ON THE ENERGY EFFICIENCY DESIGN INDEX (EEDI) OF RO-RO PASSENGER AND RO-RO CARGO SHIPS
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1 ON THE ENERGY EFFICIENCY DESIGN INDEX (EEDI) OF RO-RO PASSENGER AND RO-RO CARGO SHIPS Aimilia G. Alisafaki and Apostolos D. Papanikolaou National Technical University of Athens - Ship Design Laboratory, School of Naval Architecture and Marine Engineering 9, Heroon Polytechniou, 5773 Athens-Zografou, Greece ASTRACT This paper proposes alternative formulations of the correction factor f jroro pertaining to Ro-Ro Cargo and Ro-Ro Passenger ships, as defined in the Energy Efficiency Design Index (EEDI) equation according to IMO Resolution MEPC 245(66) on the 24 Guidelines on the method of calculation of the attained Energy Efficiency Design Index (EEDI). The alternative formulations were derived by studying a large sample of Ro- Ro Cargo ships and Ro-Ro Passenger ships, built in the period The estimation of ships resistance and powering was conducted by use of Holtrop s method. Obtained formula s exponent values were compared with corresponding ones from latest IMO studies on EEDI and they appear to better represent and fit to the energy efficiency and environmental impact of the operating fleet of Ro-Ro Cargo and Ro-Ro Passenger ships.. INTRODUCTION The 67 th session of the IMO Marine Environment Protection Committee (MEPC 67, October 24) recently confirmed a very optimistic prediction of the 3 rd edition of the IMO study on the greenhouse gas (GHG) emissions for the international shipping sector in the period 27-22; namely the fact that the global shipping industry GHG emissions were reduced from 2.8% of the world s total GHG emissions in year 27 to 2.2% in year 22 (IMO MEPC 67/6/INF.3), which corresponds to a decrease of 2% of the shipping GHG emissions within a five years period! This is a remarkable reduction that was made possible with the introduction of operational efficiency measures in the existing and newly introduced fleet worldwide. Ro-Ro Cargo and Ro-Ro Passenger ships dispose in general wide diversity in mission profile, as well as in terms of design and operational conditions. Their relatively high-installed power, in combination with the enhanced service speed being an integral part of their service to the society, lead to a wide EEDI scatter. This, in turn, required the introduction of suitable correction factors in order to get a proper EEDI reference line for this type of ships. This was the reason why these ship types were excluded from the implementation of the required EEDI in the first phase. It was not until April 24 when the method to include the Ro-Ro Cargo and Ro-Ro Passenger ship types into the IMO energy efficiency regulatory framework was finally adopted by the Resolution MEPC 245(66). The impetus for conducting the research described in the present paper was triggered by the IMO studies submitted by Denmark and Japan, MEPC 65/4/8, focusing on Comments on the method to include the Ro-Ro Cargo and Ro-Ro Passenger ship types into the IMO energy efficiency regulatory framework as proposed in MEPC 64/4/4 and MEPC 65/4/4, which both were submitted by Germany, Sweden, Community of European Shipyard Associations (CESA) and INTERFERRY. In the present paper, we propose alternative formulations and values for the exponents of the f j correction factor for Ro-Ro Cargo ships and Ro-Ro Passenger ships, namely f jro-ro, which resulted from a regression analysis of a large number of vessels, built between (source of original data: IHS Fairplay database). The prediction of resistance and powering was conducted by Holtrop s method (984); the obtained exponent values were compared with corresponding data of Kristensen (22). Derived values are compared with the latest IMO developments concerning EEDI and despite their difference they appear to rather better represent the energy efficiency and environmental impact of the operating fleet of Ro-Ro Cargo and Ro-Ro Passenger ships.
