517
1 INTRODUCTION
When a ship sails at sea, it will be affected by
environmental disturbances such as wind, waves,
currents, and ice. These impacts on the speed, fuel
consumption, safety and performance of the ship.
Optimalshiprouteisaparticularvoyagewithsafest
and shortest route for avoiding dangerous
sea
condition.Thisisessential fornavigatingtheshipto
avoid adverse weather conditions that could cause
serious injury or structural damage to ships,
machineryandequipment.
Inthe past,variousresearchershaveinvestigated
an optimal route of a ship based on optimization
algorithm, e.g. the modified isochrones method,
Dijkstra’s
algorithm,thedynamicprogra mming(DP),
and the three‐dimensional modified isochrones
(3DMI). Hagiwara and Spaans (1987) proposed the
modified isochrones method which used to find the
effectivelyoperationshipinoceancrossvoyages.The
minimum time route and minimum fuel route of
40000 dwt product tanker were predicted using
environmental data
of the North Pacific Ocean.
Otherwise,Calvertetal.(1991)carriedoutastudyof
the optimal route to minimize fuel cost for trans‐
Atlantic passage by using dynamic programming
techniques. They used dynamic programming (DP)
whichwasoriginallydevelopedbyBellmantoreduce
fuel consumption. Afterthat, Vlachos (2004)
studied
ontheoptimalrouteforsmallandmediumsizeships.
Hecarriedoutthecalculationtheinitialroutesinthe
caseofthepresentofobstacles,definitionoftheroute
costandrouteoptimization.Inhistheory,routecost
is assigned in every possible route between two
points. More recently,
the minimal time route of a
ship has been reported by Padhy et al. (2007), by
usingwaveheightinformationfromGeodeticSatellite
Development of Solution for Safe Ship Considering
Seakeeping Per
H.K.Yoon,V.M.Nguyen&T.T.Nguyen
ChangwonNationalUniversity,Changwon,Korea
ABSTRACT:Inrecentyears,safetyofashipshasbecome oneimportantissuesneededto solvedassoonas
possibleinshipnavigation.Optimalweatherroutingisoneofbestsolutionforensuringsafeoperationofa
ship with a with short passage time or minimum
energy to avoid a certain excessive motion. This paper
introducedthedevelopmentofsolutionforsafetyandoptimalweatherroutingashipconsideringseakeeping
performancebasedonmodeltestresult.ThisstudyintroducedhowtoapplyA*algorithmbasedonresultof
the seakeeping model test for determining the optimal
ship routes. Seakeeping model test of 8600 TEU
containershipwascarriedoutinChangwonNationalUniversityʹsseakeepingbasinanditsRAOsatvarious
frequencieswereusedtopredicttheRMSmotionvaluesinirregularwaves.Thespeciallymodelledpath‐cost
functionandthesafetyconstraintswereproposedforfinding
theoptimalpathoftheship.Thecomparisonof
shipperformancesestimatedbygreatcircle’s pathandestimatedoptimalrouteduringthevoyageoftheship
wasinvestigated.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 12
Number 3
September 2018
DOI:10.12716/1001.12.03.10
518
(GEOSAT) altimeter record. In their study, the
minimum distance between two nodal points was
estimated by Dijkstra’s algorithm. Next, Sen and
Padhy (2010) developed the development of a ship
weather routing algorithm based on a form of
Dijkstra’salgorithm. Wave model and ship’s motion
isusedastheinputdata
fordeterminingoptimalship
route in the Arabian sea and Bay of Bengal. As
indicated in Panigra et al. (2011), the optimal
trajectory was introduced by inverting speed
reduction of the ship to weight function for coastal
path in Indian. They have used the Dijkstra’s
algorithm for determining the shortest
path
consideringtheWAMwavemodel.Andthen,Linet
al. (2013) have proposed the three‐dimensional
modified isochrones (3DMI) method to calculate the
optimization of ship weather routing to enhance
speedperformance.Theyhavechosenthegreatcircle
routeasthereferencevoyage when constructing the
floating grid system. Their
numerical simulation,
covering the speed performance under different sea
conditions,fuelconsumptionandtotalpassagetime,
werefoundincomparisonwiththegreatcircleroute.
