235
1 INTRODUCTION
In sailing regattas the success is impacted by crew
andsailingvesselparameters. The roleofcrew is in
making decisions to choose suitable directions of
sailing, according with weather conditions and sea
state. Experience and knowledge of crew are very
useful in decision‐making, but through time a
ppear
solutions that help make the decision. In the last
article(Życzkowski,2016)presentedashortreviewof
sailboat routing. Current solutions include e‐
navigation aspect (Weintrit & Wawruch, 2007) to
supportthedecisiontochoosetheappropriatesailing
route. However, some facts are noteworthy, the big
regatta yachts such as in the Americaʹs Cup, Cowes
Races whether Mug Races, have possibilit
y to
optimize sailing routes. However the required data
and optimization algorithms are not available for
sailingsociety.Lackofsailingvesselparametersfor
scientistsisanimpediment.Despitethesedifficulties
inthearticlesyoucanfindavarietyofa
pproachesin
thesearchfortheoptimalroute(Philpott,Sullivan,&
Jackson,1993), (Verwerft& Keuning,2008),(Dębski,
2016).In this article sailing vessel parameters are
achievedduetoasimulationmodelingoftwoboats.
However, other result of different vessel modelling
canbealsoused.
The aim of thi
s work is consideration of new
different sailing criteria than in the last article
(Życzkowski, 2016), which are presented in the
followingsection.
2 OPTIMISATIONPROBLEM
Theaimoftheresearchistoproposeamethod,which
finds optimal sailing vessel route according to
specifiedcriteria,whilesatisfyinggivenconstraints.
The first crit
eria is taking account of navigation
safety in the vicinity of shore and isolated danger
marks and all dangerous situations, according with
COLREGS and good marine practice (COLREGS,
1972), (Jurdziński, 2003). The second criteria is a
penalty time for altering course which increased the
totalti
meofthevoyage.
Further considerations take into account the
impactofthesefactorsontheoptimizationcriterion.
Sailing Vessel Routing Considering Safety Zone and
Penalty Time for Altering Course
M.Życzkowski
GdanskUniversityofTechnology,Gdansk,Poland
ABSTRACT:Inthispaperweintroducenewmodelforsimulationseavesselrouting.Besidesavesseltypes
(polardiagram)andweatherforecast,travelsecurityandthenumberofmaneuversareconsidered.Basedon
thesedataboththeminimaltravellingcostsandtheminimalprocessingtimearefoundfordifferentvessels
anddifferentroutes.Totestourmodeltheapplicat
ionsSailingAssistancewadimproved.Theobtainedresults
showsthatwecanobtainquiteacceptableresults.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 2
June 2017
DOI:10.12716/1001.11.02.04
236
In consequence the applicationdeveloped by author
thispaperandcalledSailingAssistanceconsidersboth
these criteria. To make such possibilities the
applicationwas modified towards layered structure.
Using the application tests for two different sailing
vesselswereperformed. Duringtestingboth safety
navigationandthepenaltytimeforacourse
altering
on route of sailing vessel movement is considered.
Moreover the type of sailing vessels, the weather
forecast,penaltyforalteringcoursesandgranulityof
thenavigationalareaarealsotakenintoaccount.The
aim of the research is proposed method to find
optimal sailing vessel route contains new
optimizationcriteriaexplainedbelow.
In the previous paper (Życzkowski, 2016), only
one level of granulity was assumed for the whole
navigationalzone.Then,allvesselmanoeuvringwas
modelled with the same accuracy. However in a
literal zone precision of vessel sailing should be
increased.Thereforeinourconsiderationweassume
that sailing area is described by two levels of
granulity. The open sea is represented by basic
(initial) grid with the suitable granulity, defined
below(seeFigure2).Awayof conversion seamap
onaseagridisshowninarticles(Mannarini,Coppini,
Oddo, & Pinardi, 2013), (Tsou
& Cheng, 2013),
(Szlapczynski,2006).
Granulity of sea area z is determined by the
formula(1):
max max
φφ λλ
min min
OB
z
mn mn
(1)
whereφ
max (λmax),φmin (λmin) indicate the minimum
and maximum latitude(longitude) in degrees.φ
min =
min{φ
i,i=1,2,..,m},λmin=min{λi,i=1,2,..,n},
φ
max=max{φi,i=1,2,..,m},λmax=max{λi,i=1,2,
..,n}.Ifzissmallerthenamountofsquaresinagridis
higher.
