99
1 INTRODUCTION
Sea navigators of today face several important tasks
intheirwork.Oneofthemostimportantnavigatorʹs
tasks is to ensure shipʹs safety during its passage at
sea.Thereareseveralcriteriacurrentlyusedforship
safetyassessment.
Anintensifyingdebatehasbeenheldforthepa
st
five decades on the use of the ship domain for
analysisand evaluation of thenavigational situation
(i.e.Fuji&Tanaka1971,Coldwell1975,Śmierzchalski
& Weintrit 1999, Pietrzykowski & Uriasz 2009,
Wielgosz2016).
Theproblemofshipdomaindeterminationisstill
uptodateduetoalargenumberoffact
orsaffecting
itsshapeandsize,sogreatthatforpracticalreasons
inthe actual domaindeterminationmethod some of
thesefactorsaretakenintoaccount.Inmanyexpertsʹ
opinion, the most important domain determinants
includethesizeandspeedofthevesselandthetype
ofseaareaopenorrestricted. 
The ship domain as a crit
erion for assessing the
safety of navigation is of great importance for
navigationinwaterswithhightrafficintensity,where
thevesselhaslimitedavailablemanoeuvringareadue
to physical and legal limitations and in open sea
areas, with less traffic and a large av
ailable
manoeuvringarea.
The observed behaviour of marine navigators
reveals large differences in distances kept to other
vessels encountered and passed in either type of
navigable area, which directly translate into
differencesinthesizeandshapeofthedomain.
In this paper the ship domains in open sea area
andrestrictedareahavebeencompared.
Ship Domain in Open Sea Areas and Restricted Waters:
an Analysis of Influence of the Available Maneuvering
Area
M.Wielgosz
M
aritimeUniversityofSzczecin,Szczecin,Poland
ABSTRACT:Ashipdomainisnowadaysanimportantnavigationalsafetyassessmentcriterion.Itsshapeand
sizedependonmanyfactors.Theavailablemaneuveringareaseemstobeoneofthemostimportantofthem.
Thisarticleexaminestheinfluenceoftheavailablemanoeuvringareaontheshapeandsizeofshipdomainin
theopenseaandrestrictedwaters.Theresearchwasconductedusingasimulationmethod.Expertnavigators
part
icipated in simulations using the ECDIS system. The domains of ship passages in open sea area and
restrictedareahavebeencompared.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 1
March 2017
DOI:10.12716/1001.11.01.11
100
2 SIMULATIONRESEARCHANDTHEMETHOD
OFSHIPDOMAINDETERMINATION
2.1 Simulationresearch
A simulation research was conducted in ECDIS
(Electronic Chard Display and Information System)
simulatorlab. To analyze passing distances between
shipskeptbyexpertnavigators,thedatatransmitted
in the Automatic Identification System (AIS) were
registered at
one second discretization. Shipsʹ
positions(latitudeandlongitude),coursesandspeeds
wereusedforfurthercalculations.Astherearemany
domain models found in the literature with
differently interpreted domain boundaries, this
author decided to determine three effective domain
boundaries: minimum, mean and maximum. An
example of the examined domains
is presented in
Figure1(Wielgosz&Pietrzykowski2012).
The current stage of author’s research on ship
domain, herein concerning the open sea area,
includedtheexecutionandanalysisof305singleship
encounter situations (scenarios were prepared in
advanceforthreetypesofships),performedbyexpert
navigatorsin
theECDISsimulator.
Fiverelevantscenariosforeachsizeofshipwere
preparedandrecorded,thusallowinglatertorepeat
theinitialsituationwiththepossibilityof individual
maneuvers by attending experts‐sea navigators. A
detailed description of the research and analysis
methodisdescribedinauthor’searlierpublications).
Themain
purposeoftheconductedresearchwas
to determine the influence of the available
maneuveringareaconditionsontheshipdomain.
Figure1. An example of the analyzed domains in a
restrictedarea.
2.2 Theshipdomaininarestrictedarea
The problem and models of ship domain in the
restricted area have been described in many
publications lately (Hansen et al. 2013, Wielgosz &
Pietrzykowski 2012, Wielgosz 2015). Most of the
domainshaveanellipticalshape.
In this paper the author implements a
model of
anticollisiondomaindevelopedthroughhisresearch
(Wielgosz2015).Theadoptedmodelisanellipsewith
anoffsetcentre,describedbyparametricequations(1
to6),whichtakesintoaccountthesizeandspeedof
thevessel.
