723
1 INTRODUCTION
Marinevesselsspendabout80%oftheirtimeinthe
opensea,whilethisperiodoftimeaccountsforabout
20% of all ship accidents. The remaining 80% of
accidents occur in the areas of confined waters of
fairways,canals,near‐portandportwaterareas.The
reason for this distribution is the proximity of
navigational marks, the presence of navigational
hazardsandtheavailabilityofcyberattacksthatlead
toemergencyevents.
Thevulnerabilityofshipsystemsto cyber‐attacks
and their management are closely related to
navigational risks, but the methods of combating
themarefundamentallydifferent.
So,forexample,to
managethelevelofnavigation alrisk,itisnecessaryto
use high‐precision methods of planning the
coordinatesofthepathbytrajectorypoints(TP).
When controlling the movement, to monitor the
position of the vessel the satellite method in
differential mode is used, the radial
mean square
error, which is several times smaller than the
correctionforthepositionofthesatelliteantenna,the
abscissaofthecentreofgravityofthevesselandthe
turningpole. At the sametime,suchship positional
data can be cyber‐secure as long as it is not
Cybersecurity of the Processes of Manoeuvring in
Confined Waters
I.Surinov
1
&D.Shumilov
2
1
NationalUniversityOdessaMaritimeAcademy,Odessa,Ukraine
2
ColumbiaShipmanagement,Odessa,Ukraine
ABSTRACT:Inthiswork,theroutesforinbound/outboundfromeachberthintheportofChornomorskwere
designed according to the ship’s pilotage plan for navigational purposes. On the basis of the received
information, a computer‐aided planning of recommended routes for pilotage of
all types of vessels, which
wouldcall theport of Chornomorsk, was developed. The results ofthe automaticanalysisbythecomputer
programaredesignedasthematrixofcoordinatesforinbound/outboundattheport.Inordertoverifythe
cybersecurityoftheintroducedmodelofautomaticplanningof
thepathbythecoordinatesoftrajectorypoints
andusingthedecisionsupportsystemsfortheautomaticcontroloftheparametersofmaneuveringbytechnical
methods,radarobservationswerecarriedout.Afterobservationthecomparinganalysisoftheaccuracyofship
and shore radar systems was done, the methodology of
the observations for coastal systems developed.
Conducted radar observation of 300 arrivals and 200 departures of vessels from the port of Chornomorsk
accordingtothedevelopedplansforeachberthintheport.Therecommendedrouteswereintegratedintothe
expandedcomputerprogram«PathPlanningIS»,whichmadeitpossibleto
obtainthematrixesofcoordinates
oftheobservations.Acomparativeanalysisofthecomputersimulationandpracticaltransitionofshipsinthe
recommendedwaterareaoftheportdemonstratedthattheintroducedmodelisconfirmedbytheresultsofthe
observations.Onthebasisoftheanalysis,itisdetermined
thatthedevelopedmodelensuresthecybersecurity
oftheprocessesofmaneuveringincon finedwaters.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 17
Number 3
September 2023
DOI:10.12716/1001.17.03.25
724
broadcastedbyautomaticidentificationsystem(AIS).
Atthesametime,thepresenceofacyber‐attack can
be determined only by means of a comparative
analysis of the same parameter of maneuvering in
different ways, one of which a priori should not
respondtoacyber‐attack.
In the case
of a significant deviation of the
coordinates of the shipʹs position from the planned
ones, first, it is necessary to determine the cause of
such an impact‐navigationrisks oras a result of a
cyber‐attack. Information on the presence of
navigational risks and their types is given
in
informational documents – charts, sailing directions
andnoticestomariners.Forcybersecurity,suchdata
is not given in a systematic form, so the navigator
mustdeterminethesourceofthedangerhimselfand
make a decision. Recommendations of the
International Maritime Organization (IMO) on
methodsofdeterminingthepresence
ofcyber‐attacks
andmakingdecisionsaboutreducingtheirimpactare
given in the Guidelines on maritime cyber risk
management (MSC‐FAL.1/Circ3, Guidelines on
maritimecyberriskmanagement)[1].
2 LITERATUREREVIEWANDPROBLEM
STATEMENT
InJuly2020,anonlinecybersecurityforumreporteda
900 percent increase in cyberattacks on
operational
technologysystemsinthemaritimeindustry[2].Ina
reportoncyberreadinessbyAcronis(AcronisCyber
ReadinessReport),basedonasurveyofexpertsfrom
3,400 multinational companies, it was reported that
due to the COVID‐19 pandemic, 92% of surveyed
enterprises work remotely. It is obvious that the
actions of hackers are aimed at ships and maritime
enterprises that work remotely [3]. In the last three
monthsof2020,39%ofcompaniessurvivedattackson
Zoom, Cisco Webex, and Microsoft Teams video
conferencing applications [4‐5]. Ransomware attacks
have increased significantly during the pandemic,
with31% of companies
reportingdaily cyberattacks,
and50%experiencingthematleastoncea week[6].
AccordingtoestimatesbyLloydʹsofLondon,theloss
from cyberattacks in the maritime industry is
estimated at 200 billion dollars [7]. All these data
clearlydemonstratetherelevanceofcreatingacyber
defensestrategyinthe
maritimesector.Thisrequires