By extending Panigra’s work, Sen at al. (2015) have
developed an algorithm for optimal ship route
considering the weather conditions and realistic
practicalconstraintsduring
theship’svoyage.Inthe
author’s former works, Nguyen et al. (2016) the
optimization of the ship route by only considering
wind, wave conditions and safety values was
modeled as a function to avoid slamming and deck
wetness.
Overall, the majority of these studies are applied
only to single purpose routing
problems, and the
ship’s safety is the only constraint value to avoid
adverse weather conditions. This paper focused on
the development an optimization algorithm that
combines the available technologies in the area of
weatherforecastwiththeseakeepingperformanceof
a ship, in conjunction with comprehensive ship
operation cost. The
present paper introduces the
development of the algorithm to find an optimal
weather route considering the seakeeping
performanceobtainedfromthemodeltestresult.The
modeltestofthe 8600TEU containership is carried
out in Changwon National University (CWNU)’s
seakeepingbasin.Theresultsoftheoptimalweather
routeof
aship can inform a captain aboutpotential
risk during navigation. In addition, the effects of
temperature, wind and wave that change the total
ship’sresistanceareconsidered.
2 MODELTEST
2.1 Testfacility
Figure 1 shows CWNU’s square towing tank, in
whichthemodeltestwasconducted.Awave
maker
is installed at the end of the towing tank and wave
absorberisattheoppositesite.Thewavemakercan
make waves with a height up to 20 cm, and a
wavelength up to 3 m. Table 1 lists the principal
dimensionsoftheCWNUsquarewavebasin.
Figure1.TheCWNUsquarewavebasin
Figure 2 shows motion measurement device and
wave probe. Heave, roll, and pitch are measured
usingeachpotentiometer.
Figure2.Motionmeasurementdeviceandwaveprobe
Sincetheexperimentisperformedatvariouswave
directions and wave frequencies, it is necessary to
evaluate the quality of the waves. Right photo in
Figure 2 shows the wave probe that is used in this
experiment.
2.2 Testcondition
Inthe presentstudy,the 8600 TEU containership is
selected
in this experiment. Table 1 shows the
principaldimensionsofthemodelshipof8600TEU
container ship. Most tests in regular waves are
concernedwiththeexperimentaldeterminationofthe
motion response amplitude operator (RAO). The
experiment is carried out in regular waves in seven
wavedirections.Thetest
conditionsare105wavesfor
15wavefrequencyconditions.Table2showstheset
valuesforeachtestconditioninregularwaves.
Table1.Principaldimensionsofmodelship
_______________________________________________
Particulars Unit RealModel
_______________________________________________
Scaleratio ‐ 1285.630
pp
L m 322.61.129
Bm 45.60.160
Dm 24.60.086
T(design) m 130.046
B
C ‐0.59080.5908
m31129830.0048
kg 115909259.7 4.974
LCBm‐6.625‐0.023
GMm 1.50.0053
519
Table2.Testconditionsinregularwaves
_______________________________________________
λ/L λ Wavefrequency WaveWave
[m] [rad/s]period[s] height[cm]
_______________________________________________
0.50.56 10.450.60 1.4
0.60.68 9.540.66 1.4
0.70.79 8.830.71 1.4
0.80.90 8.260.76 1.4
0.91.02 7.790.81 1.4
1.01.13 7.390.85 1.4
1.21.35 6.740.93 1.4
1.31.47 6.480.97 1.4
1.41.58 6.241.01 1.4
1.51.69 6.031.04 1.4
1.6
1.81 5.841.08 1.4
1.71.92 5.671.11 1.4
1.82.03 5.511.14 1.4
1.92.15 5.361.17 1.4
2.02.26 5.221.20 1.4
_______________________________________________
2.3 Wavemakercalibration
Sinceseakeepinganalysisisdonefortheassessment
of the ship motion in waves, the was characteristics
shouldbe checked in advance. The wave evaluation
valuesare obtained through the amplifier and wave
probe device in the model test. Figure 3 shows the
process of wave
probe calibration, and the typical
relationshipbetween wave height and output signal
voltageoftheamplifier.
