347
1 INTRODUCTION
The aim of this paper is to show how the major
problems were solved as the research aim is to
incorporatethedynamicsofthedamagedro‐roships
during assessing the ship performance and safety at
thepreliminarystageofdesign.
The contribution of the paper is
connected with
presenting some information on development of a
newmodelforassessmentofperformanceofthero‐ro
ships in damaged conditions. The research is a step
forwardregardingtheresearchwhichwasconducted
at the Gdańsk University of Technology between
2007‐2010 and then from 2010 to
2012 (Gerigk 2010,
Gerigk2012,Gerigk2014a).
A Hybrid Model of Flooding of the Ro-Ro Ships in
Damaged Conditions
M.K.Gerigk
GdanskUniversityofTechnology,Gdańsk,Poland
J
.Jachowski
GdyniaMaritimeUniversity,Gdynia,Poland
J
.Sargun
GdanskUniversityofTechnology,Gdańsk,Poland
ABSTRACT:Thepaperpresentssomeresultsoninvestigationsconcerningdevelopmentofahybridmodelfor
assessmentofperformanceofthero‐roshipsindamagedconditions.Themodelisdevotedtowardsassessing
theperformanceofthedamagedro‐roshipsatthepreliminarystage
ofdesign.Thekeyproblemsassociated
withpreparingofsuchthemodelareassociatedwithworkingoutamethodofassessmentofthedamagedro‐
ro ships performance, investigating all the phenomena which associated with the flooding process of the
damagedro‐roshipsandpreparingthemodelitself.Introducing
themethodofassessmentofthedamagedro‐
ro ships performance it has been assumed that there is a dependence between the arrangement of internal
spaces of a ro‐ro ship and flooding process. The major phenomena which have been decided to take into
accountwhenconsideringfloodingofthero
‐roshipsarethefloodingunderstoodastheflowofexternalwater
intothe datadamagedcompartment,impactofthefloodingwaterontheshipstructureanddamaged ro‐ro
shipmotion. Knowing thedamaged ro‐ro ship motion characteristicsin time domain it is relatively easyto
assessthe
damagedro‐ro ship performance according to the heeling angle and assess the ro‐ro ship design
accordingtothedataarrangementofinternalspaces.Thelastresearchissueistoinvestigateiftheproposed
modelmaybeappropriatetoolforassessingtheperformanceofthero‐roshipsindamaged
conditionsatthe
preliminarystageofdesign.Theaimofthispaperistoshowhowtoincorporatethedynamicsofthedamaged
ro‐ro ships when assessing the ship performance and safety at the preliminary stage of design. The basic
informationon themodel for estimation of the damaged
ro‐roship behavior during the flooding process is
presented.Thecomplexityofthismodelisshowndependingontheapproachappliedtoconsidertheflooding
processitself.Themodelisdevotedtowardsassessmentofperformanceofthedamagedro‐roshipsanditis
stillunderthedevelopmentaccording to
a Ph.D.research attheFaculty ofMechanical EngineeringGdańsk
UniversityofTechnology.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 13
Number 2
June 2019
DOI:10.12716/1001.13.02.11
348
There are a few problems associated with
developmentofsuchthemodel.Firstofall,amethod
whichshouldenabletoassesstheperformanceofthe
ro‐roshipsindamagedconditions.Workingoutsuch
themethoditshouldbe underlinedthat themethod
structure has to be according with
the requirements
existingwithinthecurrentregulations(SOLAS2009),
IMO 2008. The next issue is to have a possibility to
analyze the impact of all the phenomena appearing
during the flooding on the damaged ro‐ro ship
performanceandsafety.Thelastresearchproblemis
toevaluateifsuchthe
modelmaybeanappropriate
andreliabletooltoassesstheperformanceandsafety
of ro‐ro ships in damaged conditions at the
preliminarystageofdesign.
Generally, the method of safety assessment of
commercialshipsindamageconditionsincludingthe
ro‐roshipsisbasedontherequirementsincluded in
theSOLAS2009regulations(IMO2005a,IMO2005b,
IMO 2008). This method is of prescriptive character
and generally is based on the experience in ship
designandoperationofships.Thismethodseemsto
be reliable form the practical point of view. It is
harmonized and very much devoted for
the design
purposes. It is difficult to apply this method when
operating the ships to support the emergency,
evacuationorshipsalvageprocedures.