the development of international and national
regulatory documents and recommendations, the
organization of special state units and information
support, similar to what exists in the area of
navigationalrisks.
But organizing such a structure for maritime
shippingasawholeisacumbersometask,therefore,
using
an analogy that is acceptable for navigational
risks,wesuggeststartingwiththevoyagecycleofsea
vessels. For this purpose, we will use the existing
system of organizing information on navigational
risks[8‐10]duringthevoyagecycleandimprovethe
recommendations on ways to identify cyberattacks
anddevelopedmethods
ofmanagingtheirlevel.This
approach is justified by the fact that, based on a
generalized table of existing accident‐prone areas of
the voyage cycle, the shipmaster can determine the
areas where cyber‐attacks can be expected, and
preparetoreducetheirnegativeconsequences.
Theproposedapproachcharacterizesthe
relevance
of creating a cyber securitystrategy inthe maritime
sector,whichbeginswiththeshipʹsvoyagecycle,then
moves to ports and extends to the entire maritime
industry.
Thecentralissue,whichhasnotyetbeenresolved,
isthemethodofpreparationoftheshipʹsnavigation
planfor
theentry/exitoftheshipfromtheport,which
should be used during pilotage. The existing
recommendations for the preparation of the pilot
passageplanoftheshipʺPilotpassageplanʺarenot
intended for navigational purposes. For this reason,
thecaptainhastousethepersonalexperienceofthe
pilotinmanagingtheshipwhenenteringthisport.
Thedevelopedplanningmethod[11‐12]oftheship
navigation pilotage plan when entering/exiting the
port and the developed program for automatic
calculation of the matrix of planned coordinates of
trajectory points [13] by the route method for
implementationinthepractice
ofworkintheportsof
Ukraineneedverification.
3 FORMULATIONOFTHEGOALSOFTHE
ARTICLE(STATEMENTOFTHETASK)
The aim of this work is to verify the analysis of
possiblevulnerabilitiesandcyberrisksinthevoyage
cycle on the basis of a generalized table of accident
prone areas of navigation risks and to compile a
registerofvulnerabilitiesofnavigationequipmentin
relation to cyber‐attacks and to determine the
proceduresforimplementingacyber‐securitystrategy
on each accident‐prone section of the route. [14‐16].
This will makeit possible to organize cyber defense
on
ships in the areas of expected cyber‐attacks and
reduce losses from cyber‐crimes after the
implementationoftheappropriateresponseplan[17‐
24].
4 PRESENTATIONOFTHERESEARCH
MATERIALWITHAFULLJUSTIFICATIONOF
THEOBTAINEDSCIENTIFICRESULTS
4.1 Calculationoftheaccuracyofthecoastalradarstation
(CRS)
The estimation of the trajectory of the shipʹs motion
accordingtotheplannedcoordinatesisbasedonthe
determinationofthedisplacementofthepointofthe
centreofgravityrelativetothetrajectorypoints(TP).
Atthesametime,theamountofrudderturning,and
thefrequencyofadjustment
depends ontheratioof
the amount of lateral shift and the radial root mean
square error (RMSE) of the determination of the
vesselʹs position. In order to verify the proposed
modelforcalculatingtheplannedcoordinatesofthe
TPwhenentering/exitingofthevessel,itisnecessary
to
determinetheirvaluesaccordingtothewaypoints
(WP), maneuvering characteristics of the vessel and
the selected rudder turning angle for curvilinear
trajectories.Itisnecessarytocomparetheaccuracyof
725
theplannedcoordinatesaccordingtothereadingsof
the navigation device, whichisthe mostaccurateof
the existing ones. The shipʹs radiolocation station
(Radar), Automatic Identification System (AIS) and
shoreradiolocationstationarethedevicesatdisposal
ofthenavigator.Tochooseacontroldevice,wewill
perform a comparative analysis of the accuracy of
each method and determine its resistance to cyber‐
attacks.
Letʹs consider the errors of determining the
position of the ship by comparing the planned
coordinatesanddeterminingthepositionoftheship
usinghigh‐precisioncyber‐independentmethods[25‐
26].Errorsdue
tovarioussourcesoftheiroriginare
classified as instrumental, methodological and
calculationerrors.
Instrumental errors are associated with the final
accuracy of the presentation of the original
information. They are caused, for example, by the
roundingoftheinputvaluesortheaccuracyoftheir
measurements.
Methodological errors are
due to the fact that
many calculations are solved approximately using
specialnumericalmethods.This, inparticular, refers
to trigonometric, logarithmic, exponential and other
functions.
Errorsinthecalculationresultsarecausedbythe
propagation or transformation of the errors of the
original data during their passage in the calculation
algorithm
throughanumberofintermediateresults.
Inmosttechnicalcalculations,thelevelofaccuracy
of the result, in which its ma ximum relative error is
from0.1to5%,isconsideredsatisfactory.
A qualitative solution to the problem of
determining the accuracy of any calculated quantity
with random values of the
arguments requires the
establishment of the RMSE for the definition of the
function:

