 > 0.2083(Lhun> 2
-
4.83 (category II)
RM90=gA,,,.GZ90 > 0.1042(Lhun '2
-
2.42 (category III)
Reasons for Requiring a Minimum Value
of the Area Under the Righting Moment
Curve
5.3.2
Proposals for the Area Under the Righting Moment Curve
To derive criteria for mono-hulls, a detailed list of
stability particulars for Dutch sailing barges and
similar sailing vessels with little or no ballast and
with a good track record with respect to stability,
was collected. On plotting the area under the righting moment curve up to the heel angle at which
the maximum righting moment occurs, a well-defined relationship with displacement weight was
obtained. For vessels sailing on the IJsselmeer for
example (which need to comply with the requirements of stability category III) according to the
(category IV)
When Lhun is less than 6 mete1 :
(category I)
(category II)
(category III)
111
prevailing wave height and wind speed), all of the
points for the different vessels considered are positioned above a curve with the following formula:
6.
6.1.
DEVELOPMENT OF SINGLE STABILITY
INDEX
Introduction
A1oGZmax = gl\,,(12.9 - 0.0 l 7g<'.lm)
Late in 1995 and early in 1996 it became apparent
to all members of Working Group 22 that unanimous agreement on the required minimum values
for each of the important stability parameters, as
given in the preceding paragraphs, was unattainable.
Where one country, for example, wanted a moderate minimum value of the angle of vanishing stability and a high minimum value of the downflooding angle, another country wanted a relative high
minimum value of the angle of vanishing stability
and a moderate minimum value of the downflooding angle. It was then decided to appoint a small
group of experts to study and, if possible, develop a
system in which a high value of one parameter
could be traded-off against a low value of another
parameter, wherever possible. This group worked
through the summer of 1996, resulting in the concept of a single STability Index (STIX). At the
meeting of WG 22 in Paris on 9 September 1996, it
was unanimously decided to adopt this STIX concept for the assessment and categorization of the
intact stability and buoyancy of mono-hull sailing
craft with a (hull) length between 6 and 24 m. The
sub-working group was composed of the French,
Netherlands, Swedish and UK delegates to WG 22.
This method will form the basis of ISO 12217-2 for
mono-hulls. Use of this method resulted in the
correct stability categorization of every yacht and
sailing vessel selected from the data bases provided
by France, The Netherlands, Sweden and the UK.
No other method devised by WG 22 in the past
gave such good results.
In this formula gl\,, is the weight of the vessel in
kNewton, in the minimum sailing condition.
For displacement values greater than 40 tons, no
further reduction in the area under the GZ curve
with increasing displacement (the part of the expression in brackets) is noticeable. On using the
same differences in righting moment requirements
between the various stability categories as for ballasted mono-hulls, it was possible to develop the
following proposed requirements:
For L\,, < 40 tons:
A1oozmax > gl\,,(38.6 - 0.05lg<'.lJ (category I)
A1o GZmax > gl\,,(25.7 - 0.034g<'.lm) (category II)
A1o GZmax > gl\,,(12.9 - 0.017g<'.lm) (category III)
A1o GZmax > gl\,,( 6.4 - 0.008g<'.lm) (category IV)
For L\,, > 40 tons:
Ato GZmax > l 8.2gl\,,
(stability category I)
Alo GZmax > 12 .1 gl\,,
(stability category II)
(stability category III)
(stability category IV)
On applying these values to ballasted mono-hulls
such as the J24, usually the same stability category
is assigned as would be assigned using Paragraph
5 .1.2. The following example illustrates this.
6.2.
The Factors Involved
The following factors were defined for incorporation into the calculation of the STIX value:
The J24 has a value for <l>v of about 115 degrees
and when using Paragraph 5.1.2 is assigned stability
category III according to the proposed criteria. The
value for gllm is about 16. 7 kN and the area under
the positive part of the righting moment curve, up
to the heel angle where the maximum righting moment occurs, is approximately equal to 224
kN.m.deg. According to the above formulae, the
minimum requirement for category III is equal to
gl\,,(12.9 - 0.017 x 16.7) which equals 210.7
kN.m.deg. Hence, here also, stability category III is
assigned.
