« Not All That Guzzles is Olds | Main | Spotlight on AXP Letter of Intent Teams »


Chris Ellis

This is a great summary, apart from the phrase 'but you never get back what you lose going up'. On most downgrades most drivers seldom use their brakes, because the potential energy their vehicle gained going up, five minutes before or a hundred miles away, is now being used to overcome air and tire resistance, etc. Of course, with a hybrid, any gentle braking required will result in energy being recovered for later use. Only going down a steep mountain pass will some of the potential energy gained in reaching altitude be lost, and then not all of it. But then I'm still young enough to accelerate out of downhill hairpin bends... Most vehicles spend less than one mile in a thousand going down really steep, long hills, so clearly the phrase is wrong and should be dropped. Then the 'The Car Equation' may become the definitive primer. I would't have bothered with this blog if I didn't think it could....

Ken Fry

This is an excellent summary, John.

At the risk of over-complicating things, I’ll reinforce that what is being calculated is a force: tractive force. The equation applies to one instant for a particular car, on a particular grade at a particular speed and acceleration.

To get from force to power, we need throw v (velocity) into the equation again. From power, we can say how much energy a car will consume per minute.

Which leads us to the other equation: given that one needs, let’s say, 10 kW to move a particular vehicle at 60 mph along a flat road, then how to best supply that? Generate electricity at 38% efficiency (although the DOE says 33%) cranking out a lot of carbon in the process… or generate gasoline at 82% efficiency? Once the energy source has reached the vehicle, do you drive on electricity at 85% efficiency (including battery charging, through the controller, and through the motor to the motor output)… or do you drive at the 38% (peak) efficiency of a Prius engine (ignoring the hybridization factors which improve the vehicular efficiency). Using the DOE figure, the Prius is more efficient than the electric car: 82% x 38% > 85% x 33%. Using the 38% figure for overall electrical generation sometimes heard, the tables turn… but in practical terms, the > or < symbols might just as well be =.

But then 49% of our power is generated with coal, which creates about 50% more carbon per million BTU than gasoline. So today, in the real world, an efficient gasoline-powered car is perhaps less egregious, environmentally, than an electric car. The DOE predicts that the percentage of electricity generated by coal will increase to 57% by 2030. The use of renewables will increase in kW terms but not as a percentage of the total. See: http://www.eia.doe.gov/oiaf/aeo/electricity.html

Is that a dismal prospect, or what??

Having written all this, however, I’d have to say that the Tesla, especially, will help to change things in a fundamental way. Electric vehicles are clearly the way to go in the long term, and great credit should go to Tesla for making the technology attractive, today. While either my own Pod One microcar or an Aptera can squeeze about twice as many miles out of a chunk of coal as a Tesla, it’s the Tesla that says, today, that driving an electric car can be a blast – and that an electric car can compete (in coolness) with a Porsche, head to head, dollar for dollar. In the not too distant future, all cars will be full electric. As we, as a country and as a world, actually begin to think, really think, about how we use energy, the move to renewables, and especially solar, will come. People will start to think about how profoundly foolish it is use up all the resources we have so little of while ignoring the one we have so much of. A single year’s solar input is far greater than all the fossil fuels we can ever use. But this graph of energy usage has to be expanded in scale twice for solar voltaic usage to even become visible: .04% of total energy usage.
See: http://en.wikipedia.org/wiki/Image:World_energy_usage_width_chart.svg

Even today, solar voltaics are competitive economically with grid electricity in many parts of the US. In the future (probably near future), that will only improve. My hope is that the Automotive X Prize will stimulate enough real thought to speed that transition to solar power. In the meantime, PHEVs are a great stepping stone.

