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796 Guidelines for the calculation of the coefficient fw for decrease in ship speed
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Interim guidelines for the calculation of the coefficient fw for decrease in ship speed in a representative sea condition for trial use

  dd-mm-yyyy = Entry into force
Document

MEPC.1/Circ.796

12-10-2012

Ingangsdatum: 12-10-2012

Interim guidelines for the calculation of the coefficient fw for decrease in ship speed in a representative sea condition for trial use

  dd-mm-yyyy = Entry into force
Document

MEPC.1/Circ.796

12-10-2012

Introduction

Ingangsdatum: 12-10-2012

Introduction

The purpose of these guidelines is to provide guidance on calculating the coefficient fw, which is contained in the Energy Efficiency Design Index, in paragraph 2.9 in the 2012 Guidelines on the method of calculation of the attained Energy Efficiency Design Index for new ships (EEDI), adopted by MEPC.212(63).

fw is a non-dimensional coefficient indicating the decrease in speed in a representative sea conditions of wave height, wave frequency and wind speed.

fw should be determined by conducting the ship specific simulation on its performance at representative sea condition following the procedure specified in part 1: Guidelines for the simulation for the coefficient fw for decrease in ship speed in a representative sea condition.

In cases where a simulation is not conducted, fw should be determined based on the standard fw curves following the procedure specified in part 2: Guidelines for calculating the coefficient fw from the standard fw curves.

Sample simulation and calculation of the coefficient fw are shown in respective appendices to part 1 and part 2, and the procedures for deriving standard fw curves are shown in appendix 2 of part 2.

Part 01 Simulation for the coefficient fw for decrease in ship speed

Part 1: Guidelines for the simulation for the coefficient fw for decrease in ship speed in a representative sea condition

Ingangsdatum: 12-10-2012
Part 1: Guidelines for the simulation for the coefficient fw for decrease in ship speed in a representative sea condition

01 General

Ingangsdatum: 12-10-2012

1 - General

1.1Application

1.1.1 The purpose of these guidelines is to provide guidance on conducting the simulation to obtain the coefficient fw for an individual ship, which is contained in the EEDI.

1.1.2 These guidelines apply to ships of which ship resistance as well as brake power in a calm sea condition (no wind and no waves) is evaluated by tank tests, which mean model towing tests, model self-propulsion tests and model propeller open water tests. Numerical calculations may be accepted as equivalent to model propeller open water tests or used to complement the tank tests conducted (e.g. to evaluate the effect of additional hull features such as fins, etc., on ship's performance), with approval of the verifier for the EEDI.

1.1.3 The design parameters and the assumed conditions in the simulation to obtain the coefficient fw should be consistent with those used in calculating the other components in the EEDI.

1.1.4 fw may also be determined by the verifier's acceptance of the tank test and/or simulated data from the ship of the same type's performance in representative sea condition.

 

1.2 Method of calculation

1.2.1 Symbols

PB

:

Brake power
RT

:

Total resistance in a calm sea condition (no wind and no waves)
Vref

:

Design ship speed when the ship is in operation in a calm sea condition (no wind and no waves)
Vw

:

Design ship speed when the ship is in operation under the representative sea condition
Rwave

:

Added resistance due to waves
Rwind

:

Added resistance due to wind

:

Propulsion efficiency

:

Transmission efficiency
Subscript w refers to wind and wave sea conditions.


1.2.2 The basic procedures in calculating decrease in ship speed is shown in figure 1.1. (See section 4 for more information.)


Figure 1.1: Flow chart of calculation for the decrease in ship speed

 

1.2.3 Relation between the power and the decrease of ship speed is shown in figure 1.2

Figure 1.2: Relation between power and the decrease in ship speed

02 Representative sea condition

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2 - Representative sea condition

2.1 Representative sea condition

2.1.1 The representative sea condition for all ships is Beaufort 6, listed in table 2.1.

Table 2.1: Representative sea condition for all ships


2.1.2 The direction of wind and waves are defined as heading direction, which has the most significant effect on the speed reduction.