2
22
2
, ,...,
ZX Y t
zz z
ZfXY tm m m m
x
yt









(1)
whereX, Y, ...,t – measured parameters,andm
x,my
….m
t–theirRMSE.
The situation of approaching ships (Fig. 1) is
consideredinthefollowingway.
At the initial moment of time t
1, the oncoming
vesselС
cwasatadistanceD0АfromthevesselСv.At
the moment of time t
2, the mark of the oncoming
vessel travelled the distance S
о by the LRM and the
bearingB
2changedbythevalueΔB,andwaslocated
atthedistanceD
6А.TheanglebetweentheLRMand
bearingB
1wasα1,andbetweenbearingB2wasα2.The
oncomingvesselpassesatadistanceCPArelativeto
itsown.
The value of the traveled relative distance S
о is
determinedfromtheobtusetriangleС
vСcСcʹbythe
formula:
22 22
006 06
2cos
AA AA
SDD DD B (2)
Given that the values of angles α
1 and α2 are
unknown, we determine their values using the
theoremofsinesfromthesametriangle:
6
1
0
sin
sin
A
DB
S

(3)
0
2
0
sin
sin
A
DDB
S

(4)
Foreachmethodofdeterminingthepositionofthe
ship[26‐28],therearecalculationschemesthatallow
establishing the error of determiningthe position of
the ship relative to the Earthʹs surface, which is
usuallyrepresentedasacircleontheplane.Theuse
forestimatingthe
positionoftheerrorellipse(Fig.1)
has not been widely used, as it requires the use of
threeparameters–theminorandmajorsemi‐axesand
the direction of its location. In order to use a more
accurateestimatethantheellipse,acharacteristicwas
introducedintothepractice
ofnavigation–theradial
RMSE,which,withasafetymargin,outlinesthearea
oftheprobablelocationofthevesselalongtheradius.
AccordingtotherequirementsoftheIMO,fora95%
probability, it is necessary to multiply the results of
thecalculationsby2,thatis,to
taketheradiusequal
tothemajorsemi‐axisoftheellipse.
Figure1. Probable assessment of the situation of
approachingships.
Foramorerigorousassessmentoftheaccuracyof
determiningthelocationofthevessel,formula(1)is
used sequentially for functions (2)‐(4), as a result,
formula(1)iswritten:
000
00 6
06
22
2
2
AA
AA
SSS
SD D B
DD
mm m m












(5)
00 6
2
22
0
2
06 60 06
000
cos cos sin
57.3
AA
AA AA BAA
SD D
D
DB DDBmDDB
mm m
SSS


 






(6)
726
6
1
0
sin
arcsin
A
DB
S



(7)
16 0
60
22
2
2
111
A
A
DSB
DS
mm m m
B





 





(8)
16 0
2
22
0
2
11 1
60
57.3
A
B
DS
A
tg tg m tg
mm m
D
StgB









(9)
01
sin
A
CPA D
 (10)
01
01
2
2
2
A
A
CPA CPA
CPA D
D
mm m











(11)
0
1
2
2
CPA
01
CPA
A
D
A
m
m
m
Dtg









(12)
01
0
cos
A
D
TCPA
V
(13)
010
010
22
2
2
A
A
TCPA TCPA TCPA
TCPA D V
DV
mm mm











(14)
00 1
2
22
01 01
1
TCPA
2
00
0
cos sin
cos
A
AA
DV
DD
mm m m
VV
V









(15)
Intheobtainedformulas(5)‐(15),eachvalueofthe
RMSE includes all three types of errors –
instrumental, unavoidable and inherited from
calculations.
Asyou can see,thecalculationof the SCP of the
calculated values of theparameters accordingtothe
formulas (5)‐(15) make it possible
to create correct
formalized calculation schemes for estimating the
accuracyoftheplaceforcomparativeevaluation.
When measuring the relative distance and
directionusingradar(Fig.1),thevalue of theradial
RMSEisdeterminedbytheformula:
2
2
B
0
57,3
D
Dm
m