John Shore

Chris Ellis and I had a side conversation after his comment on "The Car Equation", above. I believe I convinced him that "you never get back what you lose going up", but I may have oversimplified by not mentioning the many relevant variables (speed, cornering, braking, regeneration, etc.), and I realized that the basic reason for energy loss may not be obvious. Consequently, I edited and then republished the post, in particular replacing this:

• hills - how often you go up them and how steep they are (what goes up, must come down, and the sign of the last term becomes negative when you go down; but you never get back all you lose going up)

with this:

• hills - how often you go up them and how steep they are; (the sign of the last term becomes negative when you go back down, but you never get back all you lose going up. Although there are many variables involved - speed, cornering, braking, regeneration, etc. – at best you can recover most of the potential energy gained by climbing the hill. However, the energy spent going uphill is considerably greater than that potential energy gained since engines and drivetrains are not 100% efficient. The difference is lost forever.)


John Prikkel PE

I am pleased to see that weight reduction is a prominent factor to be considered. liteflex LLC has been designing and manufacturing light weight springs (leaf and coil) for automotive (Corvette 25+ years) and truck applications (Peterbuilt, Freightliner etc). Weight is reduced 60 to 75%) while performance is improved (ride, handeling, durability etc).
Concerning reducing rolling resistance, Liteflex has developed a low cost alternative to run flat tires. better rolling resistance and no need for a heavy spare tire. Fell free to contact me if interested cell 937-469-3962. John P

Bruce McHenry

Regarding Chris Ellis' comment above:
"Generate electricity at 38% efficiency (although the DOE says 33%) cranking out a lot of carbon in the process… or generate gasoline at 82% efficiency? Once the energy source has reached the vehicle, do you drive on electricity at 85% efficiency (including battery charging, through the controller, and through the motor to the motor output)… or do you drive at the 38% (peak) efficiency of a Prius engine (ignoring the hybridization factors which improve the vehicular efficiency). Using the DOE figure, the Prius is more efficient than the electric car: 82% x 38% > 85% x 33%. Using the 38% figure for overall electrical generation sometimes heard, the tables turn… but in practical terms, the > or 85% (PEV storage) x 33% (Electric generation + distribution):

The quoted 38% Prius efficiency quoted must be for the peak efficiency of the engine. The engine is not always operated at peak efficiency which is also substantially reduced when the output is stored and retrieved from the battery. My guess is that that round-trip loss averages more like 40% than 15%. Can you find any data on that? Overall, I'd expect average Prius' efficiency around 25%, not 38%.

When electric utilities use natural gas in new turbines, efficiency is 55% or better, presumably because combustion inside the turbine is more efficent. Higher efficiency should also be expected for atomized liquid fuels such as gasoline and oil. I assume the 33% DoE figure you quote includes transmission losses. What are they? If 15%, the fuel equivalent utility power is .55 * .85 = .47 efficient.
Revising your equation yields .82 * .25 = .21 for Prius versus .47 * .85 = .40 for electric, twice as good. Say this goes down to .33 * .85 = .28 for coal. If your 1.5X carbon from coal is correct, coal power is also carbon equivalent.

Not factored into the calculation above is the weight of the on-board power plant which results in higher power needs. Going all-electric seems to reduce weight, but how much at a given range?

Going all-electric with high speed, long range power coming from the directly from the grid would allow most of the on-board batteries to be eliminated which will probably reduce weight relative to traditional vehicles by about 40%. Such vehicles would weigh much less than the equivalent Prius, PHEV and PEV.

How can vehicles be powered while cruising down the arterials? How do you power them when off-grid? See http://roadtrains.us for some ideas in development.


hi all
sorry, but overall prius eff. is much lower than 38%, even a lot lower than 25%. the avg. prius driver uses 5 liters premium for 100km. that's 5 x 8900Wh/l or 44,5 kWh. let's say we're doing an avg. of 60 km/h. drag, rolling res. & friction losses will sum up to about 6kW power demand at that speed. therefore, total eff. is somewhere around 14%. it's still a clever thing, though, at least in terms of marketing.

Jim Bullis

I need to reiterate my concern about the MPGe method since I read your plans for the competition. On a separate issue, I appreciate your inclination to allow tandem seating.

