MPG for Electric Cars?

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A typical efficient car in the U.S. market gets about 40 MPG (miles per gallon) running on gasoline. A hybrid car like the Prius typically gets 50–55 MPG. In a previous post, we looked at the physics that determines these numbers. As we see more and more plug-in hybrid or pure electric cars on the market, how do we characterize their mileage performance in comparison to gasoline cars? Do they get 100 MPG? Can they get to 200? What does it even mean to speak of MPG, when the “G” stands for gallons and a purely electric car does not ingest gallons?

This post addresses these questions.

Using the Wrong Measure

Okay, first of all, MPG (called fuel economy) has always been a poor choice of units. We don’t usually put a gallon of gas in the car and drive as far as it might take us. Rather, we tend to have a destination in mind and care about how much gas it will take to get there. The inverse, GPM (called fuel consumption), would therefore be a better measure, and is akin to the measure used in some parts of the world (e.g., Europe’s liters per 100 km).

Besides this philosophical advantage, the GPM approach has a numerical advantage. If you have an old truck that gets 12 MPG and car that gets 30 MPG (let’s say both travel comparable distances in a year) and you want to replace one of the vehicles, are you better off replacing the truck with a 16 MPG model or the car with a 40 MPG model? Framed this way, the car looks like a better choice: a gain of 10 MPG vs. 4 MPG.

Let’s say for numerical simplicity that you want to go 240 miles in both. In your initial situation, it takes 20 gallons for the truck and 8 gallons for the car, for 28 gallons total. If you replace the car, the same journey will take 6 gallons for the car for a total of 26 gallons. If you replace the truck, the new one takes only 15 gallons for a total of 23 gallons. It’s a much better deal to replace the truck, even though the MPG gain seemed less impressive. We would have had to replace the 30 MPG car with one that gets 80 MPG to achieve the same 23 gallon result. If we had been using GPM instead of MPG, we’d never get confused on this point, and would therefore make smarter decisions. Try adding the values of 1/MPG to see that this is true, as in the following table.

Scenario truck MPG car MPG gal/240 mi truck GPM car GPM total GPM
Original 12 30 28 0.0833 0.0333 0.1167
Replace Car 12 40 26 0.0833 0.025 0.1083
Replace Truck 16 30 23 0.0625 0.0333 0.0958
Equivalent Car 12 80 23 0.0833 0.0125 0.0958

A New Measure for All Cars: Electric and Gasoline

With this lesson in mind, we would like a measure of energy per distance traveled. I’m a big fan of picking a universal energy unit and applying it to all forms of energy we use. Among the zoo of energy units: Joule, kilocalorie, Btu, Therm, kilowatt-hour, gallon of gas, barrel of oil, etc., I prefer the kilowatt-hour as a common standard. I like this because my favorite unit is the Watt (is it wrong to have a favorite?), and using the kWh makes it straightforward to flip between energy and power. Like ya do.

So I’ll bow to both the American and the scientist in me and try a unit as schizophrenic as an American scientist must be when it comes to units: kWh/mi. Lovely.

Let’s look at our 40 MPG sedan. A gallon of gasoline contains 36.6 kWh of heat energy when combusted, in this case taking us 40 miles down the road in the process. So this car uses 0.915 kWh per mile.

We tend not to be fond of puny fractions: especially in America where we like our numbers BIG. So let’s take a hint from the Europeans and use kWh/100-mi. Now our sedan has an energy consumption of 91.5 kWh/100-mi. Using this measure, we desire a smaller number for our car. Energy consumption in these units for gasoline-driven cars can be calculated as 3660/MPG kWh/100-mi. A 12 MPG Hummer has an energy consumption of 305 kWh/100-mi, while a Prius, at 50 MPG has an energy consumption of about 73 kWh/100-mi.

How do electric cars or other electric/hybrids stack up? In order of performance: the Chevy Volt gets 35 miles from a 16 kWh battery for a consumption of 45 kWh/100-mi (see note below); the Nissan Leaf gets 73 miles from its 24 kWh battery for 33 kWh/100-mi; and the pricey Tesla has a 244 mile range using a 53 kWh battery, for 22 kWh/100-mi. The MPG equivalent of these three figures is approximately 80, 110, and 170, respectively. All are much better deals than gasoline cars deliver, primarily because the electrical drive system is far more efficient than the typical 20% gasoline engine.

