ographic
k ping
ng
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Lab. y.
ScheepsbouwkUn
ARCHIEF
Tedinische
Hogeschool
Deift
Advances in
Underwater Technology,
Ocean Science and
Offshore Engineering
i4ITTEE
Volume 9
Stationing and Stability of Semi-su bmersibles
rf Energy
edited by
Lduc!W12
C. Kuo
½'echnology
Proceedings of an international conference (Stationing and Stability of Semi-submersibles) organized by the University of Strathclyde and the Society for Underwater Technology co-sponsored by the Royal Institution of Naval Architects and held at the University of Strathclyde, UK, 16-18 June 1986
Published by
Graham & Trotman
The Study ofa New Procedure
for Assessing Stability
of Ships and Offshore Structures
J.S. Pawlowski, National Research Council, St. John's,
Newfoundland,Canada and M.K. Deb, Memorial University of Newfoundland, Canada
ABSTRACT
In the existing prodecures for assessing stability of ships and floating structures, the qualities of the vessel* are represented by righting arms curves in calm water. As a result, dynamic effects of the interaction of the vessel with the environment
cannot be rationally taken into account. It is possible to say that in general, no
sufficiently comprehensive and coherent conceptual framework exists at present for the establishing of fully rational procedures for stabilityassessment.
In the chapter a new procedure is described which relies on a direct application of stability criteria to the generalized configuration (defined interms of absolute
and relative motions) of the vessel. The procedure relates
the generalizedconfiguration to a set of control parameters which are regulated by the designer
and operator of the vessel, and provides a unified approach to problems of intact
and damage stability. Dynamic effects of the interactionbetween the vessel and
environment are explicitly taken into account and can be evaluated either by
means of model tests or through a numerical simulation. The procedure is
therefore entirely rational and can be applied at various levels ofadvancement. the term vessel is used here to denotea ship or a floating structure.
Advances nz (Jndei-water Technology, Ocean Science and Offshore Engineering, Volume 9; Stationing and Stability oJSenz-submersjb1es
(&) Sooety for Underwater Technology (Graham & Trotman, 198)
7
-¿
INTRODUCTION
The need to rationalize the existing procedures for assessing stability of ships and
floating offshore structures appears to be widely recognized'10. Reviewing
what has recently been written on the subject three main factors can be identified as contributing to that recognition:
new types of ships and structures do not easily fit in the format of existing
rules and regulations;
losses of floating units, involving tragic losses of human lives, challenge the adequacy of existing rules and regulations;
the substance of existing rules and regulations has become incommensurable with available knowledge of dynamics of floating bodies.
In spite of the tendency to introduce appropriate rationalizations, attempts to
this effect are being found difficult to succeed. It can be argued that the difficulty
arises from the nominality of current procedures, as in fact regulating the GZ curve of a vessel.8,11 The evaluation of stability according to these procedures is
nominal since the GZ curve does not directly represent the behaviour of a vessel
in the seaway; see refs 7 and 8 for relevant comments with respect to rules
applicable to offshore structures. The nominality of the procedures hampers
rationalizations motivated by (a) and (c) listed above because, with respect to (a):
without gathering an appropriate experience it is virtually impossible to judge if
nominal criteria apply to a new type of vessel, and with respect to (c): there is no clear cut relation between the dynamics of vessel motions and nominal criteria of stability. Considering factor (b), and assuming the nominal criteria to be adequate,
it should be observed that stability assessments according to nominal criteria
cannot be sufficiently related with other design considerations to provide efficient
assessment procedures. This aspect of the present discussion will be further elaborated.
It follows from the above that possible rationalizations of current procedures for
assessing stability depend upon working out of a new non-nominal conceptual frame. In the remaining part of the chapter a proposition of such a conceptual frame, first described in ref. 12, is presented together with limited examples of application which utilize stability criteria adapted from the existing stability assessment procedures.