2 2. THEORETICAL ACKGROUND The attained new ship Energy Efficiency Design Index (EEDI) is a measure of ships' energy efficiency [g/t nm] and is calculated by the following formula (MEPC 245(66), Annex 5): g EEDI att [ t nm ] n nme n npti n j = f j )( i= P ME i C FME i SFC ME i + P AE C FAE SFC AE + (( f j P PTI i eff n f eff i P AEeff i )C AE SFC AE ) ( eff j = i= f eff i P eff i C FME SFC ME ) i= i= = f i f c f l Capacity f w V ref () In the above Eq. (), the subscripts ( ) ME(i) and ( ) AE(i) refer to the main and auxiliary engine(s) respectively. In the numerator, the P corresponds to the power of the main and auxiliary engines, measured in [kw]. The P ME(i) is 75% of the rated installed power (MCR) for each main engine ( ) (i). The P AE is the required auxiliary engine power to supply normal maximum sea load including necessary power for propulsion machinery/systems and accommodation, at the reference speed V ref [kn]. In case shaft motor(s) are installed, the P PTI(i) is 75% of the rated power consumption of each shaft motor divided by the weighted average efficiency of the generator(s). The P eff(i) is the output of the innovative mechanical energy efficient technology for propulsion at 75% main engine power. The P AEeff (i) is the auxiliary power reduction due to innovative electrical energy efficient technology measured at P ME(i). The C F is a nondimensional conversion factor between fuel consumption measured in [g] and CO 2 emission also measured in [g] based on carbon content. The SFC stands for the certified specific fuel consumption, measured in [g/kwh], of the engines. The Capacity is defined as the deadweight for Ro-Ro Cargo and Ro-Ro Passenger ships. The f eff(i) is the availability factor of each innovative energy efficiency technology. The f i is the capacity factor for any technical/regulatory limitation on capacity and equals to. (one) for Ro-Ro Cargo and Ro- Ro Passenger ships. The f l is the factor for general cargo ships equipped with cranes and other cargo-related gear. The f w is a non-dimensional coefficient indicating the decrease of speed in representative sea conditions of wave height, wave frequency and wind speed (factor accounting for the added resistance and increased powering of the ship operating in realistic environmental conditions). 2. Correction factors for Ro-Ro Cargo and Ro-Ro Passenger ships In order to adjust the introduction of the Ro-Ro Cargo and Ro-Ro Passenger ships into the EEDI framework, the capacity correction factor f cropax for Ro-Ro Passenger ships and the ship design correction factor f jroro for both Ro-Ro Cargo and Ro-Ro Passenger ships were introduced in MEPC 64/4/4. Noting that in Eq.(), f c is the cubic capacity correction factor and should be assumed equal to one (=.) if no necessity of this factor exists. Ro-Ro Passenger ships designed for large passenger accommodation capacity and associated spaces are, compared to cargo ships, adjusted by the introduction of the cubic capacity correction factor f cropax. This cubic capacity correction factor f cropax is applicable only to Ro-Ro Passenger ships exhibiting a (DWT/GT)-ratio of less than the fleet average, which was found to be approximately.25; it is defined as follows (MEPC 245(66): f CRoPax = (2), where GT is the gross tonnage in accordance with the International Convention of Tonnage Measurement of Ships 969, annex I, regulation 3. DWT GT.25.8
3 Finally, the f j is a correction factor that accounts for ship specific design elements. For both Ro-Ro Cargo and Ro-Ro Passenger ships, this correction factor f jroro is calculated as follows (MEPC 245(66)): f jroro = (F α nl Β Τ 3 (3) where L pp is the ship s length between perpendiculars [m], is the ship s breadth [m], T is the ship s draught [m], is the ship s volumetric displacement [m 3 ] and F nl is the Froude number defined as F nl =,544 V S g (4) where g is the gravitational acceleration [= 9.8m/sec 2 ] and V ref is the ship s reference speed [kn]. If f jroro >, then f jroro =. It is noted that both correction factors f cropax and f jroro are used in the calculation of the attained EEDI, as well as for the development of the EEDI reference line. 2.2 Ship Design Variable (SDV) The denominator of the fraction in Eq. (3) is defined as a Ship Design Variable SDV (MEPC 64/4/4). That is: SDV = F α nl so the Eq. (3) can be also written as follows: f jroro = (F α nl Β Τ Β Τ 3 3 δ = δ SDV ) = δ ) (5) The Ship Design Variable (SDV) is the product of (F nl ) α and the non-dimensional ratios, all of which have a significant influence on the ship-power performance. 2.3 Estimated EEDI Index Value The Estimated EEDI Index Value for each Ro-Ro Cargo sample ship is calculated as follows (MEPC 23(65)): Estimated EEDI Index Value = 3.44 (f jroro 9 P MEi + 25 P AE ) Capαcity V ref (6) Likewise, the Estimated Index Value for each Ro-Ro Passenger sample ship is calculated as follows (MEPC 23(65)): Estimated EEDI Index Value = 3.44 (f jroro 9 P MEi + 25 P AE ) f cropax Capαcity V ref (7) The auxiliary power P AE for Ro-Ro Cargo ships with a total installed propulsion power of,kw and above is calculated as follows (MEPC 23(65)): P AE =.25 nme i= MCR ME(i) + npti i= P PTI(i) (8) For Ro-Ro Cargo ships with a total propulsion power below,kw the formula is modified as follows (MEPC 23(65)):