 

2.2 Wind condition

2.2.1 The mean wind speed and wind direction are given in table 2.1.

 

2.3 Wave condition

2.3.1 Symbols

DAngular distribution function
EDirectional spectrum
HSignificant wave height
SFrequency spectrum
TMean wave period
Angle between ship course and regular waves (angle 0(deg.) is defined as the head waves direction)
Mean wave direction ( = 0 (deg.))
Circular frequency of incident regular waves

 

2.3.2 As ocean waves are characterized as irregular ones, the directional spectrum should be considered.

2.3.3 The significant wave height, mean wave period and mean wave direction are given in table 2.1. To obtain the mean wave period from the Beaufort scale, the following formula derived from a frequency spectrum for fully-developed wind waves is used.

where, H is the significant wave height in metres and T is the mean wave period in seconds.

2.3.4 The directional spectrum (E) is composed of frequency spectrum (S) and angular distribution function (D).


03 Ship condition

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3 - Ship condition

3.1 The assumed ship conditions yield to the 2012 Guidelines on the method of calculation of the attained energy efficiency design index for new ships (EEDI), adopted by MEPC.212(63) (EEDI calculation guidelines, hereafter), constant main engine output (75 per cent of MCR, to be consistent with the one used in the EEDI calculation guidelines), and operation in steady navigating conditions on the fixed course.

3.2 The current effect is not considered.

04 Method of calculation

4 - Method of calculation

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4 - Method of calculation

04.01 General

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4.1 - General

4.1.1 The total resistance in the representative sea condition, RTw, is calculated by adding Rw, which is the added resistance due to wind and waves derived at 4.3, to the resistance RTderived following the procedure specified in paragraph 1.1.2.

4.1.2 The ship speed Vw is the value of V where the brake power in the representative sea condition PBw equals to PB , which is the brake power required for achieving the speed of Vref in a calm sea condition.

4.1.3 Where PBw can be derived from the total resistance in the representative sea condition RTw, the properties for propellers and propulsion efficiency () should be derived from the formulas obtained from tank tests or an alternative method equivalent in terms of accuracy, and transmission efficiency () should be the proven value as verifiable as possible.

The brake power can also be obtained from the reliable self-propulsion tests.

4.1.4 The coefficient for decrease of ship speed fw is calculated by dividing Vw by Vref as follows:

04.02 Total resistance in a calm sea condition

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4.2 - Total resistance in a calm sea condition:RT

4.2.1 The total resistance in a calm sea condition is derived following the procedure specified in paragraph 1.1.2 as the function of speed.

04.03 Total resistance in the representative sea condition

4.3 - Total resistance in the representative sea condition: Rtw
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4.3 - Total resistance in the representative sea condition: Rtw
04.03.01 The total resistance in the representative sea condition
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4.3.1 The total resistance in the representative sea condition, RTw, is calculated by adding Rwind, which is the added resistance due to wind, and Rwave, which is the added resistance due to waves, to the total resistance in a calm sea condition RT.

04.03.02 Added resistance due to wind: wind
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4.3.2 Added resistance due to wind: windRwind

4.3.2.1 Symbols

 

AL

:

Projected lateral area above the designated load condition
AT

:

Projected transverse area above the designated load condition
B

:

Ship breadth
C

:

Distance from the midship section to the centre of the projected lateral area (AL); a positive value of C means that the centre of the projected lateral area is located ahead of the midship section
CDwind

:

Drag coefficient due to wind
LOA

:

Length overall
Uwind

:

Mean wind speed

:

Air density (1.226(kg/m3))

4.3.2.2 Added resistance due to wind is calculated by the following formula on the basis of the mean wind speed and wind direction given in table 2.1.

4.3.2.3CDwind should be calculated by a formula with considerable accuracy, which has been confirmed by model tests in a wind tunnel. The following formula is known for the expression of CDwind, for example:

 

04.03.03 Added resistance due to waves
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4.3.3 Added resistance due to waves: Rwave

4.3.3.1 Symbols

H

:

Significant wave height
T:

:

Mean wave period
V

:

Ship speed

:

Angle between ship course and regular waves (angle 0(deg.) is defined as the head waves direction)

:

Mean wave direction

:

Amplitude of incident regular waves

:

Circular frequency of incident regular waves


4.3.3.2 Irregular waves can be represented as linear superposition of the components of regular waves. Therefore added resistance due to waves Rwave is also calculated by linear superposition of the directional spectrum (E) and added resistance in regular waves (Rwave).