[Note: a reader informs me that his Volt uses 30 kWh/100-mi, the difference being that the battery is only allowed to use 10.4 kWh of its 16 kWh capacity.]

If you pay $0.10/kWh for electricity, these three cars travel 100 mi for costs of $4.50, $3.30, $2.20, respectively (triple this for Hawaii). At $3.50 per gallon of gasoline, a car getting 50 MPG will cost $7.00 to travel the same distance. So in almost all cases, the “fuel” cost is less to the consumer at current prices.

Theoretical Expectations

Are the energy consumption numbers we calculated good? Besides being obviously better than gasoline cars, are they close to the theoretical limit? To get at this, we follow the analysis developed in the earlier post on gas mileage. The energy it takes to fight air resistance when traveling a distance D at velocity v is E = ½cDρADv², where cD is the drag coefficient (0.25 for the Prius, for example), ρ=1.3 kg/m³ is the density of air, and A is the frontal area (<2.5 m² for a deliberately efficient small car). Putting in 160,934 meters for D to represent 100 miles, and converting the result (in Joules) to kWh by dividing by 3,600,000 J/kWh, we get 16 kWh/100-mi when traveling at a freeway speed of 30 m/s (67 m.p.h.).

If we add rolling resistance, at about 1% of the car’s weight, we get an additional tax of about 5 kWh/100-mi for a 1000 kg car, independent of speed. Therefore, the low 20’s is about as good as you might ever see at freeway speeds. For city driving, regenerative braking and the much smaller contribution from air resistance will reduce the theoretical expectation, approaching the rolling resistance limit in extreme cases. The Tesla figure of 22 kWh/100-mi, for example, represents a combined profile of driving conditions/speeds. The energy consumption at freeway speeds is undoubtedly higher than the combined figure, and not in danger of challenging the theoretical limit. But on the whole, not a bad show for the first wave of mass-market electric cars.

Not So Fast

The present analysis leaves out two important bits. First, the energy consumption (and electricity costs) I calculated for the Volt, Leaf, and Tesla simply use the battery capacity—not the electricity delivered for charging. Charging efficiency may be anywhere from 70% to 90%. But that’s a small caveat compared to the second issue (and similar to the 25% energy overhead for refining gasoline from oil—which itself has an energy overhead of only about 5% in the extraction/delivery process).

In order to deliver 30 kWh to your house to fully charge the Leaf’s 24 kWh battery bank, for example—incorporating the charge efficiency this time, the source of electricity becomes a highly relevant factor. Two-thirds of our electricity comes from fossil fuel plants, typically converting 35% of the fossil fuel thermal energy into electricity. Only 90% of this makes it through the transmission system, on average. If your electricity comes from a fossil fuel plant, the 30 kWh delivered to your house took about 95 kWh of fossil fuel energy. The 73 miles the Leaf travels on a full charge now puts it at an energy efficiency of 130 kWh/100-mi. The MPG equivalent number is 28 MPG. From a carbon-dioxide standpoint, you’d be better off burning the fossil fuel directly in your car.

I’m not saying that transitioning to electric or hybrid cars is not a good idea. I think it’s an imperative, if we want maintain a car culture, given that fossil fuel supplies are going to decline eventually, starting with oil. Obviously, if your power comes from hydroelectric, solar, wind, or even nuclear, you don’t have the same concerns. Also, emissions controls (for things other than CO2) are vastly better for fossil-fuel power plants than for automobiles, so electric cars are less polluting. But if your priority is either reduced resource consumption or climate change and CO2 reduction, let’s focus on getting electricity from carbon-free sources before transforming our fleet of cars to electric—or at least accomplish the two in tandem.

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15 thoughts on “MPG for Electric Cars?”

  1. If you really want to be pedantic, shouldn’t we be comparing the energy contained in the raw fossil fuel, including the losses associated with refining, etc?

    My suspicion is that a lot more energy is expended when extracting and refining oil than is lost extracting and refining brown coal. I’m not sure what wins when comparing Gas and Oil, but liquifying LPG for delivery must be an energy intensive process.

    These sorts of comparisons seem kind of silly for the above reason. The sensible comparison in my view is the cost per 100-Mi after applying a suitable ground-to-consumer carbon cost.

