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
up‐to‐dateduetoalargenumberoffact
orsaffecting
itsshapeandsize,sogreatthatforpracticalreasons
inthe actual domaindeterminationmethod some of
thesefactorsaretakenintoaccount.Inmanyexpertsʹ
opinion, the most important domain determinants
includethesizeandspeedofthevesselandthetype
ofseaarea–openorrestricted.
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
anti‐collisiondomaindevelopedthroughhisresearch
(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,b2v–speedinfluencecoefficients;
t – relativebearing;
p
x,qx,rx–X‐axiscentredisplacementcoefficient;
p
y,qy,ry–Y‐axiscentredisplacementcoefficient.
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
_______________________________________________
parametershipsize
small medium large
_______________________________________________
typeCoaster LO‐RO 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 forʹfull 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 ofthesemi‐axes
3.2.1 Restrictedarea
Detaileddataconcerningthelengthofsemi‐major
and semi‐minor axis for 3 types of the examined
domainsintherestrictedareaarepresentedinTable
2.
Table2.Semi‐axislengthinrestrictedarea
_______________________________________________
semi‐axis domaintype shipsize
small medium large
_______________________________________________
majorminimum529 537 865
mean1093 1341 1524
maximum1730 1719 2667
minor minimum226 439 441
mean332 534 697
maximum477 829 1035
_______________________________________________
3.2.2 Openseaarea
The lengths of elliptical domain semi‐axes in the
openseasarepresentedinTable3.
Table3.Semi‐axislengthinopenseaarea
_______________________________________________
semi‐axis domaintype shipsize
small medium large
_______________________________________________
majorminimum1058 1680 2044
mean1672 2312 2915
maximum2166 2470 3226
minor minimum602 992 1170
mean992 1464 1760
maximum1295 1826 2371
_______________________________________________
The research results are also presented in a
graphicalforminFigures5and6forsemi‐majorand
semi‐minoraxis,respectively.
102
Figure5.Lengthofthesemi‐majoraxesinanopenseaarea.
Figure6.Lengthofthesemi‐minoraxesinanopenseaarea.
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 semi‐axes) was also analysed.
TheresultsarepresentedinFigure7.
3.4 Comparison
oftheresultsforexaminedseaareas
The resulting length of semi‐axes in both sea areas
concernedareshowninFigures8and9forthemajor
andminorellipsesemi‐axes,respectively.
Figure8. Length of the semi‐major axis in restricted and
openseaareasforselectedships
A comparison of the resulting domain areas is
presentedinFigure7.
Figure9.Length ofsemi‐minor axisinrestricted andopen
seaareaforselectedships
Anotherapproachtoanalyzing theobtaineddata
isto calculate the coefficient of change (ratio) of the
examinedparametervaluesfromthetwoseaareas‐
therelativemagnitudesoftwoquantities.
Theratiooflengthtosurfaceareaoftheanalysed
domainparametersinthewatersunderconsideration
ispresentedin
Figure10.
103
Figure10.Ratiooflengthtoareaoftheanalyseddomain
parameters
Asexpected,allthreeanalysedparametersshowa
significant increase in the open sea domain area in
comparisonwiththerestrictedwatersdomain.
A mathematical description (function) of
increasing the length of ship domain semi‐axes in
transition from the restricted to open sea area has
been developed. A curve fitting
tool in the Matlab
environmentwasusedforapproximation.
It follows from Figure 11 that the change of the
analysed ratio is of linear character, which allows
using a linear function (7) for approximation and
mathematicaldescription.
f
xmxn (7)
Figure11.Thelengthtoarea ratioof the analyseddomain
parameters.
Describedbyfunction(7),thechangeintheellipse
parameterswhilea shiptransitsfromtherestrictedto
the open sea area can be used to modify a domain
modeladoptedfortherestrictedarea(1,2,3,4,5,6)
forapplicationintheopenseaarea.
