Reanalysis of the revised EEDI parameters for inland ships of Bangladesh

A revision of the Energy Efficiency Design Index (EEDI) formulation was previously proposed to be useful for inland ships of Bangladesh. The study incorporated the shallow water effect using Schlichting’s method which has been developed in 1934 based on a large number of ship model tests to show how a ship’s resistance in shallow water deviates from that in deep water. However, the evaluation and presentation of Schlichting’s results did not cover all range of ship parameters. This reanalysis has considered the shallow water effect by actual measurement of 15 inland ships of Bangladesh. Later, the results of Schlichting’s method were compared with (a) actual investigation, (b) an improved version of Schlichting’s method proposed by Lackenby in 1963, and (c) a new method proposed by C B Barrass in 2004. It was found that the deviations of Schlichting’s results are much higher than Lackenby and Barrass’s methods in comparison to the investigated results. In a previous analysis of the inland ships of Bangladesh, the Maximum Continuous Rating (MCR) of the main engine was considered by using the Holtrop-Mennen method. As this method requires too much ship data, that analysis had assumed some unknown required ship data. This reanalysis has overcome that problem by the physical investigations of the same 15 inland ships of Bangladesh. The average MCR for inland cargo ships and oil tankers of Bangladesh are measured as 70% by the investigations, whereas it is 80% for passenger ships.


Introduction
The adopted EEDI formulation by the International Maritime Organization (IMO) 1 in 2011 to increase the energy efficiency of sea-going ships is successful so far. 2 The fourth IMO greenhouse gas (GHG) study states that the overall carbon intensity has improved between 2012 and 2018, which is approximately 11.32%. 3 At the same time, inland shipping had only a 0.22% share of global shipping. Though the global share of Carbon Dioxide (CO 2 ) emission from inland shipping is relatively very small (more than 11 times smaller) the absence of appropriate energy and emissions benchmark for inland waterway self-propelled ships is a large impediment to performance improvements of inland ships. 4 Due to different types of additional restrictions on inland ship design, EEDI by IMO is not suitable for assessing the energy and environmental efficiency of inland navigation vessels. 5 In general, inland ships require more power at the same speed in comparison to similar types of open water/seagoing ships, 6 primarily because of the shallow water effect. Since this effect varies with channel depth and width, a generalized EEDI reference line is not possible in a similar fashion to IMO. For these reasons, the emission levels of existing inland ships of each country shall be known first.
Due to several features and changes in the design of inland ships compared to seagoing ships, some modifications to the formulation are required to estimate the energy efficiency of inland ships. 7 For the inland ships of Bangladesh, the prime differences are shallow and restricted water effects, different fuel qualities (to reduce operational cost), increase in engine power requirement, reduction in carrying capacity, cargo availability, limited access to design data, etc. These differences forbid the use of existing EEDI formulation for inland waterways of Bangladesh. A study by Hasan and Karim 8 in 2020 has considered the problem. However, the procedure followed for shallow water effect calculation by them was the famous Schlichting method. 9 The evaluation and presentation of Schlichting's results did not cover all range of ship parameters. The assumption of equal wave resistance by Schlichting in deep and shallow water when the lengths of the ship-generated waves are the same is questionable. 10 For the frictional resistance, Schlichting derived an empirical correction in terms of an assumed overspeed along the hull dependent on the ratio of hull midship area and depth of the water. However, its value was derived from his model-test data, to cover the remaining gap in total resistance after the wave correction had been made, and with some support from velocity measurements in the model basin. Now this wave resistance correction is a severe simplification. It assumes that ship waves propagate with the same speed as the ship, which is only true for transverse waves. Also, the wave resistance depends not just on wavelength but also wave amplitude. An effect of additional sinkage in shallow water is disregarded. Therefore, the wave resistance correction cannot be expected to be accurate; and its deviations are implicitly incorporated in the frictional-resistance correction, found by correlating with the model-test data. Moreover, Schlichting's model tests were just for three cruisers of that era, with extreme slenderness and rather high speeds.
International Towing Tank Conference (ITTC) 11 approved two procedures for power trials in shallow water, namely Lackenby 12 and the Raven 13 methods. Lackenby 12 extended the well-known Schlichting method toward smaller effects and has cast it into a simpler form. This method is approved internationally and by ITTC and is much easier to be used for research purposes where many ships are under consideration. The seventh Asia-Pacific workshop on marine hydrodynamics 14 compared the experimental data to evaluate the Lackenby method. When computational fluid dynamics (CFD) and experimental findings are compared, Lackenby's shallow water resistance yields a higher total resistance value. Raven 15 also mentions this result, stating that the Lackenby approach yielded greater total resistance estimates. Barrass 16 on the other hand has produced a very simple formula and is easy to use for all channel configurations. However, his formula overestimates ship squat due to its simplicity. Moreover, using bigger squat values than real ones can be considered a precautionary measure in terms of navigation safety in shallow waters.
Though both Lackenby's 12 and Barrass's 16 methods have limitations, this research selected the method described by Lackenby for theoretical calculation which has been approved by ITTC. 17 In addition to that, the procedure as proposed by Barrass 16 has also been calculated to compare both theoretical results. Finally, both results have been evaluated with the physical measurement for Bangladeshi inland ships.