Figure3.Waveprobecalibration
Table3.Evaluationinputstrokeforeachwavefrequency
_______________________________________________
Input WaveMeasured Target Error
Stroke period Wavevalue [%]
[cm][s]height[cm][cm]
_______________________________________________
1.790.60 1.431.40 2.46
1.620.66 1.421.40 1.70
1.550.71 1.351.40 3.56
1.510.76 1.381.40 1.76
1.510.81 1.451.40 3.33
1.500.85 1.371.40 2.11
1.480.93 1.381.40 1.29
1.490.97 1.371.40 1.80
1.511.01 1.381.40 1.41
1.521.04 1.391.40 0.49
1.54
1.08 1.401.40 0.34
1.581.11 1.421.40 1.26
1.591.14 1.431.40 1.97
1.581.17 1.381.40 1.31
1.641.20 1.361.40 2.60
_______________________________________________
Wave maker calibration is also necessary for
evaluationofthewavequality,andfindingtheinput
stroke of the wave maker system for each wave
frequency. Wave maker calibration at different
frequenciesareperformedatthe centerof thebasin,
in order to find the input stroke value in
the wave
maker system. Table 3 lists the results of the input
strokevaluesofthewavemakersystem.
2.4 Pre‐test
Intheseakeepingtest,itisveryimportanttoexactly
matchthemassdistributionofthemodelshiptothe
designwaterline.Inordertoapproximatethevertical
and
longitudinal mass distributions, the mass
momentsofinertiaaboutlongitudinalandtransverse
axisandmetacentricheight (GM)mustbe thesame.
Theballastedmodelshipwasperformedasshownin
Figure4.
Figure4.Ballastingofmodelship
The GM value is obtained through the inclining
test.AccordingtothetargetGM,Eq.1 determinesthe
angle of inclination at the time of application of the
inclined moment by a small weight. Figure 5 shows
movingtheweightinordertochangetheGMduring
thetest. Tables 4~5
show the results of the inclining
test.
1
y
wl
tan
WGM
(1)
Table4.Targetvalueofmetacentricheight
_______________________________________________
ItemModel
_______________________________________________
Mass[kg]4.974
GM[m]0.0053
Movedweight[kg]0.1
Lever
y
l
[m]0.03
Heelangle
(deg.)6.49
_______________________________________________
Table5.Measuredheelangle
_______________________________________________
ItemMeasured RealError
angle[deg.] angle[deg.] [%]
_______________________________________________
Startpoint‐0.3‐‐
MoveweighttoPort ‐6.86‐6.561.04
MoveweighttoStbd 6.046.342.35
_______________________________________________
Figure5.Incliningtest
520
According to ITTC (International Towing Tank
Conference) recommendation, the radius of gyration
in pitch motion is 0.25 of the ship length. In this
study, inertia test was performed by inertia swing.
Figure6showstheinertiaswing, andtheprocessof
inertia swing calibration. Inertia swing calibration
was performed with
4 kgf weight and different
distancefromthecenterofinertiaoftheinertiaswing.
Then,targetmomentofinertiaandmeasuredmoment
ofinertia valueofthemodelshipare0.3963kgm
2
and
0.3925kgm
2
,respectively.
Figure6.Inertiaswingcalibrationandinertiatest
2.5 Experimentalsetup
Themodelisattachedtothemotionmeasuringdevice
inthe middle of the measuring frame of the towing
carriage. The center of gravity of the model should
matchthethrustlineasmuchaspossible.Thewave
probeisinstalledat1.703minfrontofthe
centerof
themodelontherightedgeoftheyawtable,inorder
toavoiddisturbancecausedbythemodel.Figures7~8
showthedetailedsetupofthisexperiment.
