Annex – 2014 Guidelines on the Method of Calculation of the Attained Energy Efficiency Design Index (EEDI) for New Ships, as Amended

 CONTENTS

1 Definitions

2 Energy Efficiency Design Index (EEDI), including equation

• 2.1 C_F ; Conversion factor between fuel consumption and CO₂ emission

• 2.2 V_ref ; Ship speed

• 2.3 Capacity

  • 2.3.1 Bulk carriers, tankers, gas carriers, LNG carriers, ro-ro cargo ships (vehicle carriers), ro-ro cargo ships, ro-ro passenger ships, general cargo ships, refrigerated cargo carrier and combination carriers

  • 2.3.2 Passenger ships and cruise passenger ships

  • 2.3.3 Containerships

• 2.4 Deadweight

• 2.5 P ; Power of main and auxiliary engines

  • 2.5.1 P_ME ; Power of main engines

  • 2.5.2 P_PTO ; Shaft generator

  • 2.5.3 P_PTI ; Shaft motor

  • 2.5.4 P_eff ; Output of innovative mechanical energy efficient technology

  • 2.5.5 P_AEeff ; Auxiliary power reduction

  • 2.5.6 P_AE ; Power of auxiliary engines

• 2.6 V_ref, Capacity and P

• 2.7 SFC ; Specific fuel consumption

• 2.8 f_j ; Correction factor for ship specific design elements

  • 2.8.1 f_j ; Ice-class ships

  • 2.8.2 f_j ; Shuttle tankers

  • 2.8.3 f_jroro ; Ro-ro cargo and ro-ro passenger ships

  • 2.8.4 f_j ; General cargo ships

  • 2.8.5 f_j ; Other ship types

• 2.9 f_w ; Weather factor

• 2.10 f_eff ; Availability factor of innovative energy efficiency technology

• 2.11 f_i ; Capacity factor

  • 2.11.1 f_i ; Ice-class ships

  • 2.11.2 f_i ; Ship specific voluntary structural enhancement

  • 2.11.3 f_i ; Bulk carriers and oil tankers under Common Structural Rules (CSR)

  • 2.11.4 f_i ; Other ship types

• 2.12 f_c ; Cubic capacity correction factor

  • 2.12.1 f_c ; Chemical tankers

  • 2.12.2 f_c ; Gas carriers

  • 2.12.3 f_cRoPax; Ro-ro passenger ships

  • 2.12.4 f_{c bulk carriers designed to carry light cargoes}; Wood chip carriers

• 2.13 Lpp ; Length between perpendiculars

• 2.14 f_l ; Factor for general cargo ships equipped with cranes and other cargo-related gear

• 2.15 d_s ; Summer load line draught

• 2.16 B_s ; Breadth

• 2.17 ▽ ; Volumetric displacement

• 2.18 g ; Gravitational acceleration

• APPENDIX 1 A generic and simplified power plant

• APPENDIX 2 Guidelines for the development of electric power tables for EEDI (EPT-EEDI)

• APPENDIX 3 A generic and simplified marine power plant for a cruise passenger ship having non-conventional propulsion

• APPENDIX 4 EEDI calculation examples for use of dual fuel engines

1 Definitions

1.1 MARPOL means the International Convention for the Prevention of Pollution from Ships, 1973, as modified by the Protocols of 1978 and 1997relating thereto, as amended.

1.2 For the purpose of these Guidelines, the definitions in chapter 4 of MARPOL Annex VI, as amended, apply.

2 Energy Efficiency Design Index (EEDI)

The attained new ship Energy Efficiency Design Index (EEDI) is a measure of ships' energy efficiency (g/t · nm) and calculated by the following formula:

* If part of the Normal Maximum Sea Load is provided by shaft generators, SFC_ME and CF_ME may – for that part of the power – be used instead of SFC_AE and C_FAE

** In case of P_PTI(i) > 0, the average weighted value of (SFC_ME · C_FME) and (SFC_AE · CF_AE) to be used for calculation of P_eff

• Note: This formula may not be applicable to a ship having diesel-electric propulsion, turbine propulsion or hybrid propulsion system, except for cruise passenger ships and LNG carriers.

