Fuel to speed “cube rule” not as good as thought

Sep 17 2020

A study by 3 academic researchers found that the well-known cube rule for fuel consumption to speed does not work unless you are near the design speed.

Everybody in shipping ‘knows’ the cubic rule for how fuel consumption varies with speed. Double the speed and the fuel consumption goes up 8 times, triple the speed and fuel consumption goes up 27 times – and the same with small increments of speed. The lesson is that lowering the speed a little means lowering fuel consumption a lot.


The trouble with this rule is that it does not match real life, according to work by researchers at Norwegian School of Economics, Kedge Business School and University of Nantes.


The researchers looked at the speed consumption relationship based on 11,000 noon reports for 6 suezmax and 10 Aframax oil tankers on global trade. 


The noon reports contain data about daily fuel consumption, voyage data and prevailing weather conditions at noon every day the vessel is sailing, compiled by people (not machines).


The study found that the ‘cube rule’ is only true near the design speed, but at slower speeds, the fuel consumption has a more linear relationship with the speed. 


This calls into question the benefits of "slow steaming" and fuel levies, to encourage vessels to go slower, the authors say.


Companies do not usually have a good model of the vessels' fuel consumption as a function of sailing speed, which they would need to work out the best speed economically. 


Today, it is very common for vessels to operate at much lower than the design speed. 


In October 2019 Clarkson Research reported reductions in average fleet speeds of 16% for bulkers, 18% for tankers and 24% for containership compared to 2008. 


The researchers propose use of a new variable "speed elasticity" which changes with vessel speed, and is estimated from real data from vessel operations, taking weather into account. 


This speed elasticity should also take into account draft, trim, sea current, wave, wind and its interaction with the ship heading, they say.


The "findings can also be used to challenge the general political view that a large reduction in CO2 emissions can be achieved through further speed reduction and that an increase in fuel price (through for instance the implementation of a bunker levy) would force ship operators to reduce speed and therefore CO2 emissions,” they say.


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