4.3.3.3 Added resistance in irregular waves Rwave should be determined by tank tests or a formula equivalent in terms of accuracy. In cases of applying the theoretical formula, added resistance in regular waves Rwave is calculated from the components of added resistance primary induced by ship motion in regular waves, Rwm and added resistance due to wave reflection in regular waves Rwr as an example.

Rwave = Rwm + Rwr

As an example, Rwm and Rwr are calculated by the method in 4.3.3.4 and 4.3.3.5.


4.3.3.4 Added resistance primary induced by ship motion in regular waves

(1)Symbols

:

Gravitational acceleration
H(m)

:

Function to be determined by the distribution of singularities which represent periodical disturbance by the ship
V

:

Ship speed

:

Angle between ship course and regular waves (angle 0(deg.) is defined as the head waves direction)

:

Fluid density

:

Circular frequency of incident regular waves

 

(2)Added resistance primary induced by ship motion in regular waves Rwm is calculated as follows:

 

4.3.3.5 Added resistance due to wave reflection in regular waves

(1)Symbols
B

:

Ship breadth
Bf

:

Bluntness coefficient, which is derived from the shape of water plane and wave direction
Cu

:

Coefficient of advance speed, which is determined on the basis of the guidance for tank tests
d

:

Ship draft

:

Froude number (non-dimensional number in relation to ship speed)

:

Gravitational acceleration

I1

:

Modified Bessel function of the first kind of order 1

K

:

Wave number of regular waves
K1

:

Modified Bessel function of the second kind of order 1

 

Lpp

:

Ship length between perpendiculars
V

:

Ship speed

:

Angle between ship course and regular waves (angle 0(deg.) is defined as the head waves direction)

d

:

Effect of draft and frequency

:

Fluid density

:

Amplitude of incident regular waves

:

Circular frequency of incident regular waves

 

(2)Added resistance due to wave reflection in regular waves is calculated as follows:

Figure 4.1: Coordinate system for wave reflection

 

(3)Effect of advance speed u is determined as follows:

 

(4)The coefficient of advance speed in oblique waves  is calculated as follows:


(5) The aforementioned coefficient is determined by tank tests. The tank tests should be carried out in short waves since Rwr mainly works in short waves. The length of short waves should be 0.5 Lpp or less.

(6) Effect of advance speed in regular head waves U is calculated by the following equation where  is added resistance obtained by the tank tests in regular head waves, and Rwm is added resistance due to ship motion in regular waves calculated by 4.3.3.4.

(7) Effect of advance speed U is obtained for each speed of the experiment by the aforementioned equation. Thereafter the coefficient of advance speed  is determined by the least square method against Fn; see figure below. The tank tests should be conducted under at least three different points of Fn. The range of Fn should include the Fn corresponding to the speed in a representative sea condition.

 


Figure 4.2: Determination of the coefficient of advance speed

Appendix Sample simulation of the coefficient fw

Ingangsdatum: 12-10-2012

Appendix - Sample simulation of the coefficient fw

Sample: Bulk carrier

The subject ship is a bulk carrier shown in the following figure and the following table.

Figure 1: Subject ship

Table 1: Dimensions of the subject ship
DimensionsValue
Length between perpendiculars217m
Breadth32.26m
Draft14m
Ship speed14.5knot
Output power at MCR9,070kW
Deadweight73,000ton

Calculation of fw from the ship specific simulation

The definition of symbols and paragraph number are followed by the Guidelines for the simulation for the coefficient fw for decrease in ship speed in a representative sea condition.

  1. The total resistance in a calm sea condition RT  is derived from tank tests* in a calm sea condition as the function of speed following paragraph 4.2 as shown in the following figure.