By promoting the MPGe term, harm is done to the overall intention to limit carbon dioxide and its equivalent compounds. The harm is that the public sees the MPG part and is led to think that we will make great progress against global warming by simply changing to electric power systems.

I offer evidence in the fact that, today, Tesla claims on the headline page of their website at www.teslamotors.com that their roadster gets 135 miles per gallon equivalent.

Since last summer when I first objected to this criterion I have looked at "Mechanics, Heat and Sound by Sears, 1950 (probably more engineers learned freshman physics from his very clear writings than from any other). Hopefully my argument is now more refined.

Obviously electricity does not come in gallons, so the desire to make some sort of equivalent is understandable. An incorrect formulation can result in statements that mislead by a factor of 3 or more. The "miles per gallon equivalent" measure is only valid for electricity that falls from the sky, meaning hydro-electric, solar, (lets include) wind and geothermal, where the heat engine process is not required. However, by far the most electrical energy comes by making heat from some sort of fuel and running it through a heat engine of some kind. The second law of thermodynamics now stands in the way. If we are talking about fossil fuels, which is the only way to get electricity that is not already spoken for, then the USA efficiency in 2006 for electrical energy produced from fossil fuel is 34%. Without worrying about distribution losses, this means that the Tesla roadster example of which is claimed 135 mpg(equivalent) has to be divided by about three. It might be claimed that in California, the mix of electric sources allows a divisor of about two. So taking these as a range of reasonable, the Tesla gets between 45 and 68 mpg(equivalent). So I think it is clear that this is marketing over-done. The shame is that the Tesla is quite a remarkable achievement, where sports car performance is obtained, while being more economical than a Prius.

The outcome of this is that there is an unwarranted sense in the media and hence, the public, that such cars put us on track to solve global warming, and since they are so attractive, no further effort is called for.

The good side of this exercise in outrage is that it has made me realize that, not only are we excessively wasteful due to operation of inappropriate cars, we are similarly wasteful in electric power generation. The system of central power plants where heat rejected by the heat engine is thrown away is all wrong. Rather, a distributed power generation system, where a cogeneration process is carried out at our respective households would allow full use of that otherwise wasted heat. If this were to be the way we make the electricity, then MPGe is actually a valid unit of measurement.

A key requirement for such cogeneration is that the motor-generator be sized appropriately for the household such that all heat can be used effectively.(PGE rebate rules make a looser but similar statement).

If high efficiency cars include motor-generator systems, then distributed cogeneration of power, using those motor-generators in those cars can be implemented with very little additional cost. Conduits for heat transfer to the household from the car and piping to supply natural gas from the household to the car are anticipated.

It is amazingly fortuitous that this combination could put us on the 7% Kyoto CO2 reduction track much faster than previously thought possible.

I realize this goes beyond your immediate concerns, but I am interested in solving the whole problem. I think this warrants X-prize involvement in some form.

Best regard, Jim Bullis


Jim Bullis

I add to evidence on the subject of MPGe the specification for the GM Volt
that came out a year ago, where the confusion with 'MPGe' is confounded with a variation that is 'equivalent mpg' which has completely different meaning from your MPGe.

I am copying my comment to GM, which covers the problem as I currently see it:

Horrors, I looked at the specs released Jan 7, 2007. The snake oil salesmen are back. Do we really have to pass a law regulating motor vehicle and global warming emissions claims. Maybe we could let the FDA do the job. That would sure expedite things.