Where:

• .1 C_F is a non-dimensional conversion factor between fuel consumption measured in g and CO₂ emission also measured in g based on carbon content. The subscripts _ME(i) and _AE(i) refer to the main and auxiliary engine(s) respectively. C_F corresponds to the fuel used when determining SFC listed in the applicable test report included in a Technical File as defined in paragraph 1.3.15 of the NO_X Technical Code ("test report included in a NO_X technical file" hereafter). The value of C_F is as follows:

• • In case of a ship equipped with a dual-fuel main or auxiliary engine, the C_F-factor for gas fuel and the C_F-factor for fuel oil should apply and be multiplied with the specific fuel oil consumption of each fuel at the relevant EEDI load point. Meanwhile, gas fuel should be identified whether it is regarded as the "primary fuel" in accordance with the formula below:

  • 

  • f_DFliquid = 1 - f_DFgas

  • where,

  • f_DFgas is the fuel availability ratio of gas fuel corrected for the power ratio of gas engines to total engines, f_DFgas should not be greater than 1;

  • V_gas is the total net gas fuel capacity on board in m³. If other arrangements, like exchangeable (specialized) LNG tank-containers and/or arrangements allowing frequent gas refuelling are used, the capacity of the whole LNG fuelling system should be used for V_gas . The boil-off rate (BOR) of gas cargo tanks can be calculated and included to V_gas if it is connected to the fuel gas supply system (FGSS);

  • V_liquid is the total net liquid fuel capacity on board in m³ of liquid fuel tanks permanently connected to the ship's fuel system. If one fuel tank is disconnected by permanent sealing valves, V_liquid of the fuel tank can be ignored;

  • ρ_gas is the density of gas fuel in kg/m³;

  • ρ_liquid is the density of each liquid fuel in kg/m³;

  • LCV_gas is the low calorific value of gas fuel in kJ/kg;

  • LCV_liquid is the low calorific value of liquid fuel in kJ/kg;

  • K _gas is the filling rate for gas fuel tanks;

  • K_liquid is the filling rate for liquid fuel tanks;

  • P_total is the total installed engine power, P_ME and P_AE in kW;

  • P_gasfuel is the dual fuel engine installed power, P_ME and P_AE in kW;

  • .1 If the total gas fuel capacity is at least 50% of the fuel capacity dedicated to the dual fuel engines , namely f_DFgas ≥ 0.5, then gas fuel is regarded as the "Primary fuel," and f_DFgas = 1 and f_DFliquid = 0 for each dual fuel engine.

  • .2 If f_DFgas < 0.5, gas fuel is not regarded as the "primary fuel." The C_F and SFC in the EEDI calculation for each dual fuel engine (both main and auxiliary engines) should be calculated as the weighted average of C_F and SFC for liquid and gas mode, according to f_DFgas and f_DFliquid, such as the original item of P_ME(i)· C_FME(i) · SFC_ME(i) in the EEDI calculation is to be replaced by the formula below.

  • P_ME(i) · (f_DFgas(i)·(C_{FME pilot fuel(i)} · SFC_{ME pilot fuel(i)} + C_{FME gas(i)} · SFC_{ME gas(i)}) + f_DFliquid(i) · C_{FME liquid(i)} · SFC_{ME liquid(i)})

• .2 V_ref is the ship speed, measured in nautical miles per hour (knot), on deep water in the condition corresponding to the capacity as defined in paragraphs 2.3.1 and 2.3.3 (in case of passenger ships and cruise passenger ships, this condition should be summer load draught as provided in paragraph 2.4) at the shaft power of the engine(s) as defined in paragraph 2.5 and assuming the weather is calm with no wind and no waves.

• .3 Capacity is defined as follows:

  • .1 For bulk carriers, tankers, gas carriers, LNG carriers, ro-ro cargo ships (vehicle carriers), ro-ro cargo ships, ro-ro passenger ships, general cargo ships, refrigerated cargo carrier and combination carriers, deadweight should be used as capacity.

  • .2 For passenger ships and cruise passenger ships, gross tonnage in accordance with the International Convention of Tonnage Measurement of Ships 1969, annex I, regulation 3, should be used as capacity.