    * The tank tests are conducted in the conventional ship design process for the evaluation of ship performance in a calm sea condition.



    Figure: Resistance in a calm sea condition

  2. The added resistance due to wind Rwind is calculated following paragraph 4.3.2. For the subject ship, the drag coefficient due to wind Dwind C is calculated as 0.853.

  3. In the guidelines, the added resistance in regular waves Rwave is calculated from the components of added resistance primary induced by ship motion in regular waves Rwm and the added resistance due to wave reflection in regular waves Rwr.


    Rwm and Rwr are calculated in accordance with paragraphs 4.3.3.4 and 4.3.3.5, respectively.


    Here CU in head waves is determined following the paragraphs from 4.3.3.5 (5) to (7).* For the subject ship, effect of advance speed U in head waves is obtained as shown in the following figure, and CU is determined as 10.0.


    * CU is determined by tank tests in short waves. Since the ship motion is very small in short waves, the tests can be simply conducted with the same setting as the conventional resistance test, and the required time is about four hours.




    Figure 3: Effect of advance speed

  4. With the obtained CU , the added resistance in regular waves Rwave is calculated following the paragraph 4.3.3.3. For example, in the case of Fn =0.167, the non-dimensional value of the added resistance in regular waves is expressed as shown in the following figure.




    Figure 4: Added resistance in regular waves

  5. The added resistance due to waves in head waves Rwave is calculated following paragraph 4.3.3.2. Rwave in head waves at T = 6.7 (s) (BF6) is expressed as shown in the following figure. For obtaining the power curve, Rwave is expressed as a function of ship speed from the calculated Rwave at several ship speeds. In the sample calculation, Rwave is expressed as a quartic function of ship speed.




    Figure 5: Added resistance due to waves

     

  6. The total resistance in the representative sea condition RTW is calculated following paragraph 4.3, and the brake power in the representative sea condition PBW is calculated following paragraph 4.1.3. That is, RTW is calculated as a sum of RTRwind , and Rwave as shown in the following figure and PBW is calculated by dividing RTWV by the propulsion efficiency in the representative sea condition and the transmission efficiency .




    Figure 6: Total resistance in the representative sea condition

     

  7. The self-propulsion factors and the propeller characteristics for the subject ship are shown in the following figures. Here (1 - w) is the wake coefficient in full scale, (1 - t ) is the thrust deduction fraction,  is the propeller rotative efficiency, J = Va / (nD) is the advance coefficient, Va is the advance speed of the propeller, n is the propeller revolutions, D is the propeller diameter, KT is the propeller thrust coefficient, and KQ is the propeller torque coefficient.

  8. The propulsion efficiency is expressed as follows:





    Where  is the propeller efficiency in open water obtained by the propeller characteristics.

    Figure 7: Self-propulsion factors

    Figure 8: Propeller characteristics




  9. The power curve in the representative sea condition is obtained by solving the equilibrium equation on a force in the longitudinal direction numerically.


    The representative sea condition is BF6. The brake power in a calm sea condition (BF0) and that in the representative sea condition (BF6) are calculated as shown in the following figure.




    Figure 9: Power curves

  10. Following paragraph 4.1.4, the coefficient of the decrease of ship speed fw is calculated as 0.846 from Vw = 12.10(knot) and Vref = 14.31(knot) at the output power of 75 per cent MCR: 6802.5(kW).


    In the EEDI Technical File, fw is listed as follows:

Part 02 Calculating the coefficient Fw from the standard Fw Curves

Part 2 - Guidelines for calculating the coefficient Fw from the standard Fw Curves

Ingangsdatum: 12-10-2012

Part 2 - Guidelines for calculating the coefficient Fw from the standard Fw Curves

01 Application

Ingangsdatum: 12-10-2012

1 - Application

1.1 The purpose of these guidelines is to provide guidance on calculating the coefficient fw from the standard fw curves, which is contained in the EEDI.

1.2 These guidelines apply to ships for which a simulation is not conducted to obtain the coefficient fw following Guidelines for the simulation for the coefficient fw for decrease in ship speed in a representative sea condition.