Figure1.Increasinggranulityofareainvicinityofshore
Figure2. Descritazed chart with constant granulity of area
withexampleofroutefromstartpoint AtofinishpointB
with 32 possible movements of a sailing vessel from each
point P
k, illustratedare 9 points Pk, where in point
designedby7,8,9iscourse
For sea area near the shore and any obstacles it
shouldbedescribedbyhighergranulity.Forthiscase
onesinglesquareisdecreased2
s
timeincomparison
thebasicsquare,wheresisgranulitycoefficientand
inourconsiderationsisequals1.
Below it is assumed that in vicinity of shore,
isolateddangerous,orothersituationsrequirehigher
awareness. In consequence it is necessarily to apply
higher granulity of the area. Because this
increases
accuracy of route optimization, and safe navigation.
Highergranulityoftheareaisalsoplacedaroundthe
peninsula. Such zones, in this article, is called the
safety zones. The safety zone area is determined by
minimal radius R from contour shore or contour
others obstacles to open navigation zone. Figure
1
shows such a grid, which corresponds to one small
partoftheFigure2.Thewayofncreasinggranulityof
areaisdefinedbyfollowingformula(2):
ifcheckRadius(P
ij,unnavigablezone)<R{ (2)
forx=0;x=2
s
;x++
fory=0;y=2
s
;y++
createnewpoint
}
where checkRadius is a function which determined
the fragment of sea grid determined by the contour
shore or contour others obstacles and distance R of
from them. Parameter R determines safety zone
radius(R=1is equal onediagonal ofa squarein the
basic grid), parameter s is the
coefficient of
granulation in the safety zone when s=1 than one
square of grid represents four new safety squares,
whens=2thaninonebasicsquarethereissixteennew
squares.Formula(2)allowstoindicatenewallpoints
forallpossibledirectionsofvesselsailingfrom
pointP
ij. Coordinatesx,y directly shows location of
allpoints
These points directly follow from the neighbors
points existent in the grid area. If these points are
situatedinthesafetyzone,thanhighergranulitymust
be considered. To take in account the time penalty
relatedtomaneuvers ofvesselweshouldcalculatean
angle determined by previous position P
k‐1, current
237
positionP
k=PijandoneofnextpositionsPk+1= .
inthegrid.Tooptimizethenextvesselmovementto
two known criteria such as the weather forecast in
points P
k and Pk+1 and the polar diagram of specific
sailing vessel (Stelzer & Jafarmadar, 2012) must be
take into account. These possibilities was
implemented in SailingAssistance application
(Życzkowski,2016).Additionallytwonewcriteriacan
be added: the safety zone and penalty time of the
current vessel movement. Moreover we can also
consider
thepossiblenumberofvesselflowdirection
from point P
k to Pk+1. In practice is determined by
coefficientwr,whichcanbeoneofthreevalues:8,16,
32.Infurther consideration weassume theambition
valuewr = 32. The penalty timeof vesselmaneuver
frompoint P
k to point Pk+1 can be corresponded to
angleΩdeterminedbythreevesselpositioninpoints:
P
k‐1,Pk,Pk+1(seeFigure3).Inthefurtherconsiderations
it is assumed that difficulty of maneuver execution
correspondingtovalueofangleΩ.IfangleΩishigher
than difficulty of maneuver is alsohigher and takes
more time. Such time delay can be evaluated by
formula(3).
PenaltyTime(Pk‐1,Pk,Pk+1) (3)
{
X=Pk;Y=Pk‐1;Z=Pk+1;
1
Ω 180 cos
||
X
YXZ
X
YXZ
360
ΩΩ
wr
if( 0.5*wr)
=0.5*wr‐
returntimeTochangeCourse= *p;
}
where p be specific coefficient following from
characteristicsofasailingvessel.Ifconsideredpoints
existing on boundary of basic and safety zone the
required calculations of the above parameters are
morecomplicated.
Tocalculatethenextacceptabledirectionofvessel
sailing we consider all possible maneuvers for
different possible
points Pk+1.For each of them we
calculate also possible values of penalties time for
alteringcourse.Takingintothepolardiagramofthe
sailingvesselandcurrentweatherinthesepointswe
can evaluate admissible maneuvers basic on
algorithm calculating the optimal safety route
(Stelzer, 2012). This can be printed out
by
SailingAssistance.application.