Literature review
Since the adoption of EEDI by IMO in 2011, the formulation and guidelines have been updated since then. This kind of up-gradations is quite normal for new regulations The latest update was adopted in the 77th Marine Environment Protection Committee (MEPC) session by the member states of IMO in 2021. 18 In this MEPC session, a new index to improve the energy efficiency of existing seagoing ships called the ''Energy Efficiency Existing Ship Index (EEXI)'' was adopted. The EEXI is the extension for existing ships of the new building-related EEDI, most procedures will be the same as for the EEDI, with some adaptations regarding limited access to design data. The aim of the Energy Efficiency Existing Ship Index (EEXI) is to measure ships' energy efficiency under operating conditions. EEDI formula and guideline have both options to improve the energy efficiency of the ship, that is, by improving the ship hull performance and by adopting more energy-efficient technologies. European Commission (EC) report 19 has suggested 14 technologies to improve energy efficiency. However, it has been in the report that, though the low-cost technologies provide lower payback time, the improvement in efficiency is less than 5%.
Proposal for modification of EEDI formulation and definitions for specific ships is not new. Ancˇic´et al. 20 have proposed a new approach to the EEDI definition for ro-ro passenger ships. The proposal introduced a reference surface instead of a reference line like EEDI of IMO. This is a fairly new approach to energy efficiency calculation for ro-ro passenger ships.
Federal German Ministry of Transport and Digital Infrastructure has evaluated the energy requirement of inland vessels using energy efficiency indices. 21 The study was based on the EEDI by IMO where they have differed some parameters specific to inland navigations. The study found that inland ships on the Rhine River use significantly lower power than the installed engine power. For this reason, the study could not use the MCR as suggested by IMO. This finding is also true for the inland ships of Bangladesh, which were physically investigated under this study. The study also acknowledged the restricted draft problem and the percentage of deadweight capacity to be used to quantify the energy efficiency. Specific fuel consumption (SFC) was generalized to be 220 g/kWh (Gram kilowatt-hour) which they claim to have from the test-bed reports for inland vessel engines. However, in the case of the inland ships of Bangladesh, it is very difficult to generalize this SFC.
Aleksandar Simic agreed that the amount of effort/ research on benchmarking inland waterways' selfpropelled ships concerning energy and emission efficiency is not enough. 4 He investigated 111 existing inland waterway self-propelled cargo ships and deduced that EEDI introduced for seagoing ships cannot be applied for proper benchmarking of inland ships due to various reasons, including geographic restrictions.
A study on the inland waterways of Ukraine assumed that the energy efficiency of inland shipping is much higher than is technically possible. 22 However, this assumption is very risky to adopt for inland ships of other countries because of the geographical and technical differences.
Holmegaard Kristensen 23 developed a computer model for systematic investigation of container ship design which can be used to calculate exhaust gas emissions from container ships, including CO 2 . This kind of model is very much helpful for specific conditions and design. The model investigated different ship design parameters to check the influence of the ship design parameters on EEDI as well. This is quite normal for a new regulation to get modified over time. This modification is adjusting the regulation to different conditions and increases its adaptability. This paper deals with modifying a possible corollary of the energy efficiency regulation adopted by the IMO for sea-going ships. As inland ships plys within the national boundary, unique research, and suggestions on modifying EEDI formulation are required. This paper is one of those efforts.

