481
1 INTRODUCTION
There are numerous criteria that can be used for
estimating the safety of navigation in the restricted
sea areas. Yet, most of them are not standardized,
whichcancauseproblemswithdistinguishingthesea
areas difficult for navigation and the restricted sea
areas and classify them as ‘easy’ or ‘difficult
for
navigation. It is also hard to present the ‘scale of
difficulty’innavigatinginagivenseaareabymeans
ofnumbersorsymbols,assuchasystemhasnotbeen
establishedsofar[4].
In this article we try to establish, if possible, the
standard, i.e. universal method to classify the sea
areas difficult for navigation with regard to the
conceptofuniformsafety system of tra
nsportin the
seaarearestrictedbyasafetymargin,definedbythe
outlineofathreedimensionaldomainofaship[6].
The risk analysishas been prepared for PS Cla
ss
container vessels Emma Maersk” from AE10 Far
East AsiaEurope Service in the Deep Container
Terminal(DCT)GdanskPortPolnocny.Navigational
risk for the ships manoeuvring in the restricted sea
areahasbeenestimatedwithrespecttovariedouter
interference (average and extreme condition) on the
approach to Gdańsk Port łnocny DCT termi
nal
alongside the currentlyexploited eastern fairway by
meansofathreedimensionalmodelofship’sdomain
[6],[7].
2 NAVIGATIONALRISKANALYSESWHEN
PROCEEDINGINRESTRICTEDSEAAREAS
Inthischapterwepresentmethodsthatcanbeused
forestimatingsafetyofnavigation(navigationalrisk)
intherestrictedseaareas by mea
ns of the modelof
the ship’s domain [6], the definition of the
navigational risk [7] and the simple ship’s domain
formulas(from[6])forestimatingtheship’sdomain
parameters (see Fig.1): including the depth of the
ship’s domain (G
D), the height of the ship’s domain
(W
D), the length of the ship’s domain (DD) and the
beamoftheship’sdomain(S
D).Then,usingallabove
informationbymeansofthethreedimentionalmodel
oftheship’sdomainandknowingtheparameters,we
aregoingtotrytoestablishthenavigationalriskina
vertical(R
NG,RNW)andhorizontal(RNDdz,RNDr,RNSpand
Safety of Shipping when Navigating on the PS Class
Container Vessel “Emma Maersk” While Approaching
DCT Terminal in Gdańsk Port Północny
G.Rutkowski
GdyniaMaritimeUniversity,Gdynia,Poland
ABSTRACT:Inthispaperauthorpresentsthemethodsthatcanbeusedforestimatingthesafetyofshipping
(navigationalrisk)intherestrictedseaareasoftheGulfofGdanskbymeansofathreedimensionalmodelof
ship’s domain specified for the PS Class container vessels
Emma Maersk”. The essence of the method
suggestedinthethesisisthesystematicapproachtoaseavesseloperationintheaspectofestimatingitssafety
whileapproachingDCTterminalinGdańskPortłnocnyinthedivergentexteriorconditions.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 10
Number 3
September 2016
DOI:10.12716/1001.10.03.13
482
R
NSl)planeforaPSclassContainervessellike“Emma
Maersk”intheballastand/orloadedconditionwhen
navigatingontheeastfairwaytoDCTTerminalinthe
Gulf of Gdansk (sea area restricted with the overall
dimensions350metersinbreadth,17metersindepth
and253,6073,6 direction)
in the divergentexterior
conditions(averageandextreme).
According to the ship’s domain definition [6],
every ship will be safe (in navigational meaning) as
longassheistheexclusiveobjectwhichcangenerate
dangerwithinherdomain.