"Why," you might ask,"do you say such mean things?"
And I say, "because the spec tries to confuse the public by using the term 'equivalent mpg'."
This is not literally dishonest, since 'equivalent mpg' is not really defined. The fault is only an intent to mislead, or possibly, really not understanding what you are talking about.
In the spec for the Volt, a careful look will turn up the likelihood that 'equivalent mpg' really relates only to the gasoline and the word 'equivalent' does not relate to energy in general, as you might suppose. Thus, it completely ignores the equivalent electric energy part. "Why do you care," you might ask. I say, "because it results in a false implication about the overall energy usage and the global warming implications. Shame on GM"
GM is not alone in this. Others that seem to have an intent to mislead, have come up with 'mpg+' which is gibberish and 'MPGe' which stands for 'miles per gallon equivalent' which seems to stand for something related to the fact that electricity has to be recognized as a form of energy.
Unfortunately,the problem with the way 'MPGe' is used is also indefinite, since it depends on how the electricity was produced. It takes more than four letters to deal with this.
A convenient way to handle this 'MPGe' ambiguity is to ignore the process of electricity generation and the generally required heat engine and the Second Law of Thermodynamics, where such details dictate an enormous loss of energy, given the way power is usually generated in fossil fuel power plants.
Now, if we are only considering electricity that falls from the sky, such as hydro, solar, wind, (lets also include) geothermal, the MPGe formulation can be justified as honest. But it sure is misleading, since there is not much chance of electricity from these sources getting into the car batteries. I hope GM can dig up someone that remembers enough freshman physics to come up with a forthright way to specify the critical aspects of auto performance.
Once I get through to the truth it seems that there is a good design here, and I am not against progress in small steps.

Ken Fry

I notice that several people have assumed that the 38% figure given for engine efficiency in the Prius was an engine average figure, or a vehicular average efficiency figure. When I wrote “or do you drive at the 38% (peak) efficiency of a Prius engine,” I was referring to the peak efficiency of the engine (if that is not already clear). Although it spends more time near its peak than the engines in most cars, it does not operate at that peak for anything close to the majority of the time. Overall vehicle efficiency is of course much lower, although not as low as Roger has suggested. Based on US EPA fuel consumption figures, the Prius would have to consume very close to 9kW at 60, so overall efficiency would be around 20%.

Fuel efficiency can mean many different things. A 100 mpg moped is unimpressive. A 100 mpg Hummer, on the other hand, is so impressive as to be unbelievable. One recently publicized Hummer uses biodiesel, large quantities of hydrogen, and grid electricity (it’s a plug-in hybrid). Obviously, when it is running on grid power alone, it is using no biodiesel, so it gets infinite mpg. If it you go five miles on grid power, the engine starts, and then you stop the test at 6 miles, then you can quote a very very high mpg figure. That figure could be technically correct (on 1/20 gallon of liquid fuel, the vehicle went 6 miles: 120 mpg) but extremely misleading – because it treats electricity as if it falls from trees; ditto for hydrogen, currently one of the least efficient energy carriers imaginable.

The 20% mentioned above for the Prius means that the Prius is fairly efficient at moving itself around. That same figure could apply to a much heavier, lighter, bigger, or smaller vehicle. In fact, it could be applied to a Hummer with a diesel. It also applies to a VW diesel. The VW and the Prius, however are fairly efficient at moving a couple people around – the Hummer is atrocious: you are spending your fuel on pushing around tons of metal with bad aerodynamics. Smaller, lighter, more streamlined vehicles transport a couple people around with much higher overall efficiency even when the fuel tank to wheels efficiency (percentage) is the same as a Prius. Vehicles like the Aptera, and my own Pod One are small, light, and streamlined, so no matter what the energy source: coal or natural gas (grid power), biodiesel, gasoline… they simply use less energy per person-mile. Smaller vehicles also have large advantages in overall resource usage, and are less likely to kill others.

Several years ago, the DC area electric vehicle association came out with a white paper hyping electric vehicles. In it, they pegged the EV1 as 59 mpg equivalent. The Tesla aerodynamics are much worse, so it would be reasonable to expect a lower figure for the Tesla. The DC people used essentially the same figures I used above, which are also the figures the EPA uses to begin calculating CAFÉ ratings for electric vehicles. But the EPA then adds a fudge factor to promote electric vehicles, which multiplies the reasonable calculation by 6.67. It you look at the fine print on the Tesla website, they give the section of law used, which is easy to look up in the web.