)cos()(
0
taxtx
(1)
)sin()(
0
tbyty
(2)
vv
L
bb
vL
b
L
vacLaa
11
1
2
111
(3)
vv
L
bb
vL
b
L
vacLab
22
2
2
222
(4)
xxx
rvqLpx
0
(5)
yyy
rvqLpy
0
(6)
where:
L ship’slength[m];
v ship’sspeed;
a
1L,b1L,c1L,a2L,b2L,c2L lengthinfluencecoefficients;
a
1v,b1v,c1v,a2v,b2vspeedinfluencecoefficients;
t relativebearing;
p
x,qx,rxXaxiscentredisplacementcoefficient;
p
y,qy,ryYaxiscentredisplacementcoefficient.
2.3 Theshipdomaininanopenseaarea
Implementingthesamemethodasforrestrictedareas
(Wielgosz2015),threetypesofdomainwerestudied
for the analyzed ships. In order to determine the
shapeandsizeofadomainintheopensea
area,the
authorcontinuedtheresearchdescribedabove,using
thesameshipmodelsofdifferentsize,consideredto
berepresentativefortoday’sshipping.
Selected parameters of the ship models are
presentedinTable1.
Table1.Selectedparametersofshipmodels
_______________________________________________
parametershipsize
small medium large
_______________________________________________
typeCoaster LORO Tanker
length[m]95.0 174.0 261.0
breadth[m]13.0 23.0 48.0
displacement[T] 3510.0 19512.0 63430.0
speed[knots]11.1 16.3 16.3
_______________________________________________
The research was conducted only forʹfull aheadʹ
speed,typicallydevelopedwhentheshipproceedsin
theopenseaarea.
Detailed results obtained in open sea area (after
implementation of generic algorithms for
approximation)arepresentedinSection3below.
101
3 COMPARISONOFTHERESULTSIN
RESTRICTEDANDOPENSEAAREAS
The data published herein consist of previously
presenteddata for the restricted area and the newly
obtainedresultsfortheopenseaarea.
3.1 Thedomainshape
As expected, the domain shape in the open sea
remainselliptical,as
presentedinFigures2,3and4.
These figures are drawn in the ship coordinate
system,withthevertical Xaxis(Xaxisiscommonly
used in navigation as the longitudinal axis of
symmetry)andthehorizontalYaxis.
Approximated data for “small”, “medium” and
“large” ship are visualised in
Figures 2, 3 and 4,
respectively.
Figure2.Comparisonofthestudieddomainsfora“small”
ship.
Figure3. Comparison of the studied domains for a
“medium”ship.
Figure4.Comparisonofthestudieddomainsfora“large”
ship.
3.2 Length ofthesemiaxes
3.2.1 Restrictedarea
Detaileddataconcerningthelengthofsemimajor
and semiminor axis for 3 types of the examined
domainsintherestrictedareaarepresentedinTable
2.
Table2.Semiaxislengthinrestrictedarea
_______________________________________________
semiaxis domaintype shipsize
small medium large
_______________________________________________
majorminimum529 537 865
mean1093 1341 1524
maximum1730 1719 2667
minor minimum226 439 441
mean332 534 697
maximum477 829 1035
_______________________________________________
3.2.2 Openseaarea
The lengths of elliptical domain semiaxes in the
openseasarepresentedinTable3.
Table3.Semiaxislengthinopenseaarea
_______________________________________________
semiaxis domaintype shipsize
small medium large
_______________________________________________
majorminimum1058 1680 2044
mean1672 2312 2915
maximum2166 2470 3226
minor minimum602 992 1170
mean992 1464 1760
maximum1295 1826 2371
_______________________________________________
The research results are also presented in a
graphicalforminFigures5and6forsemimajorand
semiminoraxis,respectively.
102
Figure5.Lengthofthesemimajoraxesinanopenseaarea.
Figure6.Lengthofthesemiminoraxesinanopenseaarea.
Figure7.Domainareainarestrictedandopenseaareafor
selectedships
3.3 Thedomainarea
Thedomainareacanalsobeanalysedasacriterionof
navigational safety assessment, so the area of the
domains(here countedas an area of an ellipsewith
known length of the semiaxes) was also analysed.
TheresultsarepresentedinFigure7.
3.4 Comparison
oftheresultsforexaminedseaareas
The resulting length of semiaxes in both sea areas
concernedareshowninFigures8and9forthemajor
andminorellipsesemiaxes,respectively.
Figure8. Length of the semimajor axis in restricted and
openseaareasforselectedships
A comparison of the resulting domain areas is
presentedinFigure7.
Figure9.Length ofsemiminor axisinrestricted andopen
seaareaforselectedships
Anotherapproachtoanalyzing theobtaineddata
isto calculate the coefficient of change (ratio) of the
examinedparametervaluesfromthetwoseaareas‐
therelativemagnitudesoftwoquantities.
Theratiooflengthtosurfaceareaoftheanalysed
domainparametersinthewatersunderconsideration
ispresentedin
Figure10.