The measure of a damaged ship safety in the
current regulations is the probability of surviving a
collision known as the attained subdivision index A
(IMO2005,SOLAS
2005,Gerigk2010,IMO2014).
The major criteria of the method included in the
SOLAS 2009 regulations is the condition (1) (IMO
2005a,IMO2005b,IMO2008):
A>R (1)
where A = attained subdivision index calculated for
the draughts d
s, dp and dl defined in regulation 2,
accordingtotheformula(2),IMO(2005):
A=∑p
isi (2)
where p
i= probability that only the compartment or
group of compartments under considerationmay be
flooded,asdefinedinregulation7‐1;s
i=conditional
probability of ship survival after flooding the
compartment or group of compartments under
consideration, as defined in regulation 7‐2; R =
required subdivision index given with the
regulations.
Theprobabilitiesp
iandsiarecalculatedaccording
tothewellknown formulaeacceptedbyIMO, (IMO
2005a, IMO 2005b, IMO 2007). A typical process of
safetyassessmentofashipindamagedconditionsat
thedesignstageisdirectedtosatisfythecriteria(1).
Thes
iconditionalprobabilityofshipsurvivalafter
floodingthecompartmentorgroupofcompartments
under consideration is estimated according to the
formulae,IMO(2008):
s
i=minimum{sintermediate,iorsfinal,i smom,i} (3)
where s
intermediate,i = conditional probability of ship
survivalafter floodingthe compartment orgroup of
compartments during all the intermediate stages of
flooding untill the final stage of flooding and it
should be calculated according to the formulae
included in regulations, IMO (2008); s
final,i =
conditionalprobabilityofshipsurvivalafterflooding
thecompartmentorgroupofcompartmentsduringin
thefinalstageoffloodinganditshouldbecalculated
accordingtotheformulae includedinregulationsas
well, IMO (2008); s
mom,i = conditional probability of
ship survival after flooding the compartment or
group of compartments taking into account the
moments following from all the possible impacts of
thewind,survivalcraft,passengersimpacts,etc.and
it should be estimated according to the formulae
includedinregulationsaswell,IMO(2008).
The
most important information following from
application of the above method to the designers is
that this method does not take into account a
damagedshipdynamicsinwaves. Accordingtothis
method the damage stability parameters as
hydrostatics‐relateddataareobtained.
Applyingthismethodinpracticethescenariosof
flooding
concernfloodingofallthesinglewatertight
compartments and groups of compartments under
consideration. The key damaged ship performance
data concern the ship damage stability parameters
and characteristics obtained for the preliminary,
intermediateandfinalstagesofflooding.
Thedynamicsassociatedwiththefloodingprocess
isnotconsidered.
Thedamaged
shipdynamicshasa big impacton
the performance and safety of the ro‐ro ships in
damaged conditions. And this is one between the
most important reasons why it has been decided to
renew the investigations towards developing the
modelwhichisbrieflyintroducedinthepaper.From
the practical
point of view suchthe model may one
between the most important tools a ship designer
shouldhavein hisdisposalto improvethe safety of
ships.
2 METHODOFASSESSMENTOFPERFORMANCE
ANDSAFETYOFTHERO‐ROSHIPSIN
DAMAGEDCONDITIONS
Working out the method of assessment of
performanceandsafetyofthero‐roshipsindamaged
conditionsitwasassumedthatthemethodshouldbe
akindofperformance‐orientedrisk‐basedmethod.
Theabovemethodisofnon‐prescriptivecharacter
because any case of compartment flooding may be
considered to assess a damaged ro‐ro ship
performance. It may be treated as a prescriptive
method from the formal point of view as the
requirementsincluded in the current regulations are
takenintoaccountaswell.
Theproposedmethodisbasedontheassumption
that the safety assessment of a damaged ro‐ro ship
should be done
according to assessment of the
damaged ship performance followed by the risk
349
assessmentunderstoodasconsideringallthepossible
casesofflooding.
Assessmentofperformanceofthe damaged ro‐ro
shipcanbedoneaccordingtoestimationofthemajor
characteristics describing the behavior of the ship
duringthefloodingprocess.