3.4.1 Thesemi
‐majoraxislengthincrease
The result of ratio increase approximation
referringtothesemi‐majoraxisispresentedinFigure
12anddescribedbyequation(8).
Figure12. The ratio increase−theresultofapproximation
forsemi‐majoraxis.
Thelinearmodel:
111
f
xmxn
(8)
where:
x–shipsizefactor(tobecalculated,seeTable4),
m
1,n1–functioncoefficients.
Thecoefficients(with95%confidencebounds):
m
1=0.19(0.19,0.19),
n
1=1.34(1.34,1.34).
Thegoodnessoffit:
SSE:2.958e
‐031
R‐square:1
adjustedR‐square:1
RMSE:5.439e
‐016
3.4.2 Thesemi‐minoraxislengthincrease
Figure 13 depicts the result of ratio decrease
approximation concerning the semi‐minor axis,
describedbyequation(9).
Figure13.Ratiodecrease−the resultof approximationfor
thesemi‐minoraxis.
Thelinearmodel:
222
f
xmxn
(9)
104
where:
x–shipsizefactor(tobecalculated,seeTable4),
m
2,n2–functioncoefficients.
Thecoefficients(with95%confidencebounds):
m
2=‐0.235(‐0.345,‐0.125),
n
2=3.22(2.982,3.458).
Thegoodnessoffit:
SSE:0.00015
R‐square:0.9986
adjustedR‐square:0.9973
RMSE:0.01225.
Table4.Shipsizefactor“x”forequation(8)and(9).
_______________________________________________
shipsize
verysmall small medium large verylarge
_______________________________________________
length[m] 60,0 95.0 173.5 261.3 294.0
factor(x) 0.51 23 3.5
_______________________________________________
Thevaluesfor“verysmall”and“verylarge” ship
are suggested only‐for extrapolation‐and to be
verified in the future research, as preliminary
research has been conducted only for such size of
ships. Intermediate values from 1 to 3 are to be
interpolatedforaspecificshiplength.
Inconclusion,thelengthofellipticaldomainsemi‐
axesintheopenseaareacanbepresentedas(10,11):
01
afxa (10)
02
bfxb (10)
where:
a
o – length of semi‐major axis of elliptic domain in
openseaarea,
a
‐ length of semi‐major axis of elliptic domain in
restrictedarea,asdescribedinequation(3),
b
o – length of semi‐minor axis of elliptic domain in
openseaarea,
b
‐ length of semi‐minor axis of elliptic domain in
restrictedarea,asdescribedinequation(4),
f
1(x),f2(x)‐functionvaluedescribedabove.
Thesearealternativeformsoftheaboveequations:
0
0.19 0.34axa (12)
0
0.235 3.22bxb (13)
4 CONCLUSIONS
Ithasbeenobservedthat,generally,thedomainsize
changes distinctly depending on available
maneuverable area dimensions. The simulation
researchprovesthatnavigatorsmaneuveringinopen
seaareastendtokeepalargerdomaincomparingto
restrictedarea.
In particular, the following changes have been
observedfor
navigationintheopensea:
1 increaseinlengthofsemi‐majoraxis;
2 increaseinlengthofsemi‐minoraxis;
3 increaseinthesizeofthedomainarea;
4 changeddisplacement ofellipse centre (x0,y0) is
proportional to length increase of the relevant
semi‐axis.
Another important observation
is that the
proportionsofdomainaxeschanges‐domainsinthe
open sea are relatively wider and more oval than
thoserelativelysliminrestrictedareas.
Regularityisobservedintheincreaseofsemi‐axis
lengthinrelationtoshipsize.Itispossibletodescribe
itbyequations(10
and11or12and13).
Isseemspurposefultoverifytheresultswithreal
datafromAISbasedresearchasproposedbyHansen
etal.(2013)forarestrictedarea.
This research outcome has been achieved under
theresearchprojectNo1/S/ITM/2016financedfroma
subsidy of the Ministry of
Science and Higher
Educationforstatutoryactivities.
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