Roll
Pitch
Amplifier
A/D
Converter
SDCL
Computer
Data
Analysis
Heave
Yaw t abl e
Carriage
1.5m
1.703 m
Wave probe
Electrical line
Figure7.Modeltestsetup
Figure8.Realmodeltestsetup
2.6 ResponseAmplitudeOperator(RAO)
The results of heave, roll, and pitch RAOs of the
model for 7 wave directions in 15 wave frequencies
wereobtainedasshowninFigures9~11.Therelative
vertical motion and relative velocity at bow were
estimatedfromresultofmodeltestbasedonARJM’s
method.
The relative displacement and relative
velocity at the bow can be determined by Eqs. 2~3,
respectively.InEq.2,
isthelocalwavedepression,
3
and
5
are the heave and pitch response,
respectively.Figures 12~13 showthe relative motion
and relative velocity at bow depending on wave
direction for finding probability of slamming and
deckwetness.
315RB
x
(2)
RR
(3)
0
0.4
0.8
1.2
0.4 0.8 1.2 1.6 2 2.4
/L
-180
-90
0
90
180
Z
A
/A
Phase [deg.]
0
0.4
0.8
1.2
0.4 0.8 1.2 1.6 2 2.4
/L
-180
-90
0
90
180
(a) 180
o
(b) 150
o
(c) 120
o
Z
A
/
A
Phase [deg.]
0
0.4
0.8
1.2
0.4 0.8 1.2 1.6 2 2.4
/L
-180
-90
0
0
0.4
0.8
1.2
0.4 0.8 1.2 1.6 2 2.4
/L
-180
-90
0
90
(d) 90
o
(e) 60
o
(f) 30
o
0
0.4
0.8
1.2
0.4 0.8 1.2 1.6 2 2.4
/L
-180
-90
0
90
(g) 0
o
Figure9.HeaveRAO
521
/kA
Phase [deg.]
/kA
Phase [deg.]
/kA
Phase [deg.]
(a) 180
o
(b) 150
o
(c) 120
o
/kA
Phase [deg.]
/kA
Phase [deg.]
(d) 90
o
(e) 60
o
(f) 30
o
/kA
Phase [deg.]
(g) 0
o
Figure10.RollRAO
0
0.2
0.4
0.
6
0.4 0.8 1.2 1.6 2 2.4
/L
-180
-90
0
90
180
0
0.2
0.4
0.
6
0.4 0.8 1.2 1.6 2 2.4
/L
-180
-90
0
90
180
/kA
Phase [deg.]
(a) 180
o
(b) 150
o
(c) 120
o
0
0.2
0.4
0.
6
0.40.81.21.6 2 2.4
/L
-180
-90
0
90
180
0
0.2
0.4
0.
6
0.40.81.21.6 2 2.4
/L
-180
-90
0
90
180
(d) 90
o
(e) 60
o
(f) 30
o
0
0.2
0.4
0.
6
0.4 0.8 1.2 1.6 2 2.4
/L
-180
-90
0
90
180
(g) 0
o
Figure11.PitchRAO
522
0.3 0.4 0.5 0.6 0.7
[rad/s]
0.4
0.8
1.2
1.6
2
2.4
2.8
Wave direction
180 degree
150 degree
120 degree
90 degree
60 degree
30 degree
0 degree
Figure12.Relativedisplacementatbow
Figure13.Relativevelocityatbow
3 WEATHERROUTINGALGORITHM
3.1 Weatherroutingclass
Figure 14 illustrates the implementation of Optimal
Weather Routing Setting Unit class (OWRSU) in a
flowchart.First,ship’sdataandweatherforecastdata
areinitialized byReadData function which is stored
inthe Weather classand OwnShip class. These data
relatetoship
informationandweatherforecastdata.
Then, Initialize function is called, and it is used to
initializeOwnShip,Weather,andRouteclasses.Next,
FindRoutefunctioniscalledtoestimatecostofapath
basedonspeedreductiontoenvironmentalcondition
and safety constraint value. The last two stages are
PrintDataand
Finalize.
Figure15showstheprocessusedinthissystemto
provide a safety solution for ship operation at sea.
There are two stages (SHORE and SHIP) in the
processoffindingsafetyoperationofashipundera
givenseastate.InputandoutputofOWRSUclassare
shownin
Figure16.
ReadData
OWRSU class
Initialize
FindRoute
PrintData
Finalize
Weather class
OwnShip class
ReadData
Route class
ReadData
Initialize
Initialize
RouteCost
GetData
GetData
SpeedLossWindWave
SpeedLossSlamming
SpeedLossDeckWetness
CostParametricRolling
SpeedLossTemperature
Figure14.Flowchartforroutefinding
Figure15.Flowchartforroutefinding
Figure16.Flowchartforroutefinding
3.2 Modelsofcostfunctions
InordertoapplyA*algorithmforoptimalshiproute,
thepathcostwasproposedasanadditiveevaluation
function
() () (),
f
ngnhn
where ()gnis the path
cost and
()hn
is the heuristic cost which includes
geographic information and weather constraint.
Possibleareasencompassing of aoptimal ship route
and weather condition are discretized by candidate
nodes.Inthisstudy,thecandidatenodesthatcanbe
traversedarebuiltaroundthegreatcircle’spath.f(n)
value of a node combines the
environmental data
withtheship’sdataandcanbeestimatedbyEq.4.
111iii
f
gh
(4)
By optimizing the evaluation function
1i
f
for
the complete path, A* algorithm achieves the
minimumtime route orminimum fuel consumption
routeofaship.Inaddition,parametricrollingissetas
thesafetyconstraintvalue.Inordertoavoidlandand
islands, this algorithm treats these hazards by
assigningaverylargedefaultvalueof
theevaluation
function to these grids. To implement the optimal
route search algorithm, two models are proposed to
523
minimize the arrival time and minimum energy
requirement.Intheminimumarrivaltimemodel,we
assume that the engine of the selected vessel can
provide constant power output and ship speed can
changed due to weather condition. The ETA
(Estimated Time to Arrival) is used to set a shorter
route
fromdepartureporttodestinationportnodeby
applyingtheweatherforecastdata.Inthismodel,the
pathcost functioncanbe estimatedas asthesailing
time.Intheminimumenergymodel,weassumethat
theshipʹsenergyoutputcanbechangedtokeep the
speed constant. It
can be seen that when a vessel
operatesundertheinfluenceofenvironmentsuchasa
windand wave, more energyshould be supplied to
the vessel than in case the vessel operates in clam
water. Therefore, the path cost function can be
estimated as the minimum energy to maintain a
constantshipspeed.
3.3 Variousspeedreductionparameters
The method for avoiding parametric rolling is
recommendedbyIMOcirc.1228,thecourseandthe
speed of the ship should be chosen avoiding these
condition, encountering period
E
T close to the ship
rollperiod
R
T (
ER
TT )oronehalfoftheshiproll
period
(0.5)
ER
TT .
In ship navigation, the speed reduction of a ship
can be divided into two types, voluntary and
involuntary speed reduction. Involuntary speed
reduction can be estimated from empirical formulae
suggestedbymanyresearchersinthepast.Weused
Kwon’s method (1981, 2005) to predict involuntary
speedreductionunderdifferentweather
condition.In
addition,theeffectoftemperatureisalsoconsidered
intermsofinvoluntaryspeedreduction.
Ontheotherhand,foravoidingacertainexcessive
motion, voluntary speed reduction was reduced the
ship’scaptain in dangeroussea condition. However,
this method depends not only on the caption’s
decisionbutalso
onhislong‐standingexperience.In
this study, the involuntary speed reduction of the
vessel wasmodeled as to avoid slamming and deck
wetness phenomena for avoiding excessive motion.
The probability of slamming and deck wetness is
usually estimated by relative motion and relative
velocityatbow.Inordertoapply
theresultsofmodel
test at various wave heading angle for the optimal
ship,therelativeverticalmotionandrelativevertical
velocity at bow should be calculated from RAOs
motionofthemodeltestinwavesbased onARJM’s
method
4 SIMULATIONANDRESULTS
4.1 Simulation
Weather data sets are
updated every 12 hours and
obtainedfromSAS.Environmentalconditionsthatare
used in the simulation of this study include swell
direction,swellheight,windspeedandtemperature.
Thesampleweatherdataaregivenateachnodewith
gridsizeof0.1degreeinlongitudeand0.1degreein
latitude.
The
weather data at any particular time and
position of the ship are obtained by linear
interpolationofthesurroundingenvironmentaldata.
InordertoconfirmtheabilityoftheA*algorithmin
the OWRSU class, and investigate how the weather
conditions influence the optimal weather route, the
8600 TEU
container ship was selected for this
simulation.
Table 6 shows the route of container ship which
was simulated in this study. Two simulations were
performed to evaluate the effectiveness of the two
models that were suggested in this study for the
optimalshiproute.Incase1,modelofminimumthe
arrival time of the ship is applied and optimization
index is the shortest time under environmental
conditions. In case 2, model of minimum energy is
used,andtheoptimizationindexistheenergyofthe
vessel provided so that the vessel can keep the
constant speed under the influence of
the
environmentalconditions.
Table6.Simulationcondition
_______________________________________________
PortLocation
_______________________________________________
DepartureTokyo,Japan139
o
East,35
o
North.
Destination:SanFrancisco,US 122
o
West,38
o
North.
_______________________________________________
4.2 Results
Figure 17 shows the shipʹs speed comparisons
estimated by both the Great Circles (GC) and the
optimal weather route found by the A * algorithm
duringa shipʹsvoyage.Speedreductionofashipin
the GC’s route has significant difference with that
estimated by the
A* algorithm. Speed reduction is
verysmallincasesofshipfollowsthepathsuggested
by the A * algorithm, whereas speed reduction is
significantinthecasewhentheshipfollowsthepath
suggested by the GC. The reason is that the GC
cannotconsidertheweatherconditionfor
findingthe
optimalshiproute,leading tothe shipbeing ableto
gointodangerousareastoreduceitsapparentspeed.
The shipʹs arrival time can save 9.10% using the A*
algorithmlistedinTable7.A*suggestsshorterroutes,
fasterthanoneissuggestedbyGC.
Figure17.Comparisonofspeedandtimeincaseofconstant
powercondition
524
Table7.ComparisonofETA
_______________________________________________
Algorithm ETA[hours] Timesavingratio[%]
_______________________________________________
GC268.61‐
A*244.179.10
_______________________________________________
In case of constant speed conditions, energy
consumption will become less if ship goes by the
route suggested by the A * algorithm as shown in
Figure 18. In particular, when ship follows the path
suggested by the A * algorithm, the energy
consumptioncansaveabout5.47%as
listedinTable
8.However,thearrival time of a shipin caseof the
ship passes the route suggested by the GC will be
faster than the route suggested by A * because the
great circle distance is the shortest route. Figure 19
showstheoptimalshiprouteinthis
simulation.
Table8.Comparisonofestimatedenergyconsumption
_______________________________________________
AlgorithmETA[hours] Energy[KJ] Energysaving
ratio[%]
_______________________________________________
GC 166.39 3.4037E+10‐
A*168.06 3.2175E+105.47
_______________________________________________
Figure18. Comparison of energy and time in case of
constantspeed
Latitude [deg.
]
Latitude [deg.]
Wind Spee
d
[knots]
Tokyo, Japan
San Francisco, US
Figure19.Optimalweatherroute
5 CONCLUSION
In this paper, the seakeeping model test of the 8600
TEU container ship was carried out in Changwon
National University’s square wave basin, and its
RAOs at various frequencies were modeled for
finding the optimal weather route minimizing the
arrivaltime or minimum.A* algorithmfor avoiding
hazard situations
has been proposed as an
optimizationmethod.Theconcludingremarksareas
follows:
First,themeasuredshipmotionsinvariouswaves
andheadingconditionsbyperformingthemodeltest
in the square wave basin. The effect of wavelength
and wave direction have a clear effect on the RAO
motion of
8600 TEU container ship. The relative
vertical motion and relative vertical velocity at bow
wereestimatedfromRAO’smotionofthemodeltest
in waves. In particular, the experimental results of
thisstudyhavebeenusedtofindtheoptimalrouteof
aship.
Second, A* algorithm was applied to 8600
TEU
container ship. It is clear that the A* algorithm is
effective in finding the optimal route based on
weather forecast data and experimental result. This
studyproposes anoptimalsolution for optimalship
routetoensurevesselsafetyaswellassavetimeand
fuelforthevessel.Users
canselectETAorconsume
shippower.Thesimulationresultsshowthatthepath
suggestedbythealgorithmA*isbetterthantheGC
with minimum arrival time and minimum energy.
Userscanchoosetosavetimeaswellassaveenergy
easily. From the simulation results, the path
suggested
by the A* algorithm is better and more
efficientthantheroutesuggestedbytheGC.
Finally,theinfluenceofenvironmentaldata,such
as the influence of temperature, wind and waves,
changes the resistance of the entire ship, has been
considered. The special feature of this study is that
the
speedestimationisbasedonnotonlythetimeand
location of the vessel, but also the updating of the
weatherdataandonthelocationofthecurrentvessel.
Developmentofthis studycan usedto contributeto
thedevelopmentoftheship.
ACKNOWLEDGEMENT
This research was supported by “Development
of
SolutionforSafetyandOptimalNavigationPathofa
ShipConsideringtheSeaState”sponsoredbyKorean
EvaluationInstituteofIndustrialTechnology(KEIT).
REFERENCE
ARJM,L.1998.Seakeeping:shipbehaviorinroughweather,
EllisHorwoodLtd.
Calvert, S., Deakins, E. and Motte R. 1991. A dynamic
system for fuel optimization Trans‐Ocean, The Royal
InstituteofNavigation,Vol44:233‐265.
Hagiwara, H. and Spaans, J. A. 1987. Practical weather
routingofsail‐assistedmotor
vessels.TheRoyal Institute
ofNavigation,Vol40:96‐119.
InternationalMarineOrganization,2007.Revisedguidance
to the mas t er for avoiding dangerous situations in
adverse weather and sea conditions, IMO circular no.
1228.
525
Kwon,Y.J.1981.Theeffectofweather,particularlyshortsea
waves, on ship speed performance (Ph.D. thesis),
UniversityofNewcastleuponTyne
Kwon,Y.J.,Kim,D.Y.2005.AResearchontheApproximate
Formulae for the Speed Loss at Sea, Journal of Ocean
EngineeringandTechnology,19(2):90‐93.
Lin,Y.H.,
Fang,M.C.,Yeung,R.W.2013.Theoptimization
of ship weather‐routing algorithm based on the
compositeinfluenceofmulti‐dynamicelements,Applied
OceanResearch,43:184‐194.
Nguyen, V.M., Jeon, M., Yoon, H.K. 2016. Study on the
optimal weather routing of a ship considering
parametric rolling, slamming, deck wetness, PRADS’
2016
Padhy, C.P., Sen, D., Bhaskaran, P.K. 2007. Application of
wave model for weather routing of ships in the North
IndianOcean,NatHazards:373‐385.
Panigrahi, J.K., Padhy, C.P., Sen, D., Swain, J., Larsen O.
2012. Optimal ship tracking on a navigation route
betweentwoports:ahydrodynamicsapproach,
Journal
ofMarineScienceandTechnology,Vol17:59‐67.
SenD.andPadhy,C.2010.Developmentofashipweather‐
routing algorithm for specific application in North
Indian Ocean Region, Proceeding of the International
ConferenceonMarineTechnology(MARTEC):21‐27.
Sen,D.,Padhy,C.P.2015.Anapproachfor
developmentof
ashiproutingalgorithmapplicationintheNorthIndian
Oceanregion,AppliedOceanResearch,50:173‐191
Spyrou, K.J. 2005. Design Criteria for Parametric Rolling,
OceanicEngineeringInternational,9(1):11‐27.
Vlachos,D.S.2004.Optimalshiproutingbasedonwindand
wave forecasts, Computational Mathematics, Vol 1:
547‐
551.