Brief description of EEDI by IMO
EEDI in its simplest form can be expressed as follows 24 In June 2021, new amendments were adopted to the IMO's International Convention for the Prevention of Pollution from Ships in the MEPC. 18 These amendments include new energy efficiency requirements called EEXI, which measures CO 2 emissions per transport work, purely considering the ship's design parameters. EEXI has the same formula as EEDI but is used for the existing ship. Existing ships falling into the scope of EEDI requirements can use their attained EEDI calculated by the EEDI guidelines. 24 Equation (1) of EEDI (or EEXI) contains different constants and coefficients. The definition and meaning of those are described in the MEPC resolution, 18,24 as shown in the following Table 1. The detailed definition and calculation methods of these parameters are presented in the resolution.

Methodology to revise EEDI parameters for Inland Ships of Bangladesh
This reanalysis is based on the work by Hasan and Karim. 8 They have given an effort to revise EEDI parameters to be useful for inland cargo ships of Bangladesh. It was proven by them that, a generalized EEDI formulation is not possible like IMO defined EEDI because of many reasons. As found in that research, EEDI parameters need to be revised for many reasons, one of the major reasons is to counter the shallow water effect on speed. There are more issues like fuel quality, capacity to be considered for calculation, etc. also been addressed.
The effort by Hasan and Karim 8 on revising EEDI parameters to be useful for inland ships was first for Bangladesh. Further studies of that analysis have found more required corrections. For example, the speed drop was calculated by empirical formulas developed by Schlichting 9 and Barrass. 16 However, since the shallow water effect on ship speed is a hydrodynamic problem which is not uniform, this research has conducted physical investigations on speed drops because of shallow water.
The previous method mainly focused on theoretical/ empirical methods. To fix the MCR of the ship at service speed, Holtrop-Mennen methods [25][26][27] were considered. These methods are very well-known and dependable methods at the design stages but do not consider the shallow water effect. For this reason, MCR at service condition was very less than the investigated MCR. Therefore, physical measurements are required to fix the MCR of the main engine. Table 2 summarizes the required changes in the methodology of the previous 8 analysis. The methodology for fixing capacity based on cargo availability and carbon content of fuel remained the same as proposed in the previous analysis. 8 Theory of speed drop due to the shallow water effect Ships plying on shallow water can easily be affected by the limited draft due to the squat effect. The water velocity is accelerated around the hull as the draft Table 1. Definitions* of different EEDI parameters.

Parameter
Definitions of EEDI parameters 24 Definitions of EEXI parameters 18 P ME 75% of the main engine MCR in kW after having deducted any installed shaft generator(s). Ship engines are usually not operated near 100% MCR. Instead, they are designed with two margins in mind. One is a sea margin that can be accessed to provide higher speed operations, for example, to make up for a port delay. The other is an engine margin that is only used to keep a ship safe during adverse weather operations. In general, a sea-going ship runs at 70%-80% of MCR. For this reason, IMO has fixed 75% MCR for EEDI calculation.
In cases where an overridable Shaft/Engine Power Limitation is installed P ME(i) is 83% of the limited installed power (MCR lim ) or 75% of the originally installed power (MCR), whichever is lower, for each main engine. In cases where the overridable Shaft/Engine Power Limitation and shaft generator(s) are installed, MCR ME should be read as MCR lim . P AE Required auxiliary engine power to supply normal maximum sea load including necessary power for propulsion machinery/systems and accommodation, for example, main engine pumps, navigational systems and equipment and living on board, but excluding the power not for propulsion machinery/systems in the condition where the ship engaged in a voyage at the speed (V ref ) under the design loading condition of Capacity.
The same guideline is used in EEDI. However, under some special circumstances, EEXI has a different calculation process. P PTI(i) 75% of the rated power consumption of each shaft motor is divided by the weighted averaged efficiency of the generator(s).

Same as EEDI 24
P AEeff(i) the auxiliary power reduction due to innovative electrical energy-efficient technology measured at P ME(i) .

