# Cost of driving: electricity vs. gasoline

Hello All,

I'm trying to get a sense of the cost of using electricity e.g., plug-in hybrid vs. the cost of operating the same vehicle using gasoline. I've read a comparison using the btu value of gasoline vs watts/btu but I'm not sold on that idea since the vast majority of thermal energy in an automobile goes out the tailpipe. What I was thinking of was choosing a 'standard' car like a Ford Taurus, operated on a highway at a steady state for one hour. Using horsepower as the common denominator between gasoline and electricity As far as gasoline consumption, I would propose dividing the miles travelled in the hour by some reasonable highway MPG. Just for sake of example, I have read that steady-state 50 MPH driving uses 40 HP. Figuring 25 MPG highway, gasoline at $4.00/gal and electricity (746 W/hp * 40 hp. for one hour = 29.84 KWH. At$0.10/KWH, driving the 50 miles cost $2.98 using electricity or 2 gallons of gas =$8.00.

Obviously, the example is greatly simplified, but is it a fair comparison?
Wordsmith

russ_watters
Mentor
You are right that most of the energy goes out the tailpipe. The efficiency is somewhere around 30%. The easiest way to deal with that is to divide the fuel economy by the efficiency to find the equivalent economy of a plug-in hybrid.

Ie, a car that gets 40mpg would get an equivalent 40/.3= 133 mpg.

There are certainly other complicating factors, but that should get you in the ballpark.

RonL
Gold Member
Although I don't agree with all he says, there are a lot of things worth considering in this presentation.

It might be a little help to some.

http://ludens.cl/philo/electric.html

Although I don't agree with all he says, there are a lot of things worth considering in this presentation.

It might be a little help to some.

http://ludens.cl/philo/electric.html

this looks interesting. even though i am an electric car advocate (and had been for some time), i am not sure that i disagree with this guy (the author, Manfred Mornhinweg, XQ2FOD, looks like he's an amateur radio operator licensed in Chile) about the facts.

when you take a Thermodynamics course in mechanical engineering, you will learn about the ideal Carnot Cycle, entropy, and the difference between "high-grade energy" (ordered mechanical energy such as the twist of a shaft or electricity) and "low-grade energy" (essentially heat). when converting from Joules of heat to Joules of ordered mechanical energy (via an ideal Carnot Cycle), there is a theoretical maximum efficiency of

$$1 - \frac{T_{in}}{T_{exhaust}}$$

where the temperatures are relative to absolute zero, like Kelvin. so, if fuel is burnt to make electricity, the cost of a Joule of electriciy must cost more than a Joule of heat from some combustible fuel (by a factor of at least the reciprocal of that efficiency). so you have to consider the cost of the electric Joules compared to the cost of the gasoline Joules with figure divided by the reciprocal of the efficiency of the engine (from point of sale of the energy source to the axels of the drive wheels). that's how to compare these apples to oranges.

the reason why i might not agree with that ludens.cl guy is that i think that centralized power plants (where the chemical energy of a fuel is converted to heat and then to mechanical power) are far more efficient than the miniature power plants we drag around with us when we drive our conventional cars around (although the technology of both are getting better, but i think that the electric power plants' efficiency is closer to their limit than car engines).

another cost you have to consider in the cost of a pure electric car, is the cost of replacing the batteries after their expected life. traction-motor batteries (deep-cycle rechargable batteries either lead-acid or of some modern technology like lithium-nickel) ain't cheap, and after some, i dunno, 10000 kilometers (maybe more, i dunno what the mean lifespan of a battery is, nor precisely the cost), you have to replace and responsibly recycle those batteries. that costs money. serious bucks.

another cost you have to consider in the cost of a pure electric car, is the cost of replacing the batteries after their expected life. traction-motor batteries (deep-cycle rechargable batteries either lead-acid or of some modern technology like lithium-nickel) ain't cheap, and after some, i dunno, 10000 kilometers (maybe more, i dunno what the mean lifespan of a battery is, nor precisely the cost), you have to replace and responsibly recycle those batteries. that costs money. serious bucks.

Yeah, like a couple grand if I remember correctly. So, the cost effectiveness drops drastically.

