393
1 INTRODUCTIONANDMOTIVATION
The Sub‐committee on StabilityandLoadLines and
on Fishing Vessels Safety (SLF) completed the work
on revision of the International Code on Intact
Stability in 2008 [13]. The Code was adopted by
ResolutionMSC.267(85)on4
th
December2008.PartA
of this Code becamemandatory on 1
st
July 2010 via
corresponding amendments to SOLAS and Load
Lines conventions. At present the Sub‐committee on
Ship Design and Construction (SDC) has been
workingonthe2
nd
GenerationIntactStabilityCriteria
‐forexample[2],[4],[8].
Oneofthemandatorystabilitycriterioncontained
inthe2008ISCodeisspecialcriterionforpassenger
shipsthattakesintoaccountanangleofheelinturns.
Thephenomenonanditseffectsonthesafetyofa ship
fromthest
abilitypointofviewarewidelyexplained
intheliterature,forexamplein[6].Accordingtothe
frameworkfor2
nd
GenerationIntactStabilityCriteria
[1] this criterion is classified as deterministic
performancebasedcriterion.
The purpose of this criterion is to prevent
passenger ships (and other if the criterion has been
applied–forexamplecontainerships)fromascenario
that may be described in following points. Such
scenario could be easily presented using TRIPOD
method[7].
1 Theshipsailswiththeservicespeed.
2 There is a need of immedia
te turn to avoid a
collisionorobstacle.
3 Therudderhasbeenlaid.
4 The ship enters into turn and large angle of heel
occurs.
5 Theheelcausescargoshiftoranot
herphenomena
increasingtheangleofheel.
6 Theheeltransitsintocapsizing.
The Need of the Revision of Passenger Ships’ Stability
Criterion on Account of Turning
Z.Szozda
M
aritimeUniversityofSzczecin,Szczecin,Poland
ABSTRACT:Theangleofheelonaccountofturningisoneof the mandatorystabilitycriteriaforpassenger
ships.FormulausedforcalculationsofthiscriterioncontainedintheInternationalCodeonIntactStability[13]
is criticized at present. Agendas of the Sub‐committee on Ship Design and Constructi
on (SDC) for the first
(2014) and the second (2015) sessions contain the item on revision of this criterion and corresponding
regulation.Thepaperpresentssomeshortcomingsofthecriterion.Turningtestsofafreelymaneuveringmodel
ofapassengershiphavebeenexecutedaimingatgatheringdataforthefut
urediscussionanditsfacilitation.
The paper presents results of the tests together with preliminary conclusions that confirm the need of the
revisionoftheregulationandputforwardconcernsonapplicationofsuchvaluesasinitialmetacentricheight
(GMo)andrightinglevercurve(GZ(φ))calculatedfora shiplayingst
illforcalculationofaship’sheelcaused
byturn.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 8
Number 3
September 2014
DOI:10.12716/1001.08.03.10
394
Some sources claim that the sequence of events
presentedabovemightbeacauseofthecapsizingof
thepassenger shipSewolinSouthKorean’swatersin
April2014
1
.
“Asof17April,theROKCoastGuardhasconcluded
that an unreasonably sudden turn to starboard, made
between 8:48 and 8:49 a.m. (KST), was the cause of the
capsizing.AccordingtotheCoastGuard,thesuddenturn
caused the cargo to shift to the left, causing the ship to
experience an incline and to eventually become
unmanageable for the crew. The existence of the sudden
turn has been confirmed by the analysis of the shipʹs
AutomaticIdentificationSystemdata.Thecrewoftheferry
has agreed that the main cause was the sudden turn.
ExpertssuchasLee
Sang‐yun,aprofessorandheadofthe
environment/maritimetechnologyinstituteofthePukyong
NationalUniversity,havealsoagreed”.
Thecorrespondingtextoftheregulationrelatedto
thisphenomenon([13],PartA,Chapter3,regulation
3.1.2)isquotedbelow.
“Inaddition
2
,the angleof heel on account of turning
shall not exceed 10° when calculated using the following
formula:
2
2.0
2
d
KG
L
v
M
WL
o
R
(1)
where:
M
R–heelingmoment[kNּm],
v
o–servicespeed[m/s],
L
WL ‐lengthofshipatwaterline[m],
Δ–displacement[t],
d–meandraught[m],
KG – height of the centre of gravity above baseline
[m]”.
