539
1 INTRODUCTION
The navigation safety of ships that maneuver on
inshore waters mostly depends on the size of
availableunderkeelclearance(UKC).Thedecisionto
allowagivenvesselinoroutoftheportisinfluenced
by many factors, among them, for example: wind
waves,heightofwatersurface,draftandheelofthe
vessel, ship sq
uatting, taking into account possible
errorsincalculatingthesevaluesatthesametime.
Inorderforboththeportandtheshipoperatorto
achieve optimum profit, a system was created with
the main objective to determine and predict the
dynamic under keel clearance (DRWPS) for ships
suchasQ‐flextypeLNGtankerstha
tenterthePortof
Swinoujscie.
The DRWPS system is a computer program that
determines the under keel clearance based on the
methodofconstantreservesusingaccuratemodelsof
squatting and change of the position of the lowest
pointofaship’shullasaresultofit
smovementofthe
wave.It is dynamicallylinkedtowith water gauges
and the reading of the height and direction of the
wave. It can work in the mode of planning the
maximumspeedordefiningbasedonthespeedgiven
forthepredictedUKC.
Thesystemisba
sedonthemethodofcomponents
where each component of the clearance is described
asamodel(squatting,ship’smovementonthewave)
orconstantonethatcanbechangedbyanauthorised
user. The DRWPS takes into account both the
analytical model of sq
uatting that downloads data
from a database in the program which can be
calibrated with respect to the data from the echo
sounderfittedoneachship,andtheinfluenceofwind
waveswhich maybe subject tocalibrationbased on
the current reading from the ships inclinometer.
Onlineaccesstodataonwaterlevelandwindwaves
increases the accuracy of the system. Maximum
va
luesofthefollowingerrorshave been adopted as
thesystem’sconstants:
Errorindeterminingtheconstantheel
Errorindeterminingthevessel’ssquatting
Errorindeterminingthewaterlevel
Errorinsoundings
Error in silt
ation taking into account the time
passedbetweensoundings
System for Determining Dynamic Under Keel Clearance
of Vessels Entering the Port of Swinoujscie (DRWPS)
L.Gucma,M.Bilewski,J.Artyszuk&K.Drwięga
M
aritimeUniversityofSzczecin,Szczecin,Poland
ABSTRACT:Thearticlepresentsasystemfordeterminingdynamicunderkeelclearance.Inordertobuilda
DRWPS system, a mixed model was created based on the analysis of math models. The system includes
advisorysoftwarefordefiningtheconditionsfortheenteringoflargeLNGvesselsinthecontextofunderkeel
clearance and software was built to support the decision‐ma
king of operators who are responsible for
introducingthesevesselstothePortofSwinoujscie.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 3
September 2017
DOI:10.12716/1001.11.03.21
540
Other errors and constants as agreed with the
orderingparty.
2 DESCRIPTIONOFTHEMATHSMODEL
APPLIEDINTHEDRWPSSYSTEM
In order to define safety with respect to dynamic
under keel clearance, the following methods are
applied:
1 Method of constant component reserves where
reservesaredefinedas
constantvalues;
2 Methods based on math models of reserves,
including methods that apply probabilistic
models;
3 Mixedmethods.
Anotherdivisiondifferentiatesbetween:
1 Staticmethods;
2 Dynamicmethods.
ThemodelcreatedfortheDRWPSsystemshould
be deemed as a mixed (two reserves components –
squatting and wave influence,
are modelled using
mathmodels)anddynamicmodel,i.e.amodellinked
to external sensors and possible changes in a ship’s
speed and movement when it enters the port are
takenintoaccount.
2.1 Methodofconstantcomponent reserves
Themethodofconstantcomponentreservesadopted
assumes that in order to
ensure a safe under keel
clearance for actual vessels draft T under the most
unfavorableconditions,itisnecessaryto:
1 Determine the influence of the most important
factors on reserve for UKC (the so‐called
componentreserves);
2 Determine the maximum or the most probable
valuesofeachreserve
componentRi;
3 Add reserves individually and determine the so‐
calledcriterionreserveRk=∑Ri;
4 DeepenthebasintothedepthofH=T+Rk;
5 Avoid introducing vessels when the sum of
reserve components taking into account the
changeinsquattingandwaterlevelissmallerthan
thevalueof
thecriterionreserve.