    That measure approximately captures both the environmental impact, and market signals regarding the future scarcity of natural resources.

    • A shortcut: the energy return on energy invested (EROEI) for conventional fossil fuels tends to be in the 20:1 ballpark, meaning 5% of the delivered energy goes into producing it. Such small corrections are in the noise for this kind of calculation. Tar sands and oil shale are much worse off, but not a large share of today’s fossil fuel activity.

      • [edited down by moderator]

        The EPA testing uses the wall-to-wheels efficiency of the vehicle. Test procedure is simple. Charge vehicle all the way. Run test until car won’t run any more. Charge vehicle all the way and record kWh. Repeat until satisfied with result. And the results from the EPA:

        Roadster: 30 kWh / 100 mi
        LEAF: 33 kWh / 100 mi
        Volt: 36 kWh / 100 mi

        The cars in EPA testing are far closer to one another than your rough calcs. Not too surprising that the lighter cars are more efficient – the Volt is the heaviest of the bunch.

        Most gas [electric generation] these days is combined cycle or cogen (you know you have a few cogen plants right there at UCSD by the Physics buildings) – combined cycle plants are about 50% efficient today – cogen can be up to 90% depending on how much of the heat is able to be used. The cogen plant you have there at UCSD appears to be about 75% efficient overall. Way over 90% of gas generation in California is either combined cycle or cogen. I’ve calculated the carbon emissions of a coal powered EV about the same as a 45-50 mpg car. In other words – worst case powered by coal, an EV is about as efficient as the most efficient gas car on the market – and you’re likely doing much better and will continue to do better as the grid becomes less fossil fuel intensive.

    • That’s a lot of faith you’ve put in market signals… but I definitely agree that including the costs of the refining process would be prudent.
      I think most people view our dependence on oil primarily based on its role as a fuel source, when the really tricky aspect of our dependence is on its role as a battery – that is, as high-density energy storage so we can put energy in during refining and take energy out at the point-of-use. Even if extracting and refining oil cost more energy than we got out of it, we’d still be locked in – sad.

  2. [edited down by moderator]

    If you use Argonne National Labs’ GREET model, you’ll find that the greenhouse pollution from a gallon of gasoline is about 25% greater than the greenhouse pollution from burning the gallon of gasoline in the vehicle. For example, see http://www.fueleconomy.gov/feg/sbs.htm which uses GREET for its greenhouse numbers. Unfortunately they haven’t supplied the greenhouse numbers for the 2011 Nissan Leaf yet. However, try comparing the 2002 Toyota RAV4-EV to the 2002 Toyota RAV4; that’s an interesting one.

    FWIW, my Nissan Leaf averages 250 Wh/mi battery-to-wheels, and about 295 Wh/mi plug-to-wheels. I usually use 92% efficiency for the grid, giving 320 Wh/mi for plant-to-wheels. Also, it only takes about 150 ft^2 of PV on my roof to power my annual Nissan Leaf driving. In my case, my transportation fuel is sunshine.

    Finally, EVs don’t cause any more water to flow through dams, or U235 to be split, or coal to be burned. Those sources run flat out, EV or no EV. What happens when you plug in EVs to the grid is that utilities fire up NG plants to supply the load. You will find a detailed analysis of this sort of thing in GREET, and also from the Pacific Northwest National Laboratory, and from EPRI.

  3. In the electric utility industry, we generally accept that for every kWh delivered there were three produced at the generator (for fossil fuel generation at least). My off-grid solar/wind hybrid system at home doesn’t have appreciable transmission losses, but the embodied energy in the equipment, along with getting it delivered and then installing it was substantial. It always seems to be that the embodied energy of a power plant is ignored by the utilities, most likely because they wouldn’t like the information. It’s easier to attack solar and wind installations based on their low capacity factor and variable output rather than efficiency of generation or EROI.

    For the sake of the current post, I just picked up an electric motorcycle to use for my daily 10 mile round trip commute. It will be charged using my solar array, and I plan to keep track of my “mileage”, using kWh/mile (or per 100 mile). Using Lithium iron phosphate batteries, I expect the charge efficiency to be similar to lead acid, perhaps a little lower.

    By the way, it’s a blast to ride- 65 mph on electricity.