Same as EEDI 24
P eff(i) The output of innovative mechanical energyefficient technology for propulsion at 75% main engine power Same as EEDI 24 SFC ME SFC is the certified specific fuel consumption, measured in g/kWh, of the engines. The subscripts ME and AE refer to the main and auxiliary engine(s), respectively.
In cases where an overridable shaft/engine power limitation is installed, the SFC corresponding to the P ME should interpolate by using SFCs listed in the applicable test report included in an approved NOx Technical File of the main engine. Notwithstanding the above, the SFC specified by the manufacturer or confirmed by the verifier may be used. For those engines which do not have a test report included in the NOx Technical File and which do not have the SFC specified by the manufacturer or confirmed by the verifier, the SFC can be approximated by SFCapp defined as follows: SFC ME,app = 290 (g/kWh) SFC AE,app = 215 (g/kWh) SFC AE C FME C F is a non-dimensional conversion factor between fuel consumption measured in g and CO 2 emission also measured in grams based on carbon content. The subscripts ME and AE refer to the main and auxiliary engine(s) respectively. limitation restricts the water flow. This increase in water velocity results in a higher drag and eventually reduces the ship's hull efficiency. After a certain speed of the vessel, this shallow water effect becomes very pronounced. Any ship (regardless of its size) navigating through restricted waterways is heavily affected by these hydrodynamic effects.
International Towing Tank Conference (ITTC) guideline. ITTC recommended in the ''Procedures and guidelines for preparation, conduct and analysis of speed/power trials'' 11 that, if the water depth is less than the larger of the values obtained from the following two formulas, shallow water correction may be applied: Where, h: Water depth in meter B: Ship's breadth in meter T M : Draught at midship in meter V S : Ship's speed in m/s g: Acceleration of gravity in m/s 2 If the above conditions are satisfied and the effect of shallow water on a ship's speed needs to be predicted, ITTC recommended the Lackenby method 12 or the Raven shallow water correction method. 13 Raven method 13 does not provide any formulation, it is a procedure for a series of tests, which starts with CFD analysis. Later, this analysis is validated with model test and trial data. This is a very accurate process in practice, but not a generalized process. In addition to that, the builder, owner, and verifier must agree upon this process, as stated in the ITTC 11 guideline. On the other hand, the Lackenby method 12 provides simple formulas   [25][26][27] The engine output of the main engine was taken from the engine curve.
The use of engine curve will provide more accurate information on MCR and guidelines which are very handy. For this reason, Lackenby's 12 method is considered in this study.
Ship speed loss prediction (Lackenby's method). The shallowwater correction method most often used is that of Lackenby. 12 It modifies the speed-power curve by correcting the measured speed, assuming unchanged power. Lackenby 12 extended Schlichting's 9 diagrams toward smaller effects and has cast them into a simpler form. This speed correction follows from: Assumptions on the considerations of the effects of confined waters on ship resistance. In this research, the effect of the riverbank on the resistance has not been considered and is assumed to have a negligible effect. As stated in the ITTC report 17 the influence of the riverbank is negligible when the channel width (W) to the ship breadth (B) ratio is greater than 4. Without any exception, the maximum breadth of the inland ship in Bangladesh is 14 m. Only very few passenger ships have a breadth larger than that. A vessel with a 14-meter breadth when moves through a channel of width less than 56 m, only then the riverbank effect will increase the resistance. However, it is very unlikely in Bangladesh that, a vessel having a breadth of 14 m, plys through a narrow channel of width less than 56 m.
The water depth of a certain route is not uniform. For this reason, the effect of shallow water will not be uniform as well. This research relies on the river water depth data at certain points only, which are measured daily by different government organizations in Bangladesh. Therefore, in this research, the average speed as measured in a certain route has been considered as the gained speed after overcoming the average effect of shallow water. In addition to that, the measured highest speed in each case has been considered as the achieved speed without any effect of shallow water, because in these routes there may be certain regions where the depth of water may be quite high than the measured depth at various locations.