(16)
Table1.Comparativeevaluationofthecharacteristicsof
shipradarandshoreradar
________________________________________________
NoParameterParameter Parameter
valueof valueof
shoreradar ofshipradar
________________________________________________
1. Therealresolutionofthesystem 0.3° 1.0°÷2.0°
bydirection,notworse:
2. Therealresolutionofthesystem 12м 15м
byrangeonscalesupto2miles,
noworse:
3. Measurementerrorofthe 5‐7м/ 1м/0.8°÷1.0°1м/0.8°÷1.0°
systemforastationary 5°
‐10°
pointtargetatD=5miles 15m 30m 30m
atP=0.95,notworse:by
range/angle,byroute
coordinate
4. Measurementerrorofthe 7м/0.13° 20м/0.3° 20м/0.3°
movementparametersof 0.13 – –
thetarget
beingfollowed 2°≈4°÷8°≈4°÷8°
atthestageofthestablecar
escortisnoworsethan: 0.5knots≈1÷1.5knots≈1÷1.5knots
routecoordinates:bydistance/
anglegeographicalcoordinates
bylatitudeanddeparture,
shipʹscourse,shipʹsspeed
5. Thenumberofaccompanying 200–
autotargetsisnotlessthan
6. Carrierfrequency 3.34–3.42GHz 3.34–3.42GHz
7. Minimumdetectionrange,no 20m 50‐70m
morethan:
8. Minimumsensitivity,nolessthan: –130dB –120dB
9. Impulsepower:10kWt 7‐100kWt
10.Durationofprobingpulses:
‐inshortpulsemode
 0.045ms 0.1ms 0.1ms
‐inthelongpulsemode 0.15ms 0.5÷1.0ms 0.5÷1.0ms
11.Antennatype:waveguide waveguide
slot slot
11.1 Antennapolarization:А2‐circular,horizontal
А3‐circular,linear,A3
horizontal
linear
11.2 Thewidthoftheantennaʹs 0.23degree 1.0°÷2.1°
directional
pattern(expanded
L=2.5m)inthehorizontalplane
11.3 Thewidthoftheantennapattern7deg 20°÷25°
intheverticalplane
A2–pseudocosecantquadratic 3deg –
12.Antennagain:А2:6000,(дБ) Antenna Antenna
gain: gain:
A2:6000, A2:6000,
13.А
3:18000(дБ)А3:18000 А3:18000
14.Supplyvoltagesingle‐phasesingle‐phase
variable variable
50Hz 50Hz
220±22 220±22V
________________________________________________
Basedonthedatainthetable.1radar,theaccuracy
ofdeterminingtheparametersoftheclosestapproach
wascalculatedusingMathlab,theresultsofwhichare
showninFig.2(X=m0radar)andFig.3(y=D;z=
M).
727
0.2
0.4
0.6
0.8
1
0
5
10
15
0
0.1
0.2
0.3
0.4
m
°
radar
D, miles
M, miles
Figure2. Accuracy surface under the condition of error
m
D=0.005D
0.2
0.4
0.6
0.8
1
0
5
10
15
0
0.1
0.2
0.3
0.4
M, miles
D, miles
m
°
radar
Figure3. Accuracy surface under the condition of error
m
D=0.002D
To determine the calculation error in the VTS of
theconvergenceparametersandthelocation,wewill
assume that the two ships are moving as shown in
Fig.4.
Figure4. The situation of displacement of vessels in the
modeofrealmovement
BearingsanddistancesforthevesselЦА–BАand
D
А; for a vessel ЦВ – BВ and DВ. Errors in the
measurementsofbearingsB
А,BВanddistancesDА,DВ
are random. The distance between ships is
determinedbytheformula:
1/ 2
22
2cos
AB AB
DDD DD



(16)
where–thedifferenceinbearings,thevalueofwhich
isdeterminedbytheformula:
BA
BB
 (17)
22
2
А B
AB
BB
BB
mm m








(18)
00
22
180
BA
BB
mmm

(19)
After applying formula (10) to equation (16), we
get the absolute error in determining the distance
betweenships:
22
2
2
AB
DD D
AB
DDD
mm m m
DD









(20)

22
222222
2
22
cos cos sin
2cos
AB
AB D B A D AB
D
AB AB
DD m DD m DD m
m
DD DD

  

(21)
Significantlyaffectsthesituationofdivergenceand
the regularity of relative movement, which is
providedbythecourseangleLRM–β.
From Fig. 4, we get the dependence for
determiningtheangle–β:

.sin
.cos
BAB
A
BAB
VTCTC
tg
V V TC TC

(22)
Fromhereweget:

.sin
.cos
BAB
AB A B
VTCTC
arctg
V V TC TC





(23)
Aftersimpletransformations,weget:
2222
2
BA A B
BA A B
V V TC TC
V V TC TC
mm m m m




 



(24)


22
220 0
2
2
2
sin
180 180
2Cos 1
AB
ABF TC TC
AB
TC TC m m H m C
m
F F TC TC








(25)
A
B
V
F
V
(26)
22 22
2
4
BA
AV BV
F
B
Vm Vm
m
V





(27)

2
Cos 1
AB
H F TC TC

(28)

2
Cos2 Cos
AB AB
CTCTCFTCTC

(29)
728
To calculate theerror in determining the angleθ
fromthetriangle0Ц
АЦВ,weobtainbythetheoremof
sines:
sin sin
B
DD
(30)
sin
sin .
B
D
D
 (31)
.cos
cos
AB
DD
D

. (32)
Fromformulas(31‐32)weget:
sin
cos
B
AB
D
tg
DD


(33)
sin
cos
B
AB
D
arctg
DD





(34)
22
2
2
.
AB
AB
DD
DD
mm m m











(35)
By differentiating formula (35) in partial
derivatives,weobtain dependencies for determining
theerror:
2
2
4
K
N
m
D
(36)
Informula(36)thenotationsareadopted:

22222
sin
BA
AD BD
KDmDm
, (37)

cos
BA B
NmD D D

. (38)
Todeterminetheerrorincalculatingthedistance
oftheshortestapproachfromthetriangleМЦ
АЦВwe
obtain:

CPA sin sin
AA
DDBTC
 
(39)
After differentiating formula (39) in partial
derivatives,weget:
22
2
2
2
2
AA
AA
CPA CPA CPA CPA CPA
CPA D B TC
DB TC
mm m m m m

















(40)


22 22 0 0
sin cos
180
AA
CPA D AA AA BB
Pi
m m BTC D BTC m m m m





.(41)
From the given analytical dependencies, it is
possibletostartdeterminingtheerrorindetermining
thetrajectoryofshipsatseabycoastalVTS.
A comparative analysis of the accuracy of
establishing the positions of ships while moving
showed that the total RMSE of the ship radar is
approximately
3 times higher than that of the shore
radar.ThetotalerrorwhenusingAISinnormalGPS
modegiveserrorsthatare comparabletoradar, and
whenusingDGPSitisalmost5timesmoreaccurate.
Basedontheseprerequisites,itcanbearguedthat
itisadvisableto
useinformationfromradarandAIS
in VTS, giving preference to the more accurate of
them.Calculationschemes,accordingtothedefinition
oftheparametersofdangerousapproach,musthavea
minimuminheritedRMSE.
Takingintoaccountthatthecoordinatesoftheaxis
of the shore antenna are determined by geodetic
methods, it doesnothave alinearmovementandis
unknowntotheattackerswhoorganizecyber‐attacks,
itcanbearguedthattheradarindicatorscanserveto
verify the TP coordinate planning model when the
shipenters/leavestheportfornavigationpurposes.
4.2 Constructionofa
matrixoftrajectorypointsofthe
vessel’sapproachtotheportofChornomorskunder
theconditionsofcybersecurity
The essence of the TP route planning method is the
high‐precision calculation of the coordinates of the
givenpointsbasedontheplannedpoints(WP)ofthe
rectilinearpathandthe
turningcharacteristicsforthe
selectedrudder turning angleandtheir presentation
intheformofalinearmatrixofturningcoordinates.
Atthesametime,thecalculationalgorithmwillbe
as follows: according to the coordinates of the way
point,theangleofthesteeringwheelisselectedbythe
segmentmethodandthestartingandendingpointsof
theturnaredetermined;basedonthecoordinatesof
thestartingpointoftheturn,thecoordinatesoftheTP
arecalculatedbythesegmentmethod after3°,5°or
10°,dependingonthescaleofthemapandtheangle
of
the turn; form a matrix of coordinates of the TP
turn at a given waypoint, which starts from the
startingpointoftheruddershift,thentheTPandthe
endpointofthecirculation..
TheTPmatrixoftheturnfromthefirstWPtothe
secondcanbe
writtenasfollows:


11
11 21 1 1
12
11 21 1 1
11
, , ,...,, ,...,, , ,
nn
nk
in
nk
in
nn
M






foralland ∈ {1,...,n},wherenisthenumberofTP
ofthecurvilineartrajectoryforthegivenWP.
Inthefuture, the coordinates of the pointsofthe
rectilineartrajectoryfromtheinitialfirstpointtothe
beginningoftheturnarecalculatedandtheTP
array
isformedintheformofthefirstmatrixoftheroute.
The calculation of points is carried out according to
theformulasofwrittencalculation,uptothefifthsign
oftheminuteandthenextroundinguptofour.Such
accuracy is necessary due to the small
distance
betweenthepointsthatdeterminethepositionofthe
centre of gravity, and the high accuracy of
determining the location of the vessel by satellite
729
systems in differential mode, whentheradial RMSE
reachesavalueof±2m.
ToformTPmatricesoftheentiretransition,form
arraysofroutematricesandTPturnmatricesforall
waypointsinthefollowingorder:
М01,Мп12,М12,Мп23,М23,...,Мпі(і+1),Мі(і+1),...Мп(m‐1)m,М(m‐1)m
where
М
01–is the TP matrixofthelinearsectionfromthe
initial0thWPtothepointofsthesteeringwheelshift
command;
M
12–theTPmatrixoftheturnfromthefirstWPto
thesecondfromthebeginningofП
1totheendofК
1
ofthecurvilinearsegment;
M
12, M
23, M
i(i+1), M
(m01)m – matrices of segments of
turns;
М
12,М23,Мі(і‐1),Мі(і+1) – TP matrices of rectilinear
segments.
AftercalculatingtheplannedTPcoordinates,they
will be optimal, since they are obtained for the
maneuveringcharacteristicsofaspecificvesselwitha
marginofcontrolinfluencesandaresafeinrelationto
navigationalhazards.
The task of guaranteed safe management of the
movementprocesswillbetheneedtomovethecentre
of gravity of the vessel along the line of the given
route, taking into account the actual width of the
maneuvering offset, controlling the position of the
vesselbyhigh‐precisionmethodsof determiningthe
locationandusingexistingdecisionsupport
systems
for timely and adequate actions to correct emerging
deviations. At the same time, it is necessary to take
into account the characteristic points of the vessel,
which determine the accuracy of determining its
positionandthewidthofthemaneuveringoffset.
Theseinclude:thecontrolcentre(CC)–the
point
on theshipʹs bridge, where the navigator is located,
who assesses the shipʹs condition in relation to the
signsofthenavigationalsituation;turningpole(TP);
centreofgravity(CG);extremecharacteristicpoints‐
bowoftheleftsideНл,bowofthestarboardsideНп,
aft of
the left side Кл, aft of the right side Кп; the
lengthofthevesselbetweentheperpendicularsL;the
maximumlengthofthevessel.
5 DISCUSSIONOFRESULTS
Asanexample,thestagingoftheshipʺLadyLagunaʺ
usingtrajectorypointmatricestoBerth5intheport
of
Chornomorsk, which was developed using the
programʺPath Planning ISʺ, is shown. Below is the
mathematical base of calculations used by the
program.
1. According to hydrographic recommendations, the
pilotdevelopstheapproachrouteofthevesselto
the pier, which he transmits to the vessel in
advance in
the form of coordinates of the
recommended approach route of the vessel. For
these coordinates, formulas (42‐46) are used to
calculatethecoursesthattheshipwillfollow(TC),
the angles of turns (Θ) and thedistance between
waypoints(S).