Another way to look at the efficiency of a vehicle is simply look at the energy required to move it down the road. In this case, the Tesla is 600 lb heavier than the Lotus equivalent, which is a 23 mpg vehicle. The Tesla must deliver more energy to its wheels per mile. Fortunately, it uses energy more efficiently than a gasoline-powered equivalent – but not 6 times as efficiently. From motor to wheels, losses are comparable for all car types (electric car, PHEV, traditional gasoline car, etc.). The real differences are in where the fuel is burned and with what efficiency the energy gets to the motor output: that is the reason I quoted the figures I did above. Certainly, using peak efficiency gives the Prius an unfair advantage, but a similar series hybrid would run at peak efficiency virtually all the time. So suppose we fudge downward a couple points on battery charging through motor output to 82%, and call power generating efficiency 33%. Then we bump the engine efficiency down to 33%, (almost 10 percent lower than a VW TDI) and use 82% for gasoline generation and transport. That’s a wash: on a well-to-wheels basis, electric vehicles and efficient hybrids are about the same in energy efficiency. (Bruce makes the point that natural gas powerplants can be 55% efficient, which is correct. But that does not reflect the actual US mix. Certainly, if all our electricity were generated by wind and solar, electric cars would look better yet. But that is also not the case – and it is something we should work toward, rather than pretend it has already happened.)

So it seems silly, as Jim Bullis points out, to consider electric vehicles to be ultra-high MPGe. Measuring from plug-to-wheels completely ignores where the energy is consumed and pollution generated – at the power plant. Around the world, we need to work on generating efficiency as much as we need to work on vehicle efficiency. A plug/pump to wheels standard for judging completely ignores where electricity comes from, and makes us feel ever-so-virtuous for driving electric cars that consume our fossil fuel resources and generate pollution at rates far too close to the status quo. There are no Zero Pollution Vehicles unless we are charging with solar and wind – and right now we are doing anything but. The DOE projects no change in renewable percentage through 2030. That percentage needs to change, and pretending that electricity falls from trees is not the way to do it.

New Cars

Very interesting article. I do think the uncontrolled variables such as speed, acceleration, and terrain have a significant impact on the equation overall.


July 22, 2008

Cars, Vehicles, Modes of transport, these are very important elements of a much broader equation.

Are you prepared to now vest interest and support for vital ecocentric systems?

Think - Act - Repeat



Shouldn't the rolling resistance term include a cos(θ)?


How I doing to know more??

skid steer tires

Your tire pressure can change allot about the performance of your vehicle. not enough air in your tires will slow you down, cause you to be all over the road, hurt your allignment, cause accidents, etc.

solid tires

Gary Samler

Hello All,
I am impressed with the calculation estimates mentioned above, after all I'm an ME that loves numbers. From my point of view, there is a bigger picture here though. Probably 99% of the vehicles on the road today are being powered by gasoline engines, whether hybrid or not - that's the problem! We have all contributed to the largest transfer of wealth in the history of mankind and driving gasoline powered automobiles is a large part of the problem. In my opinion, electric vehicles is the best solution, since we can charge them up at home, would not have to gas up at a gas station ever again and would easily be accomodated by building more nuclear powered facilities, which has been proven safe for 50 years or more. No matter what the calculations say, we MUST convert to electric vehicles or our country is destined to fail, we are already broke and losing jobs at an alarming rate. I think that a fully electric vehicle is 1000 times better than the internal gas combustion engine from the 1800's. Had we started designing & building electric cars and new battery technolgies, since the 1970's during the first big energy crisis under Carter, I think more than half of us would be driving electric vehicles today. Instead we are again too late with our paradigm shift. I am a believer in ZAP's electric vehicles and I hope their ZAP Alias wins the Progressive Automotive X-Prize and finally draws the attention toward electric vehicle transportation. I'm enjoying the calculations mentioned above nonetheless, but let's remember the bigger picture when looking at these calculations!

The comments to this entry are closed.