Thisregulationmaybe expressedby the formula
(2).
10
R
(2)
where:
φ
R– angleof heel produced by the heeling moment
M
R.
Thecoefficient0.2 informula(1)istheresultofthe
assumptionthatradiusoftheturningcircleRisequal
to five lengths of a ship at waterline L
WL(actually it
conflicts with the standards for manoeuvrability
adopted by resolution MSC.137(76), what may be
perceivedasanotherissueforconsideration):
R=5L
WL=>
WL
LR
1
2.0
1
Itshallbestressedthattheformula(1)giveninthe
2008ISCodedefinesthemethodofcalculationofthe
1
http://en.wikipedia.org.wiki/Sinking_of_the_MV_Sewol.Asthe
investigationhasnotbeencompletedtillnowthisquotationshall
notbereadasthefinalconclusionregardingthecausesoftheacci‐
dent.
2
InadditiontogeneralcriteriagiveninPartA,Chapter2,regula‐
tion2.2and2.3.
heeling moment on account of turning MR but a
method of calculation of the angle of heel due to
turningφ
R is not defined there. It may be seen as a
kindofashortcominginthe2008ISCode–thereis
no final formula for the angle of heel which is the
criterion.
Theformulaexpressingthecriterionfortheangle
ofheelinturns‐formula(1)‐hasbeen
criticizedby
IMO. It has been recognized that this formula is
unsatisfactoryandneedstobeamended.Anumberof
differentissueshavebeenidentifiedwhichrequireto
be addressed [3]. The most important from the
author’sperspectivearelistedbelow:
1 The criterion requires the use of the simplistic
prescriptiveformulafortheheelingmomentdue
toturning.
2 Maximum permitted angle of heel stipulated by
theregulationrelatestotheangleoccurringinthe
steady state of the turn while the maximum heel
occursatthefirststageoftheturnanditsvalueis
considerablyhigherthanthisinsteadystate.
3 Theformulaemployed
intheregulationdoesnot
take into account the varying turning ability of
different vessels which strongly affects the
magnitude of the heeling moment and hence the
resulting angle of heel. This would pose a
significant hazard to the safety of the personnel
onboard,aswellastotheship
itself.
4 It is not clear in 2008 IS Code what formula or
methodshallbeusedforcalculationoftheangle
ofheelwhichactuallyisthecriterion.
Therearetwomethodsofcalculationoftheangle
of heelφ
R used in practice. The first one is by
comparison of the heeling lever l
R(φ) with righting
leverGZ(φ)–Figure1.
)cos(
g
M
)(l
R
R
where:
M
R–heelingmoment[kNm],
Δ–displacement[t],
g–accelerationduetogravity[m/s
2
].
RRR
GZl
Figure1.AngleofheeldeterminedusingGZcurve
The second method (widely used in stability
calculations)isderivedasasimplificationofthefirst
one.ThismethodusesinitialmetacentricheightGM.
Itispresentedbyformula(3).
395
GMg
M
)(tg
R
R
(3)
It shall be also noted that in the view of the
frameworkdevelopedbySLF51[1]wherethe“trio”:
criterion,standard,regulationweredefinedas:
criterionisaprocedure,analgorithmoraformula
usedforjudgmentonlikelihoodoffailure;
standardisaboundaryseparating
acceptableand
unacceptablelikelihoodoffailure;
regulation is a specification of a relationship
between a standard and a value produced by a
criterion;
andinordertomaketheprocedureunambiguous
thefinalformofthecorrespondingregulationshallbe
writtenasfollows:
φ
R=formula≤standard (4)
In ship design and ship operation both above
mentioned methods use values GZ(φ) and GM
o
calculated for static conditions – for the ship laying
still.However,inrealitythesubmergedpartofthe
hull is being flown round by water during turning
manoeuver.Thereforeactualhydrodynamicpressure
distribution in turn is different from the static one.
Thiscreatesthesituationwheretherestoringmoment
and
metacentricheightinturnmaydifferfromthese
calculatedfortheshiplayingstill.Thismayquestion
approachdescribedintheFigure1andbyformula(3)
and delivers another issue for the consideration of
acceptabilityoftheexistingregulation.
