International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 3
Number 4
December 2009
401
1 INTRODUCTION
In the late years, the ship operation cost increased
due to the raise of oil prices and the reduction of
CO
2
and NO
x
gas emission have become a urgent
matter to protect the environment.
Up to now, various researches on the weather
routing (here after WR) had been conducted and var-
ious calculation methods were developed in order to
find the safest route, shortest time route, minimum
fuel route. But until now WR researches are per-
formed focusing on the operation of ocean going
ships. Being mainly developed for long voyages
with a wide choice of routes, WR cannot be directly
applied for ships sailing on confined coastal water
(Haibo 2005).
In the recent years there have been tremendous
advances in weather forecasting techniques, forecast
of current also greatly progressed. Taking ad-
vantages of these progresses we developed a routing
method with minimum fuel consumption for coastal
ships.
In this paper we present a method for calculating
the minimum fuel consumption route (here after
MFR) for a specified voyage time for coastal ships
using precise weather forecast data and ship’s per-
formance model, the results of the simulation study
with this calculation method will also be discussed.
2 CALCULATION OF MINIMUM FUEL ROUTE
USING DJIKSTRA’S ALGORITHM
For calculating the minimum fuel route, Djisktra’ s
algorithm was used. This algorithm was developed
by Edsger W. Dijkstra in 1959; it is one of the most
common algorithms for solving the shortest path
problem, it finds the shortest path from a single
source vertex to other vertices in a graph that is
weighted (non negatively weighted), directed and
connected.
Setting the departure point as P
0
and the destina-
tion point as Ps, the standard route from P
0
to Ps is
constructed. A set of vertex (nodes) is constructed
on the perpendicular to the standard route (hereafter
we call all the nodes lying on the same perpendicular
from the standard route “vertex line”) (Takashima
2008).
The distance between the vertex lines is a func-
tion of the ship’s type and average speed and can be
easily changed to accommodate the type of voyage;
the distance between each vertex on a vertex line is
set to 2 miles in this work but it can also be changed.
In the method, we propose the propeller revolu-
tion number is kept constant during the voyage and
only the course can be controlled, which is more in
accordance with the practice onboard ship where
propeller revolution number is not constantly being
changed but kept constant and the course is gradual-
ly adjusted.
On the Fuel Saving Operation for Coastal
Merchant Ships using Weather Routing
K. Takashima & B. Mezaoui
Graduate School, Tokyo University of Marine Science and technology, Tokyo, Japan
R. Shoji
Tokyo University of Marine Science and technology, Tokyo, Japan
ABSTRACT: It is well known that Weather Routing is one of the effective ship operation methods to reduce
fuel consumption and many studies have been conducted to develop the effective calculation methods. How-
ever, most studies were performed focusing on the ocean going ships, and there were few studies made for
coastal ships. The authors propose a minimum fuel route calculation method for coastal ships that use the pre-
cise forecasted environmental data and the propulsion performance data of the ship on actual seas. In the pro-
posed method, we use the Dijkstra’s algorithm to calculate an optimum minimum fuel route suitable for
coastal ships. Simulation study was carried out to evaluate the effectiveness of the proposed method using
two coastal ships. As the result of study, the authors confirmed that the proposed calculation method is effec-
tive for fuel consumption reduction and is applicable for the operation of coastal merchant ships.
402
Figure 1. Grid points of DP to calculate minimum fuel route.
The propeller revolution number is determined so
as to reach the destination point at the desired time
of arrival. We will look for the minimum propeller
revolution number that will allow us to reach the
destination at the desired time of arrival, by doing so
we will find the most practical minimum fuel route
for the desired voyage time.
Ship’s position can be described by the following
equation:
),,,( CSxtfx =
(1)
Where t is the time, x the position of the ship, S the
speed and C the control parameter, which in our case
is dependent only on rudder angle since the propeller
revolution number in kept constant.
The speed of the ship at any instant is function of
ship’s heading and response to the external weather
elements, such as wave, wind and current.
),,,( currentwindwavefS
θ
=
(2)
Knowing the weather elements we can determine the
speed of the ship, and knowing this later allows us to
compute the time needed to travel from one node to
another.
Let the i-th node on the k-th vertex line from P
0
be G(k, i). The ship starts from G(k, i) at time t
k
and
reaches the node G(k-1, j) on the k-1-th vertex line at
time t
k-1
(see fig.1 for more details).
The minimum time route from the departure point
P
0
to the destination Ps is obtained by solving the
following iterative equation:
( )( ) ( ) ( )( ) ( )( ){ }
jkGTikGjkGTMinikGT
j
,1,,,1,
minmin
−+−=
(3)
(k=1,2,…,N+1)
where T
min
(G(k, i)) represents the minimum passage
time from the departure P
0
to the node G(k, i), and
T(G(k-1, j), G(k, i)) represents the passage time from
the previous node G(k-1, j) to the node G(k, i).
Eq.3 means than the minimum passage time from
departure point P
0
to any point G(k, i) can be deter-
mined by finding the minimum of the sum of pas-
sage time from G(k-1, j) to G(k, i) and the minimum
passage time from departure point P
0
to G(k-1, j)
(when k reaches N+1, G(N+1) is Ps ).
If the T
min
obtained by solving (3) is not equal to
the desired voyage time the propeller revolution
number is changed and (3) resolved, we will gradu-
ally adjust the propeller revolution number until we
get a T
min
as close as possible to the desired voyage
time.
The route thus obtained can be considered as the
minimum fuel route for the specified voyage time.
Here after we will refer to this route as MFR.
The MFR obtained by this method is not the true
minimum fuel route from the mathematical point of
view, but it can be regarded as the sub-optimal route
that will allow us to reach destination at the desired
time with a minimum consumption and a fixed pro-
peller revolution number. In this method since the
only control parameter is the ship’s course the
amount of calculation is largely reduced
3 ENVIRONMENTAL DATA
The environmental data used for carrying simulation
with this calculation method are forecasted data of
surface winds, waves, ocean and tidal currents, these
data were used to calculate the ship’s speed trough
the water and over the ground. The forecast data are
available for each 1 hour, extending for a period of
72 hours, the forecast data are updated 8 times a day
(i.e. base time of forecast: 00,03,06,09,12,15,18,21
UTC).
3.1 Wind and wave data
The wind data comprises mean wind direction and
mean wind speed; the wave data comprises the sig-
nificant wave height, predominant wave direction
and significant wave period.
For the forecast period up to 15 hours ahead the
forecasted data are the result of the input of the sur-
face winds from the mesoscale numerical forecast
model of the Japan Meteorological Agency into the
3
rd
generation wave forecast model “WAM” of the
Japan Weather Association, the data are given for
grids of 2 by 2 miles .
For the forecast period from 16 to 72 hours
ahead, the data are from the output of the wave fore-
cast model of the Japan Meteorological Agency, the
data are given for grids of 6 by 6 miles.
403
3.2 Ocean and tidal current data
The ocean current forecasted data are the output
from the Japan Coastal Predictability Experiment
operated by Frontier Research Center for Global
Change; the data are given for grids of 5 by 5 miles.
The Tidal current forecasted data are from the
output of the tidal calculation program developed by
the National Astronomical Observatory of Japan.
The data are given for grids of 2 by 2 miles. The da-
ta are given for grids of 2 by 2 miles
4 SPEED AND ENGINE PERFORMANCE IN
SEAWAY
Two ships, A roll-on/roll-off container ship plying
between Tokyo and Tomakomai/Kushiro in Hokkai-
do (north of Japan) and a cement career plying be-
tween Ube in Yamaguchi (south-east of Japan) and
Tokyo were used for the simulation to investigate
the effectiveness of the proposed minimum fuel
route calculation method, hereafter we refer to the
Ro/Ro container ship as “model ship-A” and to the
cement carrier ship as “Model ship-B”. The princi-
pal characteristics of the two ships are shown in Ta-
ble 1 and Table2.
Table 1 Principal particulars of the model ship-A
161.13 m
150.00 m
24.00 m
6.424 m
7,323 ton
Diesel engine x 1
16,920 kW
14,380 kW
23.00 kn
50 trailers (12 m)
200 containers (12 feet)
Table 2 Principal particulars of the model ship-B
159.7 m
152.5 m
24.2 m
9.016 m
13,787 ton
Diesel engine x 1
6,960 kW
13.0 kn
The speed through the water of the two ships was
calculated by numerically solving the equilibrium
equation between total resistance (sum of the still
water resistance, the wind resistance and the added
resistance due to waves) and the propeller thrust
(Kano 2008). For various rpm, wind conditions and
Figure 2. Speed performance curve of model ship-A at 142
RPM.
Figure 3. Speed performance curve of model ship-B at 157
RPM
wave condition we get the corresponding speed
through the water. In figure 2 and 3, speed perfor-
mance curve 142 rpm (for model ship-A) and 157
rpm (for model ship-B) for various wave heights and
wave direction from the bow are shown. When
drawing these curves, the wind speed (m/s) was tak-
en to be four times the significant wave height (m),
the wind direction was assumed to be equal to four
times the square root of the significant wave height.
It can be clearly seen that the speed reduction in-
crease with the decrease of the wave direction from
the bow. In the elaboration of these performance
curves, operational limits due to excessive ship’s
motion and accompanying dangerous phenomena
are not considered when elaborating these curves.
The fuel consumption F in kg per hour of the
model ship is calculated using the following equa-
tion
KPF =
(4)
Where K is the specific fuel consumption of the ship
(for model ship-A, K=0.180 kg/kW h, for model
ship-B, K=0.182 kg/kW h) and P is the engine pow-
er in BHP (kW) of the model ship.
142RPM
14
16
18
20
22
24
26
0 1 2 3 4 5 6 7
SIGNIFICANT WAVE HEIGHT [M]
SHIP'S SPEED [KNOT]
180
165
150
135
120
105
090
075
060
045
030
015
000
WAVE DIRECTION
FROM BOW [DEG]
157RPM
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7
SIGNIFICANT WAVE HEIGHT [M]
SHIP'S SPEED [KNOT]
180
165
150
135
120
105
090
075
060
045
030
015
000
WAVE DIRECTION
FROM BOW [DEG]
404
5 RESULTS OF MFR SIMULATION
We conducted MFR simulation for the two ships
(model ship-A and model ship-B) using the pro-
posed calculation method. For demonstrating the ef-
fectiveness of the proposed calculation method, we
also simulated the fuel consumption for the route
usually used by the ship (hereafter UR). A suitable
propeller revolution number is set, the propeller rev-
olution number is set to be constant during the voy-
age, according to this and using the environmental
data, speed and engine performance data, the voyage
time is calculated.
If the voyage time is not close to the desired voy-
age time, the propeller revolution number is changed
and the voyage time recalculated, the calculation
will be stopped when the difference between the cal-
culated voyage time and desired voyage time reach-
es ±0.1 hour. The fuel consumption thus obtained is
assumed to be the UR fuel consumption.
The simulation has been conducted for the condi-
tion shown as follows.
Model ship-A
− Route: From Kushiro to Tokyo (South bound)
− Term of simulation: November 2008
− Departure time: at 15:00(UTC) on each day
− desired voyage time: 26 hours
Model ship-B
− Route: From Ube to Tokyo (East bound)
− Term of simulation: November 2008
− Departure time: at 15:00(UTC) on each day
− desired voyage time: 29 hours
5.1 Comparison of fuel consumption in MFR and
UR
For achieving a good comparison between the MFR
and UR fuel consumption it would be better to use
weather data with as small error as possible. For
achieving this, we use only the first three hour fore-
cast data of each weather forecast report, hereafter
we refer to this data as Analyzed Wx and to the orig-
inal data as Forecast Wx.
Using the Analyzed Wx, we simulated MFR and
UR fuel consumption for 1 month (November 2008).
The results for ship model-A and ship model-B are
shown in figure 4 and 5 respectively.
The O marked curve shows MFR fuel consump-
tion, the △ marked curve shows the UR fuel con-
sumption and the bar graph represents the saving of
fuel between the two routes.
For both model ships, there is an evident fuel sav-
ing between MFR and UR; for model ship-A the av-
erage saving is 2.4%, the largest is 6.9%; for model
ships-B the average saving is 18.4% and the largest
saving amount is 22.1%.
The MFR routes obtained are shown on figure 6 for
ship model-A and figure 7 for ship model-B, we can
notice that the MFR tends to be farther from the
coast line than the UR.
Figure 4. Fuel consumption and fuel saving amount for model
ship-A.
Figure 5. Fuel consumption and fuel saving amount for model
ship-B.
Figure 6. Comparison between MFR ad UR for November
2008 for model ship-A.
Figure 7. Comparison between MFR ad UR for November
2008 for model ship-B.
model ship-A(RO/RO container ship)
0.0
10.0
20.0
30.0
40.0
50.0
60.0
11/2
11/3
11/4
11/5
11/6
11/12
11/13
11/14
11/15
11/16
11/17
11/18
11/19
11/20
11/21
11/22
11/23
11/24
11/25
11/26
11/27
11/28
11/29
Date of departure
Fuel consumption [tons]
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
The amount of fuel saving
[%]
amount of saving MFR UR
model ship-B(cement carrier ship)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
11/1
11/2
11/3
11/4
11/5
11/6
11/12
11/13
11/14
11/15
11/16
11/17
11/18
11/19
11/20
11/21
11/22
11/23
11/24
11/25
11/26
11/27
11/28
Date of departure
Fuel consumption [tons]
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
The amount of fuel saving
[%]
amount of saving MFR UR
405
Figure 8 and 9 show the sea current data for the
voyages with the largest amount of fuel saving. We
can notice that the MFR avoids regions with oppo-
site current and takes advantage of the regions where
current flows in the same direction as the ship’s
route. We also compared the difference between the
speed over ground and speed through the water for
the MFR and the UR, for the MFR, nearly all along
the voyage the speed over ground is higher that
speed through the water, which demonstrates that
the MFR is the route that takes advantage of the
ocean and that for the Japanese coasts, the ocean
current has a large influence on fuel saving.
Figure 8. Ocean current data for 20/12/2008.
Figure 9. Ocean current data for 27/12/2008.
5.2 Recalculation of MFR using updated
environmental forecast
Practically using Analyzed Wx for the calculation is
impossible; In fact there is a time lag of about 9
hours between the forecast and its publication, so at
any time only the forecast Wx data is available, the
Analyzed Wx data will not be available until the
time lag has passed, which means it can not be really
used for calculation.
Using the latest available Forecast Wx data, we
calculated the MFR for model ship-A, the departure
time is 17/12/2008 at 15:00 UTC from Kushiro in
Hokkaido to off Tokyo.
Hereafter we call the MFR obtained using the
Forecast Wx data as MFR-F and the MFR obtained
using Analyzed Wx data as MFR-A.
We can notice from figure 10 that shows both
routes, that the MFR-F tends be farer from the coast
than the MFR-A and this due to the error in the fore-
cast; we checked the accuracy of weather forecast
data and found that the Forecast Wx wind data tends
to be smaller than the Analyzed Wx wind data.
Figure 10. Comparison between MFR obtained using only An-
alyzed Wx data and using Forecast Wx data
To palliate the error on the route generated this
error on the forecast, we use rerouting; rerouting
consists on recalculating a new route from the pre-
sent position to the destination point every time
there is a change in the weather data, the ship starts
from the departure point and sails on the MFR calcu-
lated using the available Forecast Wx data, when a
new weather forecast is available the MFR is recal-
culated from the actual position of the ship to the
destination point using the newly available data.
Figure 11 shows the simulation of the MFR ob-
tained using forecasted data updated every three
hours. The rerouting points are shown with O marks,
the rerouting has been done 9 times in this voyage.
We also calculated the difference on arrival between
the MFR-A and the MFR-F calculated on each re-
routing. If the ship arrives ahead of the desired time
the error is deemed positive and it arrives late the er-
ror is negative.
Figure 12 shows the error on arrival time with re-
gards to the number of rerouting calculation, without
406
any rerouting the error on arrival time is around +28
minutes, with one rerouting recalculation the error
decreases to +9 minutes and with a maximum num-
ber of recalculation the error is around +3 minutes.
Using rerouting calculation the error on arrival
time can be reduced to an acceptable value.
Figure 11. MFR obtained using Forecast Wx data with recalcu-
lation every 3 hours
Figure 12. Error of arrival time with regards to the number of
recalculation
6 CONCLUSIONS
In this paper, a method for achieving energy saving
for coastal merchant ships using weather routing was
proposed. An optimization method based on Dijks-
tra’s algorithm using weather forecast data was pro-
posed. Two ships, one is a RO/RO container ship
plying between Kushiro in north Japan and Tokyo,
another is a cement carrier plying between Ube in
west Japan and Tokyo were taken as models, the
speed and engine performances in waves of both
ships were determined, simulations were also con-
ducted.
The results of one month simulation shows that
the MFR obtained using the proposed calculation
method allows to save a large amount of fuel, the
average saving for two model ships is 2.4% and 18.4
%, the maximum saving is 6.9% and 22.1% respec-
tively.
There is a strong oceanic current along the Japa-
nese coast, the proposed MFR calculation method,
takes advantage of this current and achieves a good
energy saving.
Recalculation of the MFR based on the updated
weather forecast data during the voyage allows to
reduce the effect of the forecast error.
For the further development of this research, a
concept of risk of delay will be introduced to the
calculation algorithm, using the information on the
accuracy of wind/wave forecast, the possible error
on the arrival time is determined and a minimum
fuel route arriving at the destination point with a
specific probability of the risk of delay can be calcu-
lated.
This study was done as a part of the “Research
and Development of Environment-Harmonized Op-
eration Planning Support System for coastal ships”
by New Energy and Industrial Technology Devel-
opment Organization (NEDO).
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Kano. K. & et al. 2008. Energy Saving Navigation Support
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Takashima, K. & et al. 2008. Energy Saving Operation for
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Dijkstra, E. W. 1959. A Note on Two Problems in Connexion
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model ship-A(RO/RO container ship)
-5
0
5
10
15
20
25
30
0 1 2 3 4 5 6 7 8
number of recauclation
error on arrival time [minutes]