4 P AE =.5 nme i= MCR ME(i) + npti i= P PTI(i).75 (9) The auxiliary power P AE for Ro-Ro Passenger ships is calculated as follows (MEPC 23(65)): P AE =.866 GT.732 () 2.4 P ME as a function of SDV and The required EEDI is expressed as (MARPOL 73/78, Annex VI, Regulation 2): Required EEDI a (Capacity) c () Hence, when applying to the left hand side of the above Eq. () the estimated EEDI value from the Eq. (6), the correction factor f jroro as described in the Eq. (3), and noting that the largest influence on the emitted CO 2 on their numerator is by far coming from P ME, and based on the assumption that the capacity (DWT for these ship types) is linearly proportional to ship's displacement volume, then the Eq. () is reformulated to the following expression for P ME : P ME Const. L PP 2 F nl a+ L PP (2) The relation between the main engine power P ME (=75% MCR) and the relevant ship particulars, as expressed on the right hand side in the Eq. (2) is investigated. The right hand side of the Eq. (2) is introduced as the Main Engine Power Ship Design Variable SDV PME : SDV PME = L PP 2 F nl a+ L PP Β Τ Β Τ L PP L PP 3 3 δ δ ε ε (3) 3. METHODOLOGICAL APPROACH The aim of the present study is the calculation of suitable values for the exponents α,,, δ and ε of the Ship Design Variables SDV (Eq. 5) and SDV PME (Eq. 3). The study was conducted by using Holtrop s method (984) for the estimation of the powering of the sample ships and Normand s relational method (Papanikolaou, 24) for the calculation of suitable values for the exponents α,,, δ and ε. Normand s relational method leads in general to estimations of ship s displacement for small variations of ship s dimensions and speed with respect to a basis (reference) ship; it can only be applied when the deviations from the values of the parent ship are relatively small (in the range of %). The parent ship for each investigated ship type is assumed corresponding to the average ship of the relative sample (relevant operating fleet) and her main characteristics are presented in Table : Table. Reference parent ship for each ship type Average Parent ship( Index ) Ro-Ro Cargo Ro-Ro Passenger L PP [m] [m] T [m] V [kn] C [m 3 ] Δ [ton]
5 According to IMO MEPC 64/4/4, for both ship types under study, the main engine power P ME was linearly proportional to Ship Design Variable SDV PME. Β Τ ε 3 (4) The above Eq. (4) can be further analyzed after some mathematical arrangements to the following: P ME = Const. 2 F nl a+ δ P ME = Const. V α+ α 2 ++δ Β + Τ δ 3 +ε (5) y keeping constant the four out of the five ship parameters of Eq. (5), and applying differential calculus to the each selected parameter, the exponents were calculated as follows: a + = P ME V P ME = P ME V V P ME for ΔV V. (6) α + + δ = P 2 ME = P ME P ME L PP P ME for ΔLpp Lpp. (7) + = P ME Β P ME = P ME Β Β P ME for ΔΒ Β. (8) Τ = P ME = P ME P ME Τ Τ P ME for ΔΤ Τ. (9) δ 3 + ε = P ME = P ME P ME P ME for Δ. (2) Further details can be found in Alisafaki (23). 3. Sample Presentation The ship types under study are defined in regulations 2.34 and 2.35 in Annex VI of Chapter of MARPOL 73/78. The statistical sample was generated for the relevant ship types, namely for Ro-Ro cargo and Ro-Ro passenger ships, built between 99 22, by use of the IHS Fairplay (IHSF) World Shipping Encyclopaedia version 2. database. Data relating to existing ships of 4GT and above were used. The noted IHSF database service speed is used as reference speed V ref and likewise the IHSF database field giving ship s total installed main power is used for the identification of MCR ME(i) respectively. The Ro-Ro Cargo ships sample consists of 54 ships (8 ships built between and 73 ships built between 2-22) of the following ship subtypes: Ro-Ro Cargo Ship, Statcode-5 A35A2RR: Ro-Ro Cargo Ship Ro-Ro Cargo Ship, Statcode-5 A35A2RT: Rail Vehicles Carrier The following Figs., 2 and 3 represent the main Ro-Ro Cargo ships sample characteristics.