Base Size Factor (FBS). The Base Size Factor is
based on length. The size of a vessel is considered
as the single most important factor in resisting the
excitation forces on a vessel;
Area under the righting moment curve or Righting
Energy Factor (FRE). This factor is particularly
important for vessels with mainly form stability. It
is based on the area under the righting moment
curve up to the angle of vanishing stability or the
downflooding angle in the case the downflooding
angle is less than 90 degrees and less than the angle
112
thus determined (conservative) value is insufficient
to obtain the wanted stability category, it is necessary to carry out the full set of calculations however, requiring the actual GZ curve as a function of
heel angle, at least up to the angle of vanishing
stability, or 90 degrees, whichever is greatest.
of vanishing stability;
Inversion Recovery Factor (FIR). This factor accounts for the recoverability "rom an inversion and
is based on the value of the ''anishing angle, or the
downflooding angle in the case the downflooding
angle is less than 90 degrees ;md less than the angle
of vanishing stability;
In all, 7 factors need to be evaluated when the
downflooding angle is greater than 90 degrees, and
8 factors need to be evaluated when the downflooding angle is less than 90 degrees.
Knock-Down Recovery Fact< 1r (FKR). This factor
accounts for the recoverabilit:, after a knock-down.
Rather than base this factor )n a righting moment
or a righting arm (GZ) value at 90 degrees alone, it
was decided to base this fact >r on the value of the
righting moment at 90 degrees, divided by the area
of the sailplan times a lever. The resulting value is
indicative of the ability of f vessel to spill water
out of the sails after being ( otally) knocked down
to about 90 degrees of heel;
6.3 Downflooding Openings
In the calculation of some of the factors described
above, the value of the downflooding angle plays
an important role, particularly in the case the downflooding angle is less than 90 degrees. This
downflooding angle is the heel angle at which a
critical amount of water downfloods into the nonselfdraining part of the vessel. The combined crosssectional area of openings causing critical downflooding (after a knock-down for example), is considered to be greater than that defined in ISO
12217-2 in the context of determining the minimum
Specifically, downflooding through
freeboard.
hatches and companion ways are the causes of
dangerous downflooding during a typical knockdown. Accordingly, it was agreed that openings
with a cross-sectional area of 0.18 m 2 or greater
constitute openings for the calculation of the downflooding angle (not the downflooding height) in the
context of the calculation of the STIX value. In the
calculation of the downflooding angle for the evaluation of the various factors as described in Paragraph 6.4 below, the above definition of downflooding openings is utilized.
Displacement Length Factor 1 FDL). Since the Base
Size Factor is based on lengt 1 only, it is necessary
to include a factor which ace· mnts for the displacement since a heavy yacht fo1 a given length has a
greater resistance to being kn• •eked down;
Beam-Displacement Factor ( ~BD). This factor accounts for the beam and the degree of top-sides
flare (i.e. the ratio between 3hull and BwL). This is
considered necessary since ;1 vessel with a large
value of BhuufBwL• when l roadside to breaking
waves, experiences a greater 1 langer;
Wind Moment Factor (FWM) In the case of vessels
with a downflooding angle le: :s than 90 degrees it is
necessary to determine the w nd speed at which the
vessel attains a heel angle equal to that of the
downflooding angle (without reefing the sails). If
such a heel angle occurs at 1JW values of the wind
speed, the vessel is at great1 :r risk than when this
occurs at high wind speeds;
6.4 Formulation of the Individual Factors
The formulae involved in the evaluation of each of
these factors are as follows:
Downflooding Angle Factor (FDF). The danger of
downflooding is largely dep~ ndent on the value of
the downflooding angle.