LURCH
I have done considerable figuring on this topic, but took a very different approach from the one in the OP. I took numbers from the one highway EV that I know of (the Tessla), and multiplied the number of kW/h per mile by the price of electricity on my electric bill that month. My conclusion was that driving 25mi would require a certain amount of electrical energy (I think it was about 4kW/hrs; I'll look it up), which I then reffered to as an electric gallon, or EG. From my calculations, driving about on electrical energy would be about $1.00/USgal (that's assuming the electricity gets taxed like petrol, about$.40/EG).

I also figure the CO2 emmisions would be about 1/2 that of gas (and that assumes no improvement over current rates of CO2 per kW/hr).

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rcgldr
Homework Helper
I also figure the CO2 emmisions would be about 1/2 that of gas (and that assumes no improvement over current rates of CO2 per kW/hr).
Unless your source of electricity is from a coal burning plant.

Unless your source of electricity is from a coal burning plant.

How would CO2 emissions compare if it were from a coal burning plant?

rcgldr
Homework Helper
How would CO2 emissions compare if it were from a coal burning plant?
I don't know the exact numbers, but...

Coal is the major fuel used to generate electricity worldwide, but burning it adds more carbon dioxide, a greenhouse gas, to the atmosphere per unit of heat than does burning other fossil fuels like oil and natural gas.

http://www.america.gov/st/washfile-english/2007/May/20070530134219lcnirellep0.6537592.html

How toxic are the li-poly batteries used in electric vehicles? Can these be recycled? What's the loss in energy in having to produce electricity, transmit it, charge up batteries, which have to store it, then convert it into linear power to propel a car, as opposed to extracting, tranporting, and storage of gasoline, where all the conversion into linear power occurs within the car?

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LURCH
Unless your source of electricity is from a coal burning plant.

No, that's assuming the electricity comes from nothing but a coal-burning power plant, one with no better carbon control techniques than those currently in use.

LURCH
Ah, here is that research I did:

As can be seen from this site...
http://www.teslamotors.com/efficiency/well_to_wheel.php [Broken]
...the Tesla requires about 110Wh to travel 1km. This translates to about 160Wh/m. According to the EPA, the average passeneger vehicle gets about 25mpg, so multiplying 160Wh/m by 25mpg, we get 4000Wh = 1gal. This is to establish what I call the Electric Gallon (or EG), which is the amount of electrical energy required to drive the same distance as 1 gallon of gasoline; 4 kWh.
Looking at my electric bill from last month, I see that I am paying about 10 cents per kilowatt hour, including all taxes and service fees. So...
$.10 per kilowatt hour times 4 kilowatt hours gives me about$.40 per EG. Of course, if electricity is being sold as fuel for vehicles, the taxes usually charged for gasoline will have to be charged for that electricity in order to maintain roads. Also, if gas stations begin selling electricity, the electric utilities will have to charge at a higher rate, due to the very high current the stations would require. And of course, the fuel stations themselves would have to mark up the price in order to make a profit. Depending on the state in which one lives, gasoline taxes can be anywhere between $.30 and$.50 per gallon...
http://www.energy.ca.gov/gasoline/statistics/gas_taxes_by_state_2002.html [Broken]
... and the national average is about $.40, bringing the price of electrical energy as automotive fuel up to$.80 per EG. So, even if the electric utility and the fuel distributor really gouge the customer at $.10 per Equivalent Gallon apiece, the price still only goes up to$1.00/EG.

It can also be seen from this DOE web site:
http://www.eia.doe.gov/cneaf/electricity/page/co2_report/co2report.html#electric
that burning coal to generate electricity creates about 2 pounds of CO2 per kilowatt hour. Multiplying by 4 kWh, this renders about 8 pounds of CO2 per EG. By comparison, according to this EPA web site:
http://www.epa.gov/otaq/climate/420f05001.htm
burning gasoline generates approximately 20 pounds of CO2 per gallon; roughly double the amount.

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Nice research, Lurch.

I'd add that converting power from the mains to recharge the batteries obtains losses in both battery heat and power conversion, perhaps 15%.