21 1
sin
sin sin cos
Lon
Lon
D
TC arctg
tg D





(42)
where
TC‐trueheadingfromthepreviouspointtothenext;
D
Lon‐thedifferencebetweenthelongitudesoftheend
andstartpoints;
1‐latitudeofthestartingpoint;
2‐latitudeoftheendpoint.
1Lon i i
D
 (43)
1ii
TC TC
(44)
where
–turningangle.
cos
Lat
D
S
TC
(45)
where
S–distancebetweenwaypoints.
1Lat i i
D
(46)
Table2.Calculationofturningangles
________________________________________________
WP Latitude Longitude S,cable TC,° Θ,°
________________________________________________
0 46⁰18,94ʹN 030⁰41,56ʹE 0 0 0
1 46⁰19,17ʹN 030⁰40,46ʹE 0,8 286,6 78
2 46⁰18,83ʹN 030⁰40,19ʹE 0,39 208,8 67,1
3 46⁰18,84ʹN 030⁰40,05ʹE 0,1 275,9 0
________________________________________________
2. Findtheangleofthesteering wheelforeachturn
accordingtotheconditions(40):
530
10 30 60
560
if less than
if
if more than




(47)
Table3.Turningselection
________________________________________________
WP LatitudeLongitude S, cableTC,° Θ,°δ,°
________________________________________________
0 46⁰18,94ʹN 030⁰41,56ʹE 0 0 0 0
1 46⁰19,17ʹN 030⁰40,46ʹE 0,8 286,6 78 15
2 46⁰18,83ʹN 030⁰40,19ʹE 0,39 208,8 67,1 15
3 46⁰18,84ʹN 030⁰40,05ʹE 0,1 275,9 0 0
________________________________________________
3. Withthehelpofformulas(41‐42),thedistanceson
the track lines from the point of turn to the
beginningandendoftheturnarecalculated.The
coordinatesoftheturningpointaretakenaspoint
ʺMʺ.SegmentsМПandМКrepresentthedistance
frompointMon
thetracklinetothestartandend
pointsoftheturn,respectively.Fortheaccuracyof
calculations,itisbettertoleave6decimalplaces.
1
22 2
TT
DD
MC l tg




(48)
where
l
1–shiftingofthevesselduringcirculation;
D
T–thetacticaldiameterofthecirculation.
730
2
2
ME l tg




(49)
where
l
2–directshifting.
Table4.Calculationofstartandendsegmentsofturns
________________________________________________
WP Latitude Longitude МC,cableМE,cable
________________________________________________
0 46⁰18,94ʹN 030⁰41,56ʹE 0 0
1 46⁰19,17ʹN 030⁰40,46ʹE 2,97482 2,12863
2 46⁰18,83ʹN 030⁰40,19ʹE 2,58613 1,774288
3 46⁰18,84ʹN 030⁰40,05ʹE 0 0
________________________________________________
4. Foreachturn,itisnecessarytocalculatesegments
every 10° using formulas (41‐42), where the
turninganglewilltakethevalue10,20,30,…,
.
5. Theobtaineddataintheformofsegmentsmustbe
convertedintogeographiccoordinates.Thiscanbe
doneusingformulas(50‐56).
cos
i
Lat i i
DMCK
(50)
where
і–turningangleevery10°;
К
і–thecoursethevesselfollowstothenextpoint.
i
Lon i i
DDMPtgK (51)
where
DMP
і–thedifferenceofthemeridionalpartsforeach
segmentoftheturn.
45
2
3437,75 ln
45
2
E
C
tg
DMP
tg