Figure3 Penalty time for altering course, where possible
sailingmovementwr=8.SailingvesseliscomingfromP
k‐1
to Pkand following to Pk+1. For wr = 8 sailing vessel
possiblemovement.Frompictureonthetoprighttodown
left :Ωis 0°,45°, 90°,135°,180°,225°,270°,315°and penalty
timeatp=1equals:0,4.5’,9’,13.5’,18’,13.5’,9’,4.5’.
3 ENLARGMENTOFFUNCTIONALITYOF
SAILINGASSISTANCEAPLICATION
The present architecture of the application
SailingAssistanceisshowninFigure 4.Itconsists of
threelayers:USERSresponsibleforcooperationwith
sailors,ROUTEdeterminingthefastandsafetyroute,
DATA allowing to collect the required set of data.
Eachlayerconsistsofmany
functions,whichsomeof
them are shown in Table 1. Such architecture is
flexibleandallowstomakefurthermodifications.
USER
ROUTE
DATA
Figure4.SailingAssistancelayerstructureapplication
238
Table1.SailingAssistancefunctions.
_______________________________________________
FunctionLayer Description
_______________________________________________
Input(SV,A,B,cr) DATA StartpointA,finishpointB,
sailingvesselSV,crcriteria
fixed.
Create(OB,m,n)DATA Createm∙ngridofOB
specificarea.
ChangePD(PD) DATA PolardiagramPD
transformationtomatrixC
ab
Area(P
ij,t)DATA ReadareastateinPijpointatt
time,ie.S(P
ij,t)=Area(Pij,t)for
i=1,2,..,m;forj=1,2,..,n.
Object(P
ij,t) DATA Determineobjectstateinpoint
P
k=Pij
CreateRoute ROUTEImplementationofDijkstraʹs
(A,B,wr,t)algorithm(Dijkstra,1959)
(Neumann,2014)forgraphG
(V,E,O,S)withfixed
Parameters(avariantof
movement wr,and
withapredeterminedcriteria.
Theresultisalistofwaypoints
fromstartpointAtofinish
point
B.
Timeto(P
k,Pk+1) ROUTETimefromPktoPk+1,(potential
nextpointindefinedroute.)
IncGranulity(R,s) DATA Increasegranulityinsafety
zone,Rissafetyzoneradius
withcoefficients.
PenaltyTime ROUTECalculatepenaltytimefor
altering
(Pk‐1,Pk,Pk+1)courseduringsearching
anotherwaypoints.
DisplayUSER Displayonassumedchart
(chart,route)waypointsofdesignatedroute
_______________________________________________
4 THERESULTSFORTWOSAILINGVESSELS
OBTAINED
SailingAssistanceapplicationcarriesouttestsfortwo
specific sailing vessels: Conrad and Oceania. Some
technicaldetailsfortheseboatsareinTable2.
Table2. Technical details of Conrad 1200 RT and R/S
Oceania
_______________________________________________
Parameters CONRAD1200RT R/S*OCEANIA*
_______________________________________________
Sailarea[m
2
]80520
SailtypeBermudarigSch.3masted
Length[m]12.0048.50
Beam[m]4.049.00
Draught[m]23.60
Freeboard[m]1.082.00
Waterplane[m
2
]32.889430.133
Lwl/Bwl[‐] 3.1614.711
Bwl/T[‐]4.8443.000
_______________________________________________
SAS_VPPN.v03program (developed in The
FacultyofOceanEngineering)hasbeenusedtocreate
a polar diagram based knowledge of sailing vessel
design details. The result of program are presented
belowas Table 3.It isfragment of polardiagram of
sailing vessel Conrad. The first row means wind
speed equals 1 knot, the second equals 2 knots, the
first column means sailing direction equals N, the
secondNbEattruewindfromN.Duringtestingwe
usedthefollowingssettings:granulitygr
1isequal293
10
‐6
for 42 n points and 84 m points. The dedicated
area is designed by rectangleφ
min
(λmin) =54.217 N
(18.069 E) andφ
max
(λmax) =54.936 N(19.508 E), and
granulitygr
2 isequal7310
‐6
for168npointsand84
mpointsvariantsofsailingvesselmovementwr=32.