How toxic are the li-poly batteries used in electric vehicles? Can these be recycled? What's the loss in energy in having to produce electricity, transmit it, charge up batteries, which have to store it, then convert it into linear power to propel a car, as opposed to extracting, tranporting, and storage of gasoline, where all the conversion into linear power occurs within the car?

Lithium batteries are still an evolving technology. In the form that I've read about, the lithium is in the form of an olivine, lithium iron phosphate; no heavy metals, which is nice to see. At one time I looking up electric power generation and transmission efficiency. I think 39% is close to nominal.

The cost of coal is about $100 per ton Nominally 20*10^6 BTU per ton (varies from about 16 to 26 MBTU) 1000 BTU = 293 Watt-hours about 39% efficiency for delivered energy from the mains ---------------------------------------------------------------- Cost in coal, alone, for delivered power: 4.4 cents per kilowatt-hr I would have guessed 6 to 7 cents out of 10. But the numbers do seem to be in the right ball park. So how does gasoline compare to coal in cost? Coal: 88 KBTU per dollar (using the 10c per KWhr figure) Gasoline: 125 KBTU per gallon, at$4.00 per gallon obtains 31 KBTU per dollar

Each delivers about 20 - 25% efficiency to the axle.

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Unless your source of electricity is from a coal burning plant.

you are comparing a car's motor efficiency with a power plant efficiency...........

anyway, when doing some kind of effectiveness evaluation, you must know what the degree of accuracy you want. first you were only considering a first approximation of the equation: electric versus gasoline, then you start putting terms about battery, and then about effectiveness of electrical energy produced in power plants versus mechanical energy produced by the car with gasoline or with electrical energy. So, at this time, you have already some variables.

however the point is: if you want to know how you do the calc, is one thing, if you want to know what are the variables of it, is other thing... physics can give you both and can give you an equation relating every variable and the optimum solution(if it exists), but you have to say at what level of accuracy you want, otherwise, more some days and we are arguing that at your living place, energy chargers are at x miles, so you will waste more energy to go there than to a conventional fuel station...xD

I've done a little more reasearch in the mean time on coal fueled electric power generation. They are not as efficient as I beleved. Some years ago the hot technology was internal combustion coal dust turbines, but this technology doesn't seem to have made it to general use, so the less efficient boiler-driven steam-turbine seems to be the common motive source.

The efficiency of coal burning electric power generatation is about 35%.
The efficiency of delivery over the power grid (US) averages about 93%.
Overall efficiency. 0.35*0.93 = 32.5%

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Has anyone ever considered the use of Geothermal driven power plants to generate the electricity for electric cars?
Yellowstone has enough geothermal energy to drive all the geothermal electric power plants we would ever need. The only cost would be for plant construction and maintenance. (I know it would require congressional approval to use Yellowstone.)
I can envision the government selling the electricity through separate meters with the electric cars being required to charge at night in order to receive the special pricing and not overload the grid. The revenue from the sales could be used to fund (pick your favorite unfunded liability) or reduce income taxes ... whatever. This would also result in zero CO2 emissions. The revenue could also be used to help lower income families purchase their first electric cars and get the older (cheap) gas hogs of the streets.

This could also be the initial step towards the fuel-cell cars with hydrogen being produced through electrolysis from this new found excess of electricity.

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LURCH
Has anyone ever considered the use of Geothermal driven power plants to generate the electricity for electric cars?

Everybody, but that's a different thread, I think.
This could also be the initial step towards the fuel-cell cars with hydrogen being produced through electrolysis from this new found excess of electricity.

If you've alerady got the cars running on electricity that's produced with zero emissions, what do we need fuel cells for?

OmCheeto
Gold Member
Hello All,......I have read that steady-state 50 MPH driving uses 40 HP. Figuring 25 MPG highway, gasoline at $4.00/gal and electricity (746 W/hp * 40 hp. for one hour = 29.84 KWH. At$0.10/KWH, driving the 50 miles cost $2.98 using electricity or 2 gallons of gas =$8.00.