Therehasbeen asubstantial amount ofliterature
published on intact
ship stability. However, at the
sametimeitishardtofindmanystudiesontheeffect
ofship’sforwardspeedonrestoringmomentandin
particular initial metacentric height. Furthermore,
thereareexamplesofreportssupportingthenecessity
oftheresearchinthisfield–forexample[12]where
onemayread:“Aquitestrangebehaviorwasobservedat
thestandardturningcircletestendingwithapull‐out.The
maximumrollangle was about 28° and when the rudder
wasputamidshipsforthepull‐out,theyawrateandroll
anglewerefirstdecreasedasexpected,but
thenincreasedas
speed was picked up. …. The reason for this unstable
behaviorwasnotobvious”.
ExtensivediscussionsatIMOareexpectedbefore
anydecisionconcerningamendmentstoPartAofthe
2008 IS Code, regulation 3.1.2 might be taken. The
authorofthispaperdecidedtoexecutean
experiment
–modeltestsoftheturning manoeuvre.Severaltrials
with the use of a freely manoeuvring model of a
passenger ship have been executed in Iława Ship‐
handling Research and Training Centre in Poland.
The purpose of the experiment was to contribute to
the work of SDC Sub‐committee
by submission a
sample of experimental results in order to facilitate
future discussions. In particular, this paper aims at
addressingtheissueoftheeffectofforwardspeedin
turn on initial metacentric height as an additional
argument (not discussed by IMO till now) for the
needofrevisionof
abovementionedcriterion.
2 DESCRIPTIONOFTHEEXPERIMENT
ThemodeltestswereperformedonSilmLakeinJuly
2013.Themodelofapassengershipthatwasusedfor
theexperiment(scale1:16)isshowninthepictures
presentedinFigure2.Mainparticularsofthemodel
andBodyLinesare
presentedbelow.
Mainparticulars
L
WL=11.529m
B=1.78m
Blockcoefficient=0.687
BodyLines
a)generalviewb)lastpreparationsbefore
thetests
Figure2.Themodelusedforthetests
Theexperimentconsistedofthreestagesdescribed
inTable1.Thefirststageaimedatfindinghydrostatic
data of the model in the loading condition as
prepared for the experiment: the ma ss (Δ) and the
heightofthemetacentrepointaboveBaseLine(KM).
Thesecondstageaimedatfinding
initialmetacentric
heightforthemodellayingstill(GM
o)andtheheight
ofthecentreofgravityaboveBaseLine(KG).Thelast
stage aimed at measuring the model’s position,
trajectory and angle of heel versus time caused by
layingtherudder.Theweatherduringtheexperiment
was calm – there was no influence of the wind and
waves
ontheresultsofthemeasurement.
396
Table1.Stagesoftheexperiment
__________________________________________________________________________________________________
Stage DescriptionMeasuredvaluesOutcomeNooftrials
__________________________________________________________________________________________________
1. Draftsmeasurement Fore,Aft,MeanDrafts;.Volumeofdisplacement,massofthemodel, 1
specificdensityofthewater.heightofthemetacentrepoint.
2. IncliningtestsStaticangleofheelproducedby Initial metacentricheightinstandstill(GMo);7
shiftingoftheknownmass. heightofthe
centreofgravityaboveBaseLine.
3. TurningtestsModel’sgeographicalposition, Model’strajectory,speed,radiusoftheturning 7
3
rudderdeflection,angleofheel –allparametersversustime.
–allparametersversustime. circle
__________________________________________________________________________________________________
3
Actuallytentrialswereperformed.Duetoahumanelementthreeofthemhavebeenneglected–therewasnotpossibleto
determineinitialstableangleofheelatthemomentwhentherudderstartedtomove.Suchtrialthathasbeenneglectedis
shownintheFigure3.
A 2‐dimensional inclination sensor IS2AxxP20
withvoltageinterfacewasusedforthepurposeofthe
measurement of the angle of heel. According to the
manufacturer’s information technical parameters of
the device are as follows: data resolution (at zero
point) is ±0.01 [deg] and calibration accuracy is ±0.3
[deg].Furthermoretheaccuracy ofthe measurement
ofthegeographicalpositionoftheantennax=x(t)and
y=y(t) in the area of Silm Lake is ±0.03 [m]. The
frequency of measurement was 0.1 [s] (ten readings
persecond).
