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 decisionmaking, 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
vesselswereperformed. 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)
whereφ
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, illustratedare 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
k1, current