Benchmarking bulkers delivered between 2010 and 2016, identifying the effect of the EEDI introduction

Pruyn, Jeroen F. J.

doi:10.1186/s41072-020-00063-1

Journal of Shipping and Trade

Table 1 Overview of indicators their formula and which improvements are considered

From: Benchmarking bulkers delivered between 2010 and 2016, identifying the effect of the EEDI introduction

Factor	Formula	Considers
EEDI	$ \frac{\left(\sum \left({P}_{ME i}\ast {SFC}_{ME}\ast {CF}_{fuel}\right)+\sum \left({P}_{AUXi}\ast {SFC}_{AUXi}\ast {CF}_{fuel}\right)\right)}{DWT\ast {V}_{design}} $(1)	Hull Shape, Lightweight materials, Air Lubrication, Hull Coating, Other Resistance Reductions, Waste Heat Recovery, Hybrid power, Power system,Propulsion efficiency devices, On Board Power Demand, Design Speed, Solar Power, Wind Power, Fuel Cells, Biofuels, LNG
EEDI (Simplified)	$ \frac{\left(\sum {P}_{MEi}+\sum {P}_{AUXi}\right)}{DWT\ast {V}_{design}} $ (2)	Hull Shape, Lightweight materials, Air Lubrication, Hull Coating, Other Resistance Reductions, Waste Heat Recovery, Power system,Propulsion efficiency devices, Design Speed
Admiralty Constant	$ \frac{\nabla^{2/3}\ast {V}_{design}^3}{\sum {P}_{MEi}} $ (3)	Vessel Size, Hull Shape, Lightweight materials, Air Lubrication, Hull Coating, Other Resistance Reductions, Power system,Propulsion efficiency devices, Design Speed, Wind Power
Power Ratio	$ \frac{\sum {P}_{MEi}}{P_{Estimated\left(H\&M\right)}} $ (4)	Hull Shape, Air Lubrication, Hull Coating, Other Resistance Reductions, Power system,Propulsion efficiency devices, Design Speed, Wind Power
Block Coefficient	$ {C}_b=\frac{\nabla}{L\ast B\ast T}=\frac{\Delta}{L\ast B\ast T\ast \rho }=\frac{DWT+ LDT}{L\ast B\ast T\ast \rho } $ (5)	Hull Shape
Lightweight (LDT) Ratio	$ \frac{LDT}{LDT_{Estimated(Watson)}} or\frac{C_b\ast L\ast B\ast T\ast \rho - DWT}{LDT_{Estimated(Watson)}} $ (6)	Hull Shape, Lightweight materials
Speed Ratio	$ \frac{V_{design}}{\left(\sqrt{g\ast L}\ast {F}_{n, Avg}\right)} $ (7)	Vessel Size, Hull Shape
Froude Number	$ \frac{V_{design}}{\sqrt{g\ast L}} $ (8)	Vessel Size, Hull Shape
Length over Width Ratio	$ \frac{L}{B} $ (9)	Hull Shape
Length Ratio	$ \frac{L}{\nabla^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}} $ (10)	Hull Shape
Area to volume ratio	$ \frac{WSA}{\sqrt{\nabla \ast L}} $ (11)	Hull Shape

∇= Displacement of the vessel in m³
Δ= Displacement of the vessel in ton can be found by adding LDT and DWT
ρ = Density of seawater in ton/m³
B = Moulded width of the vessel
CF_fuel = Carbon Factor, the amount of grams (new) CO₂ produced on combustion of a gram of fuel
DWT = Deadweight, the carrying capacity of a ship, it includes all weights that are not fixed on to the ship
g = Earth’s gravity, 9.81 m/s²
L = Length of the vessel (commonly the length between perpendiculars, as overall length is too inaccurate)
LDT = Lightweight, the total weight of the empty vessel
LDT_{Estimated(Watson)} = Lightweight estimated making use of Lloyd’s E numeral as demonstrated by Watson (1998)
P_MEi = Power of each (i) main engine
P_AUXi = Power of each (i) Auxiliary engine
P_{Estimated(H&M)} = Propulsion power estimated with the use of Holtrop and Mennen (1982)
SFC_x = Specific fuel consumption of an engine in g/kWh
T = Moulded draft of the vessel
V_design = the design speed of the vessel
WSA = Wetted Surface Area, the total area of the submerged vessel, responsible for the frictional resistance of the vessel

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Factor	Formula	Considers
EEDI	\( \frac{\left(\sum \left({P}_{ME i}\ast {SFC}_{ME}\ast {CF}_{fuel}\right)+\sum \left({P}_{AUXi}\ast {SFC}_{AUXi}\ast {CF}_{fuel}\right)\right)}{DWT\ast {V}_{design}} \)(1)	Hull Shape, Lightweight materials, Air Lubrication, Hull Coating, Other Resistance Reductions, Waste Heat Recovery, Hybrid power, Power system,Propulsion efficiency devices, On Board Power Demand, Design Speed, Solar Power, Wind Power, Fuel Cells, Biofuels, LNG
EEDI (Simplified)	\( \frac{\left(\sum {P}_{MEi}+\sum {P}_{AUXi}\right)}{DWT\ast {V}_{design}} \) (2)	Hull Shape, Lightweight materials, Air Lubrication, Hull Coating, Other Resistance Reductions, Waste Heat Recovery, Power system,Propulsion efficiency devices, Design Speed
Admiralty Constant	\( \frac{\nabla^{2/3}\ast {V}_{design}^3}{\sum {P}_{MEi}} \) (3)	Vessel Size, Hull Shape, Lightweight materials, Air Lubrication, Hull Coating, Other Resistance Reductions, Power system,Propulsion efficiency devices, Design Speed, Wind Power
Power Ratio	\( \frac{\sum {P}_{MEi}}{P_{Estimated\left(H\&M\right)}} \) (4)	Hull Shape, Air Lubrication, Hull Coating, Other Resistance Reductions, Power system,Propulsion efficiency devices, Design Speed, Wind Power
Block Coefficient	\( {C}_b=\frac{\nabla}{L\ast B\ast T}=\frac{\Delta}{L\ast B\ast T\ast \rho }=\frac{DWT+ LDT}{L\ast B\ast T\ast \rho } \) (5)	Hull Shape
Lightweight (LDT) Ratio	\( \frac{LDT}{LDT_{Estimated(Watson)}} or\frac{C_b\ast L\ast B\ast T\ast \rho - DWT}{LDT_{Estimated(Watson)}} \) (6)	Hull Shape, Lightweight materials
Speed Ratio	\( \frac{V_{design}}{\left(\sqrt{g\ast L}\ast {F}_{n, Avg}\right)} \) (7)	Vessel Size, Hull Shape
Froude Number	\( \frac{V_{design}}{\sqrt{g\ast L}} \) (8)	Vessel Size, Hull Shape
Length over Width Ratio	\( \frac{L}{B} \) (9)	Hull Shape
Length Ratio	\( \frac{L}{\nabla^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}} \) (10)	Hull Shape
Area to volume ratio	\( \frac{WSA}{\sqrt{\nabla \ast L}} \) (11)	Hull Shape