The ship behavior may be described by major
featuresandcharacteristics
ofthedamagedro‐roship
likethefloatability,damagestabilityanddynamicsof
thedamagedship.Thelatestmeansthattheinfluence
ofthepreliminary,intermediate,additional(releases)
and final events (consequences) of the flooding
process are taken into account during assessment of
performanceofthedamagedro‐ro
ship.
It was decided that the damaged ro‐ro‐ship
behaviormaybepresentedastheshipmotiontaking
into account three degrees of freedom (3DoF) as
follows:
swayofthedamagedro‐roship;
heaveofthedamagedro‐roship;
rollofthedamagedro‐ro
ship.
Themajorcomponentsofthedamagedro‐roship
motionarebrieflypresentedinFigure1.
Figure1.Themajorcomponentsofthedamagedro‐roship
motion(Author:M.K.Gerigk).
Introducing the method of assessment of the
damaged ro‐ro ships performance it has been
assumed that there is a dependence between the
arrangement of internal spaces of a ro‐ro ship and
flooding process. Therefore a criteria is to find the
bestro‐roshipsubdivisionhavingthesmallestimpact
of the flooding on the damaged ro‐ro ship
performanceandsafety.
Themajorphenomenawhichhavebeendecidedto
takeintoaccountwhenconsideringfloodingofthero‐
roshipsareasfollows:
flooding is understood as the flow of external
waterintothedatadamagedcompartment;
‐impactofthefloodingwaterontheshipstructure
shouldbeunderstoodasthemass,volume,inertia,
damping and additional heeling moment
followingfromthefloodingwater;
impactofthefloodingwateronthedamagedro‐ro
shipmotion.
Knowing the damaged ro‐ro ship motion
characteristicsincludingthe
sway,heaveandrollitis
relatively easy to assess which characteristics is the
mostimportantformperformanceofthedamagedro‐
roshippointofview.
Ithasbeendecidedthattheheelingangleintime
domain will be the roll damage function which
describesthedamagedro‐roship
performanceinthe
best way. This heeling angle in time domain
characteristics is the main data for assessing the
significantvaluetheheelingangle.Duringthedesign
processthisvaluemaybecomparedwiththeangleof
heelobtainedfromthedamagestabilitycalculations.
The roll damage function (heeling angle
in time
domain) is the key design driver for assessing the
correlation between the ro‐ro ship subdivision
(arrangement of internal spaces) and flooding. The
significant value of the heeling angle of a damaged
ro‐ro ship is the value compared with the critical
angleof heel(safety criteria)includedin
the current
regulations.
The last research issue is to investigate if the
proposed model may be appropriate tool for
assessing the performance of the ro‐ro ships in
damaged conditions at the preliminary stage of
design.
Fromthesientificpointofviewitisimportantto
add that the risk‐
based design and a formalized
designmethodologymaybeintegratedtogetherasit
was published by Gerigk, Skjong, Vassalos and the
Ship Stability and Research Centre in Glasgow
(Gerigk2010,Skjongetal.2006,SSRC2009,Vassalos
2006).Theproposedmethodisakindofperformance‐
oriented risk‐based method which
enables to assess
thesafetyofro‐roshipsindamagedconditionsonthe
basis of the damaged ro‐ro ship performance. Such
theapproachwasintroducedbyGerigkandadopted
for the current research including the necessary
changesconcerningthero‐roships,Gerigk(2010).
Generally, for assessment of
performance of the
damagedro‐roshipeitherthestatistics,investigations
usingthe physical models andnumerical simulation
techniques may be applied. They may be used all
together but such the approach is time consuming
and very expensive. The risk assessment may be
based on application of the matrix type risk
model
which is prepared in such a way that it enables to
consider almost all the possiblescenarios of events
during the flooding, Gerigk (2010). It is a big
differenceincomparisonwiththefixedsetofaccident
scenarios(flooding)asitisinthecurrentregulations.
From the ship
safety point of view the criteria is to
achieve an adequate level of risk using the risk
acceptance criteria, risk matrix or ALARP concept,
Gerigk(2010).