THE CONCEPT OF A NEW PROCEDURE FOR ASSESSING
STABILITY
The definition of the New Procedure
Considerations of so called intact stability are almost exclusively, for an exception
see ref. 3, focused on the mechanism by which a vessel is brought back to its
upright configuration after a disturbing action has occurred. The resulting
approach to stability assessment is to impose criterial conditions upon the vessel parameters which contribute to the restoring mechanism, such as the GZ curve in
existing assessment procedures, the GZ curve modified with respect to wave
NEW PROCEDURES FO1 influence (with or witho moments in applications Such an approach im. to a nominality of event linearization of the inte
(waves, winds, etc.) s precisely defined, it is mechanism of interacti.
safety of a vessel in the to the excitations but als and operating systems o
on board. Therefore an
explicit examination of
features of the vessel
ballast system, etc).
criteria are understood vessel to environmen presented here.
The concept of a new the key notions discuss
The generalized insta
parameters characteriz'
absolute configuratio
relative configuratio
surface);
accelerations due to
More generally, the
relative (with respect t
static and dynamic effec static and dynamic fo
wetness on deck, s
deck, with possible d and which may hinder o i
where loss of human
including a loss of the ve
Criteria of stability r
configurations assumed
losses described above
explained the criteria de Coni rol parameters ar
the geometry of the
submerged contribut the mass and mass di of the centre of gravi
TER TECHNOLOGY
stability of ships and
ed°. Reviewing
tors can be identified
e format of existing
lives, challenge the me incommensurable
thzations, attempts to
rued that the difficulty
ct regulating the GZ o these procedures is
behaviour of a vessel
vith respect to rules
Iprocedures hampers
e, with respect to (a):
1impossible to judge if Dect to (c): there is no and nominal criteria of
nteria to be adequate, g to nominal criteria
ns to provide efficient
.ission will be further urrent procedures for
)fl-flommal conceptual
of such a conceptual
h limited examples of
the existing stability
OR ASSESSING
ively, for an exception
is brought back to its
urred. The resulting
itions upon the vessel
uch as the GZ curve in
with respect to wave
NEW PROCEDURES FOR ASSESSING PROCEDURES 151 influence (with or without Smith's effect)13 14, or a form of restoring and damping moments in applications of Lyapunov's direct method.1516
Such an approach implicitly contains two basic sources of difficulties which lead to a nominality of eventual assessment procedures. Firstly, the approach implies a linearization of the interaction between the vessel and environmental phenomena
(waves, winds, etc.) since in general, although the exciting phenomena must be precisely defined, it is impossible to separate restoring effects from the overall mechanism of interaction between the vessel and environment. Secondly, the
safety of a vessel in the seaway does not depend solely upon its dynamic response to the excitations but also, and not to any lesser degree, on the capacity of the hull and operating systems of the vessel to remain intact and protect the crew and load on board. Therefore any fully rational assessment of stability must follow from an explicit examination of the dynamic response in conjunction with constructional
features of the vessel (such as the vulnerability of weather deck, efficiency of ballast system, etc). Both difficulties described above are avoided if stability criteria are understood as bounds limiting relevant dynamic responses of the vessel to environmental excitations. Such is the starting point for the concept presented here.
The concept of a new procedure for assessing stability is formulated in terms of the key notions discussed below.'2
The generalized instantaneous configuration of the vessel is defined in terms of parameters characterizing:
absolute configuration of the vessel (with respect to the vertical);
relative configuration and velocities of the vessel (with respect to water
surface);
accelerations due to the motion of the vessel.
More generally, the definition includes all parameters of the absolute and relative (with respect to water surface) motion of the vessel, which determine
static and dynamic effects such as:
static and dynamic force loads upon parts of the vessel and devices aboard;
wetness on deck, shipping of green water or permanent submergence of the
deck, with possible downflooding;
and which may hinder operational qualities of the vessel up to and beyond the level
where loss of human lives andior considerable damage or loss of property,
including a loss of the vessel, occurs.
Criteria of stability represent effective bounds imposed upon the generalized
configurations assumed by the vessel over its lifetime, so that the risk of possible
losses described above is reduced to an acceptable minimum. As it has been
explained the criteria depend inherently on constructional features of the vessel. Cont rol parameters are defined as parameters determining:
the geometry of the buoyant volume of the vessel, i.e. the volume which if
submerged contributes to the buoyancy force;
the mass and mass distribution of the vessel, i. e. the displacement, the location of the centre of gravity, the moments of inertia.