6.4.1
Base Size Factor (FBS)
This factor is based on a weighted average of the
length of the vessel, as follows:
For some of the above factor; an approximate value
or expression is being de• 'eloped which allows
approximate and conservativ1: evaluation thereof in
those cases the detailed riE hting moment or GZ
curve is not available. Accodingly, it is possible to
determine a conservative vah e of the stability index
without any difficulty (i.e. w thout actually carrying
Liis
= (2LwL
+ ~un)/3
where:
Base size length;
on the waterline
in the
out a calculation of the rig 1ting lever GZ - as a
Length
function of heel angle). Wh :n it is found that the
minimum sailing condition in m;
113
Length of hull as defined in ISO
8666 in m.
bility in degrees;
Downflooding angle in degrees;
Base value of the angle of vanishing stability in degrees. This is
the minimum value of <l>v considered desirable for stability category
I.
<l>o
<l>v(base)
The Base Size Factor is defined as:
FBS = 3Les = (2LwL + Lhu11)
6.4.2
Righting Energy Factor (FRE)
The formula for <l>v(base) is:
This factor is defined as:
<l>v(base) = 125 -
0.625~
< 40)
40)
in which Am is the displacement in tons, in the minimum sailing condition.
The minimum and maximum values of FIR that
may be adopted in the calculation of the STIX
value, are 0.5 and 1.5 respectively.
6.4.4
Knock-Down Recovery Factor (FKR)
This factor is defined as:
If FR> 1.5:
The base value of the area under the righting
moment curve is:
FKR = 0.875 + 0.125F R/FR(base)
If FR < 1.5:
when Am< 40
The knock-down recovery coefficient FR is defined
as:
and when Am > 40
ERM(base) = 250~
In which ~ is the displacement in tons, in the
minimum sailing condition.
and the base value of the knock-down recovery
coefficient FR(base)> considered as the minimum value
of FR desirable for stability category I, is equal to
1.5. It follows that:
The minimum and maximum values of FRE that
may be adopted in calculating the final STIX value,
are 0.5 and 1.5 respectively.
6.4.3
~
(for~>
<l>v(base) = 95
where ERM is the area under the righting moment
curve in kN.m.deg, up to the angle of vanishing
stability if the downflooding angle is equal or greater than 90 degrees or when the downflooding angle
is greater than the angle of vanishing stability. If
the downflooding angle is less than 90 degrees and
also less than the vanishing angle, the area under
the righting moment curve up to the downflooding
angle is taken. ~(base) is the base value of the area
under the righting moment curve in kN .m.deg. This
is the minimum value for ERM considered desirable
for stability category I.
(for
0.875 + 0.0833FR
If FR> 1.5:
FKR
If FR< 1.5:
FKR = 0.5 + 0.333F R
=
Inversion Recovery Factor (FIR)
This factor is defined as follows:
Here:
When <l>o > 90 degrees or when <l>o > <l>v:
Righting moment in N .m at 90
degrees of heel for the minimum
sailing displacement condition;
Projected profile area of all sails
that may be set at one time when
sailing to windward, as defined in
ISO 8666, in m 2 ;
Distance between the centre of
buoyancy and the top of the sail
plan, for a heel angle of 90 de-
and if <l>o < 90 degrees, when <l>o < <l>v:
FIR = <l>J<l>v(base)
where:
<l>v
Angle of vanishing (positive) sta-
114
grees, i.e.
hs
=
Else:
HBI + (I+P+BA ~)/2 - VCG - GZ 90
FBD
Height of I >ase of I above the
water surfact in m at zero heel;
Vertical hois: of genoa or jib in m;
Height of be om above sheerline in
m at zero he :I;
Hoist of mainsail above boom in
m;
Height of vertical centre of gravity
above water! ne in m at zero heel;
Righting le' er at 90 degrees of
heel in m.
I
BAS
p
VCG
l .25BwdBhun
Where:
where:
HBI
=
Maximum beam of hull according
to ISO 8666 in m;
Maximum beam of hull on the
waterline in m;
Displacement of vessel in minimum sailing condition, in tons.
The minimum and maximum values of FBD that
may be adopted in the calculation of the STIX
value, are 0.75 and 1.25, respectively.
6.4. 7
Wind Moment Factor (FWM)
If the downflooding angle is less than 90 degrees
the Wind Moment Factor must be calculated. When
the downflooding angle is equal or greater than 90
degrees, the value of this factor is 1.0 and FWM
does not need to be calculated.