  • .3 For containerships, 70% of the deadweight (DWT) should be used as capacity. EEDI values for containerships are calculated as follows:

    • .1 attained EEDI is calculated in accordance with the EEDI formula using 70% deadweight for capacity.

    • .2 estimated index value in the Guidelines for calculation of the reference line is calculated using 70% deadweight as:

    • 

    • .3 parameters a and c for containerships in table 2 of regulation 21 of MARPOL Annex VI are determined by plotting the estimated index value against 100% deadweight i.e. a = 174.22 and c=0.201 were determined.

    • .4 required EEDI for a new containership is calculated using 100% deadweight as:

      Required EEDI = (1-X/100) · a · 100% deadweight ^–c

      Where X is the reduction factor (in percentage) in accordance with table 1 in regulation 21 of MARPOL Annex VI relating to the applicable phase and size of new containership.

• .4 Deadweight means the difference in tonnes between the displacement of a ship in water of relative density of 1,025 kg/m³ at the summer load draught and the lightweight of the ship. The summer load draught should be taken as the maximum summer draught as certified in the stability booklet approved by the Administration or an organization recognized by it.

• .5 P is the power of the main and auxiliary engines, measured in kW. The subscripts _ME(i) and _AE(i) refer to the main and auxiliary engine(s), respectively. The summation on i is for all engines with the number of engines (_nME) (see diagram in appendix 1).

  • .1 P_ME(i) is 75% of the rated installed power (MCR^footnote) for each main engine (i).

    For LNG carriers having diesel electric propulsion system, P_ME(i) should be calculated by the following formula:

    

    Where:

    MPP_Motor(i) is the rated output of motor specified in the certified document.

    η_(i) is to be taken as the product of electrical efficiency of generator, transformer, converter, and motor, taking into consideration the weighted average as necessary.

    The electrical efficiency, η_(i) , should be taken as 91.3% for the purpose of calculating attained EEDI. Alternatively, if the value more than 91.3% is to be applied, the η_(i) should be obtained by measurement and verified by method approved by the verifier.

    For LNG carriers having steam turbine propulsion systems, P_ME(i) is 83% of the rated installed power (MCR_SteamTurbine) for each steam turbine_(i).

    The influence of additional shaft power take off or shaft power take in is defined in the following paragraphs.

  • .2 Shaft generator

    In case where shaft generator(s) are installed, P_PTO(i) is 75% of the rated electrical output power of each shaft generator. In case that shaft generator(s) are installed to steam turbine, P_PTO(i) is 83% of the rated electrical output power and the factor of 0.75 should be replaced to 0.83.

    For calculation of the effect of shaft generators two options are available:

    Option 1:

    .1 The maximum allowable deduction for the calculation of Σ P_ME(i) is to be no more than P_AE as defined in paragraph 2.5.6. For this case, Σ P_ME(i) is calculated as:

    

    • or

    Option 2:

    .2 Where an engine is installed with a higher rated power output than that which the propulsion system is limited to by verified technical means, then the value of Σ P_ME(i) is 75% of that limited power for determining the reference speed, V_ref and for EEDI calculation. The following figure gives guidance for determination of Σ P_ME(i):

    

  • .3 Shaft motor

    In case where shaft motor(s) are installed, P_PTI(i) is 75% of the rated power consumption of each shaft motor divided by the weighted average efficiency of the generator(s), as follows:

    

    Where:

    P_SM,max(i) is the rated power consumption of each shaft motor

    is the weighted average efficiency of the generator(s)

    In case that shaft motor(s) are installed to steam turbine, PPTI(i) is 83% of the rated power consumption and the factor of 0.75 should be replaced to 0.83.

    The propulsion power at which Vref is measured, is:

    Σ P_ME(i) + Σ P_{PTI(i), Shaft}

    Where:

    Σ P_{PTI(i), Shaft} = Σ (0.75 ·P_SM,max(i) · η_PTI(i))

    η_PTI(i) is the efficiency of each shaft motor installed

    Where the total propulsion power as defined above is higher than 75% of the power the propulsion system is limited to by verified technical means, then 75% of the limited power is to be used as the total propulsion power for determining the reference speed, V_ref and for EEDI calculation.