152 ADVANCES IN UNDERWATER TECHNOLOGY
These parameters of the vessel are, at least in principle, totally or partly
controlled by the designer and operator of thevessel, and in any environmental
conditions the range of generalized configurations assumed by the vessel depends primarily upon them, provided that the environmental conditions are defined in a system of reference moving with the average velocity of the vessel.
The Procedure for assessing stability isa procedure which provides means for
bounding within certain risk limits the possibility that during the lifetime of the vessel the generalized configuration assumes unacceptable values which are indicated by the criteria of stability. Since generalized configurations depend primarily upon control parameters (over
a set of considered environmental
conditions) and the control parameters evolveconstantly over the lifetime of the vessel, the fundamental purpose of the procedure isto ensure that the evolutionof control parameters does not lead to a violation of the stability criteria.
Relations between the elements of the procedure are shown schematically in
Fig. 1.
It can be observed that they fall into
two overlapping and interactingpatterns. One, the design pattern, consists of controlparameters, constructional features, criteria of stability and the decision making process. The other, the dynamic pattern, comprises environmental conditions (including the regime of
motion of the vessel through their definition,
as explained above), controlparameters and generalized configurations. As it is shown by the scheme, the
design pattern belongs to the design spiral whereby, starting from an assumed set of constructional features and control parameters and through the interaction with the dynamic pattern, the decision is made about the acceptability of the design and
if necessary the adopted constructional features and/or control parameters are revised.
The dynamic pattern comprises the evaluation of generalized configurations as uniquely dependent upon controlparameters and environmental conditions. The
dynamic pattern interacts with the design pattern by providing the evaluation of
generalized configurations to be examined withrespect to the criteria of stability
and it overlaps with the design pattern by including control parameters
as the
common element. The scheme shows therefore that
within the procedure,stability assessment becomes an inherent part of the process of design.
STABILITY ASSESSMENT PROCEDURE
C ONS T R OC T O NA L EAl uRIS CRuTEtA O STARILITY CONTROL PA RANC t( R S GENERALIZED
CONFIGURATIONS ENV IRON WE N TA LCON CITIONS
FIGURE I
NEW PROCEDURES FO
Comparison with l
In comparison with th
procedures represent
replaces the control p
directly applied, assumi
al features are satisfied are nominally taken mt limiting heel angles re.
vessel. It is seen, ther
the convention of usir constructional feature procedures.
In addition, the no
explicitly take into acc
be achieved within a below. Therefore, e. g., damage stability ente space of control param defined above, to dis
-damage conditions are
It should be reco evolution of control p
application of the GZ c
restoring effects, refe a nominal representati
evolution of control par
pattern in a resulting reference to generalize
In addition to the
generalized configurati
constitutes the other n
importance results Iron changes and shifts of le
loss
of structural me
occurrences of such e
being taken of construct
Although this provisi dynamic pattern in the
known,7. 9. 17-19 that attributable to evolutioi structural failure, syster weather conditions and
conclusions apply to lose
presented in ref. 20 w
reported as the causes
XATER TECHNOLOGY
iple, totally or partly
in any environmental
by the vessel depends
ditions are defined in a
vessel.
ch provides means for
hing the lifetime of the
ble values which are
configurations depend
sidered environmental ver the lifetime of the sure that the evolution
ility criteria.
shown schematically in lapping arid interacting
imeters, constructional
ocess. The other, the
ricluding the regime of lamed above), control vn by the scheme, the
rig from an assumed set ugh the interaction with ability of the design and
control parameters are
alized configurations as
mental conditions. The
viding the evaluation of the criteria of stability
trol parameters as the
within the procedure,
ss of design.