Finally, it may be underlined that providing a
sufficientlevelofshipsafetybasedonassessmentof
damagedro‐roshipperformanceandriskassessment
is the main objective of the work form the
methodology and practical point of view. It is the
design objective as the safety is the design objective
betweentheotherobjectives.
350
The measure of performance of a damaged ro‐ro
ship is the adequate level of the damaged ship
characteristics (floatability, damage stability,
damaged ship dynamics) enabling avoiding the
capsizing and sinking (loss of floatability). The
measureofsafetyofadamagedro‐roshipistherisk
(levelofrisk).
Thegeneralstructureofthemethodofassessment
of performance and safety of the ro‐ro ships in
damagedconditionsispresentedinFigure2,Gerigk
(2010).
Start
Requirements,criteria,limitations
Definitionofshipandenvironment
Design Hazardidentification
Scenariosdevelopment
Caseoffloodingidentification
Estimatingofdamaged
shipbehaviour
Assessingofdamagedship
performance
Riskestimation
Assessingofdamagedship
performance
Riskcontrol
Riskoptimisation
Designoptimisation
Making
decisions
End
Modification
ofdesign
Figure2. Structure of the method of assessment of
performance and safety of the ro‐ro ships in damaged
conditions(Author:M.K.Gerigk).
The method structure is based on the general
structure presented in previous work by Gerigk,
Gerigk(2010).Butthepresentedinthepapermethod
is more devoted to the performance assessment
problemsassociatedwiththesafetyofro‐roshipsin
damaged conditions. It is clear whencomparing the
structureof
themethodpresentedbyGerigkin2010
and structure of the current method introduced
briefly in this Chapter (see Figure 2). The basic
elementsofthecurrentmethodareasfollows:
requirements,criteria,limitations,objectives;
ro‐roshipandenvironmentdefinition;
hazardsandscenariosidentification(casesof
ro‐ro
shipflooding);
estimation of the damaged ro‐ro ship behavior
(floatability, damage stability, ship dynamics‐
3DoFmotion);
assessmentofthedamagedro‐roshipperformance
based on the roll damage function (heeling angel
intimedomain,heelinganglesignificantvalue);
riskestimation;
riskassessment(risk
matrix,ALARPconcept);
riskmanagement(riskcontroloptions);
selecting the ro‐ro ship design that meet the
requirements, criteria, limitations, safety
objectives;
optimizingthero‐roshipdesign;
makingthedecisionsonthero‐roshipsafety.
Theknowledge onships safety andmethodology
ofship
safetyassessmentmaybefoundinthepapers
given in References (Abramowicz‐Gerigk 2006,
Abramowicz‐Gerigk 2008b, Abramowicz‐Gerigk &
Burciu 2013, Arangio 2012, Burciu & Grabski 2011,
Gerigk 2004,Gerigk 2005, Gerigk 2006, Gerigk 2008,
Gerigk 2010, Gerigk 2012, Gerigk 2014a, Gerigk
2014b).
3 MODELOFFLOODINGOFRO‐RO
SHIPSIN
DAMAGEDCONDITIONS
Theshipaccidentsatseamayleadtothelossoflife,
loss of properties (ship and cargo) and pollution of
environment. The modern approach to safety of
maritime transportation still requires to apply the
new achievements within the ship design for safety
domain.Theeffective
assessmentofshipperformance
and ship safety assessment often require to develop
the new methods, models and tools. It concerns the
methods, models and tools for analyzing the
performance and safety of ships in damaged
conditionsaswell.
The current method included in the regulations
(SOLAS 2009) introduced in Chapter 1
is a
prescriptivemethodinitscharacter.Itisbasedonthe
combined approach to assessment of thedamaged
shipperformanceandsafety.Insomecasesthesemi‐
probabilisticcomponentsareincorporatedwithinthe
method.Themaindisadvantageofthismethodisthat
it does take into account the fixed
set of scenarios
(floodingprocess)withoutconsidering thedynamics
offlooding.Itmeansthatassessmentofperformance
and safety of the damaged ship is only based on
assessment of the the damaged ship floatability and
damage stability data. Further it means that only
static‐relateddatadecideaboutthebehaviourof
the
damaged ship and assessment of the damaged
performance (capsizing, sinking). The dynamics
associatedwiththefloodingprocessisnotconsidered
intheexistingmethod.