6 Total No. of Ships Ro-Ro Cargo Ships Sample: 54 ships Year of built Fig.. Ro-Ro Cargo ships under study: Year of uilt. 9 8 Sample: 54 Ro-Ro Cargo ships Length to eam ratio [L/] eam to Draft ratio [/T] Slenderness Coefficient [L/Vol.^(/3)] Length etween Perpendiculars [m] Fig. 2. Ro-Ro Cargo ships under study: L/, /T & L/Vol.^(/3).,9,8 Sample: 54 Ro-Ro Cargo ships,7,6,5,4,3,2,, Cb- lock Coefficient based on Lbp Froude Number DWT/Displacement Length etween Perpendiculars [m] Fig. 3. Ro-Ro Cargo ships under study: c b, Fn & DWT/Displacement. The Ro-Ro Passenger ships sample consists of 8 ships (2 ships built between and 69 ships built between 2-22) of the following ship subtypes: Passenger / Ro-Ro Cargo Ship (vehicles) Statcode-5 A36A2PR Passenger / Ro-Ro Cargo Ship (vehicles/rail), Statcode-5 A36A2PR
7 Total No. of Ships The following Figs. 4, 5 and 6 represent the main Ro-Ro Passenger ships sample characteristics Ro-Ro Passenger Ships Sample: 8 ships Fig. 4. Ro-Ro Passenger ships under study: Year of uilt. 9 8 Sample: 8 Ro-Ro Passenger ships Length to eam ratio [L/] eam to Draft ratio [/T] Slenderness Coefficient [L/Vol.^(/3)) Length etween Perpendiculars [m] Fig. 5. Ro-Ro Passenger ships under study: L/, /T & L/Vol.^(/3).,9,8 Sample: 8 Ro-Ro Passenger ships,7,6,5,4,3,2, Cb- lock Coefficient based on Lbp Froude No. DWT/Displacement ratio, Length etween Perpendiculars [m] Fig. 6. Ro-Ro Passenger ships under study: c b, Fn & DWT/Displacement.
8 4. ANALYSIS OF RESULTS AND DISCUSSION The herein obtained exponent values for Eq. (5) and Eq. (3) vary significantly from the exponent values that have been adopted by IMO. At first, we recall the definition of the EEDI reference/boundary line, which should be not exceeded (Resolution MEPC 23(65)): Max EEDI Reference line value = a (% Deadweight) c (2) It is noted that in MEPC 64/4/4 it was supposed that there is a proportional function between P ME and the mathematical expression in the right on the Eq.(4). Therefore, in our study, we calculated the sought exponent values for the case of linearity between P ME and SDV PME, as well as in case of a non-linear modeling. The results of both approaches (Non-Linear approach and Linear approach) are presented in Table 2 (for Ro-Ro Cargo ships) and Table 3 (for Ro-Ro Passenger ships). Also, the adopted IMO values are listed in the first column, which are based on a linear relationship between P ME and SDV PME. It is noted that in both Tables 2 and 3, the values according to IMO of the exponent ε of the ship s volumetric displacement follow the MEPC 64/4/4, while the IMO for the exponents α,, and δ follow the Resolution MEPC 245(66). Exponent Values Table 2 Exponent values for Ro-Ro Cargo ships. acc. to IMO present study Non-Linear approach present study Linear approach α δ ε Exponent Values Table 3 Exponent values for Ro-Ro Passenger ships. acc. to IMO present study Non-Linear approach present study Linear approach α δ ε oth our approaches resulted in an opposite sign for the values of the exponent δ of the slenderness coefficient, compared to the corresponding IMO value. Our study concluded that this value is negative, which is also in agreement with the physics of the problem in hand, namely that a high slenderness coefficient leads to a reduction of the intensity of the generated ship-bound waves, and consequently of ship s wave resistance and of associated powering, which is a significant part of the overall powering for Ro-Ro ships, operating at relatively high Froude number (Papanikolaou, 24). The derived common exponent values α,, & δ for Ro-Ro Cargo and Ro-Ro Passenger ships for the linear approach in our study lead to an efficient way for calculations in practice, since the correction factor f jroro remains the same for both shiptypes. Fig. 7 for Ro-Ro Cargo ships and Fig. 8 for Ro-Ro Passenger ships clearly show that the correlation factor of the herein derived formulas is higher (though in the range of -2%) than the corresponding one of the IMO adopted values, when applied to the same sample under
9 study, thus much better represent the properties of the currently operating Ro-Ro Cargo and Ro-Ro Passenger fleet PM.E. =,75*MCR [KW] Non-Linear approach (present study) y = 23.78,2x,82 R² =,9 Linear approach y = 8.52,57x, (present study) 5 R² =,9 IMO values y = 8859,9x,9768 R² =,896,,5,,5 2, 2,5 3, 3,5 4, SDV PM.E. Fig. 7. Ro-Ro Cargo ships under study: P ME as a function of SDV PME. 6 5 PM.E. =,75*MCR [KW] IMO values y = 5.926,54x,95 R² =,92 y = 4.674,65x,97 R² =,93 y = 28.3,3x,77 R² =, SDV PM.E. Linear approach (present study) Non-Linear approach (present study) Fig. 8. Ro-Ro Passenger ships under study: P ME as a function of SDV PME. The following Figs. 9 & show an improved fitting in the proposed reference line according to the present linear approach of our study for both ship types. In both figures the curve of EEDI original (meaning without the correction factor f jroro ) is also plotted. The correction factor f jroro reduces the EEDI value and simultaneously the scatter of the estimated index values.