L N V IRON MEN TAL
CON CITIONS
s
NEW PROCEDURES FOR ASSESSING PROCEDURES 153
Comparison with Nominal Procedures
in comparison with the procedure illustrated by Fig. 1, the existing, nominal
procedures represent the vessel by means of a
GZcurve which in a sense
replaces the control parameters and to which nominal criteria of stability are
directly applied, assuming that certain requirements with respect to construction-al features are satisfied. Environmentconstruction-al conditions and generconstruction-alized configurations
are nominally taken into account in terms of, respectively, heeling moment and limiting heel angles referred to the GZ curve and downflooding points on the vessel. It is seen, therefore, that the dynamic pattern is effectively replaced by the convention of using the GZ curve. As a result explicit relations between constructional features and criteria of stability are excluded from the nominal
procedures.
In addition, the nominal procedures for assessing intact stability do not
explicitly take into account the evolution of control parameters, although this can
be achieved within a nominal scheme of stability assessment as it is explained
below. Therefore, e.g., the transition to damage conditions (which are covered by damage stability criteria in the nominal procedures) corresponds to a jump in the
space of control parameters. In principle there is no necessity, in the procedure defined above, to distinguish between intact and damage conditions as long as
damage conditions are included in the examined set of control parameters.
It should be recognized that the exclusion of an explicit consideration of the evolution of control parameters in the nominal procedures follows from the
application of the GZcurve as a nominal vessel descriptor, whereby the focus on restoring effects, referred to above, is expressed and amplified. However, even if
a nomina' :presentation of the vessel more suitable for taking into account the
evolution of control parameters were adopted, an effective inclusion of the design
pattern in a resulting procedure would be hampered by the lack of an explicit
reference to generalized configurations.
In addition to the imposition of stability criteria as limits of admissible
generalized configurations, the inclusion of evolution of control parameters constitutes the other major characteristic of the procedure defined above. Its importance results from allowing for explicit considerations of static effects of:
changes and shifts of load andlor ballast, flooding, shipping of green water, and
loss of structural members. The procedure enforces an examination of
occurrences of such events and of their influence upon stability, with account
being taken of constructional features of the vessel.
Although this provision is a logical outcome of incorporating a non-nominal dynamic pattern in the procedure, it is also of practical significance. It is well
9. 17-19 that stability related failures of semisubmersible units are attributable to evolutions of control parameters, as described above, due to a
structural failure, system malfunction andlor human error, combined with adverse weather conditions and followed by shipping of green water and flooding. Similar conclusions apply to losses of small ships as it is shown by the investigation results
presented in ref. 20 where load shift and shipping of green water have been
reported as the causes of 81% out of 52 capsizings of fishing boats and 77% out of 87 capsizings of small cargo vessels.
Stability Diagrams
The definition, given above, of the procedure for assessing stability and the
ensuing discussion indicate that the outcome of an application of the procedurecan
be expressed as a range of allowable evolutions of control parameters, which
results from limits (stability criteria) imposed upon generalized configurations and
corresponds to an assumed set of environmental conditions. That range can be
represented in a simple form by stability diagrams.'2
A stability diagram refers to a fixed geometry of the buoyant volume and a
chosen displacement. Under those conditions an upright static configuration of the
vessel is defined. In the upright configuration the projection, K, of the centre of
buoyancy on a horizontal base plane, provides the origin of the system of
reference fixed with the vessel,
in which changes of mass distribution aredescribed. The location of the centre of gravity, CG, is consideredas evolving in a
plane perpendicular to the base plane. The coordinates of CG
are read with
respect to the axis defined by the crossing line of the plane of the evolution of CG and the base plane (the horizontal coordinate axis in Fig. 2) with the origin
at K,'
and the axis through K perpendicular to the base plane and directed upwards (thevertical coordinate axis in Fig. 2) with the origin also at K. The displacements
(shifts) of CG parallel to the base plane are denoted by GG' and the coordinate of CG measured along the axis perpendicular to the base plane is designated as KG, as shown in Fig. 2.