Figure1.Diagramofthecriterionreserve
2.2 Themodelofdynamicunderkeelclearanceadopted
The model and some of its parameters have been
basedon the [6] document that was approved of by
UMS in Szczecin titledʺProjekt systemów
zapewniających bezpieczną nawigacje i obsługę
statkówLNGnapodejściuiwporciezewnętrznym
w
Świnoujściuʺ [A project for systems that ensure safe
navigationandhandlingofLNGshipswhenentering
and staying in the external port in Swinoujscie] of
2012.
For calculations, the maximum Q‐flex type LNG
tanker of the following dimensions was adopted for
thePortofSwinoujscie:
L=315m,
B=50m,TLNG=12.5m,H=14.5m
The values for each component reserves adopted
arepresentedinTable1
WhenforecastingsafeexploitationofLNGvessels,
thesumof componentreserves (criterionreserve R
k)
hastobelargerorequalto:
2
kLNG
R
HT m (1)
The main dependence in the model is the
dependence on the reserve difference (R
r), i.e. the
value of the actual UKC reserve with respect to the
assumedcriterionreserveR
k=2mintheformof:
() 2 ()
rka a
R
RRv H T mRv H T
(2)
where:
R
k–criterionreservevaluedefinedas2mand0.9m;
R
a(v) – actual reserve comprised of component
reserveswherethereserveforsquattingiscalculated
for various, changing speeds of the ship on the
entrance;
∆H–differenceofthewatersurfacelevelwithrespect
tothezerolevelH=500cm;
∆T–differenceofavessel’sdraughtwithrespect
to
themaximumT
LNG=12.5morTMAS=13.6m.
As a result of the calculations according to the
abovedependence,twopossibilitiesappeared:
1
0
r
R
acceptable situation; a vessel can move
along the waterway with the speed defined
(Figure2.1);
2
0
r
R
unacceptable situation; the indispensable
reserveislargerthanthecriterionone(Figure2.2).
Figure2.1. An acceptable situation – the actual reserve is
smaller than the criterion one (the difference between
reservesislargerthanzero).
541
Figure2.2.Anunacceptablesituation–theactualreserveis
larger than the criterion one (the difference between
reservesissmallerthanzero).
In order to determine the criterion value of the
speedofavesselonthewaterway,reservedifferences
R
r for various speeds were calculated which are
presentedinthediagramasacurvedependingonthe
vessel’s speed. The example in Figure 3 shows two
situations:
1 SituationAwherethespeedneedstobereduced
withrespecttothemaximumone;
2 SituationBwhereduetothepositive
valueofthe
differencebetweenreservesthespeedcanbeequal
to the maximum one on the stretch. In this case,
there is a theoretical possibility of increasing the
speed on the entrance (to be decided by the
authorizedparties).
A.(maximum speed is smaller than the maximum and
equalsVpassed=7.5kn);
B (maximum speed equal the maximum,it is theoretically
possible to achieve the speed of 12kn with the sum of
reservesequalto the criterionreserve, in this situationfor
the speed of vmax=10kn the ship moves with the sum of
reserves0.5mlargerthanthecriterionreserve,whichmeans
thatthesumofallreservesis2m+0.5m=2.5mforthespeed
of10kn).
Figure3.SamplepossiblesituationsforthereserveforLNG
Table1.Componentreservesadoptedintheprogrambased
on[6]and[14]
_______________________________________________
Reserve Stretch Stretch2 unit Name
symbol
_______________________________________________
∆1 0.20.2m Reserveforanerrorin
sounding
∆2 0.20.2 m Navigationreserve
(valueadoptedas
requestedbyUMS)
∆3 0.00.1m Reserveforsiltation
∆4 0.00.0m Reservefortheheight
oftide
∆5
LNG 0.30.5m Reserveforanerrorin
determiningthestate
ofwaterforLNG
∆6 0.10.1m Reserveforanerrorin
theship’sdraught
∆7
LNG0.40.4m Reserveforthe
constantheelofthe
LNGship(1deg.)