10 EEDI EEDI 5 y =.75,7x -,45 R² =,38 EEDI original y = 594,7x -,42 R² =,63 EEDI (MEPC 245/66) y = 689,5x -,45 R² =,65 EEDI (Linear approach - present study) DWT Fig. 9. EEDI reference lines for Ro-Ro Cargo ships under study y = 2.678,3x -,4 R² =,6 y =.47,9x -,45 R² =,79 y =.22,98x -,48 R² =,8 EEDI original EEDI (MEPC 245/66) EEDI (Linear approach - present study) DWT' Fig.. EEDI reference lines for Ro-Ro Passenger ships under study. 5. CONCLUSIONS The paper presents alternative values for the exponents of the correction factor f jroro pertaining to Ro-Ro cargo and Ro-Ro passenger ships in the EEDI calculation. For both ship types under study, a non-linear relationship between P ME and Ship Design Variable SDV PME proved superior to others and of a higher correlation coefficient with respect to the representativeness of the employed ship sample. The linear approach, also developed in parallel in the present study, led also to a higher (even marginally) correlation coefficient, when calculating the EEDI reference line for a large sample of ships, compared to the corresponding one adopted by IMO(MEPC 245(66)). This diversity in the quality of fitting and the variation of the exponent values raises some justified questions regarding the maturity
11 of EEDI reference lines adopted so far by IMO. Obtained parametric relationships between the powering of Ro-Ro cargo and Ro-Ro passenger ships and basic ship design parameters can be generally exploited in parametric ship design optimization procedures in the frame of holistic ship design optimization (Papanikolaou, 2). References. Papanikolaou, A.D. (24). Ship Design: Methodologies of Preliminary Design, SPRINGER, ISN , September Alissafaki, A. (23) Research on Alternative Equation Formulations in Estimating the Energy Efficiency Design Index (EEDI) for Ro-Ro Cargo Ships & Ro-Ro/ Passenger Ships, MSc thesis, Ship Design Laboratory, National Technical University of Athens. ( 3. Holtrop, J. (984) A Statistical Re-Analysis of Resistance and Propulsion Data, International Shipbuilding Progress, Vol. 3, pp International Maritime Organization, MARPOL 73/78, Consolidated Edition International Maritime Organization, Third IMO GHG Study 24, MEPC 67/6/INF.3, Executive Summary and Final Report, June International Maritime Organization, Resolution MEPC 245(66), 24 Guidelines on the Method of Calculation of the Attained Energy Efficiency Design Index (EEDI) for New Ships, MEPC 66/2/Add., Annex 5, International Maritime Organization, Resolution MEPC 23(65), Annex 4, 23 Guidelines For Calculation of Reference Lines For Use With The Energy Efficiency Design Index (EEDI), MEPC 65/22, Annex 4, May International Maritime Organization, Comments on the Method to Include the Ro-Ro Cargo and Ro-Ro Passenger Ship Types into the IMO Energy Efficiency Regulatory Framework as Proposed in MEPC 64/4/4 and MEPC 65/4/4, MEPC 65/4/8, submitted by Denmark and Japan, 8 th March International Maritime Organization, Revised Proposal for the Inclusion of the Ro-Ro Cargo and Ro-Ro Passenger Ship Types into the IMO Energy Efficiency Regulatory Framework,,MEPC 65/4/4, submitted by Germany, Sweden, Community of European Shipyards Associations (CESA) and INTERFERRY, 8 th February 23.. International Maritime Organization, Comments on the Method to Include the Ro-Ro Cargo and Ro-Ro Passenger Ship Types into the IMO Energy Efficiency Regulatory Framework as Proposed in MEPC 64/4/4 and MEPC 65/4/4, MEPC 65/4/8, Submitted