SCHEMATIC VIEW OF STABILITY DIAGRAM
k STATIC CIAGRAB Lm,i.d by STOIC W(ATHER CORRECTION OYNA'IC DIAGRAM Lm,l.d by dynamo slObily bnl.' Q
buoyant volume being
perpendicular to the
symmetric with respect
The lines of static dia,
of CG, parallel to the
criteria imposed upon
configurations achieved
phenomena. In turn, t] limits determined by s
which the vessel ass
excitations. The differe
diagrams at the same
(positive or negative G provides a measure of t
of the vessel. The st
minimum achievable K(
maximum allowed KG terms of existing proce corresponding to the pa It should be observe distribution of mass in
dynamic diagrams are
assumed environment
distributions of the sarni
Once limitations ari configurations of the ve
given geometries of bu codes for hydrostatic c diagrams can be deteni resorting to appropriat
The allowable range described in principle
directions of stability di
configurations of its bu sufficient and forms a equivalent to a chang configuration of the y possible to evaluate th vessel. The atlas can
the vessel. The atlas
scenario of a stability f.
evidence concerning s
green water and floodin
It is shown below
diagrams from exist
configurations corres
experimentally, it is
nominal criteria of stab
s;
s,
154 ADVANCES IN UNDERWATER TECHNOLOGY
NEW PROCEDURES FO.
SG nn,an, ss (sni' of CGI
R. da ,, e a
k s Pl. proI.cp!on Dt CB
Qn In basi plan, in
VP' Obi COnhIgufaton
FIGURE 2
In the described system of reference the stability diagram consists of a pair of static diagrams and a pair of dynamic diagrams. Each pair is representedby two
lines on each side of the KG axis (corresponding to positive and negative values of
GG'). In Fig. 2, for simplicity, only the diagrams on the positive GG1 side are shown. In general, the diagrams on the negative GG' side display an analogous pattern, reflected with respect to the KG axis. In the case of a geometry of the
Moma,,, KG
'ATE R TECHNOLOGY
sing stability and the
n of the procedure can
ol parameters, which
zed configurations and
s. That range can be uoyant volume and a
tic configuration of the
n, K, of the centre of
of the system of
ass distribution are
idered as evolving in a
of CG are read with
of the evolution of CG ) with the origin at K, directed upwards (the
K. The displacements
and the coordinate of e is designated as KG, L ' RR E C lION dynOm,C rn consists of a pair of is represented by two
and negative values of
positive GG' side are
e display an analogous
e of a geometry of the
NEW PROCEDURES FOR ASSESSING PROCEDURES 155
buoyant volume being symmetric relative to the plane containing KG axis and
perpendicular to the plane of stability diagram, the pairs of diagrams are
symmetric with respect to KG axis.
The lines of static diagrams indicate for a given KG value the limits of shifts GG
of CG, parallel to the base plane, which do not lead to a violation of stability
criteria imposed upon static generalized configurations of the vessel,
i.e.configurations achieved at static equilibrium without an influence of environmental
phenomena. In turn, the lines of dynamic diagrams indicate the corresponding limits determined by stability criteria imposed upon generalized configurations
which the vessel assumes under the influence of specified environmental
excitations. The difference between GG' values read off the dynamic and static diagrams at the same KG value and on the same side of the stability diagram (positive or negative GG values) is introduced as the weather correction which
provides a measure of the influence of environmental excitations upon the stability
of the vessel. The stability diagram extends between the horizontal lines of
minimum achievable KG and maximum allowed KG. lt is shown in Fig. 2 that the
maximum allowed KG corresponds to a minimum required value of GG'. In terms of existing procedures for assessing stability the minimum allowable GM
corresponding to the particular displacement is thus established.
lt should be observed that the location of CG does not uniquely represent the distribution of mass in the sense of a dynamic model. Therefore, the lines of
dynamic diagrams are in principle determined not only from a search over a set of
assumed en
ntal conditions,but also over a set of feasible mass
distributions ( ame location of CG but varying central moments of inertia. Once limit..
are imposed in terms of stability
criteria upon static
configurations o the vessel, the lines of static diagrams can be easily found, for given geometries of buoyant volume and displacements, by means of computer
codes for hydrostatic calculations. Similarly, the points, on the lines of dynamic
diagrams can be determined, in correspondence to imposed stability criteria, by
resorting to appropriately designed model tests or numerical simulations.