Obviously, the example is greatly simplified, but is it a fair comparison?
Wordsmith

Adding together your numbers and my numbers, I come out with $1.92 for a 50 mile trip using solar power. 30 kwh required per trip 45 watts/panel 180$/panel
8 hours of sun a day
360 wh/day/panel
83.3 panels required
$15,000.00 cost of panels 13,036 miles driven a year 391,071 miles driven in a career(30 years)$0.038 $/mile over your career$1.92 cost of 50 mile trip

energy equivalent mpg at $4/gal: 104 mpg energy equivalent mpg at$5/gal: 130 mpg
energy equivalent mpg at $10/gal: 261 mpg assuming a lot of course Some time back, in another thread, I did a estimate comparing what it would take to move my car through a journey if it were powered electric, working it back through all the stages to the power station. Its not nearly as good as the varied research and approaches in this discussion, but I include the pointer here .. https://www.physicsforums.com/showpost.php?p=1509048&postcount=46" Last edited by a moderator: Some time back, in another thread, I did a estimate comparing what it would take to move my car through a journey if it were powered electric, working it back through all the stages to the power station. Its not nearly as good as the varied research and approaches in this discussion, but I include the pointer here .. https://www.physicsforums.com/showpost.php?p=1509048&postcount=46" 'Read your post, GTrax. Nicely done. There are three main concerns. 1) Fuel cost is primary. It drives the market, and for the most part determines future trend. 2) Fuel efficiency. Interesting to calculate, but does it matter except on how it drives fuel cost? 3) Pollution, which includes CO2 emmisions if we are to believe the hocky-puck graph of global temperature change. Last edited by a moderator: Thanks Phrak Re: the cost of fuel. Here (UK) it is £1.33 (ukp) per litre. That translates into$10.04 per U.S. gallon at today's exchange rate. It takes $160 to fill my car tank. It burns me up some to know that part of this is driven by those naughty blighters who speculated it up to there, and are going to make a pile later as they drive it down again while selling short. rant.. rant.. :| If every there was anyone looking hard to save on it, or seek alternatives, it is me. I find it interesting that the use of bio-fuels has increased hugely in the SA in a very short time. This may be a bit better than using ancient fossil fuel, but I think it just drives a food shortage. Thanks Phrak Re: the cost of fuel. Here (UK) it is £1.33 (ukp) per litre. That translates into$10.04 per U.S. gallon at today's exchange rate. It takes \$160 to fill my car tank. It burns me up some to know that part of this is driven by those naughty blighters who speculated it up to there, and are going to make a pile later as they drive it down again while selling short.

rant.. rant.. :| .

Yikes @ 10 bucks a gallon. Half those are taxes, aren't they? I hope you're right--about the market dropping out, that is.

If every there was anyone looking hard to save on it, or seek alternatives, it is me.

From my calculations, we should be seeing plug-in electrics merging into the market and supplanting the majority of gasoline powered private transportation within 15 years. (I hope I haven't bungled my calculations.) The fuel cost, in my estimation, will be about 30-40% that of gasoline at current prices. If I recall, England has a good deal of coal reserves. Good for fuel cost, bad for pollution.

I find it interesting that the use of bio-fuels has increased hugely in the SA in a very short time. This may be a bit better than using ancient fossil fuel, but I think it just drives a food shortage.

It's a rare person who can put the pieces together required to understand this energy issue: market forces, the most elementary thermodynamics, mechanical and electrical engineering, and some Newtonian mechanics. A little bit of each. You seem to have a good handle on a majority of it. None of the news media here made the connection, when this news was first circulating, that it could be dangerous ground to have food and methanol competing for the same food supply.

I stood at a busy intersection at rush hour, yesterday. This is an historical aberration that cannot last. Cheap and ready transportation is an incredibly luxury we take for granted. But I've wondered off the folder topic of classical physics, haven't I?

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RonL
Gold Member
Yikes @ 10 bucks a gallon. Half those are taxes, aren't they? I hope you're right--about the market dropping out, that is.

From my calculations, we should be seeing plug-in electrics merging into the market and supplanting the majority of gasoline powered private transportation within 15 years. (I hope I haven't bungled my calculations.) The fuel cost, in my estimation, will be about 30-40% that of gasoline at current prices. If I recall, England has a good deal of coal reserves. Good for fuel cost, bad for pollution.