    In case of combined PTI/PTO, the normal operational mode at sea will determine which of these to be used in the calculation.

    • Note: The shaft motor's chain efficiency may be taken into consideration to account for the energy losses in the equipment from the switchboard to the shaft motor, if the chain efficiency of the shaft motor is given in a verified document.

  • .4 P_eff(i) is the output of the innovative mechanical energy efficient technology for propulsion at 75% main engine power.

    Mechanical recovered waste energy directly coupled to shafts need not be measured, since the effect of the technology is directly reflected in the V_ref.

    In case of a ship equipped with a number of engines, the C_F and SFC should be the power weighted average of all the main engines.

    In case of a ship equipped with dual-fuel engine(s), the C_F and SFC should be calculated in accordance with paragraphs 2.1 and 2.7.

  • .5 P_{AEeff (i)} is the auxiliary power reduction due to innovative electrical energy efficient technology measured at P_ME(i).

  • .6 P_AE is the required auxiliary engine power to supply normal maximum sea load including necessary power for propulsion machinery/systems and accommodation, e.g. main engine pumps, navigational systems and equipment and living on board, but excluding the power not for propulsion machinery/systems, e.g. thrusters, cargo pumps, cargo gear, ballast pumps, maintaining cargo, e.g. reefers and cargo hold fans, in the condition where the ship engaged in voyage at the speed (V_ref) under the condition as mentioned in paragraph 2.2.

    • .1 For ships with a total propulsion power

      of 10,000 kW or above, P_AE is defined as:

      

    • .2 For ships with a total propulsion power below 10,000 kW, P_AE is defined as:

      

    • .3 For LNG carriers with a reliquiefaction system or compressor(s), designed to be used in normal operation and essential to maintain the LNG cargo tank pressure below the maximum allowable relief valve setting of a cargo tank in normal operation, the following terms should be added to above P_AE formula in accordance with 1, 2 or 3 as below:

      • .1 For ships having re-liquefaction system:

        + CargoTankCapacity_LNG ✕ BOR ✕ COP_reliquefy ✕ R_reliquefy

        Where:

        CargoTankCapacity_LNG is the LNG Cargo Tank Capacity in m³.

        BOR is the design rate of boil-off gas of entire ship per day, which is specified in the specification of the building contract.

        COP_reliquefy is the coefficient of design power performance for reliquefying boil-off gas per unit volume, as follows:

        

        COP_cooling is the coefficient of design performance of reliquefaction and 0.166 should be used. Another value calculated by the manufacturer and verified by the Administration or an organization recognized by the Administration may be used.

        R_reliquefy is the ratio of boil-off gas (BOG) to be re-liquefied to entire BOG, calculated as follows.

        

      • .2 For LNG carriers with direct diesel driven propulsion system or diesel electric propulsion system, having compressor(s) which are used for supplying high-pressured gas derived from boil-off gas to the installed engines (typically intended for 2-stroke dual fuel engines):

        

        Where:

        COP_comp is the design power performance of compressor and 0.33 (kWh/kg) should be used. Another value calculated by the manufacturer and verified by the Administration or an organization recognized by the Administration may be used.

      • .3 For LNG carriers with direct diesel driven propulsion system or diesel electric propulsion system, having compressor(s) which are used for supplying low-pressured gas derived from boil-off gas to the installed engines (typically intended for 4-stroke dual fuel engines):

        ^footnote

        For LNG carriers having diesel electric propulsion system, MPP_Motor(i) should be used instead MCR_ME(i) for P_AE calculation.

        For LNG carriers having steam turbine propulsion system and of which electric power is primarily supplied by turbine generator closely integrated into the steam and feed water systems, P_AE may be treated as 0(zero) instead of taking into account electric load in calculating SFC_SteamTurbine.

      • .4 For ship where the P_AE value calculated by paragraphs 2.5.6.1 to 2.5.6.3 is significantly different from the total power used at normal seagoing, e.g. in cases of passenger ships (see NOTE under the formula of EEDI), the P_AE value should be estimated by the consumed electric power (excluding propulsion) in conditions when the ship is engaged in a voyage at reference speed (V_ref) as given in the electric power table^footnote, divided by the average efficiency of the generator(s) weighted by power (see appendix 2).