∆8 Variabledepends m Reserveforsquatting
onthespeedadoptedasanaverage
fromthemethodsof
Huuska,Barrasa3,
Eryzulu,Icorelsand
Ankundinova
∆9 Variabledepends m Reserveforheeland
trimfromthewave
onthewaveparameters
_______________________________________________
AsthecalculationstofindthecriterionvaluefortheUKC
wereconductedwiththemethodofconstantreserved,it
wasassumedthatreservesfrom∆1to∆7willremainonthe
criterionlevelasconstantvalues,whereasdynamicreserves
∆8and∆9willbechangedintheprogram.
2.3 Stretchesofwaterwaysadopted
The program allows to determine the squatting on
threetypesofshallow‐waterbasins:
Shallowwater(Restricted),
Channel(Canal)
Deepenedwaterway(RestrictedCanal).
TwocharacteristicstretchesforLNGtankeratthe
entrancetothePortofSwinoujsciewereapplied:
1 Stretch1–
frombuoys 1‐2(km43) tobuoys9‐10
(km15);
2 Stretch2–frombuoys9‐10(km15)tobuoys15‐16
(km0).
In each of these stretches, basedon [6] the worst
sectionwasselectedasfarasthevalueofsquattingis
concerned
(Stretch1–areaofbuoys9‐10;Stretch2–
area of buoys 15‐16) and its parameters were
determined and introduced in the program. Both
stretchesrepresenttheso‐calleddeepenedwaterway.
2.4 Modelsofsquattingadopted
The analysis and description of the models of
squatting available were conducted
based on the
studies [PIANC 2014] and the precise model of
Ankundinova. The following models of a moving
ship’ssquattingwereselected:
1 Huuska(appliedbytheauthoritiesinFinlandand
Spain);
2 Barrasa3;
3 Eryuzlu(appliedbytheCanadianInshoreGuard);
4 ICORELS(recommendedbyPIANC);
542
5 Ankundinova(newmethodthatiswellverifiedin
realityandthatallowstocalculatethesquattingat
thebowandatthestern).
To calculate the final reserve for squatting ∆
8,
averagevaluesforsquattingwereappliedintheform
of:
5
1
88
5/
i
(3)
where:∆
i – values calculated through eachof the 5
modelsofsquatting.
The Huuska method overstates the value of
squatting as compared to other methods. According
to Briggs [13], the Huuska/Guliev squat method can
beusedforallthreechanneltypesanditisdefinedas:
2
2
2
1
nh
bs
pp
nh
F
D
SC K
L
F
(4)
– the squat constant, is typically used
as an average value, although Hooft (1974) had
originally used
(values from 1.9 to 2.03
wereusedattimes)
D–shipdisplacement
2.5 Modeloftheinfluenceofwavesonthebowmovement
In analysing a ship’s response (rolling) to waves, a
linear model of dynamics in 6 stages of free
movement is commonly applied, as well as the
stochastic nature of the process of waves, described
withthe function oftheso‐called spectraldensityof
thewaveenergy.
From the perspective of decreasing under keel
clearance, only 3 elementary movements are crucial:
one linear (vertical) movement and two angle
movements. These are, respectively: heave, roll and
pitch.Their
amplitudecharacteristics,calledresponse
amplitude operators (RAOs), present a ship’s
responsetotheharmonicwaveofagivenamplitude
andheight,i.e.amplitudeofavessel’srollingandits
shiftwithrespecttothewaveitself.Sixfunctionshave
beengivenascalardefinition,i.e.theamplitudeand
phasecharacteristics
foreachofthethreeenumerated
componentmovements.
Inorder todescribeaship’smovement,a mobile
(linked to the ship) clockwise system of coordinates
(Figure4)wasappliedandcriticalpointsresponsible
for UKC reduction were determined where
movements (vertical displacements) are finally
defined.Theyarethecornersofa
rectangleplacedon
the surface of the keel of the L (length between
perpendicular) and B (length all over) dimensions,
stretchedbetweenperpendicularandtheship’ssides.
Numbers and horizontal coordinates (xʹ
UKC,yʹUKC) of
criticalpointsarethefollowing:
portside starboardside
ʺ‐1ʺ‐bow
2
,
2
BL
ʺ+1ʺ‐bow
2
,
2
BL
ʺ‐2ʺ‐stern
2
,
2
BL
ʺ+2ʺ‐stern
2
,
2
BL
Amplitudecharacteristicsofelementaryrollingare
usually determined directly in the system linked to
theship’scentreofgravity–seethesystemGx
SKySKzSK
inFigure4.FortheneedsoftheUKCforecastsystem
created, condensed functions of 4 arguments were
used:waveamplitude,wavedirectionwithrespectto
theship(intheʺwheretoʺconvention),ship’sspeed,
depth of the basin determined based on the
commercial SEAWAY software [Journee, 2001;
Journee/Adegeest,2003].