It's a rare person who can put the pieces together required to understand this energy issue: market forces, the most elementary thermodynamics, mechanical and electrical engineering, and some Newtonian mechanics. A little bit of each. You seem to have a good handle on a majority of it. None of the news media here made the connection, when this news was first circulating, that it could be dangerous ground to have food and methanol competing for the same food supply.

I stood at a busy intersection at rush hour, yesterday. This is an historical aberration that cannot last. Cheap and ready transportation is an incredibly luxury we take for granted. But I've wondered off the folder topic of classical physics, haven't I?

It seems like the old saying, something like "Standing too close to a tree, keeps one from seeing the forest" might apply here(for the majority of the population). There might also be a little "war debt repayment" going on.

Ron

Oh boy - have I started to cause controversy? Still - you may have it all without bones or horns.
There now follows a little energy costs polemic. It leads back to to physics - I promise.
The tax fraction on UK fuel has an interesting history, and has at one stage reached an incredible 81.5%.
The present fraction is about 71.5% The mechanism is a fuel duty. Then, the total is re-taxed with VAT, which is a kind of 17.5% sales tax that has been allowed to morph beyond its original application concept.

As with several European countries, the stated aim is to "help the environment" by pricing cars off the road via taxes, which fortuitously also raise revenue for the governments. As to whether we actually need that much government is up for debate, but the treasury came to depend too much on the revenue raised from motorists and transport. A previous goverment introduced a "fuel escalator" where the price of fuel would automatically be raised by tax at 3% above inflation .. forever!
The arithmetic was inevitable, and the policy was abandoned in 1999. This is a place where physics fellas would say "what were they thinking?", but hardball fact does not drive these decisions. Things had to be media-managed a bit in 2000 when fuel truck drivers blockaded the refineries and depots. In the ensuing chaos, very few blamed the drivers. Universally, they blamed the goverments. For a while, the politicians in office felt real fear. I watched it happen.

Originally, using a diesel vehicle with 22:1 compression ratio, and using a fuel very much cheaper to produce than gasoline petroleum, delivered an efficiency advantage over the 12:1 petrol engines. you could go a lot further for the same spend. Arguing that diesel fuel was very polluting, the government increased the tax on diesel to "equalize" the price at the pumps. Now, it has gone further. Petrol is £1.24 per litre and diesel is £1.33 ( you work it out this time 1 US gallon = 3.785 litres). The result is that now, using diesel delivers a price payoff for a car only if you exceed 40,000 miles annually.

The UK is an oil-producing country. The present fuel crisis is not actually a crisis for the UK government. The tax could have been substantially reduced, without hurting the revenue take. But for all the hand wringing, there is no way they would do that. They want the windfall, and are able to cite "outside factors beyond their control" One irony is that modern diesel engines, aside from being a whole lot more efficient than petrol types, are now possibly also less polluting.

Of course, the scamsters will try to cash in on ignorance. . Like this ..
http://cgi.ebay.com/Water-Fuel-Cell...903673QQihZ015QQcategoryZ47103QQcmdZViewItem"

(OK - the link will maybe have a short life) but I had to persuade a friend that water is the very pits of the end of any fuel life. Its like ash! You have got to put in a whole lot of energy to tear that hydrogen back into engine-ready usefulness. We are driven to contemplate biofuel. There cannot be enough used fast food fryer oil to go around, even if we want to get up to a messy conversion process in the garage. What are we going to do? Oh yeah - we can turn whole chunks of the nation into gasahol precursor farms with the help of some genetically engineered plant that will survive the other products we dump on it to kill every other living thing. We can't sell that bio-diversity, so why do we need it? Hmm..

For me, the single greatest gain has come from just not using so much in the first place. My low tech woodburner can keep me through the worst of the winter, and is carbon neutral. A bicycle can replace some journeys. Even if the UK and all its energy use were to disappear instantly, we would offset just the increase in Chinese energy use less than a decade. Maybe only half that! We can all see the danger. We just cannot bring ourselves to give up the life. Clearly, the end result will not be equitable.

Back to physics? It just has to be fusion, if possible P+B11, but D-T via Lithium will do. We have just got to get that to work. Personal mobility need not be an electric car. It can burn Hydrogen, if the technology can make a safe way to deliver it. We can start reclaiming the stuff from the water! Optimism brothers.. it will even work in a big SUV!

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