The method presented in Chapter 1 is very
difficult to apply to certain types of ships e.g. car‐
carriers,ro‐rovesselsorpassenger ships.
Usingitin
thesecasesitmayleadtoinsufficientlevelofsafetyor
provide unnecessary design or then operational
restrictions.
Thisiswhytheaimofthispaperistoshownhow
toincorporatethedynamicsofadamagedro‐roship
for performance assessment of the damaged ro‐ro
ship (roll damage function, heeling angle in time
domain,significantheelingangle)andassessmentof
safetyofthedamagedro‐roship(capsizing,sinking).
Therefore the basic information on the new hybrid
model for assessment of performance and safety
assessmentofthero‐roshipsindamagedconditions
including the
damaged ro‐ro ship dynamics is
presentedinthepaper.
3.1 Floodingprocessandfloodwaterdynamics
The behavior of a damaged ro‐ro ship (motion:
heelingangleintimedomain)isfollowingfromthree
majormechanisms:
351
floodingprocessanddynamicsoffloodwater,
interaction between floodwater and damaged ro‐
roship,
damagedro‐roshipmotioninwaves.
The flow through the damage (opening or set of
openings) is estimated according to the equation
whichcanbe obtainedfrom theBernoulliʹs equation
for
thesteadyflowofwater.Allthepossiblephasesof
flooding (water levels) through the damageopening
duringthe damaged ro‐roship motionin waves are
presented in Figure 3 (Gerigk 2010, Gerigk 2014a,
Gerigk2014b).
Water level outside the hull
Water level inside the hull
Damage
Figure3.Possiblephasesofflooding(waterlevels)through
adamageopening(Gerigk,2010).
3.2 Interactionbetweenfloodwaterandro‐roship
dynamics
The effect of interaction between floodwater and
damaged ro‐ro ship motion can be estimated using
either the added weight or added force concept.
According to the added weight concept, the
floodwatershouldbetreatedasanaddedweightwith
amoving
centreofgravity.Thischangesthelocation
oftheshipʹsoverallcentreofgravity.Thetotalmass
of the ro‐ro ship is changed during flooding and
thereforetheinertiaforcesshouldbechangedaswell.
Itisassumedthatthefloodwaterdoesnotexperience
anegativeverticalacceleration.
In the case of the added force concept the forces
due to the floodwater are treated as external forces.
The forces due to floodwater should be calculated
using the instantaneous acceleration rather than
gravitational acceleration and by integrating the
water pressure at the compartment walls (Gerigk
2010,Gerigk2014a).
There are
three methods of modeling the
floodwater‐damaged ro‐ro ship motion interaction
asfollows,ITTC(2011):
quasi‐static with static floodwater treatment
(interaction:addedweight);
quasi‐dynamicwithdynamicfloodwatertreatment
(interaction:addedweight);
dynamic with dynamic floodwater treatment
(interaction:addedforce).
The floodwater dynamics can be
predicted using
various models ranging from the second order
ordinary differential equations through to numerical
fluidmechanics(CFD).
Takingintoaccountthemodelingoffloodwater‐
ro‐roshipmotioninteractionsithasbeendecidedto
use at this stage of research the quasi‐static model.
Obtaining the promising results of assessment
of a
damagedro‐roshipperformanceusingthismodel it
may be decided to apply the quasi‐dynamic model
afterthat.Insuchawayitispossibletocomparethe
behaviorofthedamagedro‐roshipapplyingboththe
modelsofthefloodwater‐shipmotioninteractions.
The
excitation accumulated flood water forces
should be calculated according to the following
assumptions: water in the flooded compartment
moves in the quasi‐static way and free surface of
waterinthefloodedcompartmentisflatandmovesin
differentwaydependingonthemodel.
Anexampleofthefloodwater‐shipinteractions
in
thecaseofthequasi‐staticmodelwiththehorizontal
freesurfaceispresentedin Figure 4,ITTC (2011).In
thecaseofthequasi‐dynamicmodelthefreesurface
inthefloodedcompartmentisnothorizontal.Itisflat
and changing according to the shipmotions ineach
timestep.