Investigated results on shallow water effect for the Inland Ships of Bangladesh
To find the actual shallow water effect on ship speed, ship speed at service conditions was measured for 15 vessels; five from general cargo (G.C) ships, five from oil tankers (O.T) and five from passenger vessels (P.V). Android-based app (Speedometer GPS) was used to measure ship speed using satellite. The traveled routes were different and water depths were varied. For this reason, the measured speed also varied for the same RPM (Revolution per minute) of the engine. The average speed has been considered as the gained speed after the shallow water effect.
Tables 3 and 4 present the investigated results of the five general cargo ships. Table 3, investigated ship particulars, traveled route through the inland waterways of Bangladesh, traveled distance and water depths at different points are shown. The water levels of the selected river routes in Table 3 were found from the Bangladesh Inland Water Transport Authority (BIWTA), 28 data from the ''Flood Forecasting & Warning Center'' of the Bangladesh Water Development Board (BWDB) 29 and data from the Chittagong port authority (CPA). Table 4 presents the speed measured for investigated ships at various locations. Measured top speed in each case has been considered as the achieved speed without any effect of shallow water. Since the measured speed drop due to the shallow water effect was not uniform, it has been presented in a range. To compare the theoretical speed, and drop due to the shallow water effect, the same effect has been calculated by the methods explained by Schlichting, 9 Lackenby, 12 and Barrass. 16 The deviations of calculated results from investigated results by those methods have been presented in Figure 1.
As presented in Table 4 for inland general cargo ships of Bangladesh, the results of Lackenby and Barrass are much closer to the investigated results. However, the deviation of the Schlichting method's results is remarkably high from the actual measurement. A graphical representation of these deviations has also shown in Figure 1.
In a similar process, as explained above, five inland oil tankers of Bangladesh have been investigated and presented in Tables 5 and 6 and Figure 2.
Like inland general cargo ships, the results of Lackenby and Barrass are much closer to the investigated results for inland oil tankers of Bangladesh and the deviation of the Schlichting method's results is very high from the actual measurement graphical call representation of these deviations has also shown in Figure 2.
The same process has been followed for five investigated passenger vessels of Bangladesh and presented in Tables 7 and 8 and Figure 3.
For inland general cargo and oil tankers of Bangladesh, the results of Lackenby and Barrass were much closer to the actual measurement. Investigated cases for passenger ships have given mixed results as presented in Table 8. Barrass's results can be identified as the closest to the actual results, still, the deviations are quite high. Table 9 summarizes the average speed drops in the shallow water of those investigated ships. In addition to that, the average theoretical results by Schlichting, 9 Lackenby, 12 and Barrass 16 and the average deviation from the investigated results for each type of ship are also presented.
The average actual shallow water effect varied from 19.30% to 21.10% considering 15 measured ships of each type. Since this effect depends upon the clearance under the keel, different ship drafts will produce different amounts of effect in the same channel. It is not possible to fix a single factor of speed deduction while considering the shallow water effect. As shown in Table 9, the calculated value by Lackenby 12 has provided a higher value in comparison with the actual measurement. On the other hand, the results of the  Barrass 16 method are higher for cargo and oil tankers, but lower in the case of passenger vessels. Based on the actual measurement, the average shallow water effect can be approximated as 20% and has been considered to establish EEDI BD baselines for inland general cargo, oil tanker and passenger ships of Bangladesh.
Fixing the main engine MCR and P ME considering shallow water effect A previous analysis 8 has suggested 60% MCR based on the average of verified ship data. As mentioned in Table 2, the ship data verification process was based on the Holtrop-Mennen methods, [25][26][27] which requires too much ship data/information. Unavailable ship data/ information was assumed in most cases. 8 In this study, MCR was considered from the practically measured 15 ships that were used to identify the average shallow water effect. During the physical investigation, the main engine RPM was measured when the ship started to move at continuous RPM for the maximum possible time. A digital tachometer was used for RPM measurement. The main engine load at the MCR was found from the Engine performance curve (Engine Performance Curves presented in Appendix-A). Tables 10-12 present the onboard measured RPM data and corresponding main engine loads for Inland General Cargo Ships, Oil Tankers, and Passenger Ships, chronologically.

EEDI BD parameters for Inland Ships of Bangladesh based on the reanalysis
Section 3 has explained the required changes to EEDI BD parameters proposed previously by Hasan and Karim. 8 Based on the new physical investigations, the changed values of those parameters have also been proposed. Table 13 summarizes those proposals.

Sample calculation
Based on the revised value, a good number of Inland General Cargo, Oil Tanker and Passenger ships of Bangladesh were taken into consideration to calculate EEDI BD . Tables 15-17 show sample calculations using IMO-defined EEDI formulation and using the revised EEDI parameters for Bangladesh for one inland cargo, oil tanker and passenger ship. Engines' RPMs were derived from the Engine performance curve against the required power. Deep water speeds (Ship speed without    any restriction due to shallow water) of those ships at that power and RPMs were calculated by Holtrop-Mennen methods. [25][26][27] As suggested in Section 3.2, a 20% speed drop has been considered to calculate EEDI BD with updated EEDI BD parameters for the cases to incorporate the effect of shallow water. The installed engine for each case remained the same, the MCR and power output have been updated according to the proposal presented in Table 13. The SFCs will be different at different RPMs, which were found from the engine curves for each case. Different types of factors as shown in equation (1) and explained in Table 1 have the value ''1'' for the cases of inland ships of Bangladesh. The reasons are presented in the following Table 14.
The sample calculation for cargo ships presented in Table 15 shows that the new EEDI BD values are about 33.45% higher than the previous one. This jump in on the EEDI BD value is mainly because of the shallow water effect on the speed and rise of MCR as proposed in this reanalysis. Though the deep-water speed for the updated EEDI BD parameter is 4% higher than the previous one, the reference ship speed is 16.46% less because of the adoption of the additional shallow water effect as explained in Section 3.2 and presented in Table 13. Consideration of higher MCR and drop in ship reference speed have increased the EEDI BD value more than the previously proposed EEDI BD parameters. For the case of the cargo ship's sample calculation, the EEDI BD value has been increased by 33.45%.
Like the calculation process of a cargo ship, Tables 16 and 17 present sample calculations on one inland oil tanker and one passenger ship in Bangladesh. For the sample case of the tanker, EEDI BD is 36.14% higher than the previously proposed EEDI BD . For the case of the passenger ship presented in Table 17, the value is 36.55% higher.