The allowable range of evolutions of control parameters of a given vessel is described in principle by an infinity of stability diagrams covering all possible
directions of stability diagram planes, all possible displacements of the vessel and configurations of its buoyant volume. In practice, a finite number of diagrams is
sufficient and forms a stability atlas. Any system of forces, which is statically equivalent to a change of control parameters and which disturbs the upright configuration of the vessel can be referenced to the atlas and as a result it is
possible to evaluate the effect of the action of the forces upon the stability of the vessel. The atlas can be applied in this way by the designer and by the operator of
the vessel. The atlas also provides efficient means for deducing the probable
scenario of a stability failure, if used as a tool for correct interpretation of forensic
evidence concerning such events as shift of cargo, shift of ballast, shipping of
green water and flooding.
It
is shown below that it
is possible formally to derive dynamic stabilitydiagrams from existing nominal procedures. Since ranges of generalized
configurations corresponding to diagrams derived in such a manner can be found
experimentally, it is therefore also possible to scrutinize the consistency of the
N-, 4 0-/ / / Y-II? I,:I76I
EXAMPLES OF APPLICATION
In order to illustrate their application, stability diagrams have been calculated for
three semisubmersible units. Unit No. lis the same as theone reported in reIs 18
and 19. Units No. i and No. 2 are of similar geometry whereas Unit No. 3 is
significantly different from the other two.
Figure 3 shows a stability diagram of Unit No. 1. The diagram applies to the
displacement specified by the draught of 18m in the upright configuration and to shifts of CG in the longitudinal plane of symmetry of the vessel (positive towards
the bow). Because the vessel is not symmetric with respect to the plane
containing the centre of the buoyancy in
the upright configuration and
perpendicular to the plane of the diagram, the pairs of diagram lines are not symmetric. The broken lines in Fig. 3 represent static diagrams obtained for constant limiting angle of trim, taken as equal to the downflooding angle 8 =
35.2°. The continuous lines represent dynamic diagrams obtained by applying the
rule of 1.3 area ratio between the GZ curve and thecurve of wind overturning
arms, both starting from the upright configuration, in the trim mode. Therefore, for a chosen KG, and GG' values smaller than those indicated by the dynamic diagrams, the unit satisfies the criterion of 1.3 area ratio whereas for greater
shifts of CG the criterion is not satisfied. The convention of broken and continuous lines and the criteria of limiting downflooding angle for static diagrams and the 1.3
0 2 - VS OC lOChOnS ve l'e 1170110713 FIGURE 3 IS 20 0G Cm
area ratio for dynamic di
here.
Since, if immersed ar plane of a stability thag
shown that in such a cas lines if stability criteria
all of the diagrams with No. 1, where, however be well represented by
The dynamic diagram (survival condition) and (operational condition). equilibrium correspondi
KG = lømand l8rnare
Figure 4 presents sta draughts of 18, 24 and
volumes of displacemer
diagrams clearly show
displacement, according relatively small sensitiv value of the area ratio,
14 0 IZO lo SO 20 I / 2 22 0 200 leo. ie o-C
UNIT No.. TRIN, SURVIVAL CONDITION DRAUGHT 18m
220 200 15.0-IS O E UNIT No.I
- YCSTTICTEO ST OOWSFL000ISG ANGLE
.1I7 \o. \T.0 \ 22 0 200 ISo IO
-WINO NCSTNICTNO ST O0wwL0.0 SESTRICTCO ST ASCA 5*710 LIWIT 0F ISINISUW SS STATIC TRIM 00100115 . lOCAlI _/ i -WINO 5 . NESTYC700 ST ASCA SA 7,0 II 31 STATIC Tilu ANGLE
VELOCITY 00 STY 35 500_I I / / / / I f
.1
3.I N, V3/ / I / / Smi / I / I156 ADVANCES IN UNDERWATER TECHNOLOGY NEW PROCEDURES FOI
Is e 4 0 -loo 20-lo o SO 20
I'ATER TECHNOLOGY
ve been calculated for me reported in refs 18
hereas Unit No. 3 is
liagram applies to the t configuration and to
ssel (positive towards
respect to the plane
u configuration and
iiagram lines are not liagrams obtained for
rnilooding angle 01 = tamed by applying the
of wind overturning rim mode. Therefore, rated by the dynamic whereas for greater
)roken and continuous diagrams and the 1.3
P2
inc lIrIci ions
e0
6 20 CG Cm
NEW PROCEDURES FOR ASSESSING PROCEDURES 157 area ratio for dynamic diagrams are used for all other stability diagrams presented here.
