551
1
INTRODUCTION
Almost90%oftheworld’stradesarecarriedbyships,
andforthevastmajorityofthesetrades,therearefew
or no alternatives to transporting by ships. This
resulted in the increased capacities of the ships.
Besides,theschedulesarealsotightened.Atthesame
time,therequirementsforshiproutingbecomemore
strict and the weather forecasts become more
significantintheweatherrouting.
Shiproutingdeterminesaroutetosailbetweena
starting place and a destination. The great circle
sailingshould be theshortest voyageif the oceanis
=calm=.However,thenavigationalenvironmentisfar
more complex, the strong wind, waves and ocean
currentsmayseverelyaffectshipsʹsafety,speed,fuel
consumptioninbadconditions.Thustheproblemof
how to design a safe‐economic route is a key
considerationinweatherrouting.
The problemis that howtoapplytheresults of
the weather
forecast and marine forecast into ship
routingiskernelinweatherrouting.Oneofthemost
important processes of weather routing is the
calculation of environmental factors. So this paper
focuses on summarizing the research progress in
calculationofenvironmentalfactors.
Firstly, the paper introduces the effects of
environmental factors (wind,
waves, currents), and
secondlymainlydescribesthedangerousphenomena
inthebad seaconditions.Finally, itsummarizesthe
research progress in calculating the environmental
factorsandpointsoutthedirectionofdevelopments
inthefuture.
Ship Route Design for Avoiding Heavy Weather and
Sea Conditions
Y.Cai&Y.Wen
SchoolofNavigation,WuhanUniversityofTechnology,Wuhan,China
HubeiInlandShippingTechnologyKeyLaboratory,Wuhan,China
L.Wu
SchoolofNavigation,WuhanUniversityofTechnology,Wuhan,China
HubeiInlandShippingTechnologyKeyLaboratory,Wuhan,China
DepartmentofEarthScience,UppsalaUniversity,Uppsala,Sweden
ABSTRACT: This paper covers the current state of maritime oil transportation in the Baltic Sea and the
developmentofoiltransportationinthe2000s,aswellasestimationsoftransportedoilvolumesin2020and
2030intheGulfofFinland.Thescenarioswereformulatedonthebasisofacurrent
stateanalysis,energyand
transportation strategies and scenarios and expert assessments. The study showed that the volumes of oil
transportationintheGulfofFinlandwillincreaseonlymoderatelycomparedtothecurrentstatus:9.5‐33.8%,
dependingonthescenario.Greenenergypolicyfavours renewableenergysources,whichcan
beseeninthe
smaller volumes of transported oil in the 2030 scenarios compared to the 2020 scenarios. In the Slow
development2020scenario,oiltransportvolumesfor2020areexpectedtobe170.6Mt(milliontonnes),inthe
Average development 2020 187.1 Mt and in the Strong development 2020 201.5
Mt. The corresponding oil
volumesfor the2030scenarios were165MtfortheStagnatingdevelopment2030 scenario,177.5 Mtforthe
Towardsagreenersociety2030scenarioand169.5MtintheDecarbonisingsociety2030scenario.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 8
Number 4
December 2014
DOI:10.12716/1001.08.04.09
552
2
EFFECTSOFENVIRONMENTALFACTORS
Important environmental factors in ship routing are
those elements such as the atmosphere and ocean
whichmayproduceachangeinthe statusofaship
transit. In ship routing, wind, waves, fogs, ice, and
oceancurrentsshouldbeconsidered.Theireffectson
shipnavigationareanalyzedindetailinthissection.
2.1
Effectsofwind
The effect of wind speed on ship performance is
difficult to determine. In light winds (less than 20‐
knots),shiplossspeedinheadwindsandgainspeed
slightlyinfollowingwinds.Forhigherwindspeeds,
ship speed is reduced in both head and following
winds. This is due to the increased
wave actions,
which even results in increased drag from steering
corrections in following seas, and indicates the
importance of sea conditions in determining ship
performance.
2.2
Effectsofwave
Wave height is the major factor that affects ship
performance. Wave action is responsible for ship
motions which reduce propeller thrust and cause
increased drag from steering corrections. The
relationship of ship speeds to wave direction and
height is similar to that of wind. In heavy waves,
exactperformancemaybe
difficulttopredictbecause
of the adjustments to course and speed for ship
handling and comfort. Although the effect of wind
waveandswellismuchgreaterforlargecommercial
vessel than that of wind speed and direction, it is
difficulttoseparatethetwoinshiprouting.
2.3
Effectsofcurrent
Ocean currents do not present a significant routing
problem,buttheycanbeadeterminingfactorinroute
selectionand diversion.This isespeciallytruewhen
the points of departure and destination are at
relativelylowlatitudes.Theimportantconsiderations
tobeevaluatedarethedifferenceindistancebetween
agreat
‐circlerouteandarouteselectedforoptimum
current,with theexpectedincrease inSOAfrom the
followingcurrent,andthedecreasedprobabilityofa
diversionforweatherandseasatthelowerlatitude.
Direction and speed of ocean currents are more
predictablethanwindandseas,butsomevariability
can be unexpected. Major ocean currents can be
disrupted for several days by very intense weather
systemssuchashurricanesandbyglobalphenomena
suchasElNino.
2.4
Forecastoftheenvironmentalfactors
Theweatherforecast isvital tothe weather routing.
Therearemanynumericalforecastmodelhavebeen
applied into the research of weather routing,
including MM5, WRF, SWAN, WW3, POM. The
modelsarecommonlyusedinpractice.
MM5andWRFareatmospheremodels,themodel
results mainly include surface winds, pressure,
and
temperature (Grell, 1995; Skamarock, 2005). SWAN
andWW3arewavemodels,andthemodelresultsare
significant in terms of wave height, wave length,
wave period, wave direction, frequency, and so on
(SWANteam,2009;Tolman,2002).POMistheocean
model, which is a three‐dimensional primitive
equation model.
The model calculates these
componentsofcurrentvelocity,salinity,temperature,
turbulence kinetic energy, turbulence length scale,
and free surface elevation as prognostic variables
(Mellor,1998).Besides,thereisadistributedcoupled
atmosphere‐wave‐oceanmodelwhichhadbeenfirstly
developed by Wuhan University of Technology in
China (Huang, 2005; Zhang, 2006).
The coupled
model can simulate and forecast the wind field, the
wave field and the current field at the same time,
whichisimplementedbythreeindependentmodels:
atmospheremodel(MM5),wavemodel(WW3),ocean
Model(POM).
3
HAZARDSTOSHIPSINHEAVYWEATHER
ANDSEACONDITION
Whensailinginadverseweatherconditions,ashipis
likely to encounter various kinds of dangerous
phenomena, which may lead to capsizing or severe
rollmotionscausingdamagetocargo,equipmentand
personsonboard.Infollowingsectiontheindividual
hazards due
to ship motions are explained together
withtherelevantphysicalphenomena.
3.1
Largeanglesofroll
It’s hard to quantize large angles of roll which
depends on ship characteristic, type and size. In
general, a large roll angle is defined as a roll angle
whichleadstooneofthefollowingevents:capsizing;
cargoshiftorlossofcargo;failureofimportantship
systems; any situation which
leads to an even large
rollangle.
Theoccurrenceoflargerollanglesisthereforean
evenwhichcauseshighfinanciallossesuptothetotal
loss of the ship. The reasons for the occurrence of
large roll angles may be following: parametric roll
motions;synchronousrollmotion;reductionof
intact
stabilitywhenridingawavecrestamidships.
Inanaturalseaway,alleffectsdoalwaysappearin
any possible combination. It is possible that the
combinationoftheseeffectsleadstoanamplification
of roll motion. These effects are described in the
following.
3.1.1
Parametricrollmotion
Parametric rollmotion with large anddangerous
rollamplitudesin wavesare duetothe variation of
stabilitybetweenthepositiononthe wavecrestand
position in the wave trough. Parametric roll may
occurintwodifferentsituations:
1
The stability varies with an encounter period
E
T thatisaboutequaltotherollperiod
R
T ofthe
ship(1:1resonance).Thissituationisonlypossible
553
infollowingseasatrelativelyhighspeeds.Asthe
rolldampingisnormallyhighatthatspeeds,itis
only at very low values of stability possible that
critical roll angles occur. Due to the tendency of
retardedup‐rightingfromthelargeamplitude,the
rollperiod
R
T mayadapttotheencounterperiod
toacertainextent,sothatthiskindofparametric
rolling may occur with a wide bandwidth of
encounter periods. In quartering waves a
transition to harmonic resonance may become
noticeable.
2
Thestabilityvarieswith anencounter period
E
T
thatisapproximatelyequaltohalftherollperiod
R
T of the ship (2:1 resonance). This situation is
metwhentwopitchcyclescoincidewithoneroll
cycle, and it is the most dangerous situation,
becausethewavecrestisalwaysamidshipswhen
theshipisinanuprightposition.Inthissituation,
theshipmayheeltooneside.
Iftheshiptravelsinfollowingseas,2:1resonance
canonlybemetatrelativelylowvaluesofstabilityin
low ship speeds. Due to the low stability, the
transversal accelerations may not be that large, but
large roll angles may occur, which can lead to
capsizing. Ship’s natural roll period
may strongly
varyiftheshiptravelsinfollowingseas.Becausethe
natural roll period depends on the stability of the
ship,andthestabilityalterationsbecomelarger.
If the ship travels in head seas, 2:1 resonance is
metatrelativelylargevaluesofstabilityatsmallship
speeds.Due
tothelargestabilityandtheshorttimes
on the wave crest, large roll angles are hardly
possible, but large accelerations can be found quite
often.Becausetherollperiodofshipdoesnotvaryas
much as in following seas, the resonant situation is
morepronouncedand itismore
difficultto actually
meeta2:1resonancesituationinheadseas.
3.1.2
Synchronousrollmotion
Large rolling motions may be excited when the
natural rolling period of a ship coincides with the
encounter wave period. In case of navigation in
followingandquarteringseasthismayhappenwhen
the transverse stability of the ship is marginal and
thereforethenaturalrollperiodbecomeslonger.
3.1.3
Reductionofintact stabilitywhenridingawave
crestamidships
Whenashipisridingonthewavecrest,theintact
stability can be decreased substantially according to
thechangesofthesubmergedhullform.Thisstability
reduction may become critical for wave lengths
withinrangeof0.6Lupto2.3L,whereListheship’s
length in meters. Within this
range the amount of
stabilityreductionisnearlyproportionaltothewave
height.Thissituationmayoccureitherinheadorin
following seas. The latter situation is particularly
dangerous, because the duration of riding on the
wavecrest,whichcorrespondstothetimeintervalof
reducesstability,becomeslonger.
The master shall avoid situations where the
encounter period equals one time or two times the
naturalrollperiodofthevessel.Ascountermeasures
theguidelinesproposetoreducetheshipspeedorto
alter course and speed in such a way that resonant
situationsforthegivenperiodof
theseastatecanbe
avoided.
3.2
Largeaccelerations
Largeaccelerations aredefinedasaccelerationswhich
lead to the following events: massive cargo loss or
cargodamages;heavydamagesatmachinerysystems
or vital safety systems; structural overload of safety
relevantstructuralmembers;injuriestothecrew.Itis
obviousthatlargeaccelerationleadtoheavydamages
totheship
andpotentiallytocrew,butnotnecessarily
tothetotallossoftheship.
Itmustbepointedoutthatlargeaccelerationsdo
not necessarily coincide with large roll angles and
viceversa.Evenat relativelysmallroll angles,large
accelerationscanoccurifthestabilityislargeenough
or
ifa2:1resonanceinheadseasismet.
3.3
Surf‐ridingandbroaching‐to
Surf‐ridingandbroaching‐tooccursinfollowingseas
if ship travels on a steep wave crest. Typically the
speed of a wave equaling ship length islarger than
the shipspeed,and the wave overtakes the ship. In
suchasituationitispossiblethattheovertakingwave
acceleratesthe
shipinsuchawaythatitstartstoride
on that wave (surf‐riding). If this situation is
combinedwithinsufficientstabilityonthewavecrest,
theshipmaycapsizeorexperiencelargerollangles.
Surf‐ridingalsoincreasesthe timeintervalwhenthe
shipremainsinthecrest
position.
Ontheotherhandthedangerexiststhattheship
broaches after surf‐riding. The main root of that
failure modeis yawing moment introducedinto the
ship (by the waves) or insufficient course keeping
ability. Due to the wave induced velocities, the
relative flow speed to the ship’s rudder
is
significantly decreased, which decrease the
manoeuvrabilityoftheshipfurther.Thelargeyawing
motion connected to broaching‐to cause large
centrifugalforces,whichcanleadtothecapsizingof
theship.
Broaching‐to problems are not really problems
connected to intact stability failures, because
broaching‐to cannot be avoided
by moderating
alterations ofthestability.It ismore amanoeuvring
probleminwaves.
3.4
Combinationofvariousdangerousphenomena
The dynamic behavior of a ship in following and
quarteringseasisverycomplex.Shipmotionisthree‐
dimensional and various detrimental factors or
dangerous phenomena like additional heeling
moments due to deck‐edge submerging, water
shippingandtrappingondeckorcargoshiftdue to
largerollmotionsmayoccur
incombinationwiththe
above mentioned phenomena, simultaneously or
consecutively. This may create extremely dangerous
combinations,whichmaycauseshipcapsize.
554
4
SHIPROUTEDESIGNFORAVOIDINGTHE
HEAVYWEATHERANDWAVECONDITIONS
When sailing in heavy weather and sea conditions
where there are rough seas and strong wind, ship
may encounters several hazards. So how to design
ship route for avoiding the heavy weather and sea
conditionsis verysignificantto guaranteethe safety
of crew and ship. One of the most important
processes of weather routing is the calculation of
environmental factors, so the calculation of
environmental factors is our key consideration. But
even careful weather routing cannot avoid the fact
that the ship may sometimes experience rough
weatherandsea
conditions.Therefore,inthissection,
we also focus on how to avoid the hazardous
phenomenaintheheavyweatherandseaconditions
exceptthecalculationofenvironmentalfactors.
4.1
Thecalculationofenvironmentalfactors
In the present research, the calculations of
environmental factors mainly focus on added
resistance and ship speed loss. The first section
summarizethemethodstocalculateaddedresistance,
inthesecondsectionthespeedlossisdiscussed.
4.1.1
Thecalculationofaddedresistance
4.1.1.1 Addedresistance/forceduetowind
The earliest method to calculate wind force is
suggested by Hughes in 1930, the expression as
follow:
22
(A cos A sin )
aaT L
FqC
where
a
F iswind force,
q
iswind pressure,
a
C is
the coefficients of wind force,
A
T
is orthographic
projectionareaoftheshipabovewater,
isrelative
bearingofwind,
A
L
islateralprojectionareaofthe
shipabovewater.
2
1
()
2
WF WX R a f rel
X
CAV
2
1
()
2
WF WY R a S rel
YC AV
2
1
()
2
WF WN R a S rel
NC ALV
where
WF
X
,
WF
Y and
WF
N aretheaheadforce,the
side force and the yaw moment, respectively.
WX
C ,
WY
C and
WN
C are the drag coefficients of the wind
forces.
R
is the coefficient of the relative wind
incident angle. The longitudinal and the lateral
projected areas of the ship on the wetted area are
denoted as
f
A and
S
A , respectively.
a
is the air
densityandListheshiplength.Itisnotedthat
rel
V
istherelativevelocitybetweenthewindandtheship.
4.1.1.2 Addedresistanceduetowave
Themeanaddedresistanceinanirregularwavefield
isgivenbytwicetheareaunderthespectrum,
00
0
2, ()
AW
AW R e e
R
mm S d.
Theappropriaterelationtodeterminetheresponse
spectrumcanbemodifiedas(Panigrahj,2012):
2
() ()
AW
AW
Re We
W
R
SS
.
where
AW
R
is added resistance in monochromatic
waves,
e
is the frequency of encounter,
AW
R
S
is the
added resistance spectrum,
W
S is clam water
resistance,
W
iswaveamplitude.
Furthermore, a simplified formulation for added
resistancesuggestedbyBhattacharyacanbeplugged
intothecalculations,
3
22
(b z b )
2
e
AW z a a
R
g
(1 cos )
e
V
g
where
z
a
and
a
are heave and pitch
displacements for corresponding heave (
b
z
) and
pitch(
b
)damping, V istheshipspeed,
isthe
absolute wave frequency,
is the ship heading
withrespecttothewaves.
4.1.1.3 Addedresistanceduetocurrent
Theequationsoftherelativevelocities betweena
ship in the body‐fixed coordinate system and ocean
surface currents in the inertial coordinate system is
brieflydefinedasfollows(Yu‐Hsien,2013):
sin sin
c
dx
vq
dt
cos sin
c
dy
vq
dt
where
c
V isthecurrentspeed,
c
istheattackangle
between the current incidence and the body‐fixed
coordinatesystem.
Subsequently,thecurrentforcesforashipcanbe
representedasthefollowingformulae:
22
1
(V V ) BdC ( )
2
cx cx cy cx cr
F
22
1
(V V ) LdC ( )
2
cy cx cy cy cr
F
22
1
(V V ) LdC ( )
2
ccxcycncr
N
555
where
arctan( )
cy
cr
cx
V
V
C
cx
, C
cy
and C
cn
are the
drag coefficients of ocean currents, which are determined
by the coefficient of the relative current incidence,
cr
.
is
the ship heading angle in the inertial coordinate system. B
is the width of a ship on the wetted surface.
4.1.2
Thecalculationofspeedloss
4.1.2.1 Speedlossduetowind
Highwindswillhaveagreateradverseeffectona
large,fullyloadedcontainershiporcarcarrierthana
fully loaded tanker of similar length. This effect is
mostnoticeablewhendocking,buttheeffectofbeam
winds over several days at sea can also
be
considerable (Bowditch, 2002). The effect of wind
speed on ship performance can be calculated as
follows(Chiang,2004):
aa
w
ww
CA
VV
CB
where
w
V is the increment or decrement of ship
speed dueto the windforce,
V is the wind speed,
a
C istheairdragcoefficients,
a
istheairspecific
gravity,
w
C is the sea water resistance coefficient,
w
is the sea water specific gravity, A is the side
projectionareaof thehull onthe waterline, B isthe
sideprojectionareaofthehullunderthewaterline.
4.1.2.2 Speedlossduetowave
When the ship is travelling in the ocean, she
experiences the wave with variable height and
direction hindering the ship’s speed. The effective
speedontheshipisestimatedusingtherelationship
between ship’s speed and wave characteristic by
James(Panigrahj,2008).
012
[cos ]HVV
whereVistheeffectivespeed,αistheship’scourse,β
is the direction from which the waves are
coming.
1
and
2
are constants taken from James
(1959),
0
V versusHcurve.
Some researchers also propose new formula,
according to their research results. The formula is
expressedasfollows(Tsou,2013):
6
00
(0.745 h 0.257 )(1.0 1.35 10 DV )VV qh
where V is the actual speed in the sea,
0
V is the speed in
calm water, h is the wave height, q is the angle between
ship heading and wave direction, D is the actual
displacement of the ship (tons).
Both of the two methods mentioned above mainly
consider wave height and wave direction. There are also
some methods consider other characteristic of wave expect
wave height and wave direction, when calculating the
speed loss. The formula is expressed as follows (Chiang,
2004):
vh h
Vh
h
L
h
where
v
V istheincrementordecrementofshipspeed
due to the wave,
h
is the coefficient of significant
waveheight,
thewavelength,Listheship’slength
overall,
h is the significantwaveheight,
h
is the
multiplecoefficient,
isthefrequency.
4.1.2.3 Speedlossconsideringvariousfactors
There are also some methods to calculate the speed
loss considering various factors in the present
research.Oneofthesemethodsconsideringtheeffects
of wave and current is described as follow (Chen,
1978):
sin sin
c
dx
vq
dt
cos sin
c
dy
vq
dt
where
12
(x , x )
arerectangularcoordinates，
isthe
speed of current,
is ship heading,
c
q
is current
direction,
w
q
iswavedirection, v isshipspeedwhich
canbeobtainedbyfollowingformula:
2
0
()
w
v v ah bh kq
where
0
v
is still water speed，
h
is wave height,
,,abk
arepracticalcoefficients.
Othermethodstocalculatespeedlossconsidering
waveandcurrentarequitesimilartotheoneshown
aboveandarethereforeomitted.
However, these are a method to calculate speed
according to total resistance which caused by
environmental factors, including clam water
resistance and added resistance. The
formula
expressedasfollows(Yu‐Hsien,2013):
1
3
3
(V) V
(V 2 )
A
r
R
F
V
SC
r
V is reduce speed , V is clam water speed, (V)
A
F is
the total resistance,
is the water density, S is the
wetted surface of the hull,
R
C is the coefficient of
clam‐waterwaveresistance.
4.2
Howtoavoiddangerousconditions
4.2.1 Forsurf‐ridingandbroaching‐to
Surf‐ridingandbroaching‐tomayoccurwhenthe
angleofencounterisintherange135°<α<225°andthe
ship speed is higher than
(1.8 ) / cos(180 )L
(knots).Toavoidsurfridingandpossiblebroaching‐
to,theshipspeed,thecourseorbothshouldbetaken
outsidethedangerousregion.
556
4.2.2
Forsuccessivehigh‐waveattack
Whentheaveragewavelengthislargerthan0.8L
andthesignificantwaveheightislargerthan0.04L,
and at the same time some indices of dangerous
behaviouroftheshipcanbeclearlyseen,themaster
shouldpayattentionnottoenterintothedangerous
zone. When the
ship is situated in this dangerous
zone, the ship speed should be reduced or the ship
courseshouldbechangedtopreventsuccessiveattack
ofhighwaves,whichcouldinducethedangerdueto
the reduction of intact stability, synchronous rolling
motions, parametric rolling motions or combination
ofvariousphenomena.
4.2.3 Forrollingmotions
Themastershould preventasynchronous rolling
motion which will occur when the encounter wave
periodisnearlyequaltothenaturalrollingperiodof
ship. For avoiding parametric rolling in following,
quartering, head,bowor beam seas ,the course and
speedoftheshipshouldbeselectedinaway
toavoid
conditionsforwhichtheencounterperiodiscloseto
theshiprollperiodortheencounterperiodiscloseto
one half of the ship roll period. The period of
encounter may be determined by entering with the
shipspeedinknots,theencounterangleandthewave
period.
5
CONCLUSIONANDDISCUSSION
In the present researches of weather routing,
researchers almost considered the effects of single
environmental factors. There are few methods that
consider the couple‐effect of environmental factors.
Buttheenvironmentofshipsailingisverycomplex,
the single factor or accumulation of several
environmental factors cannot reflect
the effect of
environmental factors on the ship performance.
Although Kobe university have done some research
on numerical ship navigation based on numerical
forecast models (Shigeaki,2008, 2010; T. Soda, 2012;
Chen, 2013), they didn’t give a formula about
calculating added resistance or/and shiploss. In the
futureresearchof
weatherrouting,thecouple‐effects
ofenvironmentalfactorsonshipperformancewillbe
oneofthehottopics.
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