• .6 V_ref, Capacity and P should be consistent with each other. As for LNG carries having diesel electric or steam turbine propulsion systems, V_ref is the relevant speed at 83% of MPP_Motor or MCR_SteamTubine respectively.

• .7 SFC is the certified specific fuel consumption, measured in g/kWh, of the engines or steam turbines.

  • .1 The subscripts _ME(i) and _AE(i) refer to the main and auxiliary engine(s), respectively. For engines certified to the E2 or E3 test cycles of the NO_X Technical Code 2008, the engine Specific Fuel Consumption (SFC_ME(i)) is that recorded in the test report included in a NO_X technical file for the engine(s) at 75% of MCR power of its torque rating. For engines certified to the D2 or C1 test cycles of the NO_X Technical Code 2008, the engine Specific Fuel Consumption (SFCAE(i)) is that recorded on the test report included in a NO_X technical file at the engine(s) 50% of MCR power or torque rating. If gas fuel is used as primary fuel in accordance with paragraph 4.2.3 of the Guidelines on survey and certification of the energy efficiency design index (EEDI), SFC in gas mode should be used. In case that installed engine(s) have no approved NO_X Technical File tested in gas mode, the SFC of gas mode should be submitted by the manufacturer and confirmed by the verifier.

    The SFC should be corrected to the value corresponding to the ISO standard reference conditions using the standard lower calorific value of the fuel oil (42,700kJ/kg), referring to ISO 15550:2002 and ISO 3046-1:2002.

    For ships where the P_AE value calculated by paragraphs 2.5.6.1 to 2.5.6.3 is significantly different from the total power used at normal seagoing, e.g. conventional passenger ships, the Specific Fuel Consumption (SFC_AE) of the auxiliary generators is that recorded in the test report included in a NO_X technical file for the engine(s) at 75% of MCR power of its torque rating.

    SFC_AE is the power-weighted average among SFC_AE(i) of the respective engines i.

    For those engines which do not have a test report included in a NO_X technical file because its power is below 130 kW, the SFC specified by the manufacturer and endorsed by a competent authority should be used.

    At the design stage, in case of unavailability of test report in the NO_X file, the SFC specified by the manufacturer and endorsed by a competent authority should be used.

    For LNG driven engines of which SFC is measured in kJ/kWh should be corrected to the SFC value of g/kWh using the standard lower calorific value of the LNG (48,000 kJ/kg), referring to the 2006 IPCC Guidelines.

    Reference lower calorific values of additional fuels are given in the table in paragraph 2.1 of these Guidelines. The reference lower calorific value corresponding to the conversion factor of the respective fuel should be used for calculation.

    .2 The SFC_SteamTurbine should be calculated by manufacturer and verified by the Administration or an organization recognized by the Administration as follows:

    • 

      Where:

      .1 Fuel consumption is fuel consumption of boiler per hour (g/h). For ships of which electric power is primarily supplied by Turbine Generator closely integrated into the steam and feed water systems, not only P_ME but also electric loads corresponding to paragraph 2.5.6 should be taken into account.

    • .2 The SFC should be corrected to the value of LNG using the standard lower calorific value of the LNG (48,000 kJ/kg) at SNAME Condition (condition standard; air temperature 24°C , inlet temperature of fan 38°C, sea water temperature 24°C).

    • .3 In this correction, the difference of the boiler efficiency based on lower calorific value between test fuel and LNG should be taken into account.

• .8 f_j is a correction factor to account for ship specific design elements:

  • .1 The power correction factor, f_j, for ice-classed ships should be taken as the greater value of f_j0 and f_j,min as tabulated in table 1 but not greater than f_j,max = 1.0.

    For further information on approximate correspondence between ice classes, see HELCOM Recommendation 25/7^footnote.

• • .2 The factor f_j, for shuttle tankers with propulsion redundancy should be f_j = 0.77. This correction factors applies to shuttle tankers with propulsion redundancy between 80,000 and 160,000 dwt. Shuttle tankers with propulsion redundancy are tankers used for loading of crude oil from offshore installations equipped with dual-engine and twin-propellers need to meet the requirements for dynamic positioning and redundancy propulsion class notation.

