I’m an outlier.

I’m a guy who likes to write and *loves* math. There’s an old J-School joke about people picking journalism as a major because it has one of the lowest math requirements, but I majored in engineering for three years before changing majors so I have years of pent-up math that I never get to use.

With the recent buzz about **electric trucks**, their potential and their payback I think there’s an opportunity to combine a few words with a little math and have a little fun along the way.

Electric trucks have dominated recent headlines with promises of zero emissions, which is another math equation for another day because making electricity certainly generates emissions. Electric trucks also tease carriers with the idea of reduced cost of ownership. We can’t calculate total cost of ownership because we can’t factor in the cost of purchasing, financing or leasing an electric truck since there’s not one actually yet on the market. Prices of $300,000 to $350,000 are mostly speculative. They’re probably close enough, but speculations in math aren’t cool.

What we can approximate with what we know is total cost of operation of a diesel versus electric truck over a 100,000 mile, one year period.

First of all, let’s all agree this exercise isn’t designed to prove or disprove anything. Everyone’s cost of ownership – and the calculations used to determine them – is a little different. Also, I’m not factoring in any subsidies, “free fuel” guarantees or tax credits, tires or maintenance. This is head-to-head, cash-in and cash-out on getting the truck to move.

I can buy a gallon of diesel at one of three stations not far from my house for $2.29. The national average is about $2.53, but you can use any number from any station you want. It doesn’t matter. DEF is about $2.80 per gallon at the pump, so we’ll need to factor that in, too.

If my tractor averages 6 MPG, that means for 100,000 miles I’m going to need 16,667 gallons of fuel: 100,000 miles/6 MPG = 16,667 gallons. The 6 MPG ballpark is about the national average, and that’s $38,167 in fuel: 16,667 x $2.29.

With a dosing rate of about 3 percent, I should need about 500 gallons of DEF at $2.80 per gallon over 100,000 miles. So, $2.80 x 500 = $1,400 in DEF.

Our total annual fuel cost for the purposes of this exercise will be $39,567: Fuel cost + DEF cost =$39,567/100,000 miles. That’s 39.5 cents per mile.

Our fuel cost for a truck that doesn’t use any is fairly simple to figure out: $0. Ha! That’s where many calculations go off the rails. You get an electric bill every month and the first time you plug in your Tesla or whatever-other-OEM electric tractor, that bill is going up.

Commercial electricity rates in Alabama average about 11 cents per kilowatt hour (kWh), and here’s where the math gets amped up a notch.

A gallon of diesel – primarily its 146,520,000 joules of energy – converts to about 40.3 kWh. A joule is equal to 2.777778⋅10^{-7} kilowatt-hours. The energy in kilowatt-hour [*E*_{(kWh)}] is equal to the energy in joules [*E*_{(J)] }divided by 3,600,000: *E*_{(kWh)} = *E*_{(J)} / 3,600,000 = *E*_{(J)} ⋅ 2.777778⋅10^{-7}

You’ll see some citations of an EPA-estimated 33.7 kWh gallon equivalent, but that is based on a less efficient gasoline engine and doesn’t account for waste energy, which we are about to do. I haven’t seen *any* comparison that accounts for waste energy, but I think it’s necessary.

All fuel fired in a diesel engine doesn’t do work. That’s why you have waste heat. **Diesel engines** generally convert only about 45 percent of fuel energy into mechanical energy. So, if we’re getting 40.3 kWh/gallon, the engine’s actual output will only be about 45 percent of that – 18.13 kWh/gallon at full load.

An electric motor is more efficient than a diesel – meaning it uses more of the energy generated by the motor to move the load – so, we need to back out any energy that’s wasted by the diesel. What we’re trying to measure is how much of a gallon equivalent is actually doing work. For example, 40.3 kWh of electricity (the equivalent of one gallon of diesel) would do more than twice as much work as a gallon of diesel fuel assuming the electric motor was 100 percent efficient.

With electric rates of 11 cents per kWh – the current rates I got from Alabama Power today – you would pay about $1.99 for the equivalent energy of one gallon of diesel fuel, which should give us about 20 miles per gallon equivalent (MPGe). Here is where the math becomes more black magic than exact science. There is some major back-of-a-napkin math here involving factors, figures and projections that includes everything from the truck’s aerodynamics to battery capacity. If you want to argue any of the math I’ve laid out, this is a good place to start. But so we can move forward, let’s assume we can squeeze out 20 MPGe (an improvement factor of nearly 3 versus diesel).

At 20 MPGe, fuel costs associated with an electric truck should hit you up for about $10,000 over 100,000 miles – 9.9 cents per mile.

That’s a truckload of savings, but here’s the wildcard: the battery. The cost of the fuel tank is a financially negligible add-on to a tractor’s sticker price, but in the case of an electric semi it could account for as much as half of the premium asking price.

**Tesla** claims its battery costs are below $190 per kWh, but that figure is otherwise on the low side of the going rate.

A 20 MPGe is about half a mile per kWh. If your target range is 600 miles, then you’d need about 1,200 kWh in battery power. Even if Tesla’s technology drops the cost per kWh by an seemingly unrealistic 50 percent – speculations in math still aren’t cool but let’s do it anyway – the battery cost alone will hit you for $114,000.

Under normal scenarios, the cost of the battery would fall under the cost of the truck, not a fuel expense. We don’t know how much the truck will cost, but we can get an idea of the battery’s expenses since we have a ballpark base rate on the cost of storing a kWh of energy.

If you consider a five year trade cycle and spread the battery cost out over the 5 years, then add one year’s worth back to the electric fuel cost ($114,000/5 + $10,000), you hit $32,800 – or 32.8 cents per mile. At less than 7 cents per mile, you can bank about $6,700 in savings in fuel costs alone in Alabama every 100,000 miles based on my math.

But, there are a lot of other variables in play. For example, if you dial back the efficiency of the electric motor, the gap narrows, as it does when you consider what various electric companies across the U.S. charge for energy. Electric trucks make more sense in Alabama than they do in Rhode Island, where electricity rates of about 17 cents/kWh equate to $3.08 diesel gallon equivalent.

I think the potential of electricity in transportation is fascinating and it’s certainly a precursor to autonomy, but I don’t think there’s enough information yet available to make a clear case that an electric truck offers a significant reduction in cost of ownership.