Appendix – Sample Simulation of the Coefficient fw
Clasification Society 2024 - Version 9.40
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 1: Guidelines for the Simulation for the Coefficient FW for Decrease in Ship Speed in a Representative Sea Condition - Appendix – Sample Simulation of the Coefficient fw

Appendix – Sample Simulation of the Coefficient fw

Parent topic: Part 1: Guidelines for the Simulation for the Coefficient F W for Decrease in Ship Speed in a Representative Sea Condition

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

Dimensions Value
Length between perpendiculars 217 m
Breadth 32.26 m
Draft 14 m
Ship speed 14.5 knot
Output power at MCR 9,070 kW
Deadweight 73,000 ton

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 testsfootnote in a calm sea condition as the function of speed following paragraph 4.2 as shown in the following figure.

Figure 2 Resistance in a calm sea condition

  2 The added resistance due to wind ΔRwind is calculated following paragraph 4.3.2. For the subject ship, the drag coefficient due to wind CDwind 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).footnote For the subject ship, effect of advance speed αU in head waves is obtained as shown in the following figure, and CU is determined as 10.0.

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 ΔRwave is calculated following paragraph 4.3.3.2. ΔRwave in head waves at T = 6.7 (s) (BF6) is expressed as shown in the following figure. For obtaining the power curve, ΔRwave is expressed as a function of ship speed from the calculated ΔRwave at several ship speeds. In the sample calculation, ΔRwave 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 RT , ΔRwind , and ΔRwave as shown in the following figure and PBW is calculated by dividing RTWV by the propulsion efficiency in the representative sea condition ηDw and the transmission efficiency ηS.

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, ηR is the propeller rotative efficiency, J = V a/(nD) is the advance coefficient, V a 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 ηD is expressed as follows:

where ηo 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:

Copyright 2022 Clasifications Register Group Limited, International Maritime Organization, International Labour Organization or Maritime and Coastguard Agency. All rights reserved. Clasifications Register Group Limited, its affiliates and subsidiaries and their respective officers, employees or agents are, individually and collectively, referred to in this clause as 'Clasifications Register'. Clasifications Register assumes no responsibility and shall not be liable to any person for any loss, damage or expense caused by reliance on the information or advice in this document or howsoever provided, unless that person has signed a contract with the relevant Clasifications Register entity for the provision of this information or advice and in that case any responsibility or liability is exclusively on the terms and conditions set out in that contract.