Appendix 2 – Procedures for Deriving Standard fw Curves
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Statutory Documents - IMO Publications and Documents - Circulars - Marine Environment Protection Committee - MEPC.1/Circular.796 – Interim Guidelines for the Calculation of the Coefficient fW for Decrease in Ship Speed in a Representative Sea Condition for Trial Use – (12 October 2012) - Annex – Interim Guidelines for the Calculation of the Coefficient fW for Decrease in Ship Speed in a Representative Sea Condition for Trial Use - Part 2: Guidelines for Calculating the Coefficient FW from the Standard FW Curves - 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:

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.

Parent topic: Part 2: Guidelines for Calculating the Coefficient F W from the Standard F W Curves

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.

  • (i) 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. In cases where displacement is not available, the average of draft may be used instead of the displacement.
  • (ii) Wind direction (WDIR): Heading (relative wind direction not exceeding ±67.5 degree).
  • (iii) 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.
  • (iv) The RPM (Rotational speed per minute) should be within ±5 per cent of the average RPM on the voyage.
  • (v) 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.
  • (vi) Distlog should be used under the conditions that the difference between DistOG and Distlog is within ±10 per cent of whichever is smaller.

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 SHP footnote:

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
  • Vo : 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.

Step 4: Calculation of fw for individual existing ships

fw = average of V2 corresponding 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

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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