  4. What about the cost to replace the batteries in the future? The average person can barely afford to take his car to the shop now for repairs. I shudder to think what it will cost to replace batteries in a ten year old car that fails.

    • Car battery packs are made up of many smaller modules. For example, the pack on the Nissan LEAF is made of 48 smaller textbook sized batteries.

      In a battery “failure”, this typically means that one or maybe a few of the modules have significantly degraded more than the others. To restore the pack one only has to replace the faulty module(s).

      After 10 years there should be significant opportunity for “end-of-life” use of batteries as well letting one recoup a decent amount of the cost of a pack should you need/want to replace the entire pack due to gradual capacity degradation over time.

    • It shouldn’t be any worse than replacing the transmission or engine in the car, both of which have life expectancies on a similar order as that of the batteries.

      An all-electric car (as opposed to a hybrid) does away with both the internal combustion engine and the mechanical transmission; what’s left is inherently far more reliable than any petroleum-powered car on the road today.

      Lastly, battery technology is evolving very rapidly right now. In ten years, you can expect a replacement battery to be significantly cheaper, much lighter, and have substantially more energy capacity. Worst case, it might take a bit of creativity on the part of the mechanic to retrofit a new battery into the space used by the old (assuming no sanctioned replacements or standard sizes), but even that shouldn’t be that much of a big deal.

      Cheers,

      b&

  5. In response to your 2nd to last paragraph, Be Fair. If you want to talk about source to pump/outlet, then you should breakdown all paths, not just fossil power plants. Look at the long chain that is oil to gas at a pump.

    Drill hole in ground, build pumping station over hole, pump oil out of ground and into storage container, pump oil from storage container into massive 2M barrel ship, sail ship half way around world (assume middle east origin), pump oil out of ship into storage container, run oil thru refining facility and pump gasoline into storage container, pump gasoline into massive underground distribution pipe system to various locations around the country and into storage containers, pump gasoline in to fuel trucks, drive fuel trucks to local stations and pump gasoline into underground storage tanks. Then pump gas into car from UST.

    All that infrastructure needed to be built and has to be maintained. Seems like there is a lot of math there.

    • Hard work by others (like Charles Hall) have captured all the math in the handy EROEI measure—although there can be haggling over where to draw the boundaries for such calculations. The extraction/delivery part still has high EROEI (even U.S. domestic oil EROEI has ranged between 18:1 and 35:1 over the last few decades; higher still in middle east). So this sacrifices only 5% or so. Other comments point to a gasoline refining “tax” around 25%, which is starting to be significant.

      But this blog doesn’t have the “resolution” to consider 5% effects. Even 25% effects don’t tend to change the overall conclusions. I tend to seek out places where simple physics and estimation make a clear case, so that details will seldom change the story.

  6. One thing about batteries, they often involve mining and refining things like nickel, which creates a rather nasty environmental problem. In fact, I believe I read that, over the course of its whole life from creation to destruction, a Toyota Prius actually does more environmental damage than a Land Rover Discovery, mostly due to the batteries. And at that, its practical mileage is about the same as my 8 year old VW Golf diesel’s (with my leadfooted wife driving).

    Personally, I think electric cars are at least a decade away, because you wind up carrying around a lot of extra weight (a killer in fuel efficiency, as any racing team will tell you), and because recharging takes so long. I suspect that hydrogen might be the next transportation fuel.

    • The piece you read has been widely discredited a dozen times or more. It simply made up stuff that wasn’t true. Also, 60% of nickel is used in making steel, so if you think it is such a problem, please avoid any automobile with steel in it.

      Diesels are particularly bad for global warming. The problem is not their CO2 emissions, but their black carbon (soot) emissions, which a non-gaseous greenhouse pollutant.

  7. In response to Richard above, do you think that hydrogen is a viable transportation fuel alternative? One of the problems I see is that the efficiency of creating the H2 (from water?) is low as is the conversion from H2 back into energy (and water). While both hydrogen and batteries would work for cars, what about planes?

    For aeroplanes, I doubt electric batteries will be able to replace fossil fuels as they can only drive a propeller. Hydrogen is combustible so I expect it could work in a jet engine.

    Perhaps a post on using Hydrogen as a fuel would be worthwhile?

    Cheers,
    Luke

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