Following parameters of the model that were
necessary for the third stage were
calculated as the
resultofthestagesno1and2:
d=0.425m;Δ=5.43t;GM
o=0.296m;KG=0.804m.
Theresultsofonetrial(asanexampleforthethird
stageoftheexperiment)areshowninfigures3and4
–FullAhead,rudder34[deg] toPortSide.Finally,the
experiment gave seven sets of such data. Table2
contains
summary of seven trials – together with
somepreliminarycalculations.
Figure3.Ruderangleδ(1),speedv(2)andangleofheelφ
(3)versustimet
(test:1.1.F/34/PS_1)
Figure4.Trajectoryofthemodelduringthetest
(test:1.1.F/34/PS_1)
PointS1intheFigure4correspondstotimewhen
therudderstartedtomovetoPS,pointS
2corresponds
totimewhentherudderanglereached34degreesto
PS.PointMcorrespondstothetimewhentheangleof
heelreacheditsmaximum.Atthatmomenttheradius
ofthecirculationwasRandthecentreofturningwas
in point O. R
S is an average radius of the turn in
steadystage.
3 DISCUSSIONOFTHERESULTS
Havingmeasuredgeographicalpositionofthemodel
and the angle of heel versus time and consequently
having noticed the steady stage of the turn it was
possibletoderiveotherparameterscorrespondingto
thesteady
stageoftheturn:averageangleofheelφS ,
averageshipspeedv
SandaverageradiusRS.
Onthe other hand having measured by inclining
teststheinitialmetacentricheightGM
oforthemodel
layingstillitwaspossibletocalculateanangleofheel
thatshouldbeexpectedinthesteadystageoftheturn
(φ
C) according to the theory hidden behind formula
usedinthe2008ISCode.Formula(5)shouldbeused
forthispurpose.
397
2
d
KG
GMRg
v
tg
oS
2
S
C
(5)
Furthermore Formula (5) may be used for
calculationoftheangleofheelthatwasobservedin
steadystageoftheturning(φ
S).
2
d
KG
GMRg
v
tg
SS
2
S
S
(6)
Consequently:
2
d
KG
tgRg
v
GM
SS
2
S
S
(6a)
GM
Susedinformula(6)answersthequestion:
whatvalue of initial metacentric height produces
calculatedangleofheelequaltomeasuredangleof
heel in steady stage of the turn using the theory
hiddenbehindformulausedinthe2008ISCode?
After appropriate mathematical considerations in
formulas(5)
and(6)weobtain:
C
SC
oSS
tg
GM
GM tg
(7)
If the coefficientαin formula (7) was equal 1 it
wouldmean that initialmetacentric height observed
during steady stage of the turn is equal to initial
metacentricheightobservedforthemodellayingstill
and consequently the theory hidden behind the
criterionworkswellinpractice.
Table2containstheresultsofmeasurementsinthe
thirdstageoftheexperimenttogetherwithresultsof
calculationsofparametersandcoefficientsthatcould
bediscussedinthecontextoftheangleofheeldueto
turn.Following abbreviations havebeen used inthe
descriptionofonetrial:1.1–numberof
thetrial;F/H‐
the setting of the screw revolutions (Full/Half);
25/33/35‐rudder setting in degrees; SB/PS‐
starboard/portside.