3.3 Damagedro‐roshipmotioninwaves
Generally,the2‐Dstripmethodor3‐Dpanelmethod
may be used to calculate the radiation elements
within the equations of damaged ship motion
togetherwiththedirectintegrationusedtocalculate
the non‐linear restoring forces. In some
cases the
damaged ship motion is considered in 6DoF (six
degrees of freedom) domain. During the presented
studiesitisassumedtousethe3DoFdomain:sway,
heaveandroll.Therollviscousdumpingisaddedby
the use of empirical formulae. The linear memory
effectfunction(addedmassand
wavedamping)may
be used even for the large amplitude motion and
heeling condition The particular solutions may be
found in literature (Dudziak 2008, Faltinsen 1990,
Gerigk2010).
Horizontal free surface
of water in the flooded
compartment
Water surface
Horizontal free surface
of water in the flooded
compartment
Damage
Figure4. The graphical interpretation of the quasi‐static
model with the horizontal free surface of water in the
floodedcompartment,(Gerigk2010,Gerigk2014a).
Assessingtheperformanceofadamagedshipthe
followingimpactsmaybetakenintoaccount:
gravitationalforces,
352
hydrostaticforces,
excitationFroude‐Krylovforces,
excitationdiffractionforces,
accumulatedfloodwaterforces,
cargoshiftforces.
4 PRELIMINARYRESULTSUSINGTHEMETHOD
ANDMODEL
Theshipaccidentsatseamayleadtothelossoflife,
loss of properties (ship and cargo) and pollution of
environment. The modern approach to safety of
maritime transportation still requires to apply the
new achievements within the ship design for safety
domain.Theeffectiveassessmentofshipperformance
and ship safety assessment often require to develop
the new methods, models and tools. It concerns the
methods, models and tools
for analyzing the
performance and safety of ships in damaged
conditionsaswell.
Itseemsthatthepresentedmethodofperformance
andsafetyassessmentofshipsindamageconditions
enablestoanalyzealmostforallthepossibleaccident
scenarios (flooding) including the preliminary,
intermediate and final stages of flooding. What is
moreimportantthemethodandmodelenabletotake
into account both the statics and dynamics towards
assessing the performance and safety (risk) of a
damagedship(ro‐roshipasadesigncase).
Such an approach to ship safety assessment in
damageconditionsisnecessarytopredictanyfurther
deterioration of the damage condition. As an
example,iftheshipsurvivesfloodingandisunableto
return to port under own power it is necessary to
solvetheproblemsassociatedwiththetowingwhen
waitingforanassistance.Duringthetowingtherisk
and safety assessment of the ship should
be
permanently controlled (Perera & Soares Guedes
2011, Skjong & Vanem & Rusas & Olufsen 2006,
SoaresGuedes&Teixeira2001).Thestructureofthe
entireprocedurefortheassessmentofsafetyofships
inabnormal/damageconditionsduringtheaccidentat
sea and for the salvage purposes was published by
Gerigk,(Gerigk2010,Gerigk2012).
The preliminary implementations of the method
and model itself have been done for two different
modelsofro‐roships.
Thefirstmodelisbasedonaro‐roshipshapebox
ofthedimensionsasfollows:length:L=25.0meters;
breadth:B=17.0
meters;height:H=12.0meters.The
basic information on the ro‐ro ship shape box is
presentedinFigure5.
Duringthepreliminaryassessmentofperformance
ofthero‐roshipshapeboxindamageconditionsthe
followingresultsofidentificationoftheangleofheel
(usingaquasi‐
staticapproach)accordingto thedata
valuesof thewing tank heightand breadth (printed
asʺhʺandʺbʺin Figure6) were obtainedas follows
(areasfromtherighttotheleftinFigure5:from80to
100 degrees, 60‐80 degrees, 40‐60 degrees, 20‐40
degreesand
0‐20degrees.
Figure5.Thehullformofthero‐roshipshapebox
Figure6. The results of identification of the angle of heel
according to the values of the wing tank heightʺhʺ and
wingtankbreadthʺbʺofthero‐roshipshapebox(Author:J.
Sargun).
The second model is based on a ro‐ro ferry ship
shapeboxofthedimensionsasfollows:length:L=2.0
meters; breadth: B = 0.4 meters; height: H = 0.25
meters. The basic information following from the
physical model investigationsof thero‐ro ferry ship
shape box is
presented in Figure 7, (Gerigk 2010,
Gerigk2014a).