Since, if immersed and submerged wedges are symmetric with respect to the plane of a stability diagram, centre of buoyancy remains in that plane, it can be
shown that in such a case static and dynamic diagrams are represented by straight lines if stability criteria described above are imposed. Such symmetryoccurs for
all of the diagrams with the exception of the diagrams in the heel mode for Unit No. 1, where, however, the assymetry is very small and the diagrams remain to
be well represented by straight lines.
The dynamic diagrams of Figs 3, 4 and 5 are derived for wind velocity of 100 kts
(survival condition) and those of Fig. 6 correspond to wind velocity of 70 kts
(operational condition). On diagrams of Figs 3 and 4, the angles of static
equilibrium corresponding to shifts of CG determined by the dynamic diagram at KG = 10m and 18m are shown.
Figure 4 presents stability diagrams of Unit No. i in the trim mode, derived for
draughts of 18, 24 and 26m in the upright configuration, with the corresponding volumes of displacement marked at the lines of the static diagram. The dynamic diagrams clearly show the sensitivity of the vessel to increases of draught or
displacement, according to the adopted criteria. A separate calculation indicatesa
relatively small sensitivity of the dynamic diagrams to the choice of the numerical value of the area ratio, which e.g. at KG = 15m results in changes of plus 5% and
220
200
ILO
UNIT Noi, TRIM . SURVIVAL CONDITION AT VARIOUS DRAUGNTS
- - NESTRICYCO IT eOww'Lolnc ANYLE - RESTRICTED IT AREA RATIO II5)
CTh LIST Or NITilSUM 6M
STATIC TRIS ANALE SINO VELOCITY .10001* / / I I / / IB,,l/ / / / / / / 24,n/ - ICO4IOA6ITT _24 ORI -; 2e.Os \
.\
'
\ \24,e \18RY -6e irIcIlnotlOns FIGURE 4 ve inclinations 22.0 20 0 IC O i, \ le_O 14.0 2.0 lOO 160 E C, 4 0 120 Io-O .0 / I ;/ !/ / -I I I / 26m / R/:'
¿ / / 8m E V E o EU \18 ITT VT s' \26m I \ \ \ 16 0 4 0 120 loo 80 20 16 12 B o 4 e 12 6 20 CG Cm 8m 22 0 200 IC O06 Os, 07' 06' 0_5 04 .0 0.9 0.5 01 0_5
COMPARISON OF THREE UNITS. HEEL. SURVIVAL CONDITION
RESTRICTED R,
DOWN-71.000106 ANGLE RESTRICTED 5V AREA
RATIO II SI LIMIT DF MINIMUM 00, lOI
WIND VELOCITO.I000I.
COMPARISON OF THREE UNITS HEEL. OPERATIONAL CONDITION 'o 4
\
\\
\
\
\
\
\
\
\
UNIT NO 3- -
RESTRICTED 5V DOWNFI.000IIOG ANULE- RESTRICTED ST AREA RATIO II 3)
LIMIT 0F MINIMUM 0M £
WIRD VELOCIT V.70 II.
\\
\
\
\
UNIT NO I\
\UNIINOD\
\
\
\
\
\
\
\\
\
\
\
'o 020 025 GG' IA1. FIGURE 6\\
0.30 035 040 045 050 IoNEW PROCEDURES FOF
minus 5% of allowable
comparison with the ori
It is interesting to co
reported in ref. 18. L
corresponding to 49 856
at the displacement of-e
the most critical dam
interpolating, that the
according to the dynarni However, an addition. tonnes and resulting in a
brings the mass distribi. KG of 18.45m. The ma, to the weight shift, in ti
6442 tonnes.