(52)
where
φ
C–thelatitudeofthestartingpointoftheturn;
φ
E–thelatitudeoftheendpointoftheturn.
i
nmLat
D


(53)
where
φ
n–thelatitudeofthetrajectorypointatnϵ(П1,К11,
К
12, …,К1,П2,К21,К22,…,К2, …,Пk,Кk1,Кk2, …,Кk,
whenk–crossingpointoftracklinesonthechart;01,
02,…,0η,11,12,…,1η,…,ζ1,ζ2,…,ζη,whenη–the
numberoftrajectorypointsonastraighttrackline,ζ–
waypointnumber);
φ
m – the latitude of the crossing point of the track
lines.
i
nm Lon
D

(54)
whereλ
n–thelongitudeofthetrajectorypointatnϵ
(П
1,К11,К12,…,К1,П2,К21,К22,…,К2,…,Пk,Кk1,Кk2,
…,К
k,whenk–crossingpointoftracklinesonthe
chart;01,02,…,0η,11,12,…,1η,…,ζ1,ζ2,…,ζη,
колиη–thenumberoftrajectorypointsonastraight
trackline,ζ–waypointnumber);
λ
m–longitudeofthecrossingpointofthetracklines.
Based on the obtained coordinates, we build a
matrixoftrajectoryturningpointsaftereachone10°.
6. Usingformulas(44‐47),wefindthecoordinatesof
rectilinearsectionsoftheshipʹspathevery0.2kbt.
The calculation of
the difference in latitude is
basedonthefollowingformula:
cos
i
Lat i
DK
(55)
where
βϵ(2,4,6,…,l+1)–steptocalculate.
Wesummarizetheobtainedresultsinamatrixof
rectilinearsectionsoftheroute.
7. Thecoordinatematrixofthetrajectorypointsofthe
shipʹsapproachwillhavethefollowingform:

01 1 12 2
1
...
mn nk st
M
MMMM MM M


(56)
Figure5. General view of the approach of the shipʺLady
Lagunaʺusingthematricesoftrajectorypointstoberth5in
theportofChornomorsk
Table5.GeneralviewoftheapproachoftheshipʺLady
Lagunaʺusingthematricesoftrajectorypointstoberth5in
theportof
Chornomorsk
________________________________________________
TP LatLongCourse Distance
________________________________________________
0 46⁰18,94ʹN030⁰41,56ʹE 0 0
1 46⁰18,96888ʹN 030⁰41,4219ʹE 286,8 0,1
2 46⁰18,9978ʹN 030⁰41,28378ʹE 286,8 0,1
3 46⁰19,02666ʹN 030⁰41,14566ʹE 286,8 0,1
4 46⁰19,08408ʹN 030⁰40,87086ʹE 286,8 0,2
5 46⁰19,11732ʹN 030⁰40,6929
ʹE 285,1 0,13
6 46⁰19,11906ʹN 030⁰40,62828ʹE 272,2 0,04
7 46⁰19,11324ʹN 030⁰40,56408ʹE 262,5 0,04
8 46⁰19,09998ʹN 030⁰40,50228ʹE 252,8 0,04
9 46⁰19,0797ʹN 030⁰40,44462ʹE 243,1 0,04
10 46⁰19,053ʹN 030⁰40,39272ʹE 233,4 0,04
11 46⁰
18,98358ʹN 030⁰40,31196ʹE 214 0,04
12 46⁰19,05654ʹN 030⁰40,36986ʹE 208,8 0,08
13 46⁰18,9471ʹN 030⁰40,27692ʹE 210,5 0,13
14 46⁰18,91494ʹN 030⁰40,23342ʹE 223,1 0,04
15 46⁰18,88824ʹN 030⁰40,18284ʹE 232,7 0,04
16 46⁰18,86766ʹN 030⁰40,12656ʹE 242,2
 0,04
17 46⁰18,85392ʹN 030⁰40,0662ʹE 251,8 0,04
18 46⁰18,84726ʹN 030⁰40,00332ʹE 261,3 0,04
19 46⁰18,84786ʹN 030⁰39,93978ʹE 270,8 0,04
20 46⁰18,84ʹN030⁰40,05ʹE 275,9 0,08
________________________________________________
The program outputs an xls file that is easily
transported to ECDIS or Marine Traffic. In Fig. 5
shows the construction of theʺLady Lagunaʺ
approachtoberthNo.5intheportofChornomorsk.
The technological scheme of mooring will be as
follows.Ontheapproachtothefirstpair
ofbuoysʺ1ʺ
andʺ2ʺoftheapproachchannel(TP2),thepilotmust
731
be on board and the vessel must proceed at a
maneuveringspeed,accordingtotheportrules,about
7knots.Thetowingendsshouldbetakenthroughthe
bow and stern leads as close as possible to the
diametricalplane.
The first tug is attached at point TP2, and
the
second–afterpassingthroughthechannel(TP8).
Theapproachchanneloftheport,whichis160m
wide,1400mlong,and14.5mdeep,isusedforships
entering and leaving the seaport of Chornomorsk.
Accordingtothewaterareapassport,thedepthatthe
berth is
10 m and is sufficient for slowing down to
completestop,turningonthereversecoursewiththe
useoftugsandmaneuveringduringmooring.
The length of the pier is 220 meters. Thus, the
designparametersoftheoperationalwaterareaallow
safemooringanddeparture of vesselsfrom
thepier
with a length between perpendiculars of about 200
metersandawidthofabout45musingtugs.
Figure6.Thefirstturnofthesteeringwheel
According to the given plan, at point 6, the ship
makesa15‐degreeturnoftheruddertotheportside
tosetoffonacourseof234°(Fig.6).
Inthefuture,thevesselfollowsthiscoursetopoint
TP14,whereitperformsa15‐degreerudder
shiftto
starboardandapproachestheberth(Fig.7).
Figure7.Thesecondshiftofthesteeringwheel
After approaching the mooring place, they begin
topresstheshiptotheberthandadjustthepositionof
the ship. The minimum scheme of using mooring
lines, which is recommended, is three longitudinal
and two springs from forward and aft. After the
mooring lineshavebeen tightened, the tugs may
be
freeandthemooringshallbeconsideredcomplete.
Thedevelopedroutesforthemooringsoftheport
of Chornomorsk were integrated into the computer
programʺPathPlanningISʺ,whichmadeitpossibleto
obtain the coordinates matrix of the path of field
observations. Comparative analysis of computer
modelling
andpracticalpassageofshipsthroughthe
recommendedsectionoftheportwaterareashowed
thattheproposedmodelisconfirmedbytheresultsof
observations(Fig.8).
Cyber Attack –
Incide nt
Inform SSO and Master
Use Backup
system
Inform
Crew and
Head Office
for
rectification
Proceed to incident
investigation
Perform
relevant
health checks
and bring
system online
Inform Head Office
Inform
Crew and Head
Office
Ask for external
or makers
assistance
Can we rectify
systems without
putting off-
line?
Is there a
backup
s
y
stem?
Inform Head Office
and ask confirmation.
Ensure vessel’s safety before
p
uttin
g
off-line
Shut Down
system
Rectify system
Can we rectify
systems without
putting off-line?
Danger?
System
rectified?
Confirm
the Cyber
Incide nt
No
Yes
No
No
No
No
Yes
Yes
Yes
Yes
No
Figure8.Actionsofthenavigatorduringtheoccurrenceof
cyberthreats
Based on their analysis, it can be concluded that
the developed model provides cyber security of
maneuvering processes in compressed waters,
thereforeitcanberecommendedforimplementation
intheseaportsofUkraine,tofulfilltherequirements
of the International Maritime Organization for
planningtherouteofthevoyagecyclefrom
theberth
of the port of departure to the berth of the port of
arrival(Fig.8).
6 CONCLUSIONS
The main advantage of the method of planning the
shipʹspathaccordingtothetableofwaypointsbythe
methodofcalculatingthecoordinatesofthetrajectory
points by the
angle of the rudder for curved
trajectoriesisthepresentationofthepathintheform
of the sum of linear matrices of the coordinates of
straight and curved sections and automatic
operational control of movement parameters. The
proposedmethodcanbeusedinthedevelopmentof
control tools for automated
vessels and is only
possibleforvesselswithnon‐shiftmaintenance.Also,
thisrouteconstructionmethodisveryrelevantduring
thepreparationoftheapproachandexitrouteplan,as
it reduces the risk of misunderstanding between the
captain and the pilot during navigation, and even
reducestheriskof
emergencyeventsintheprocessof
managingtheresourcesofthenavigationbridge.
Thus, optimization of information about
maneuvering, proper preparationofthebridgeteam
fortimelyassessmentoftheemergencysituationand
takingadequatemeasuresfor itsprevention make it
possibletoincreasethesafetyofmaneuvering.
To ensure cyber
security when usingʺPath
PlanningISʺ,thefollowingrulesmustbefollowed:
1. Itisforbiddentouseshipʹspersonalcomputersthat
arenotconfiguredwithsoftwareforplanningthe
routeandmanagingthemaneuveringprocess.
2. If the user accidentally enters the setup program,
they should shut
down the computer without
attemptingtochangeorsaveanychanges.
3. Use the master or any other disk containing the
software files to re‐install the software on board
732
the vessel with the prior permission of the
Company.
4. Reformatorcopythefilestothemaindisksorany
other disk containing the program files for
planningandmaneuveringintheeventoffailures
intheiroperation.
5. Itisprohibitedtoinstallsoftwarethathasnotbeen
authorizedbytheCompany.
6. Use only utility software (eg disk managers,
memorygenerators/managers,NortonUtilities).
If there is a threat during the download of the
workingfile,you mustfollow the instructions given
inFig.8.
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