TheverticalrollingofthecriticalpointzUKC,andtothe
sameextentthedecreasingUKC,foraregularwaveis
finallydefinedwiththefollowingequation:
UKC G UKC G UKC
z t z t t y' t x' x'
(5)
whereallthevaluesareexpressedinthemobileOxyz
inertial system temporarily stopped on the level of
calmwater,whereasʺprimedʺvaluesasstifflylinked
toOxyzareconstant:
z
UKC – vertical displacement (rolling) of the critical
pointintheOxyzsystem[m];
z
G– vertical displacement (rolling) of the centre of
gravityG[m];
– heelingangle(ofrolling)[rad];
– trimmingangle(ofpitch)[rad];
t – time[s],
xʹ
G – longitudinalcoordinateofthe positionofthe
ship’scentre of gravity intheOxyzsystem resulting
fromitsweightlayout[m];
xʹ
UKC,yʹUKC – longitudinal and crosswise
coordinateofthepositionofaselectedcriticalpointin
theOxyz[m]systemresultingfrom thedefinition as
above.
Theabovecalculations have to be carried out for
eachofthefourcriticalpoints.
Determining the basic parameter for defining
statistical parameters of rolling means
determining
theintegraloftherollingspectrewithrespecttothe
waveamplitudeasavariationofstochastic(random)
processofrollingortheso‐calledzeromomentofthe
spectre,markedasm
0zUKC.Oneofthembasedonthe
above‐mentioned Rayleigh’s layout is the amplitude
of rolling z
UKC0‐p%, which can be overstated with the
probabilityofp
%runbytheoperator/decision‐maker
(see [Dudziak, 1998], [Journee/Adegeest, 2003],
[PIANC,2014]amongothers):
543
z
G
x
SK
y
SK
z
SK
x
0
y
0
z
0
G
O
0
x
G
CP
(surface of symmetry)
MS
(surface of the midship)
WP
(surface of the
waterline)
x
z
y
O
motionless system
(earth)
Figure4.Systemsofcoordinates.
Figure5.Weatherparametersatbuoyno12.
0% 0
%
1
2ln
UKC p zUKC
zm
p
(6)
Thetypicalvaluesofp
%is0.05or0.01.Thesystem
of dynamic UKC designed selects the largest
amplitude of all the critical points taken into
considerationinlinewith(6).
Inordertohaveageneraloverviewas faras the
size of rolling is concerned, the so‐called significant
amplitudeofrollingz
UKC0_1/3isalsoused,whichisthe
meanoutof1/3(33%)ofthehighestamplitudes.Itis
closetotheobservedamplitude:
zUKCUKC
mz
03/1_0
2
(7)
butsmallerthantheonegivenbytheformula(6)with
typicalvaluesofp
%.
Thereisapossibilityofintroducingtheactualfull
spectre of waves if it is known. In case of a lack of
suitable statistical parameters of waves, e.g. period,
they are estimated according to the implemented
empiricalandtheoreticaldependences.
3 THEDRWPSSYSTEM
TheDRWPSsystemfordynamicunder
keelclearance
createdisacomputerprogramdividedintomodules
with the aim of a possible development. The main
assumptionofthesystemwastogatherthefollowing
inputdata:
Maximum speed allowed while maintaining the
requiredclearance
Underkeelclearanceforthespeedselected
Recording and
paintingthedatainthe form ofa
reportonavessel’sentrance.
Theinputdatarequiredare:
544
1 Statisticaldata:
Ship’s data based on the data in the program
database(foraprecisemodelofsquatting)
Maximumspeeds(portregulations)
Dimensionsofthemodelwaterway.
2 Dynamicdata(downloadedonline):
Watersurfacelevel
Waves(height,direction,period)
Wind(force,direction).
3
Datatobemodifiedbyanauthorizeduser:
Introducingconstantcomponentreserves
Introducingshipdata
Otherconstantvalues.