In the case of vessels with 1nore then I mast, the
weighted average of the value of hs for each mast is
to be used. For 2 masts this h :
The Wind Moment factor is defined as:
Here, also, the minimum anc maximum values for
FKR that may be adopted in the calculation of the
STIX value, are 0.5 and 1.5, 1espectively.
6.4.5
FWM
=
0.6 + 15000L\,.F J :Las3 (333 - 8Les))
where
Minimum
sailing displacement
mass in tons;
Base size ler gth in m.
FWM
=
VAw/17
The value of VAW is to be calculated from:
The mm1mum and maximum values for FDL that
mat be adopted in the cal~ :ulation of the STIX
value, are 0.75 and 1.25, resp•:ctively.
6.4.6
VAWNAW(base)
in which V Aw is the steady apparent wind speed in
m/sec required to heel the vessel to the downflooding angle ~ 0 when carrying the full sail plan (i.e.
without reefing) when sailing to windward. The
value of VAW(bas•> is the base value of VAW• i.e. the
minimum value for VAW• considered desirable for
stability category I. This value is 17 m/sec. It follows that:
Displacement Lengtl 1 Factor (FDL)
This factor is defined as:
FDL
=
VAw
=
(13000L\,.GZ0 /(A 5 P.lever(cos(~ 0)) 13 ))05
where:
Beam-Displacement Factor (FBD)
The FBD factor is defined as:
If Fe > 2.20 then:
If Fe< 1.45 then:
lever
115
Displacement of vessel in minimum sailing condition, in tons;
Righting lever in m at a heel angle
equal to the downflooding angle;
Projected (unreefed) profile area of
all sails that may be set at one
time when sailing to windward, as
defined in ISO 8666, in m 2 ;
Vertical distance between the geometric centres of the above-water
and below-water profiles of the
vessel, including sails, masts and
hull, with centerboards, daggerboards and leeboards in the lowered position, when the vessel is
upright;
Downflooding angle.
<l>o
The minimum and maximum values for FWM that
may be adopted in the calculation of the STIX
value, are 0.5 and 1.0 respectively.
Stability category IV:
STIX
=
5 to 14;
Stability category III:
STIX
=
14 or higher.
The total volume of non, selfdrainable recesses is
moderate or large when the factor k defined below
is greater than 0.025, viz:
Downflooding Factor (FDF)
6.4.8
if the value of the resulting value of STIX is sufficiently great. In that case the vessel is susceptible
to swamping. These vessels can only be assigned
stability category III or IV. In this case the stability
categories are assigned as follows:
The Downflooding Factor is defined as:
FDF
=
total volume of non-selfdrainable recesses in m 3
k
<l>ol<l>D(base)
= --------------------------------------- --------------------
LwL ·BwL·FM
where <l>o is the downflooding angle in degrees and
<l>D(base) the base value of the downflooding angle,
i.e. the minimum value considered desirable for
stability category I. This value is 90 degrees.
It follows that:
FDF
=
where FM is the freeboard amidships according to
ISO 8666.
From the formula for STIX and the above limits, it
follows that for vessels with a value of k (according
to the above formula) less than 0.025:
<j>J90
The minimum and maximum values of FDF that
may be adopted in calculating of the STIX value,
are 0.5 and 1.25, respectively.
When (2LwL+Lhun) is greater than 100.84 m the
vessel is always a category I vessel, except
when the total volume of non-selfdrainable
recesses is moderate or large;
6.5 Calculation of the Stability Index (STIX)
When (2LwL+Lhun) is greater than 73.95 m the
vessel is always at least a category II vessel,
except when the total volume of non, selfdrainable recesses is moderate or large;
The value of the stability index (STIX) is determined from:
STIX
=
FBS(FRE.FIR.FKR.FDL.FBD.FWM.FDF)
OJ
When (2LwL+Lhun) is greater than 47.06 m the
vessel is always at least a category III vessel;
It should be noted that in the calculation of any of
the factors described above, it is at all times permissible to simply adopt the minimum value of one or
more of these factors without any calculation.