1.3 The representative sea condition for each ship is defined in paragraph 2.1 in the Guidelines for the simulation for the coefficient fw for decrease in ship speed in a representative sea condition.

1.4 The design parameters in the calculation of fw from the standard fw curves should be consistent with those used in the calculation of the other components in the EEDI.

02 Method of calculation

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2 - Method of calculation

2.1 Three kinds of standard fw curves are provided for bulk carriers, tankers and containerships, and expressed as a function of Capacity defined in the 2012 Guidelines on the method of calculation of the attained Energy Efficiency Design Index for new ships (EEDI), adopted by MEPC.212(63). Ship types are defined in regulation 2 in Annex VI to the International Convention for the Prevention of Pollution from Ships, 1973, as modified by the Protocol of 1978 relating thereto, as amended by resolution MEPC.203(62).

2.2 Each standard fw curve has been obtained on the basis of data of actual speed reduction of existing ships under the representative sea condition in accordance with procedure for deriving standard fw curves. (see appendix 2.)

2.3 Each standard fw curve is shown from figure 1 to figure 3, and the standard fw value is expressed as follows:

standard fw value = a x ln(Capacity)+ b

where a and b are the parameters given in table 1.


Table 1: Parameters for determination of standard fw value

Ship typeab
Bulk carrier0.04290.294
Tanker 0.02380.526
Containership0.02080.633

 

 

fw = 0.0429ln(Capacity)+0.294
Figure 1: Standard fw curve for bulk carrier

 

 

fw = 0.0238ln(Capacity)+0.526
Figure 2: Standard fw curve for tanker

 

fw = 0.0208ln(Capacity)+0.633
Figure 3: Standard fw curve for containership

Appendix 1 Sample calculation of the coefficient fw

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Appendix 1 - Sample calculation of the coefficient fwfrom the standard fw curves

Sample: Bulk carrier

The subject ship is a bulk carrier shown in the following figure and the following table.

Figure 1: Subject ship

Table 1: Dimensions of the subject ship
DimensionsValue
Length between perpendiculars217m
Breadth32.26m
Draft14m
Ship speed14.5knot
Output power at MCR9,070kW
Deadweight73,000ton

Calculation of fw from the standard fw curves

The paragraph numbers are followed by guidelines for calculating the coefficient fw from the standard fw curves.

  1. The standard fw value is calculated following paragraph 2.3. Since the subject ship is a bulk carrier, the standard fw value is obtained from the following equation.


      Standard fw value = 0.0429 x ln(Capacity) + 0.294

    • Since the Capacity for the bulk carriers is deadweight, the Capacity for the subject ship is determined as 73,000 (ton). By substitution of 73,000 to the above equation, the standard fw value is obtained as 0.774.

    In the EEDI Technical File, fw is listed as follows:

    7.2 Calculated weather factor, fw
    fw                                  0.774

    Appendix 2 Procedures for deriving standard fw curves

    Appendix 2 - Procedures for deriving standard fw curves

    1. This document provides the procedures for deriving the standard fw curves on the basis of main ship particulars and operation data of approximately 180 existing ships in operation.

    2. The coefficient fw has been obtained for individual existing ships, by selecting the data that meet certain conditions as explained below.

    3. The derivation resulted in three standard fw curves for bulk carriers, tankers and containerships.

     The procedures for calculating the standard fw curves comprise the following five steps:

    Ingangsdatum: 12-10-2012

    Appendix 2 - Procedures for deriving standard fw curves

    1. This document provides the procedures for deriving the standard fw curves on the basis of main ship particulars and operation data of approximately 180 existing ships in operation.

    2. The coefficient fw has been obtained for individual existing ships, by selecting the data that meet certain conditions as explained below.

    3. The derivation resulted in three standard fw curves for bulk carriers, tankers and containerships.

     The procedures for calculating the standard fw curves comprise the following five steps:

    Step 1 To extract data from the ship's particulars

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    Step 1 - To extract data from the ship's particulars

    The data needed for calculation are Displacement, Speed, Main Engine Output as well as RPM at NOR(normal rating). In case the necessary data for fw are not obtained, the data of the ship is not used for deriving the standard fw curves.