by Denmark and Japan, 8th March 23.. International Maritime Organization, Proposal for the Inclusion of the Ro-Ro Cargo and Ro-Ro Passenger Shiptypes into the Energy Efficiency Regulatory Framework, MEPC 64/4/4, submitted by Germany, Sweden and the Community of European Shipyards Association (CESA), 29 th December International Maritime Organization, International Convention of Tonnage Measurement of Ships Kristensen, H. O. (22) Analysis of a new proposal (MEPC 64/4/4) to include the Ro-Ro cargo and Ro- Ro passenger ship types in the energy efficiency regulation framework, DTU Mechanical Engineering Report, Technical University of Denmark, November World Shipping Encyclopaedia version 2., IHS Fairplay Eds. 5. Papanikolaou, A. (2) Holistic ship design optimization. Journal Computer-Aided Design, Elsevier, Vol. 42, Issue, pp Appendix enchmarking of Exponent Values According to IMO MEPC 64/4/4, for both ship types under study, the main engine power P ME was linearly related to Ship Design Variable SDV PME. P ME = Const. 2 F nl a+ Β Τ 3 δ ε (4)
12 We benchmarked the obtained exponents & for three different ship lengths (namely for Ro-Ro Cargo ships: 2 meters, 5 meters and 8 meters, and for Ro-Ro Passenger ships: meters, 4 meters and 8 meters) and for typical main dimensions and block coefficients of the sample under study. The powering calculation was performed for three different Froude numbers (.24,.26 and.28) by using the Holtrop method (984). The resultant values were compared to the corresponding ones calculated by Kristensen (22), as presented in the following Tables 4-7. Table 4 Exponent values for - for Ro-Ro Cargo ships (L/= , /T=3.5, L/V /3 =6. C = ). L [m] (present study) (acc. to Kristensen) Fn L [m] 2,94 2,47,24 2,96 3,62,26 2 2,38 5,62,28 5,99 2,52,24 5 2, 3,7,26 5 2,43 5,77,28 8 2,2 2,55,24 8 2,3 3,77,26 8 2,47 5,87,28 Table 5 Exponent values for - for Ro-Ro Cargo ships (L/= 6.3, /T: , L/V /3 =6., C = ). (present study) (acc. to Kristensen) 2,3,86,24 2,32 2,44,26 2,57 3,46,28 5,3,88,24 5,32 2,48,26 5,58 3,52,28 8,33,9,24 8,34 2,52,26 8,6 3,58,28 Fn L [m] Table 6 Exponent values for - for Ro-Ro Passenger ships (/T = 4. ). (present (acc. to L/ C study) L/V ^ /3 Fn Kristensen)
13 Table 7 Exponent values for - for Ro-Ro Passenger ships (/T: ). (acc. to L [m] L/ (acc. to C Holtrop L/V /3 Fn Kristensen) method) The values for the exponent according to our study vary from.94 to 2.47 for Ro-Ro Cargo ships and from.89 to 2.82 for Ro-Ro Passenger ships, while the corresponding values according to Kristensen (22) varies from 2.47 to 5.87 for Ro-Ro Cargo ships and from.29 to 6.69 for Ro-Ro Passenger ships. The values for the exponent according to our study vary from.3 to.6 for Ro-Ro Cargo ships and from.77 to.85 for Ro-Ro Passenger ships, while the corresponding values according to Kristensen (22) vary from.86 to 3.58 for Ro-Ro Cargo ships and from.3 to 4.7 for Ro-Ro Passenger ships. All-in-all, the calculated values by Holtrop method are lower than the relevant values according to Kristensen (22), who used for the estimation of the powering the FORMDATA method of Guldhammer. ut in all cases, obtained exponents strongly depend on the Froude number, thus on the ship s relative speed, and they undisputedly differ from the IMO adopted values, as pointed out by Kristensen (22) and is stressed in the submission of Denmark and Japan to IMO in 23(MEPC 65/4/8).
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