When (2LwL+Lhuu) is greater than 16.81 m the
vessel is always at least a category IV vessel.
6.6 Assignment of Stability Category
This follows from the fact that the minimum value
of the product of the individual, non-dimensional
factors, to the power 0.3, is 0.2975, i.e.:
The stability categories are assigned as follows:
Stability category IV:
STIX
=
5 to 14;
Stability category III:
STIX
=
14 to 22;
the minimum value of:
(FRE.FIR.FKR.FDL.FBD.FWM.FDF)03
Stability category II:
STIX = 22 to 30;
Stability Category I:
STIX
=
0.2975.
6.7 Validation
=
30 or higher.
The above method was validated independently in 4
countries, viz: in France, in the UK, in Sweden and
in the Netherlands. Some 50 different, well-known
yachts and sailing vessels were selected and given a
In the case the total volume of non-selfdrainable
recesses of a vessel is moderate or large, the vessel
cannot be assigned stability categories I or II, even
116
stability category according to what the designer,
builder and experts involve i thought was appropriate for those vessels ac1 :ording to the known
stability characteristics and t ie experience obtained
therewith over the years. 1 hese rather subjective
assignments of stability catt gory were thoroughly
discussed until finally the ~xperts involved were
unanimous in their opinion 011 the stability category.
N.m at 90 degrees of heel for the minimum sailing
displacement condition.
In the calculation of FWM:
An expression for GZo: the righting lever in m at a
heel angle equal to the downflooding angle;
An expression for "lever": the vertical distance between the geometric centres of the above-water and
below-water profiles of the vessel, including sails,
masts and hull, with centerboards, daggerboards and
leeboards in the lowered position, when the vessel
is upright.
After each of the yachts a 1d sailing vessels involved were assigned a stability category, the STIX
stability index was calcula ed according to the
above calculation scheme. l was then found that
almost without exception the wanted stability category could be obtained by se1 ting the STIX value at
5, 14, 22 and 30 for the vru ious categories as explained above. The only ni 1table case the STIX
value did not pin-point the l ppropriate category is
the case of "Taka", the casm .lty discussed in Paragraph 4, for which STIX is well in excess of 30,
indicating that this yacht is I ossibly indeed a category I yacht, as had been contended by various
experts and the designer. Th is would seem to indicate that either the stabilit) information given in
the report prepared by the J .iippon Ocean Racing
Club (see the list of referen :es) is not correct or
some other factor (such as a structural failure) also
played a role in the sinking o · the yacht - a point of
view adhered to by various Jeople. Table 4 gives
the main results of the validat on study.
In the calculation of FDF:
An expression for <j> 0 : the downflooding angle in
degrees (from the height and off-centre distance of
the downflooding location).
7.
The subject matter dealt with in this paper, in the
context of ISO Standard 12217-2, is still in development. All of the developed criteria, presented
here, will remain subject of discussion in the Working Group until mid-1997 when the voting procedure on this standard will commence. Once the
Working Group has presented its so-called Committee Draught (CD) version of the Standard, this
will be sent to all ISO member countries for formal
consideration. It is quite likely that proposals will
be forthcoming recommending modifications, additions and deletions. As such, this paper should be
considered as a presentation of the current state of
affairs with respect to the development of the Standard as it applies to mono-hull sailing vessels. Furthermore, the opinions and remarks presented here
are not necessarily those of' Working Group 22, but
those of the Netherlands delegation only.
6.8 Approximate Formulae.
Approximate formulae are 1urrently being developed for the following variab es:
In the calculation of FRE:
An expression for Eiut: the lfea under the actual
righting moment curve in kN.1 n.deg, up to the angle
of vanishing stability (<l>v) a 1d the downflooding
angle (<j> 0 ).
8.
In the calculation of FIR:
An expression for <l>v: the
tive) stability in degrees;
an~
FINAL REMARKS
LIST OF REFERENC ES
Final Report on Safety from Capsizing", Report of
the Directors of the Joint United States Yacht
Racing Union and Society of Naval Architects and
Marine Engineers Committee, 1985.
le of vanishing (posi-
An expression for <j> 0 : the d >wnflooding angle in
degrees (from the height and off-centre distance of
the downflooding location).