  • .3 For ro-ro cargo and ro-ro passenger ships f_jRoRo is calculated as follows:

    ; If f_jRoRo > 1 then f_j = 1

    where the Froude number, F_nL , is defined as:

    

    and the exponents ɑ, β ,ɣ and δ are defined as follows:

    Ship type	Exponent:
    	ɑ	β	ɣ	δ
    Ro-ro cargo ship	2.00	0.50	0.75	1.00
    Ro-ro passenger ship	2.50	0.75	0.75	1.00

  • .4 The factor f_j for general cargo ships is calculated as follows:

    ; If f_j > 1 then f_j = 1

    Where

    ; If Fn_▽ > 0.6 then Fn_▽ = 0.6

    and

    

  • .5 For other ship types, f_j should be taken as 1.0.

• .9 f_w is a non-dimensional coefficient indicating the decrease of speed in representative sea conditions of wave height, wave frequency and wind speed (e.g. Beaufort Scale 6), and is determined as follows:

  • .1 for the attained EEDI calculated under regulations 20 and 21 of MARPOL Annex VI, f_w is 1.00;

    .2 when f_w is calculated according to the subparagraph .2.1 or .2.2 below, the value for attained EEDI calculated by the formula in paragraph 2 using the obtained f_w should be referred to as "attained EEDI_weather";

    • .1 f_w can be determined by conducting the ship specific simulation on its performance at representative sea conditions. The simulation methodology should be based on the Guidelines developed by the Organization^footnote and the method and outcome for an individual ship should be verified by the Administration or an organization recognized by the Administration; and

    • .2 in cases where a simulation is not conducted, f_w should be taken from the "Standard f_w " table/curve. A "Standard f_w " table/curve is provided in the Guidelines^footnote for each ship type defined in regulation 2 of MARPOL Annex VI, and expressed as a function of capacity (e.g. deadweight). The "Standard f_w " table/curve is based on data of actual speed reduction of as many existing ships as possible under the representative sea condition.

      f_w and attained EEDIweather, if calculated, with the representative sea conditions under which those values are determined, should be indicated in the EEDI Technical File to distinguish it from the attained EEDI calculated under regulations 20 and 21 of MARPOL Annex VI.

• .10 f_eff(i) is the availability factor of each innovative energy efficiency technology. f_eff(i) for waste energy recovery system should be one (1.0)^footnote.

• .11 f_i is the capacity factor for any technical/regulatory limitation on capacity, and should be assumed to be one (1.0) if no necessity of the factor is granted.

  • .1 The capacity correction factor, f_i, for ice-classed ships should be taken as the lesser value of f_i0 and f_{i, max} as tabulated in Table 2, but not less than f_{i, min} = 1.0. For further information on approximate correspondence between ice classes, see HELCOM Recommendation 25/7^footnote.

Table 2: Capacity correction factor f_i for ice-classed ships

• Note: Containership capacity is defined as 70% of the DWT.

  • .2 f_{i VSE}^footnote for ship specific voluntary structural enhancement is expressed by the following formula:

    

    where:

    DWT_{referencedesign} = Δ_ship - lightweight_{referenceddesign}

    DWT_{emhanceddesign} = Δ_ship - lightweight_{emhanceddesign}

    For this calculation the same displacement (Δ) for reference and enhanced design should be taken.

    DWT before enhancements (DWT_{reference design}) is the deadweight prior to application of the structural enhancements. DWT after enhancements (DWT_{enhanced design}) is the deadweight following the application of voluntary structural enhancement. A change of material (e.g. from aluminum alloy to steel) between reference design and enhanced design should not be allowed for the f_{i VSE} calculation. A change in grade of the same material (e.g. in steel type, grades, properties and condition) should also not be allowed.

    In each case, two sets of structural plans of the ship should be submitted to the verifier for assessment. One set for the ship without voluntary structural enhancement; the other set for the same ship with voluntary structural enhancement (alternatively, one set of structural plans of the reference design with annotations of voluntary structural enhancement should also be acceptable). Both sets of structural plans should comply with the applicable regulations for the ship type and intended trade.