Table2.Resultsoftheturningtestsandresultsofpreliminarycalculations
__________________________________________________________________________________________________
ParameterDescriptionofthetrial
1.2.F35.S 1.3.F35.S 1.4.H25.S 1.6.H35.S 2.2.F35.S 2.3.F33.P 2.4.F35.P Average
__________________________________________________________________________________________________
vo1.90 1.87 1.47 1.64 1.89 1.91 1.89
v
S0.95 0.92 0.73 0.85 0.95 0.82 0.81
R
S11.09 11.18 11.15 11.06 11.32 8.89 8.44
φ
S1.37 1.29 0.82 1.23 1.43 1.41 1.31
φ
Max2.68 2.61 1.45 2.06 2.49 2.78 2.40
φ
C0.96 0.89 0.55 0.77 0.92 0.88 0.90
φ
S/φC1.43 1.45 1.49 1.60 1.55 1.60 1.46 1.51
GM
S0.205 0.203 0.201 0.183 0.193 0.185 0.205 0.197
v
S/vo0.50 0.49 0.50 0.52 0.50 0.43 0.43
R
S/LWL0.96 0.97 0.97 0.96 0.98 0.77 0.73
φ
Max/φC2.79 2.93 2.64 2.68 2.71 3.16 2.67 2.80
φ
Max/φS1.96 2.02 1.77 1.67 1.74 1.97 1.83 1.85
α=GM
S/GMo 0.69 0.68 0.68 0.62 0.65 0.63 0.69 0.66
__________________________________________________________________________________________________
Following abbreviations have been used in the
Table2:
v
o–observedinitialspeedofthemodel[m/s];
v
S – average speed of the model observed at the
steadystageofaturn[m/s];
R
S–averageradiusoftheturningtrajectoryobserved
atthesteadystageofaturn[m];
φ
S–averageangleoftheheelobservedatthesteady
stageofaturn[deg];
φ
Max – maximum angle of the heel observed during
turningtest[deg];
φ
C–angleoftheheelcalculatedatthesteadystageof
aturnusingformula(5)[deg];
GM
S – initial metacentric height calculated using
formula(6a)[m];
L
WL–lengthofthemodelonthewaterline[m];
GM
o – initial metacentric height determined by
incliningtestforthemodellayingstill[m].
Parameters calculated in the Table 2 (shadowed
fields)containfollowinginformation:
1 Averageangle of the heel observed at thesteady
stageofaturnisinmoreorless150%largerthen
angleofheel
calculatedusingformula(5).Atthe
sametimecoefficientαcalculatedwithformula(7)
is equal about 0.66. It means that significant
reduction of initial metacentric height was
observedatsteadystageoftheturnincomparison
withmodellayingstill.
2 Reductionofthemodel’sspeedinsteadystageof
the
turnincomparisonwiththeinitialspeedwas
about50%for starboardturn and about43%for
theturntoport.
3 Averageradiusoftheturningtrajectoryobserved
atthesteadystageofaturnwasabout0.97%ofthe
length of the model on the waterline in
turn to
starboardandabout75%inturntoport.
4 Maximumobservedangleofheelwas280%larger
in average then calculated using formula (5) and
180% larger in average then angle of the heel
observedatthesteadystageofaturn.
Additionallyitisworthtomentionthat
theangle
ofheelcalculatedaccordingtoIMOregulationusing
formulas (1) and (3) for model’s main particulars is
equal 0.73 [deg]. This means that IMO regulation
underestimates both: angle of heel observed at the
steadystageoftheturnandmaximumangleofheel.
Observation1aboveisin
contrarytoconclusions
reported by Taylan [11] deducted on the base of
experimentsmadebySobolev[9]andObrastsov[10]
398
–“increasingforwardspeedaloneimprovesintact statical
ship stability most of the time”. It proves that more
researchisneededtoexplainthephenomenarelated
to effect of forward speed on intact stability, in
particularwhatparametersplaythemainroleinthis
phenomenon.
Coefficientαin the Table
2 (being less than 1)
containstheinformationthatthemodelinturndueto
waterflowandspecificwaterpressuredistributionon
thehullismorevulnerabletoheelingmomentsthan
in stillness. It proves that formulas (1) and(3) or
method shown in the Figure1 shall not
be used for
thepurposeofstabilityassessmentofashipinturn.
The pressure distribution on a hull surface in turn
shall be investigated in more detailed way and the
results of the investigation should be properly
applied.Itisveryimportantfindingfromthisexperiment.
Coefficientαmay be interpreted
as “reduction of
initial metacentric height GM” during turning
manoeuvre.
Fromtheauthor’sperspectiveatpresentthereare
threepossibleoptionshowtoconductthediscussion
atIMOaimingatrevisionofthecurrentcriterion.
1 Developmentofatuningcoefficientthatwilltake
into account a number of parameters
affecting
maximum angle of heel in turn. This tuning
coefficientmightreplace“0.2”containedincurrent
regulation.ThisapproachwasproposedinPolish
documentsubmittedinNovember2013tothefirst
sessionofSDCSub‐committeewhichwas held in
January2014[5].Itrequiresa lotofmodelandfull
scale tests and is very conservative one.