Start point A isφ
A
(λA)= 54.65 N(19.21 E) and end
point B isφ
B
(λB) = 54.60 N(18.60 E). We measured
suchparameters:ωnumberofchangescourse(ifP
k‐1
PkPk+1isnotonestraightlinethenω=ω+1),routetime
TandthedistancevoyageD,numberofpointP
kon
designatedrouteandtimeofworkproceduretofind
route. All simulation results are in Table 4. and are
illustrated in Figure 5 to Figure 8 ( only Conrad
sailingvesselrouteonchart).
Figure5.Conradsailingrouteforparametersgr2po
Figure6.Conradsailingrouteforparametersgr1p1
Figure7.Conradsailingrouteforparametersgr1po
239
Table3.FragmentofpolardiagramofsailingvesselConrad.
______________________________________________________________________________
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1.05 2.00 2.96 3.61 4.03 4.31 4.39 4.22 3.92 3.46 2.99 2.46 2.08 1.99
0 0 0 1.48 2.52 3.57 4.32 4.80 5.11 5.19 5.03 4.70 4.19 3.63 2.98 2.60 2.50
0 0 0 1.92 3.05 4.18 5.02 5.57 5.91 5.99 5.84 5.48 4.93 4.28 3.50 3.11
3.01
0 0 0 2.35 3.57 4.79 5.54 6.05 6.33 6.40 6.29 6.01 5.53 4.89 4.02 3.59 3.48
0 0 0 2.46 3.82 5.17 6.05 6.52 6.75 6.81 6.74 6.53 6.13 5.49 4.54 4.07 3.95
0 0 0 2.94 4.25 5.55 6.34 6.78 6.99 7.06 7.00 6.83 6.49 5.95 5.04 4.53
4.39
0 0 0 3.04 4.46 5.88 6.64 7.04 7.24 7.31 7.27 7.12 6.85 6.42 5.54 4.99 4.84
0 0 0 3.43 4.82 6.21 6.83 7.21 7.42 7.51 7.48 7.35 7.09 6.68 5.92 5.43 5.28
0 0 0 3.53 4.93 6.34 7.01 7.39 7.61 7.71 7.70 7.57 7.34 6.94 6.31
5.86 5.71
______________________________________________________________________________
Table 4 The result of testing of searching sailing route for two sailing vessel depends on penaltytime for altering
course(p1)orwithoutpenalty(po),lower(gr1)orhigher(gr2)granulity,StartpointAisφ
A(λA)=54.65N(19.21E)andend
pointBisφ
B(λB)=54.60N(18.60E).
__________________________________________________________________________________________________
ParametersCONRAD1200RTR/SOCEANIA
gr1p0 gr2p0 gr1p0 gr1p1 gr1p0 gr2p0 gr1p1 gr2p1
__________________________________________________________________________________________________
RoutetimeT[h]6.22 6.20 7.17 7.12 6.21 6.19 7.30 7.25
OveralldistanceD[NM]38.69 38.58 41.89 41.64 38.55 38.35 40.24 39.82
Sumuppenaltiestimetoforalteringcourse[h] 0 0 0.68 0.70 00 0.81 0.75
NumberofCourseChangesω[‐]5 4 10 16
55 11 18
ThenumberofP
kpointsonroute[‐]27 54 15 29 2858 15 28
Processingtimetofindtheroute frompointAto 0.93 1.91 1.06 1.91 0.80 1.54 0.96 1.52
pointB[s]
__________________________________________________________________________________________________
Figure8.Conradsailingrouteforparametersgr2p1
5 CONCLUSIONS
Modeling of the sailing vessel depends on many
factors,butmainlyPD, which aredifficultto access.
The accuracy of PD depends on maneuvers, and
consequently the travel time. An important role is
played by a granulity of area, which allows a new
look at safety as well as
the need to modify the
algorithms on the border between the two zones:
basic and safety. To analyzed more practical
situations of vessel sailing the application
SailingAssistance were improved and examples of
travels modelling of two vessels for different
conditions are consideredThe paper presents
several experiments that confirm the
correctness of
thedevelopedalgorithmsandconfirmtheusefulness
ofSailingAssistanceapplication.
Of course there is the opportunity to further
develop these algorithms in order to strive to
optimize travel time. If knowledge about sailing
vessels is deeper, weather forecasting is more true,
and sea area description is more realistic our
modelling results can be more useful for real user
competition.
ACKNOWLEDGEMENTS
The author would like to thank Bogusław
Oleksiewiczforprovidingshipmodelsgeneratedby
meansof“SAS_VPPN.v03”researchsoftware.
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