Claughton, A.R. and Handley, P., "An Investigation
Into the Stability of Sailing Yachts in Large Breaking Waves", Wolfson Unit Report, 1984.
In the calculation of FKR:
Dahle, I.E.A. and Myrhaug, D., "Risk Analysis
Applied to Capsize of Smaller Vessels in Breaking
An expression for RM 90 : the righting moment in
117
Waves", Spring Meeting of the Royal Institution of
Naval Architects, 1993.
Sailing Vessels and their Response to Gusts", 10th
Chesapeake Sailing Yacht Symposium, Society of
Naval Architects and Marine Engineers, 1991.
Deakin, B., "Methods of Assessing the Safety of
Cruising Yachts in Terms of Stability", Paper Presented at the Conference on "The Seaworthy Cruising Yacht", Royal Institution of Naval Architects,
November 1991.
Forbes, H., Laing, M. and Myatt, J., "1979 Fastnet
Race Inquiry", Royal Yachting Association & Royal
Ocean Racing Club, 1979.
Deakin, B. "Model Test Techniques Developed to
Investigate the Wind Heeling Characteristics of
Nippon Ocean Racing Club, "Report on Marine
Accident Involving the Yachts 'Marine Marine' and
'Taka' in the Japan-Guam Race 1992".
Table 4.
Main results of the validation study of the STIX single stability index concept.
FBS
FRE
FIR
FKR
FDL
FBD
FWM
FDF
STIX
Category
given
Category
wanted
Muscadet
17.3
0.64
0.99
1.07
0.92
1.11
1.00
1.17
16.2
III
III
Gib Sea 242 CB
19.7
0.50
0.96
0.96
0.95
1.08
1.00
1.17
16.5
III
III
Gib Sea 242 K
19.7
0.62
1.06
1.05
0.93
1.13
1.00
1.17
18.7
III
III
Sangria
19.6
0.71
1.00
1.16
1.04
1.04
1.00
1.18
19.8
III
III
Ecume de mer
18.8
0.85
1.05
1.16
1.00
1.02
1.00
1.17
20.2
III
III
Folie Douce
22.5
0.82
0.99
1.18
1.07
1.08
1.00
1.22
24.6
II
II
Super Challenge
22.8
1.09
1.28
1.31
0.94
0.99
1.00
1.17
28.1
II
II
Comet 910
23.6
0.70
1.01
1.13
1.03
1.05
1.00
1.17
23.7
II
II
First 310
26.5
0.74
0.95
I.OJ
0.90
0.99
1.00
1.22
24.6
II
II
Neptune 940
25.0
0.90
1.03
1.12
0.97
I.OJ
1.00
1.20
26.5
II
II
Feeling 326 Di
25.9
0.69
0.89
1.03
0.97
1.02
1.00
1.17
23.6
II
II
Sun Rise K
27.0
0.98
0.99
1.09
0.93
0.91
1.00
1.17
27.4
II
II
Romanee
26.7
1.02
0.99
1.14
1.01
0.75
1.00
1.17
26.9
II
First 35 (79)
28.8
0.87
0.97
I.I I
1.01
1.07
1.00
1.17
30.2
I
I
Selection
29.5
0.82
0.96
1.02
0.86
1.00
1.00
1.17
27.7
II
II
Sun Odyss 371
31.0
0.82
0.92
1.03
0.96
0.99
1.00
1.17
29.6
II
I/II
Gin Fizz
30.1
1.00
0.99
1.19
1.10
1.07
1.00
1.17
34.9
I
I
Sun Fast 39
31.8
1.13