Results
Physical investigation of speed drops due to shallow water effect on 15 inland ships of Bangladesh have shown a very close range. For cargo ships, the average effect is 19.90%, for oil tankers, it was 19.30% and for passenger ships, it was 20.10%. Consideration of average is logical because the effect of shallow water depends on the underwater clearance and ship speed. As the ship moves, the river water depth fluctuates. Therefore, the average speed drop of a voyage is appropriate for future prediction. In this study, the vessels type and routes were different. For this reason, the average speed drops for each type of ship have been averaged again to standardize which was approximately 20%.
Empirical formulas proposed by Lackenby 12 and Barrass 16 are closer to the actual shallow water effect in comparison to the method explained by Schlicting. 9 However, the inconsistency in the results of Lackenby 12 and Barrass 16 made the use of these two-method unusable for prediction. For instance, as presented in Table 9, Lackenby's 12 result deviated by 10.10%-19.17% for cargo and oil tankers, but for passenger ships, the deviation was 43.83%. Similarly, Barrass 16 result show quite uniformity with the actual result for cargo and oil tanker, but for passenger ships, the result was inconsistent with the actual measurement. The average MCR varied from 64.50% to 80% for the five investigated five cargo ships. The same for oil tankers and passenger ships varied from 65%, 77%, 70%, and 90% respectively. Like fixing the speed drop, the average MCR were averaged again for each type of ship. The second averaged values were 71.90% for cargo ships, 69% for Oil tankers and 80.40% for passenger ships. The values for cargo and oil tanker are approximated at 70% and for passenger ships, it is approximated at 80%. Several interviews with captains and staff have also suggested the accuracy of MCR value fixed for these three types of inland ships of Bangladesh. According to the ''Inland Shipping Ordinance'' of Bangladesh, 12 ''Except to proceed to the assistance of any vessel, craft or person in distress, no inland ship shall proceed on any voyage or be used for any service when there is hoisted or announced a danger signal of the storm or where there is a reasonable apprehension of a storm.'' For this reason, the value of f w is assumed 1.0 for inland ships of Bangladesh. fi The capacity factor for any technical/ regulatory limitation on capacity. As per MEPC resolution 6 fi should be assumed to be 1.0 if no necessity of the factor is granted.
fi 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.
For inland ships of Bangladesh, no requirement of this factor was found and therefore considered as 1.

Conclusion
The Revised EEDI Parameters for Inland Ships of Bangladesh have been reanalyzed in this research. This reanalysis has considered the shallow water effect by actual measurement of 15 inland ships of Bangladesh. The average speed drops because of shallow water have been considered in this reanalysis rather than calculated with empirical formulas. Since this effect mainly depends upon the clearance under the keel, different ship drafts will produce different amounts of effect in the same channel. Practically it is not possible to fix a single factor of speed deduction while considering the shallow water effect. Based on the actual measurement, a 20% speed drop can be approximated due to the shallow water effect to establish EEDI BD baselines for inland general cargo, oil tanker and passenger ships of Bangladesh. EEDI BD for any new inland Bangladeshi ship, the individual amount of shallow water effect can be calculated theoretically at the design stage. The calculated values by Lackenby 12 and Barrass 16 methods are nearer to the actual. However, for all three types of vessels, the results calculated by Schlichting 9 are much lower than the investigated results. Therefore, both Lackenby 12 and Barrass 16 can be used for new ships.
The revised EEDI BD formulation proposed in this research can be used on the existing inland ships of Bangladesh. Plotting those results of EEDI BD against deadweight (Gross Tonne for passenger ships), EEDI BD  reference lines for several types of ships can be developed like IMO reference lines for the ocean-going vessel. This will set up a benchmark of CO 2 emission for helping the ship designers and regulating authorities to improve ship energy efficiency from the current stage.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.