WithreferencetoaverticalplaneOZofthethree
dimensionalco
ordinatesXYZestablisheddownfrom
thecentralpointofthelocalship’sreferencesystem,
one can affirm unambiguously that every ship will
remainsafeaslongthevalueofG
Dissmallerthanthe
real value of the sea depth h (see Fig.1). Therefore,
componentR
NGofRNcanbereferredtoasthevertical
component of the navigational risk that concerns
keeping under keel clearance, or risk concerning
under keel clearance. The component mentioned
above can be depicted by means of the following
formulas:
max
max
when1
when10
when0
Th
GhT
Gh
R
D
D
NG
(1)
Formula (1) indicates that the value zero of the
navigational risk [7], deriving from factors (objects)
A
i, signifies total navigational safety with respect to
thesefactors(objects).Consequently,accordingtothe
formula(1),assumption
D
Gh canbedefinedasthe
guarantee of the safe shipping‐navigation with
reference to all underwater objects or obstructions
immersedonthedepthsmallerthanh.Ifseadepthh
is smaller or equal to the ship’s draft T, that is
max
Th ,accordingtotheformula(1)seapassagecan
be unfeasible
13
or highly risky. In that situation the
valueofthenavigationalriskR
NGwillequalone(see
formula (1)), and in all probability it will signify
unquestionable (100%) risk of collision with some
underwaterobjectsimmersedon thedepthlessthan
h.
Furthermore, we can also say that the value of
navigational risk R
NG for the sea depth h limited
between T
max and GD (Tmax<hGD) will be limited
between zero andone (R
NG [0,1]) (seeformula (10)
themiddleline).Generalformula,whichcanbeused
to estimate navigational risk R
NG, depending on h
factor from the range (
D
GhT
max
), is presented
below:
max
TG
hG
R
D
D
NG
(2)
Similarly, risk analyses that refer to all objects
hangingintheairabovethewater(seeFig.1)canbe
carried out just as it was done in case of all
underwater objects i.e. obstructions. Therefore,
componentR
NWofthenavigationalriskRN(let’scallit
the vertical component of navigational risk that

13
Inouranalysesweexcludethesituation,whentheshipcanchangeher
draftduetoforexampledeballastingoperation.
concerns keeping air draft clearance, or shortly risk
concerning air draft clearance) can be depicted by
meansofthefollowingformulas:
No
DoN
ND
oD
Do
NW
HH
WHH
HW
HW
WH
R
when1
when
when0
(3)
where:
H
o ‐distancebetweenwaterlevelandtheheightof
the nearest objects hanging above the water (for
bridgeverticalclearanceaboveHW(highwater),[m];
H
N‐ship’sairdraft,(distancebetweenwaterlineto
thehighestpointontheship’shull),[m].
Similarly, with reference to horizontal plane OX
(see Fig.1) R
NDdz and RNDr components of the
navigational risk R
N (let’s call them horizontal
components of the navigational risk that concern
keeping safe distance from the nearest danger
adequately ahead and astern of the ship, or just the
riskconcerningsafedistanceaheadandastern)canbe
depictedbymeansofthefollowingformulas:
RdNdz
DdzNdzRD
RDDdz
NdzDdz
DdzNdz
NDdz
Ld
DdL
LD
dD
Dd
R
when1
when
when0
(4)
and



RdNr
DrNrRD
RDDr
NrDr
DrNr
NDr
LLd
DdLL
LLD
dD
Dd
R
when1
when
when0
(5)
Interpretation of formulas (4) and (5) will be
carried out similarly to the presentation of
navigational risk R
NG and RNW in case of vertical
navigational reserve. Hence, the assumptions d
Ndz >
D
Ddzfromformula(4)aswellasdNr>DDrfromformula
(5) constitute the guarantee of safety of shipping
(navigation) with reference to all objects
(obstructions) detected adequately ahead d
Ndz and
asternd
Nroftheship.Whenanalysingformula(4)one
can also notice that the value of navigational risk
limited between zero to one (R
NDdz(0,1)) will come
into being only if the value of the distance to the
nearest danger ahead of the ship d
Ndz will be either
lessorequaltothelengthoftheship’sdomainahead
D
Ddz. In all probability, assumption dNdz<LRD will
signify navigational accident or collision with some
objects (obstructions) detected ahead of the ship or
unquestionable (100%) risk of collision with those
objects . A questionable situation concerns those
objects that move with some speed and have their
owndomain,thevalueofwhichnormally decreases
d
Ndzparameter.
SimilarlywithreferencetothehorizontalplaneOY
(see fig. 1) distinguishers R
NSl and RNSp of the
navigational risk R
N (let’s call them horizontal
components of the navigational risk that concern
keeping safe distance to the nearest danger
adequatelyonportandstarboardsideoftheship,or,
in short, risk of keeping safe distance to port and
starboard side) can be depicted by means of the
followingformulas: