Development and Evaluation of Optimal Routing System

Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering OMAE2008 June 15-20, 2008, Estoril, Portugal

OMAE2008-57345

( DRAFT ) DEVELOPMENT AND EVALUATION OF OPTIMAL ROUTING SYSTEM Gunil Park/Samsung Heavy Indutries Co.,Ltd.

Jinho Lee/ Samsung Heavy Indutries Co.,Ltd.

Jaewoong Choi/ Samsung Heavy Indutries Co.,Ltd.

Munsung Kim/ Samsung Heavy Indutries Co.,Ltd.

Yuntae Kang/ Samsung Heavy Indutries Co.,Ltd.

Changseon Bang/ Samsung Heavy Indutries Co.,Ltd.

Munkeun Ha/ Samsung Heavy Indutries Co.,Ltd.

ABSTRACT To improve the safety and efficiency of trans-ocean voyage, authors developed a new onboard weather routing system (so called SORAS). The system utilizes weather forecasting data to evaluate seakeeping performance and to generate optimized route plan with respect to fuel consumption and sailing time. The system can provide decision support for navigator in real time. For this feature, onboard wave measurement system and hull stress monitoring system are integrated to provide real time wave information and actual hull stress and bow acceleration. The optimal route depends on not only weather condition but also ship’s propulsion performance. We performed a simulation study to determine the accuracy limit of mathematical model for propulsion performance. To evaluate the system, we compared calculation results with actual voyage data. The estimation results of speed reduction and fuel consumption showed good coincidence with measurement results. The wave bending moment was estimated on the forecasted wave condition. The results were compared with measured wave bending moment. For optimal route, it was confirmed that the efficiency of optimal route is superior to the efficiency of the actual route which planned by captains or officers, and the improvement of efficiency would be significant.

mainly performed because there were not sufficient computing systems and the forecast services were not so practical to use on board. Recently, the successful development of information systems and more active satellite communication have enabled the usage of weather forecast onboard. And 5 or 10 days' forecast can be used to make a route plan in these days. It means that objective and quantitative estimation tools have become more popular, which the navigators can make more safe and efficient route plan with. (Chen,1998) On this background, the related research works and developments have been carried out by the authors since 2001. And we performed several validation tests for the developed system, so called SORAS(Samsung Optimum Route Assessment System), on container ships.(Park,2004) (Han Yu,2006) The main purpose of those validation tests was to evaluate the economical effect of optimal routing by the authors’ system and the accuracy of its performance estimation results. In this paper we introduce the major features of the system and the results of the validation tests.

NOMENCLATURE SORAS : Samsung Optimum Routing Assessment System IMO : International Maritime Organization ISO : International Standards Organization RAO : Response amplitude operator MMG : Mathematical Modeling Group in Japan HSMS/HHMS : Hull Stress(Health) Monitoring System VDR : Voyage Data Recorder ETA : Expected Time to Arrival

INTRODUCTION Due to the recent rapid increase of oil price, the needs for the practical technologies have been increasing, which can improve the efficiency of voyage as well as its safety. The optimization of route plan with respect to safety and efficiency has been researched for long time.(Chen,1978) In the early stage of the research, theoretical and conceptual studies were

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1. MAIN FEATURES OF THE OPTIMAL ROUTING SYSTEM

(M.S. Kim, 1997) (H. H. Chun, 1997) And the added resistance in waves can be evaluated by using 3D diffraction and second order potential theory.

In general, captain and officers make a route plan with weather forecast before departure. Also during voyage, they make modified route plan to keep the voyage safe and efficient in the continuously varying weather condition. Since serious accidents can be caused from bad weather and inadequate operation of ship can happen, objective and quantitative decision support systems are required to estimate risks and the efficiency of the route plan. To supply those kinds of supports for navigators the following features are included in authors’ system.

1.3 Estimation of sailing time and fuel consumption In addition to seakeeping performance estimation, the estimations of sailing time and fuel consumption are required to estimate the efficiency of route plan accurately. The effects of current, wind, wave and water depth are considered in the mathematical models of the system. And the resistance, propulsion and maneuvering characteristics of the specific vessel are used to evaluate efficiency of voyage. Major parts of mathematical model are based on the analysis procedure in the ISO 15016. Table 2 shows the summary of major parameters in the system and how to determine the parameters (data source)

1.1 Providing long term weather forecast Weather forecasting data can be supplied via satellite communication such as wind, wave, swell, current, surface temperature, pressure, front, ice.

Table 2. Summary of major parameters in mathematical model

Table 1. Summary of weather data information

Data Source

Weather data available in the system • type: daily analysis and 15 days forecast • resolution: 1x1 degree • basic items: • surface pressure • wind direction/force • wave direction/force • ocean current, observed current • tropical storms • additional items • bathymetry • marine bulletin information

Major parameters Resistance in calm water Propeller Characteristics Thrust reduction factor Wake fraction Wind force and moment Added resistance induced by wave Yaw motion due to wave Hydrodynamic derivatives Rudder force AutoPilot Model Shallow water effect

The sources of weather data are NCEP, National Hurricane Center, U.S. Navy, In-house model of weather service company, and local governments. All data are updated at 1800 GMT. There are further updates of any storm tracks and text bulletins at 0500, 1100, and 2300 GMT.

M S D E T C O O O O O O O O O O O O O O O O O O

O

O

O O O O

Data Source M: Model test, S: Sea trial, D: Database of similar ships E: Empirical formula, T: Tuning by actual voyage data, C: Calculation by theory

1.2 Estimation of seakeeping performance

With the forecasted wind, wave, current conditions between two waypoints, the equilibrium equations for surge, sway, yaw motions are used to determine speed over ground, drift angle, rudder angle and shaft power. The iterative calculation method is used to solve these implicit equations. Generally, the parameters related to calm water propulsion performance are mainly determined by model tests and sea trial. If the model test results are not available, the database of similar ships can be used. The wind force and moment are based on model test, and the added resistance due to wave is determined by calculation method. The equations of ship motion are similar with those of MMG, which are generally used to describe maneuvering motion under wind and current.

To protect crew, ship and cargo from extreme conditions and avoid structural damage, it is necessary to estimate seakeeping performance as accurate as possible. In the system, the following items are estimated. Heave, pitch, roll, yaw Motion Local acceleration (Vertical, Lateral) Slamming, green water, propeller racing probability Wave bending moment Parametric roll safety Added resistance due to waves 3D Panel Method is used to calculate RAOs for 6 DOF motion. And the directional wave spectrums based on the weather forecasting are used to calculate ship motion in waves.

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1.4 Optimization of route plan with forecasted weather condition

But in favorable weather condition, economy aspect can be considered as important as safety aspect.

The optimal route means the successive waypoints which lead to arrival point from departure point and minimize the cost function. The cost function in this system may be expressed in a function of the sailing time, fuel consumption, wave height and roll response or their combination. The detailed explanation on the cost function can be found in Annex. The search algorithm for optimal route uses Dijkstra and Dynamic Programming methods to minimize the cost function.(Chen,1998) Users can impose such constraints as the restricted area and wave height in this search.

Regression The Relation of sailing time Plot and fuel consumption on the Transpacific Route Fuel100 = -2226.50 + 24.9186 Time100

S = 21.3272

R-Sq = 94.0 %

R-Sq(adj) = 93.8 %

Fuel Consumption (ton) Fuel100

2500

Safety First!!! 2400

2300

Safety First? 2200 180

Good Weather

185

Time100 Sailing Time (hours)

190

Bad Weather

Fig. 2 Variation of sailing time and fuel consumption on North Pacific route

1.5 Real time measurement of wave condition during voyage In addition to the forecasted weather condition, the real time wave condition is used to enhance the safety of voyage, supplied by the onboard wave measurement system. The seakeeping performance can be calculated with directional wave spectrum. The onboard wave measurement system can be used to detect the different sea state from forecasted one in real time. And it can help navigators maneuver the vessel in appropriate manner in confused wave condition. For this purpose, we applied onboard wave measurement system which was developed by authors. The system uses a marine X-band radar to measure wave condition around the ship. Fig.3 shows the captured image of authors’ wave measurement system. The system displays sea clutter, directional wave spectrum and point wave spectrum.

36 Transpacific Routes From America to Japan Each voyages started at every 12 hours from 1st Dec.

Fig. 1 Variation of optimal routes in space

Fig.1 shows the optimal routes during a period for example. As shown in this figure, the set of optimal routes can be used to study the seasonal/spatial variation of route plans in a specific transoceanic route. We calculated 36 optimal routes for LA to Tokyo route during the period of 18 days from 1st Dec. of a year. The departure time of each route plan was increased by 12 hours. And there was not any constraint. The optimal route is widely distributed as shown in Fig.1. The cause of this variation of optimal routes is the change of weather condition in that area. The results in the Fig.1 can be regarded as a sample of short term variation. For long term variation, we can expect more wide variation of route plans. So, It can be easily understood that the influence of weather on variations of voyage route is significant. Also it must be difficult to make a route plan and predict the sailing time without long term weather forecasting information and reliable calculation method. Fig.2 shows the sailing time and fuel consumption for each optimal route. The range of fuel consumption is 2200ton ~2500ton. And the range of sailing time is 178~189hours. Because the only cause of this variation is weather condition, we can guess that the less fuel consumption and the less sailing time mean the more favorable weather condition for voyage. In the worse weather condition, the more sailing time and fuel consumption. And the scattering in bad weather condition is bigger than the one in good weather condition. It means there are many different routes from usual route in bad weather condition. With a viewpoint of management, the safety aspect of route plan should be emphasized first in bad weather condition.

Fig.3 Wave measurement system

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1.6 Monitoring of structural safety

cannot be expressed in the exactly equivalent error of calm water resistance. But the effect of the wake is less than the effect of resistance. Shortly speaking, we checked the variation of optimal routes caused from the error of calm water resistance instead of checking all variations due to every parameters. And we assumed there is no error in the weather forecast. In the similar manner as shown in Fig.1, we assumed 3 virtual vessels are operating on the route between LA to Tokyo. These 3 vessels have all the same parameters except for the calm water resistance. The calm water resistances of the vessels are 105%, 100% and 95% of reference value, respectively. We calculated three optimal routes for the vessels in case that the vessels would start at the same time bound for Tokyo. These 3 different optimal routes can be regarded as the variation of optimal routes due to the error of calm water resistance on the given weather condition. Additionally, to consider the change of weather condition in time and space, we calculated 3 optimal routes for the vessel with the increment of departure time by 12 hours and repeated these calculations to get 36 samples of variations. These samples of optimal routes include the variation due to the change of weather condition as well as the variation due to modeling error. Fig.4 shows the calculation results. In the figure, there are 3 sailing distances of optimal routes for each voyage number. Because these triple pair of optimal routes has almost the same waypoints, the sailing distance is used to easily represent the differences between optimal routes.

For the direct monitoring of structural safety, hull health monitoring system is adopted in authors’ system. The HHMS which was separately developed by authors (Choi J.W, 2004) can monitor the bending stress and torsional stress at midship section. And the vertical acceleration at bow area can be monitored also. Officers can use these functions in the loading and offloading procedure to check still water bending moment due to cargo and ballast water operation. Also the system can give useful information and warning on the structural fatigue and probability of bow slamming. In case of warning, user can use the real time wave measurement system to determine the actual sea state around the ship and calculate seakeeping performance with the measured wave condition. By the calculation results user can determine the adequate direction and speed of the ship to prevent structural damage and dangerous situation. 1.7 Voyage Data logging and its analysis The speed and power performance depend on the loading condition, And these performance can be gradually varied according to the fouling effect and suddenly changed by hull cleaning. Therefore, during the voyage, we used VDR to record voyage data such as ship’s position, speed, heading, rudder angle, engine rpm, power, fuel consumption, wind and current. And the recorded data are used to tune the parameters for the estimation of speed and power performance in various loading condition.

.

Variation of Optimal Route

2. SIMULATION STUDY TO DETERMINE THE REQUIRED ACCURACY LEVEL OF MATHEMATICAL MODEL

Sailing Distance(NM)

4900

The reliable estimation results of sailing time and fuel consumption are required to determine the most efficient route plan. The reliability of estimation results depends on the accuracy of weather forecast and the accuracy of mathematical modeling (including its parameters). The accuracy of weather forecast is beyond the work scope of authors. So, we discuss only the accuracy of mathematical modeling in this paper. To determine required accuracy level of mathematical model, the variations of optimal routes caused from the change of weather condition in time and space are compared with the variations of optimal routes caused from the error in the mathematical model. Generally, the estimation methods of sailing time and fuel consumption use the equilibrium equations of force and moment at the quasi-steady state. For the convenience of calculation and understanding, we assumed that the modeling error can be regarded as the equivalent error of calm water resistance. In fact, for example, the error in sailing time and fuel consumption caused from the error of wake fraction

A

4850

B 4800 4750 4700

C

4650

35

33

31

29

27

25

23

21

19

17

15

13

11

9

7

5

3

1

4600

Voyage Number 95% Rt

100% Rt

105% Rt

Fig.4 Variation of sailing distance according to change of weather condition and modeling error.

For the variation of sailing distance on a voyage number (for example, in the circle A) the main cause of this variation is the modeling error. And the mean sailing distance on a voyage number will be varied with the change of weather condition, as shown in circle B and C. As shown in the figure, the variation of sailing distance due to weather condition is much larger than the variation due to the modeling error of calm water resistance amount of +/- 5%. It

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means that if we use the mathematical model which has acceptable accuracy we can get the reliable optimal route in which weather condition is considered. Using the statistical methods such as Gage R&R, we concluded that we will be able to determine an optimal route with the resolution of +/-10 mile if the modeling error could remain within the range of +/-5% of calm water resistance. With this simulation study, we could specify the required accuracy level of mathematical models in the system.

Speed over ground (kts.)

Speed over ground 27 25 23 21 19 17 15 02-04

02-06

02-08

02-10

Measured

3. VALIDATION TEST FOR THE ACCURACY OF MATHEMATICAL MODELS

02-12

02-14

02-12

02-14

Estimated

Shaft Power

Shaft Power (kW)

50000

To confirm that the mathematical models in the system have enough accuracy required for reliable optimization, we compared the calculation results of speed and power with the measured data. Those calculations were carried out for 6 transpacific voyages. For the measurement data, mean speed over ground and shaft power for 10 minutes were calculated with the use of GPS and torquemeter data. In the estimation of speed and power, we used measured data for wind and current to separate the effects from the error of weather forecast. But we used the hindcasting data for wave and swell because there was no available measurement data during the voyages. 5810 times comparisons were carried out and the results are summarized as show in Table 3. Estimation error means the difference between the measured value and estimated value for each 10 minutes’ interval. As mentioned in the previous section, if these error levels are less than the 5% error of calm water resistance, then we can assume that the optimal route have the resolution of +/-10 mile.

45000 40000 35000 30000 25000 02-04

02-06

02-08

02-10

Measured

Estimated

Rudder Angle (deg.)

Rudder Angle 6 4 2 0 -2 -4 -6 -8 02-04

02-06

02-08

02-10

Measured

02-12

02-14

02-12

02-14

Estimated

Drift Angle

Drift angle (deg.)

Table 3. Accuracy in the speed and power estimation Speed over ground Shaft Power Test Range 18.99kts.~30.30kts. 26340Kw~47540Kw Std. Dev. Of Estimation Error 0.36 kts. 967Kw Std. Dev. Of Estimation Error(%) 1.55% 2.67%

Fig. 5 shows the comparative result between actual navigation data and estimated data by SORAS. The hindcasted weather data were used in the estimations of speed over ground, shaft power, rudder angle and drift angle, and the results show good coincidence with the measured data. The scattering in measured drift angle indicates that we need more consideration on track keeping and course keeping performance of ship’s navigation systems in our model. But it can also imply that we need to check whether the ship’s navigation systems including operational manners are appropriate.

6 4 2 0 -2 -4 -6 -8 02-04

02-06

02-08

02-10

Measured

Estimated

Fig.5 Comparisons of measured voyage data and estimated results (speed, shaft power, rudder angle, drift angle)

4. COMPARISON OF FORECASTED DATA

MEASURED

DATA

AND

The significant wave heights measured by wave measurement system (WaveFinder) were compared with forecast data as shown in Fig.6. It shows good coincidence between them. (Han Yu, 2006)

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1/100 Roll Amplitude (deg.)

Wave Height during the voayge from Port Kelang to Jeddah

9 8 7 6 5 4 3 2 1 0 09-25 09-26 09-27 09-28 09-29 09-30 10-01 10-02 10-03 10-04 10-05 10-06 10-07 10-08 10-09

Significant Wave Height(m)

6 5 4 3 2 1 0

Measured

08-24 00:00

08-25 00:00

08-26 00:00

08-27 00:00

Measured by W aveFinder (1Hour average) Forecasted on 27th Forecasted on 31th

08-28 00:00

08-29 00:00

08-30 00:00

08-31 00:00

Estimated

Fig.8 Comparisons of roll amplitude

Forecasted on 24th Forecasted on 29th Hindcast

1/00 Pitch Amplitude (deg.) 3 2.5

Fig.6 Comparisons of forecasted wave height and measured one

2 1.5 1 0.5

Wave bending moments predicted with forecasted wave data were compared with the measured wave bending moment at midship section by HSMS, as shown in the Fig 7. The good coincidence shown in this figure means that the forecast data and the estimation of wave bending moment are reliable.

0 10-12 00:00

08-26 00:00

08-27 00:00

Wave Bending Moment (ton-m) .

Measured by HSMS Predicted by SORAS on 27th's forecast Predicted by SORAS on 31st's forecast

08-28 00:00

10-15 00:00

10-16 00:00

10-17 00:00 Measured

10-18 00:00

10-19 00:00

10-20 00:00

10-21 00:00

10-22 00:00

10-23 00:00

Estimated

5. THE EFFECT OF OPTIMUM ROUTE

200000 180000 160000 140000 120000 100000 80000 60000 40000 20000 0 08-25 00:00

10-14 00:00

Fig.9 Comparisons of roll amplitude

Wave Bending Moment at midship

08-24 00:00

10-13 00:00

08-29 00:00

08-30 00:00

The fuel consumption for the real voyage route is compared with that of applying the optimum route supported by SORAS in order to confirm the voyage efficiency. The arrival time of the voyage at each route is adjusted to be same because the ETA should be kept for that voyage. It is necessary to optimize the route in SORAS repetitively at every 24 hours due to the fact that updated weather forecasting data would be supplied at every day. It is shown that the real voyage route, shortest route, optimum route using daily weather forecasting and ideal optimum route using hind casting in the Fig. 10.

08-31 00:00

Predicted by SORAS on 24th's forecast Predicted by SORAS on 29th's forecast Analyzed by SORAS

Fig.7 Comparisons of wave bending moments

Black Red Green Yellow

Fig.8 and Fig.9 show the significant amplitude of roll and pitch motion in another validation test. Fig. 8 shows the calculation results of roll motion response. In this calculation, we considered variation of GM in waves. The maximum value of GM fluctuation during the voyage was calculated at first. For the calculation of GM in waves, we calculated Froude-Krylov force on the hull at the wave condition corresponding to the maximum wave height encountered during the route. And the corrected GM was used in whole calculations of roll amplitude for the route. Consequently, the calculation results show the good agreement at around noon of Oct. 3rd when the measured roll motion response becomes the maximum. However, there are some errors for the other periods because the GM on each data points was different from the corrected GM. But this calculation approach for roll amplitude can be extended for each waypoints and to consider unexpected variation of GM.

Green : Actual Route (4525NM) Red Dot : Optimal route using updated forecast (4455NM) Yellow : Ideal optimal route using hindcast data (4463NM) dFuel >3.5% Black : Shortest Path (4415NM)

Fig.10 Comparisons of route plan

The wave height encountered the real voyage is compared with that of in the case of optimum route of SORAS as shown in Figure 11. The wave height of the optimum route is relatively higher than the real voyage. However, this wave height does not mainly affect the safety of the ship in voyage. In other words, the optimum route in SORAS can voyage efficiently as the range of allowable wave height.

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exist excessive margins, which cause unnecessary expense of time and fuel. And in some cases, it can cause unexpected late arrival or structural damages or loss of cargo. SORAS reduces the uncertainties in route planning by evaluating seakeeping performance to avoid and to survive rough sea condition. Ship master can estimate the safety and performance of his route plan quantitatively. Also, he can optimize his route plan using not only his skill and know-how but also the optimization function of SORAS.

Significant Wave Height (m) 4 3 2 1 0 08-31

09-01

09-02

09-03

09-04

09-05

Actual Voyage

09-06

09-07

09-08

09-09

09-10

09-08

09-09

09-10

Optimal Route

Swell Wave Height (m) 4 3 2 1 0 08-31

09-01

09-02

09-03

09-04

09-05

Actual Voyage

09-06

09-07

Optimal Route

ACKNOWLEDGMENTS

Fig.11 Comparison of wave heights on actual voyage route and optimal route.

REFERENCES

The voyage efficiency is compared for 4 times voyages between real route and optimum route of SORAS as shown in Table 4. To compare the actual voyage routes with optimal routes from SORAS, the performance of actual routes were evaluated using hindcasting weather data. Because there is no information about the weather condition on optimal routes except for forecast. The voyage distance becomes short and fuel consumption is economized more than 3.5% on the average using optimum route in SORAS. The differences in the fuel consumption between actual route plans and optimal route plans are mainly caused from weather condition, sailing distance and speed profile. The weather conditions on the optimal routes are more favorable than those on actual routes excepting for some short periods. Also the sailing distances of optimal routes are shorter than the sailing distances of actual routes. In the actual voyages, the speed profiles varied widely. Excepting for some cases related to safety in rough sea, sudden increases or decreases of speed to keep arrival time mean that the estimations of ETA were not so accurate. SORAS can estimate the arrival time with weather forecasting data. It can minimize the unnecessary variation of speed profile, which can save fuel consumption.

[1] Chen, H. (1978), “A Stochastic Dynamic Program for Minimum Cost Ship Route”, Ph. D Thesis, Department of Ocean Engineering, MIT. [2] Chen, Henry and Cardone, V.J. (1998), “Use of Operation Support Information System to Increase Ship Safety and Efficiency”, SNAME Transaction, Vol. 106, pp. 105-127. [3] Park G.I et al., “Introduction of Optimum Navigation Route Assessment System Based on Weather Forecasting and Seakeeping Prediction”, Journal of Korean Navigation and Port Research”, Vol.28, No.10, pp833-841, 2004. (in Korean) [4] Han Yu, Mun-Keun Ha, Jae-Woong Choi, James ShanChien Tai (2006), "DESIGN AND IMPLEMENTATION OF A COMPREHENSIVE FULL-SCALE MEASUREMENT SYSTEM FOR A LARGE CONTAINER CARRIER", Proceedings of RINA Conf., London, UK, Nov. 2006 [5] Park G.I et al, “The Application of Marine X-band Radar to Measure Wave Condition during Sea Trial”, Proceedings of 2nd PAAMES and AMEC2006, Jeju Island, KOREA, OCT. 17-20, 2006 [6] M. S. Kim, H. H. Chun, Y. R. Joo, "Design of a High Speed coastal passenger Catamaran with a superior Seakeeping Quality", 4th FAST'97, Sydney, Australia, July 1997 [7] H. H. Chun, M.S. Kim, Y. R. Joo, "Seakeeping Analysis of a 30 knots Coastal Passenger SWATH Ships", Proceedings of '97 ISOPE Conf., Hawaii, USA, May 1997 [8] Choi J.W and Kang Y.T., “Two-plane hull girder stress monitoring system for container ship”, The Society of Naval Architects of Korea, Vol.8, No.4, pp.17-25, 2004

Table 4. Summary of optimization

KHH-LAX OAK-TYO KHH-LAX OAK-TYO

Sailing Dist. Of Actual Route (NM) 5949.6 4525.3 6050.4 4839.5

Sailing Dist. Of Reduction Ratio Averaged Reduction Ratio Optimal Route of Sailing Dist. of Fuel Consumption (NM) (%) (%) 5922.0 0.5 4454.9 1.6 >3.5% 5955.4 1.6 4561.1 5.8

CONCLUSIONS Captains should make a safe and efficient route plan against such severe conditions. Therefore it is required to supply objective and quantitative decision support tools for those purposes. If there is no sufficient information and estimation tool, the uncertainties will make captains and officers consider some margin in their route plans. In some cases, there

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ANNEX A SUPPLEMENT

1. PROCEDURE OF CALCULATION AND REQUIRED PARAMETERS

Fsafety

The following diagram shows the detailed procedure of calculation and required parameters in SORAS. Preparing Input installation

Parameters

for

SORAS

r  FCR ( s )  V0 r   r ds + Fsafety α α ( 1 ) − + ∫ FCR0  V ( s ) on R  r r r = ∫ W ( H s ( s ) , φs ( s ))ds : a penalty function for risk

Fcost =

on R

R : a path line of a route plan r s : a position vector on path line r ds : a small segment of a route r r r r FCR ( s ) = f c ( P ( s ), n( s )) P ( s ) : fuel consumption rate

before

Typical Loading Condition on ship’s voyage

f c : specific fuel oil consumption r r r r P ( s ) : BHP on s n( s ) : RPM on s r r α : weighting factor V ( s ) : ship speed on s

Hull Offset Data & Hydrostatic Calculation

V0 , FCR0 : values in calm water

SeaKeeping Performance Analysis

φs : significant roll response amplitude

H s : significant wave height W : weighting function for safety Parametric Roll Assessment

α=

Model Test Results (Resistance and Self Propulsion)

w f Cost fuel wt Cost time + w f Cost fuel

w f , wt : weighting factor for fuel and time, respectively Cost fuel : cost per unit mass of fuel Costtime : cost per unit time of voyage

Sea Trial Results (Power and Fuel consumption)

For α = 0 ( w f > wt ), Fcost = V0

Actual Voyage Data Analysis for Correction factors

1 FCR (t )dt + Fsafety , FCR0 ∫

an optimal route which minimizes the cost function would Estimate route performance and Compare the results with actual voyage data

be the minimum fuel consumption route. If we assume calm weather condition on R, r r V ( s ) = V0 , FCR ( s ) = FCR0 , Fsafety = 0, Fcost = S (sailing distance of R )

2. COST FUNCTION The cost function of authors’ system can be expressed in the following formula. The cost function has a dimension of distance.

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3. ACTUAL VOYAGE DATA ANALYSIS FOR CORRECTION FACTORS (FUEL CONSUMPTION ANALYSIS) From the abstract Log data, we chose the some segments of the actual route, which could be assumed as a steady running state. And we calculated the fuel consumption rate during the segments (or legs). Using the mean RPM and the fuel consumption on each segment, we could estimate the BHP. Following figure shows the results of BHP .vs. RPM. Curve 0 was fitted from model test without considered propeller shaft generator and fouling effect. Curve 1 was fitted from model test including propeller shaft generator effect but, not considering fouling effect. The ship has a 3000KW shaft generator, so we should assume the additional power caused from this generator. Also the efficiency of the shaft generator should be considered. Curve 2 is the fitting result of BHP and RPM data analyzing on each segments including propeller shaft generator and fouling effect. The apparent differences between curve 1 and curve 2 were shown due to hull and propeller fouling. RPM vs BHP(KW) 50000 Scattered by loading condition and W eather condition

48000

46000

44000 BHP

Curve 2: Fitted curve

42000

Fouling Correction

Curve 1: Model Tes t + S haft Gen.

40000 Curve 0 : Model Tes t

38000

36000 83

85

87

89

91

93

95

RPM

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