1 Application of Coulomb’s friction law to define energy consumption of new drive-trains K Kendall*, N J Shang*, I Staffell † *Chemical Engineering,University of Birmingham,Edgbaston, UK † Imperial College, London, UK, Keywords: Coulomb friction law, electric drive train, fuel cell, hydrogen. Abstract A key argument in the transport field is about improving the energy consumption of cars. Should we go electric, ban combustion, move to fuel cells or change to renewable fuels [1-5]? This is an important research question because the number of cars worldwide is predicted to grow from 0.7bn in 2010 to 2bn in 2050, leading to a huge penalty in fossil fuel depletion, climate change and energy security in the near future [6]. But these discussions of electric cars, new battery materials and renewable fuels have missed a key point:- that the main difficulty with cars is their evolution in terms of increasing weight. Evidence shows that cars increase in weight by about 2% per annum. This paper demonstrates that car weight dominates the energy question by showing that Coulomb’s law of friction surprisingly applies to a complex system like a car, such that the energy usage, in other words overall friction force, depends mainly on weight. A new theory shows that dissipation in complex systems resolves into Coulomb’s Law. Experiments demonstrate that the results fit this theory reasonably well. We have tested a hydrogen fuel cell battery hybrid composite car of 7kN weight and present results better than all existing hydrogen cars in terms of low energy use. The conclusion is that Coulomb’s Law can be used to quantify precisely the energy consumption of cars and that lightweight designs are as important as hydrogen electric drive-trains in cutting fuel consumption. 1 Introduction Over the past century, there has been much discussion about improving vehicles in terms of energy use. Many changes have been proposed including electric drive, banning combustion, bringing in novel electrochemical devices like lithium batteries or fuel cells, and changing to renewable fuels such as hydrogen and biomass [1-5]. But the key problem shown in Fig 1 has been less evident:- the parameter which really matters is car weight, and this surprisingly follows Coulomb’s original friction law of 1773. Fig 1 shows the fuel consumption for 3800 petrol cars in China within years 2000 to 2010. The energy consumption in MJ/km, essentially the friction force in kN, was plotted against the weight in kN to reveal a linear dependence with an intercept. It is clear that there is some scatter, especially for heavier cars where fuel costs are less important for luxury buyers, but the trend of lower fuel use with lower weight and the obvious cut-off are clearly shown. This picture raises several interesting questions:- a) How can Coulomb’s Friction Law apply to such a complex system as a car? b) Why does car evolution give weight increase, such that new models are heavier than the old, increasing at up to 2% per annum c) Can the introduction of improved drive train technology such as hydrogen fuel cells reduce the energy consumption substantially by 2050 [6]? 0 1 2 3 4 5 6 7 -5 0 5 10 15 20 25 30 Figure 1 The energy usage in MJ/km (friction force F in kN) of petrol cars in China against vehicle weight W in kN showing the Coulomb Friction Law fit 2 Definition of energy consumption There are problems in comparing the energy usage of vehicles, mainly when new technologies like battery or fuel cell cars are introduced to compete with traditional combustion engine machines. For example, it was stated that a lithium battery electric vehicle travelled 313 miles on a single charge with no tank-to-wheels emissions [7]. However, it is known from experience that lithium ion battery vehicles more usually travel between 50 and 100 miles on a single F, kN W, kN