The argument for electric vehicles

A simple mathematical analysis

Photo by Crissy Jarvis on Unsplash

Introduction

The other day an old friend of mine brought up the following question: upon replacing gasoline powered engines with electric vehicles, if the electricity to charge these vehicles come from burning coal, what’s the actual gain? Aren’t we just replacing one source of carbon dioxide with an even worse one?

I thought the question did raise a good point, so I decided to do what I (almost) always do: resort to math. Like Katherine Johnson once said:

Everything is physics and math. Math is always dependable.

So let’s do some calculations, shall we?

Fuel for electricity

The first thing we’ll look at is if the statement that coal is the main fuel for generated electricity. Here are some statistics, globally and for the US in particular:

Globally

• Coal: 37%
• Natural gas: 26%
• Low-carbon sources/renewable sources(nuclear, wind, hydroelectric, etc.): 37%

US

• Coal: 24%
• Natural gas: 38%
• Low-carbon/renewable sources: 38%

So looks like we are up to a good start: replacing gasoline powered engines with electric vehicles means that at least about 38% of the energy will come from renewable or low-carbon sources.

But is that enough? What if the remaining 62% provided by coal and natural gas are still worse than gasoline? Let’s find out.

Energy density

Energy density is a number that tells us how much energy per kilogram of fuel we can get. The higher the energy density, the less fuel we need to burn to get the same amount of electricity.

So let’s look at the energy density of the 3 fossil fuels we’re comparing so far

• Coal: 24 MJ/kg
• Natural gas: 55 MJ/kg
• Gasoline: 46 MJ/kg

(MJ = megajoule = 1,000,000 joules)

So clearly coal is much less efficient than gasoline, but natural gas is better. Using the US percentages from the previous section let’s calculate how much natural gas and coal we must burn to produce the energy of 1 kg of gasoline or 46 MJ.

1. 38% will come from low-carbon sources, so we must burn enough coal and natural gas to produce the other 62% or 29 MJ
2. Using the US percentages:

24% from coal = 0.24 x 46 MJ = 11 MJ = 460 g of coal

38% from natural gas = 0.38 x 46 MJ = 18 MJ = 330 g of natural gas

Total fuel mass = 790 g

So far so good: by burning 790 g of fuel and combining it with low-carbon sources we can replace 1 kg of gasoline to get the same amount of energy.

But what does this mean? In order to find out if there’s any environmental benefit we must find out how much carbon dioxide is generated when we burn each one of these different types of fuel.

Carbon dioxide emission per fuel

We’re going to make some assumptions to simplify the calculations a bit (it’s ok, unlike Katherine Johnson we have some room for approximations).

• We’ll assume coal is 100% carbon (it is in fact a mix of carbon, nitrogen, hydrogen, sulfur and other chemicals, with carbon being the highest percentage)
• Similarly, we’ll assume natural gas is 100% methane
• We’ll assume all burning is 100% efficient, so all fuel is converted into carbon dioxide, water and heat
• Gasoline is a complex mixture of several compounds, with molecules ranging between 4 and 12 carbon atoms; to simplify the math we’ll assume it’s composed 100% by octanes, molecules formed by 8 carbon and 18 hydrogen atoms

Under these assumptions:

1. 1 kg coal =>3.7 kg of carbon dioxide
2. 1 kg of natural gas => 2.8 kg of carbon dioxide
3. 1 kg of gasoline => 3.1 kg of carbon dioxide

So, burning 460 g of coal and 330 g of natural gas gives us 2.6 kg of carbon dioxide, a 15% reduction in emissions compared to gasoline.

But we have to consider one more aspect for this to work: how much of the energy produced actually becomes useful energy at the wheel? If we have to produce 10 times more electricity at a power plant to get the same energy at the wheel as burning gasoline locally at the engine, it will of course mean a lot of extra carbon dioxide compared to gasoline.

So, let’s look at the efficiencies for each type of vehicle.

Power at the wheel

Electric vehicle

• Power plant production: 40% (meaning only 40% of the burned fuel actually becomes electricity; coal and natural gas fired power plants have roughly the same efficiency)
• Transmission: 98% (meaning 2% are lost in high-voltage transmission)
• Distribution: 96% (meaning 4% are lost in low-voltage distribution to buildings)
• Vehicle (battery to wheel): 77% (meaning 23% is lost from the battery to the wheel)

Multiplying all these percentages, between 25 and 30% of the total energy generated by burning fuels at the power plant reaches the wheel and provides useful power.

Gasoline engine

• Engine: 30% (about 60% is lost in radiator, exhaust heat, combustion, pumping, etc.)
• Drive train: 95% (about 5% is lost)
• Other parts (wind resistance, water, oil, electrical systems, etc.): 80% (about 20% lost for these reasons)

Again, multiplying all terms we get about 25% efficiency. Some literature indicates this can get to 30% in a well maintained vehicle, used mostly in highways.

In other words, in terms of efficiency, the percentage of the energy from burning fuels that is converted in useful power is roughly the same for both gasoline powered vehicles and electric vehicles.

So, in summary: based on this simplified model, switching to electric vehicles looks promising; as it is, we can start reducing carbon dioxide emissions in about 15% right away. Does not sound like a large number, but it’s a good start.

Conclusion

There are several other factors that affect the actual carbon footprint for both gasoline powered and electric vehicles, which a more rigorous mathematical approach must consider.

• Gasoline production chain (crude extraction, refining, transportation)
• Coal and natural gas production chain
• Battery production lifecycle (mining, production, battery operation, recycling, disposal)
• Production of renewable energy equipment
• Handling of spent nuclear fuel
• Vehicle lifecycle, etc.

It’s clear that simply replacing gasoline powered vehicles with electric vehicles is not enough; a shift in the way we produce electricity is paramount for the success of this transition. We must continue the move towards renewable sources of electricity; battery production, waste management and battery efficiency must keep improving; new ways to recycle and reuse spent nuclear fuel must be developed and adopted.

It does not seem unreasonable to think that carbon emissions can and will be drastically reduced by adopting these technologies. It’s a matter of, as for everything, will. And math.