  • .3 for bulk carriers and oil tankers, built in accordance with the Common Structural Rules (CSR) of the classification societies and assigned the class notation CSR, the following capacity correction factor f_iCSR should apply:

    f_iCSR = 1 + (0.08 · LWT_CSR / DWT_CSR)

    Where DWT_CSR is the deadweight determined by paragraph 2.4 and LWT_CSR is the light weight of the ship.

    .4 for other ship types, fi should be taken as one (1.0).

• .12 f_c is the cubic capacity correction factor and should be assumed to be one (1.0) if no necessity of the factor is granted.

  • .1 for chemical tankers, as defined in regulation 1.16.1 of MARPOL Annex II, the following cubic capacity correction factor f_c should apply:

    f_c = R ^-0.7 ─ 0.014, where R is less than 0.98

    or

    f_c = 1.000, where R is 0.98 and above;

    where: R is the capacity ratio of the deadweight of the ship (tonnes) as determined by paragraph 2.4 divided by the total cubic capacity of the cargo tanks of the ship (m³).

  • .2 for gas carriers having direct diesel driven propulsion system constructed or adapted and used for the carriage in bulk of liquefied natural gas, the following cubic capacity correction factor f_cLNG should apply:

    f_cLNG = R ^-0.56

    where: R is the capacity ratio of the deadweight of the ship (tonnes) as determined by paragraph 2.4 divided by the total cubic capacity of the cargo tanks of the ship (m³).

    Note: This factor is applicable to LNG carriers defined as gas carriers in regulation 2.26 of MARPOL Annex VI and should not be applied to LNG carriers defined in regulation 2.38 of MARPOL Annex VI.

  • .3 For ro-ro passenger ships having a DWT/GT-ratio of less than 0.25, the following cubic capacity correction factor, f_cRoPax, should apply:

    

    Where DWT is the Capacity and GT is the gross tonnage in accordance with the International Convention of Tonnage Measurement of Ships 1969, annex I, regulation 3.

  • .4 For bulk carriers having R of less than 0.55 (e.g. wood chip carriers), the following cubic capacity correction factor, f_{c bulk carriers designed to carry light cargoes}, should apply:

    f_{c bulk carriers designed to carry light cargoes} = R ^-0.15

    where: R is the capacity ratio of the deadweight of the ship (tonnes) as determined by paragraph 2.4 divided by the total cubic capacity of the cargo holds of the ship (m³).

• .13 Length between perpendiculars, L_pp, means 96% of the total length on a waterline at 85% of the least moulded depth measured from the top of the keel, or the length from the foreside of the stem to the axis of the rudder stock on that waterline, if that were greater. In ships designed with a rake of keel the waterline on which this length is measured should be parallel to the designed waterline. L_pp should be measured in metres.

• .14 f_l is the factor for general cargo ships equipped with cranes and other cargo-related gear to compensate in a loss of deadweight of the ship.

  f_l = f_cranes . f_sideloader . f_roro

  f_cranes = 1 If no cranes are present.

  f_sideloader = 1 If no side loaders are present.

  f_roro = 1 If no ro-ro ramp is present.

  Definition of f_cranes :

  

  where

  SWL = Safe Working Load, as specified by crane manufacturer in metric tonnes

  Reach = Reach at which the Safe Working Load can be applied in metres

  N = Number of cranes

  For other cargo gear such as side loaders and ro-ro ramps, the factor should be defined as follows:

  

  

  The weight of the side loaders and ro-ro ramps should be based on a direct calculation, in analogy to the calculations as made for factor f_ivse.

• .15 Summer load line draught, d_s, is the vertical distance, in metres, from the moulded baseline at mid-length to the waterline corresponding to the summer freeboard draught to be assigned to the ship.

• .16 Breadth, B_s, is the greatest moulded breadth of the ship, in metres, at or below the load line draught, d_s.

• .17 Volumetric displacement, ∇, in cubic metres (m³), is the volume of the moulded displacement of the ship, excluding appendages, in a ship with a metal shell, and is the volume of displacement to the outer surface of the hull in a ship with a shell of any other material, both taken at the summer load line draught, d_s, as stated in the approved stability booklet/loading manual.

• .18 g is the gravitational acceleration, 9.81m/s².