    Step 2 To extract data from the abstract log

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    Step 2 - To extract data from the abstract log

    The data required are Displacement, Wind Direction (WDIR), Observed Beaufort Scale (WFOR), Measuring duration of Distlog and DistOG (HP (hours)), Distance Log (Distlog), Distance over the Ground (DistOG), Rotational Speed per minute (RPM) and Shaft Horse Power (SHP) for every 24 hours.

    The data for calculation of fw of individual ships are subject to screening, by following the procedures provided from (i) to (vi). The data meeting all the criteria provided from (i) to (vi) are to be used. In case the data are not extracted in the following process, the data of the ship is not used for deriving the standard fw curves.

    1. Displacement should be within ±15 per cent of average displacement of the voyages which have been reported to be close to the fully loaded condition or to the 70 per cent DWT condition in the case of a containership.1 In cases where displacement is not available, the average of draft may be used instead of the displacement.

    2. Wind direction (WDIR): Heading (relative wind direction not exceeding ±67.5 degree).

    3. Beaufort Scale (WFOR) for the selected data should be 2, 3 or 6.
      The data under WFOR 2 and 3 are used to represent the calm sea condition (no wind and no waves), and the data under WFOR 6 are used to represent the representative sea condition.

    4. The RPM (Rotational speed per minute) should be within ±5 per cent of the average RPM on the voyage.2

    5. SHP should be within ±20 per cent of the 75 per cent of the rated installed power (MCR). In case where SHP is not available, the fuel oil consumption may be used instead of the SHP.3

    6. Distlog should be used under the conditions that the difference between DistOG and Distlog is within ±10 per cent of whichever is smaller.4


    1In reality, it is impossible to collect only the data which are under completely full load conditions. Data deviated too much from the object displacement cannot be calibrated by the method described in step 3-1.
    2Data with RPM deviated from the average RPM may not be on the normal operational condition.
    3Data deviated too much from 75 per cent MCR cannot be calibrated by the method described in step 3.1.
    4Data with a large difference between Distlog and DistOG may be affected by the tidal current and the ocean current.

    Step 3 Data correction

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    Step 3 - Data correction

    3.1 Calibration of the data to reflect the difference between the object condition specified in EEDI calculation guidelines and the actual operation.

    Distlog data selected in step 2 are calibrated by the following equation, in order to take into account the difference between the object condition and the actual operation in terms of displacement and SHP5:

    Where:
    75%MCR:75 per cent of the rated installed power (MCR)
    average:Average displacement on the reported voyages,
    0:Displacement in measurement
    HP:Running time (Hours propelling)
    SHP0:Output in measurement
    V0:Measured ship speed relative to water (Distlog/HP)
    V1:Calibrated velocity based on displacement
    V2:Calibrated velocity based on output

    3.2 Calculation of V2 corresponding to calm sea:
    30 per cent largest values of V2 under Beaufort 2 and 3 are extracted to represent the calm sea condition.


    5Since SHP is approximately proportional to the wetted surface and the cube of ship speed, ship speed is calibrated with two thirds of the displacement, which has the same dimension as the wetted surface, and one third of the SHP.

    Step 4 Calculation of fw for individual existing ships

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    Step 4 - Calculation of fw for individual existing ships

    fw=average of V2corresponding to BF6 / average of V2 corresponding to calm sea for all ships.

    In cases calculated fw is larger than 1.0, the data shall be removed for the averaging.

    Step 5 Development of "standard fw" curves

    Ingangsdatum: 12-10-2012

    Step 5: Development of "standard fw" curves
    Run the regression, based on the natural logarithmic function, on those fw values obtained by Step 4.

    Regression line, in the form of natural logarithmic line, is obtained from the observed fw values calculated in the above steps and the Capacity of each ship. The standard fw curves should be determined so that we can avoid fw by the standard curves would be much higher than the actual fw value. Then the standard fw curves are set to pass the lower limit of the observed fw values by changing the intercept of the regression line in the form of natural logarithmic line.

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