1.03
1.12
0.99
1.02
1.00
1.17
36.1
I
I
Sun Charm 39
31.5
0.94
0.98
1.08
0.98
1.00
1.00
1.17
32.7
I
I
Maracudja
32.7
0.68
0.85
I.OJ
1.17
1.06
1.00
1.17
31.l
I
I
First 41S5
31.9
0.95
1.00
1.08
1.00
0.99
1.00
1.17
33.6
I
I
First 45 F5
36.3
1.42
1.06
1.16
0.97
1.03
1.00
1.17
44.9
I
I
Meridien
38.0
1.03
0.89
1.04
I.I I
1.13
1.00
1.17
42.1
I
I
Emeraude
40.4
1.20
1.05
1.16
1.10
I.I I
1.00
1.17
50.5
I
I
First 53F5
43.4
1.50
1.03
1.10
0.92
1.04
1.00
1.17
52.5
I
I
Name
118
FBS
FRE
FIR
FKR
FDL
FBD
FWM
FDF
STIX
Category
given
Category
wanted
First 210
17.8
1.50
0.91
0.97
0.82
0.75
1.00
1.17
17.5
III
III
Mini Transat
19.5
1.19
0.93
0.94
0.78
0.75
1.00
1.17
17.6
III
JOD 35
28.9
0.98
0.98
1.04
0.86
0.78
1.00
1.17
26.9
II
II
Group Sceta
54.3
1.50
0.88
0.74
0.76
0.75
1.00
1.17
47.5
I
I
Generali Concordi
54.3
1.50
0.87
0.77
0.81
0.75
1.00
1.17
48.9
I
I
BOC 50
45.3
1.50
0.84
0.66
0.75
0.75
1.00
1.17
37.8
I
I
First Class 8
21.6
0.73
0.96
0.97
0.82
0.89
1.00
1.20
18.4
III
III
Noirmoutrin
15.3
0.50
0.50
0.50
I.I I
1.13
0.50
0.50
5.8
IV
IV
Drascombe Lugger
14.6
0.50
0.50
0.50
0.77
0.75
0.80
0.58
5.2
IV
IV
Squib
16.2
0.50
0.50
0.50
0.79
0.75
1.00
0.65
6.5
IV
IV
Duette
17.6
0.91
1.06
1.23
0.95
0.79
1.00
1.25
18.1
III
III
J24
21.1
1.00
1.00
1.10
0.80
0.75
1.00
1.25
19.9
III
III
J24
21.1
0.76
0.93
1.05
0.83
0.75
1.00
1.21
17.7
III
III
J24
21.1
0.88
0.93
1.05
0.80
0.75
1.00
1.21
18.3
III
III
Westerly Centaur
29.9
0.99
1.46
1.14
1.05
1.15
1.00
1.25
27.6
II
II
Sigma 33
25.9
0.84
0.72
1.21
0.96
0.95
1.00
0.97
22.8
II
II
Sigma 33
25.9
0.92
0.72
1.26
0.97
0.95
1.00
0.98
23.8
II
II
Moody 33
27.7
1.46
1.09
1.44
0.99
1.14
1.00
1.00
36.8
I
I
Victoria 34
27.9
1.27
1.13
1.16
0.98
1.09
1.00
1.00
33.0
I
I
Bowman 57
44.7
1.16
0.78
1.26
1.04
1.14
1.00
0.98
48.4
I
I
Oyster 67
53.2
1.50
0.83
1.36
1.17
1.07
1.00
0.93
65.3
I
I
Nordic Folkboat
19.9
0.50
0.53
0.50
0.98
0.99
0.90
0.72
9.3
IV
IV
Intern. Folkboat
19.9
0.81
I.I I
1.23
0.98
0.99
1.00
1.25
21.8
III
III
Dragon
20.2
0.50
0.50
0.50
0.93
1.09
0.80
0.64
9.1
IV
IV
Island Packet 27
22.9
1.19
l.Q9
1.34
1.12
I.I I
1.00
1.22
30.7
I
I
Dehler 34
26.8
1.27
1.03
1.19
0.95
1.03
1.00
1.22
32.3
I
I
Taka
39.4
1.03
0.95
1.03
0.83
1.05
1.00
1.00
37.9
I
I/II
17 m Schokker
44.2
' 0.57
0.61
0.50
1.25
1.23
0.50
0.67
21.6
III
III
17 m Schokker + selfdraining cockpit
44.2
0.58
0.67
0.50
1.25
1.23
1.00
1.00
30.7
I
I/II
Name
119