Furthermoreitisnotphysicallybased.Eventually
this coefficient may occur to be ship dependent
what would make the approach complicated in
practice.
2 Development of a method for calculation of the
“reducedinitialmetacentricheightinsteadyturn”
and consequently to keep
the formula for
calculationasitis‐providedthatcoefficient“0.2”
wouldbedeletedand“real”radiusoftheturning
circle would be used. This radius could be
obtainedfrommodelorfullscaletests,computer
simulationsorananalysisofexistingshipssimilar
to this under consideration. The maximum angle
of heel could be assumed to be twice of this in
steadystageasitmaybederivedusingsimplified
method of the calculation of so called
“dynamicalangleofheel”
4
(φD≈2φC).
3 Development of a physically based method of
calculation of maximum angle of heel in turn
(which is dynamical one) that takes into account
energybalanceofallheelingmomentsactingona
ship at the first stage of the turn, particularly
moment produced by rudder, inertia moment
(producedby
centrifugalforce),dumpingmoment
and restoring moment. Physically based method
meanshereamethodthattakesalsointoaccount
hydrodynamic pressure distribution acting on
submerged part of the ship sailing with forward
speedinturn.
4
Thiscoefficientequals1,85inthecaseofthemodelusedforthe
experiment.Itislowerthantheoreticalone(whichis2,00)dueto
ruddereffect,addedmasseffects,dumpingandothereffects.
The third option (being robust one) is the most
desirable as it is in line with performance based
approach to the second generation intact stability
criteria. But on the other hand it requires solving a
number of very complex problems related to
hydrodynamicphenomenawhichuptonowhavenot
been adequately investigated and understood. For
thisreasononeshouldnotexpectthisoptioncouldbe
appliedinthenearestamendmentsto2008ISCode.
4 CONCLUSIONS
Seventurningtestshavebeenexecutedusingamodel
of a passenger ferry. Angles of heel have been
measuredtogetherwithship’sspeedand
trajectoryas
a function of time. The test results may be
summarizedasfollows:
1 It is hard to find studies on the effect of ship’s
forwardspeedonrestoringmoment.Thiseffectis
not taken into account in mathematical models
and computer codes used for ships’ rolling
simulations.
2
A ship in turn is more vulnerable to heeling
momentsthantheshiplayingstill.Itistheresult
ofdifferentpressuredistribution onthesurfaceof
thehullinthesetwocases.
3 Initial metacentric height GMo calculated for the
shiplaying still does not describe the stiffness of
the
shipinturnwithacceptableadequacy.
4 The findings from the model tests show that
formula(1)containedinthe2008ISCodetogether
withformula(3)commonlyusedinpracticeshall
not be used for stability assessment of a ship in
turn as they underestimate actual angle of heel
(maximumItransientandaverageinsteadystage
oftheturn).
5 Three possible options how to proceed further at
IMO in order to revise current regulation were
indicated.
6 Tuningofthecoefficientusedinformula(1)may
betemporarywayoutbutthisisveryconservative
approachandmay
opennewproblems like ship‐
dependence. Development of the method for
“reduction of GM” caused by turning is another
possibility. This approach (if applied) shall be
perceivedalsoasatemporaryone.
7 Anumberofadditionalmodelandfullscaletests
followed by extensive discussion are needed
before revision
of the corresponding part of the
2008 IS Code may be agreed. Eventual
modification of this criterion should preferably
avoid application of GM
o or GZ(φ) values
calculatedfora shiplaying still. The influence of
the forward speed on these parameters may be
crucialinthiscase.
Mathematical models of ships’ rolling and
consequentlycomputercodesusedforsimulationdo
nottakeintoaccounttheinfluenceofforwardspeed
on restoring moments.
Very well known problems
with validation of mathematical models and
computercodesmaybereducedtosomeextentinthe
futureifforwardspeedisproperlytakenintoaccount
inrestoringmomentscalculation.
399
ACKNOWLEDGMENTS
The author wishes to express his thanks to the
Director and employees of the Iława Shiphandling,
ResearchandTrainingCenter,inparticulartoprof.L.
Kobyliński, for their support and making the model
availablefortheturningtests.
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[13]InternationalMaritimeOrganization,International
Code on Intact Stability, Resolution MSC.267(85),
London,2008,UK.