4 Inputdata–determinedbytheuser:
Selectionoftheship.
Selection of the work mode (determining
maximumspeedsforthemaximumclearanceselected
/determiningreserves
formaximumspeeds)
Figure6.GraphicaluserinterfacefordynamicUKC
545
4 CONCLUSIONS
The software created at the Maritime University in
Szczecin can serve as an advisory program when
takingdecisionstointroduceLNGtankersinthePort
ofSwinoujscie.Thesoftwarewasbuiltbycomparing
the constant reserve for a given ship’s entrance to
Swinoujscie while taking into account the
squatting
andwavereservewithrespecttothecriterionvalue.
Aboveall,theprogrammakesitpossibletoplanthe
maximumspeedfortheLNGvessel.
The further development of the DRWPS system
shall rely on replacing the reserve for the change in
the water level with a dynamic one
and building a
mathmodel,andreplacingthereservefortheheelby
distributing this reserve to components such as:
constant error in the list, heel caused by
turning/circulation and heel caused by the wind,
currentandtugvessels.
To achieve more accurate final readings of
DRWPS,thereserve for the
fall in the water surface
levelshouldbereplacedwithamodelofforecastthat
wasalreadyaddedtotheprogramasanextension.
Instead of the referential reserve, the target
DRWPS model should be based on (display on a
chart) only the navigation reserve and determine
other reserves through
models (accepted by the
MaritimeOffice).Thenavigationclearanceshouldbe
of about 0.3m for vessels without hazardous cargo
and0.6mor more for vessels with hazardous cargo.
The navigation reserve can be determined based on
methodsofriskestimation.
REFERENCES
[1]GucmaL.(2009):Zarządzanieryzykiemmorskim.AMw
Szczecinie.
[2]Gucma L. (2012): Zarządzanie ryzykiem w rejonie
mostów usytuowanych nad drogami wodnymi w
aspekcie uderzenia jednostek pływających. AM w
Szczecinie.
[3]PIANC 2014. Harbour Approach Channels Design
Guidelines. PIANCreport no 121. Maritime
NavigationCommission.PIANC
2014.
[4]Przepisy Portowe. Zarządzenie nr 3 Dyrektora Urzędu
MorskiegowSzczeciniezdnia26lipca2013r.
[5]Rozporządzenie Ministra Transportu i Gospodarki
Morskiejzdnia1czerwca1998r.wsprawiewarunków
technicznych, jakim powinny odpowiadać morskie
budowle hydrotechniczne i ich usytuowanie, Dz.U. nr
101
zdnia6sierpnia1998.
[6]Projektsystemówzapewniającychbezpiecznąnawigacje
i obsługę statków LNG na podejściu i w porcie
zewnętrznymwŚwinoujściu(2012): Akademia Morska
wSzczecinie.
[7]Gucma S. (ed.) (2015): Morskie drogi wodne
Projektowanie i eksploatacja w ujęciu inżynierii ruchu
morskiego.
Gdańsk.
[8]Briggs M.J., Henderson W.G.: Vertical Ship Motion
Study for Savannah, GA. Entrance Channel (2011):
ERDC/CHL TR‐11‐5, September (Final Report), US
ArmyCorpsofEngineers,ERDC,Viksburg.
[9]DudziakJ.(1988):Teoriaokrętu.WydawnictwoMorskie,
Gdańsk.
[10]Journee J.M.J. (2001): Verification and Validation
of
Ship Motions Program SEAWAY. Report 1213a, DUT,
Delft.
[11]Journee J.M.J., Adegeest L.J.M.: Theoretical Manual of
Strip Theory ProgramʹSeaway for Windowsʹ. Report
1370,DUT/AMARCON,Delft,2003.
[12]PIANC (2014): Harbour approach channels design
guidelines. Report no. 121‐2014 (Maritime navigation
commission),PIANC,Bruxelles.
[13]BriggsM.J.(2010):Comparison
ofPIANCandCADET
squatpredictions,PIANCMMXCongressLiverpool.
[14]Określanie parametrów maksymalnych statków
mogącychbezpiecznie wchodzić do portu handlowego
Świnoujście ( po modernizacji toru podejściowego do
Świnoujściaorazzmianiewarunkóweksploatacjiportu).
(2012):AkademiaMorskawSzczecinie.