Figure7. The physical model investigations of the ro‐ro
ferryshipshapebox(Gerigk,2010).
Some results obtained using the physical model
investigationsofthero‐roferryshipshapeboxasthe
angle of heel in time domain are of a stochastic
character. They vary very much depending on the
initial and boundary conditions during the
353
investigations. An example of results in the form of
the heeling angle in time domain are presented in
Figure 8. The vertical axis regards the angle of heel
andthehorizontalaxisconcernsthetimeinseconds.
Theseresultswereobtainedforthedataasfollows:
waveheight equal
toζw=0.06mand wavelength
to model length ratio equal toλ
w/Ls=0.3, (Gerigk
2010,Gerigk2014a,Gerigk2014b).
Figure8.Anexamplerolldamagefunction as theangleof
heelofthero‐roferryshipshapeboxphysicalmodelintime
domainobtainedduringtheinvestigationsattheFacultyof
OceanEngineeringandShipTechnologyGdańskUniversity
ofTechnology(Gerigk,2010).
Generally, about thirteen performance/safety
functionsmaybe usedconsideringeach sequenceof
events during flooding of a ro‐ro ship in damaged
conditions. Between these functions are as follows,
Gerigk 2010: avoiding the hazard, hull skin damage
(flooding), position and extension of damage,
equalizationoftheshipheelatthepreliminary
stage
offlooding,lossoftheshipstabilityatthepreliminary
stageofflooding,lossoftheshipstabilityduringthe
intermediatestages (andphases) of flooding, loss of
theshipstabilityatthefinalstageofflooding,lossof
theshipfloatabilityatthefinalstageofflooding,ship
is waiting for assistance, ship returns to port under
own power, ship returns to port by tow, ship is
continuingthemission,fireand/orexplosion.
5 CONCLUSIONS
Some information on the method and hybrid model
forassessmentofperformanceandsafetyassessment
of ships (design case: ro‐ro ships) in damaged
conditionsispresentedinthepaper.
The key issue to apply the methodis to have an
adequate model for performance assessment of the
shipsindamagedconditions.Someelementsofsuch
themodel called a hybrid model is presented in the
paper. The model is under construction and is
prepared for identification of the behavior
characteristics of a damaged ship including
floatability, damage stability and damaged ship
dynamics (angle of heel in time domain).At this
momentthemodelispreparedtothreemajordegrees
offreedom(3DoF)includingthesway,heaveandroll.
It is decided to use the
quasi‐static model for
estimatingthebehaviorofa damaged ship(angleof
heelintimedomain).Todothisthreemajorproblems
should be solved: flooding process and dynamics of
floodwater, interaction between floodwater and
damagedshipanddamagedshipmotioninwaves.
The key design driver for the
performance and
safetyassessmentofaro‐rodamagedshipistheroll
damagefunction(angleofheelintimedomain).
This function seems to be one between the most
importantcharacteristicsofadamagedro‐roship.
From the practical point of view, at the
preliminarydesignstage,theroll
functionenablesthe
designer to assess how much time the flooding last
from the preliminary to the final stage of flooding.
This function enables the design to predict the
extreme and significant values of the heeling angle
during the flooding including estimating the time a
captainmayhasinhis
disposaltostarttheemergency
and evacuation procedures. The entire information
concerningtherolldamagefunctionmaybeincluded
withashipstabilitybooklet.
The current research concerns further
development of the hybrid model of flooding of the
ro‐ro ships in damaged conditions. The final results
willbepublishedaccording
toaPh.D.procedureofJ.
Sargun to be accomplished at the Faculty of
Mechanical Engineering Gdańsk University of
Technology.
ACKNOWLEDGEMENTS
Some information presented in the paper was prepared
during a project conducted at the Gdańsk University of
Technology between 2006‐2007. The authors would like to
expresstheirthanks to the formerMinistryofScienceand
Higher Education (MNiSzW) for supporting the research.
The project was founded by the MNiSzW
Ministry
according to the agreement No. N509 008 31/0584. The
project title was „Alternatywna metoda oceny
bezpieczeństwastatkuwoparciuoocenęryzyka”.
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