The above comparis
examination of a design
stability, whereby the d
malfunction or misuse o
flooding. It also partly
interpretation of forensic
It is remarkable how' appear to be with respe
stability investigation. It
by the dynamic stabilit
approximately 18.5m to
trim, are close to the Ic (test 1, see Fig. 6 of ref
dynamic stability formuJ
derived from nominal cr11
In Figs 5 and 6 stabili
form for the heel mode
(especially of the dynan'
vessels as determined
by the geometry of the
CONCLUSION
A new procedure for th has been described abo organization of the ma procedures, the new pr.
it can be developed it can absorb recent
*a discrepancy of about 2r
and those in ref. 18.
l_0 NUNIT No 2 09 UNIT NR 3 UNIT No. UNIT No 2 0.0 02 03 0.4 0.5 FIGURE 5 0_S 07 05 09 00 005 0.10 Ois
NDIT ION CONDITION $6 *SGLI U
\
)39 040 045 0.50 \ \ \ 0? 08 09 IONEW PROCEDURES FOR ASSESSING PROCEDURES 159
minus 5S
of allowable GG' respectively for area ratios of 1.1 and 1.5,
in comparison with the original value at the area ratio of 1.3.lt is interesting to compare the data of Fig. 4 with the results of experiments reported in ref. 18. Taking into account the internal displacement of weights
corresponding to 49 856 tm (by the bow) in the upright configuration of the vessel, at the displacement of .36 712 tonnes* (draught of 18.62m) which was applied at
the most critical damage condition tested,' it
is found from Fig.
4, by
interpolating. that the shift of weight is well below the allowable 87 979 tin
according to the dynamic diagrams.
However, an additional flooding of bow corner columns, amounting to about 850 tonnes and resulting in an additional trimming moment of approximately 29 750 tin
brings the mass distribution to the maximum allowable GG value at the original
KG of 18.45m. The maximum amount of flooding of the bow columns, in addition
to the weight shift, in the test programme presented in ref. 18 was reported as
6442 tonnes.
The above comparison illustrates the, usefulness of stability diagrams in the examination of a design of a vessel within the proposed procedure for assessing stability, whereby the designer is forced to examine e.g. the consequences of a
malfunction or misuse of the ballast system in conjunction with the possibility of
flooding. lt also partly demonstrates how stability diagrams can be used in the
interpretation of forensic evidence.
It is remarkable how close and relevant the ad hoc criteria of dynamic stability
appear to be with respect to the values of interest in connection with a realistic
stability investigation. It should be observed that the allowable GG1 values given
by the dynamic stability diagrams of Fig. 4 at the draught of 18m and KG of
approximately 18. 5m together with the corresponding values of the angle of static
trim, are close to the lowest values describing the tested conditions in ref. 18 (test 1, see Fig. 6 of ref. 18). This supports the suggestion that useful criteria of dynamic stability formulated in terms of the generalized configuration, can be
derived from nominal criteria close to the ad hoc criteria introduced above. In Figs 5 and 6 stability diagrams of the three units are shown in a normalized
form for the heel mode in survival and operational conditions. The comparison
(especially of the dynamic stability diagrams) indicates that stability properties of vessels as determined within the presented procedure may be strongly influenced by the geometry of the buoyant volume.
CONCLUSION
A new procedure for the assessment of stability of ships and floating structures
has been described above in broad terms of basic definitions and an outhne of the
organization of the main components. In comparison with the existing, nominal
procedures, the new procedure appears to display two main advantages: it can be developed into an inherent part of the design process;
it can absorb recently acquired knowledge of the dynamics of floating bodies. * a discrepancy of about 2% is observed between displacementcalculations presented here
and those in ref. 18.
--It has been shown that within the procedure the properties of the vessel can be represented by means of conceptually simple stability diagrams. The usefulness of those diagrams has been demonstrated by using ad hoc dynamic stability criteria derived from the existing procedures for assessing stability of semisubmersibles. The examples which have been presented indicate that it may be found possibleto
elaborate new stability criteria,
limiting the components of the generalizedconfiguration of the vessel (defined in the new procedure), starting from the nominal criteria of the existing procedures. On the whole the outline of thenew
procedure appears to provide a promising point of departure in the development
of rational methods for assessing stability of floating bodies.
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