The Energy Blog

A 200 Mile Per Gallon car? The physics of MPG.

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The internet, as well as the local coffee shop, is full of claims of super secret gadgets that will make your car get 200mpg, or 300. The story is always that the only reason we don’t have these fantastic high mileage cars is that “Big Oil” has somehow managed to suppress every single company who has ever tried to make one, or has “bought out” every device that could magically do this to your car.  Well, All of them except for ONE - the person peddling it.

Well, As I have said many times on this blog (and in the coffee shop)  for any particular vehicle it takes a fixed, quantifiable amount of energy to push it around. This is based on the most basic laws of physics, the same laws that give us airplanes, microwave ovens, and, yes, the automobile. So, I’m gonna do it again.

Yes, once more, we will look at how much energy it takes to move your vehicle.  Our purpose will be to define the maximum MPG.

A vehicle will achieve the best MPG or energy efficiency traveling at a steady speed on level ground. In that condition, the only energy it needs is what is required to overcome aerodynamic drag and rolling resistance (friction).

Our test subject for this week will be My Late Model Chevy Malibu, a mid-sized four passenger sedan. It weighs 3,460 pounds, has a frontal area of 24.1 square feet, and a Coefficient of Drag of .37,  Totally Mainstream. To simplify the math, I didn’t do any. I used this calculator: http://ecomodder.com/forum/tool-aero-rolling-resistance.php.

Here is a summary of the results. Remember this is for a steady speed!

Speed	Horsepower	Watts	BTU/min
35 mph	6.15	4586	261
40 mph	7.94	5920	337
50 mph	12.64	9425	536
55 mph	15.66	11677	664
60 mph	19.17	14295	813
65 mph	23.23	17322	985
70 mph	27.87	20782	1182
80 mph	39.12	29171	1660

Before we continue, look at that chart closely. Note how the power required goes up rapidly? Aerodynamic drag is the largest force opposing your movement at any reasonable speed. That drag increases with the square of the speed. Doubling the speed creates four times as much drag. But, interestingly, power requirements increase at the cube of the speed. So that doubled speed will take eight times as much power.

You will also note, I have not mentioned MPG in that chart. It is irrelevant so far.  This chart is the amount of power the vehicle needs. It does not matter whether that power comes from a Gasoline or Diesel engine, an electric motor, compressed air, rubber bands or a hamster wheel.  The amount of force it needs to keep moving is the same.

Also, before we look at MPG, which implies liquid fuels, lets look at the chart and apply it to an electric car. Now it turns out an electric motor is very efficient, turning about 95% of the electricity fed into it into mechanical power. If you look at the 60 MPH row, you will find maintaining that speed requires 14,295 watts of power. To quantify that as energy consumed, or work, we have to add a time element. So, at 60 MPH over the course of an hour, we will go 60 Miles – duh. In that hour we will consume 14,295 Watt Hours of electricity, or 14.2 Kilowatt-hours (kWh). That works out to .236 kWh per Mile. In an amazing coincidence, this is the same as is claimed for the Chevy Volt in electric mode. The Chevy Volt, is indeed, nearly Identical in size to the Malibu.  The Tesla Roadster with a smaller frontal area, and slight better Cd, claims .217 kWh per mile in mixed driving where it’s lower weight is also a factor.

OK, Finally, lets talk about MPG. The calculator I used will give you a MPG figure for each speed based upon the efficiency of the engine and drivetrain. Putting 100% efficiency in it will yield you your 200mpg at 45 mph. (Try it!). At 60 mph, you will get 140 mpg. How did we do that? Well, there are 114,000 BTU’s in a gallon of gasoline, and we are using 813 of them per mile (minute). That is 140mpg with a perfect engine at 60 mph. Right here, we know that a 200 mpg car is impossible at any speed over 45 mph. Even if it were perfect.

Well, sad to say, nothing is perfect. Certainly not your car’s engine.

The Second law of Thermodynamics puts an upper limit on the efficiency of a heat engine. This is known as the Carnot efficiency. A modern fuel injected, steel, Otto cycle, internal combustion engine – the one in your car, can achieve a range of efficiencies from about 15% at idle, to 35% at it’s torque peak and with a wide open throttle. A diesel will achieve the upper end of that range most of the time. What that means, is in the best case, only 35% of the BTU’s in that gallon of gas are being converted to mechanical energy. The rest is wasted as heat out your radiator and exhaust pipe.

The maximum possible Highway MPG my Chevy Malibu can achieve without violating the laws of thermodynamics is thus about 49 MPG at 60 MPH. The only way to improve this number, is to improve the aerodynamics, reduce the frontal area, reduce the rolling resistance, go much slower, or only drive downhill. The Toyota Prius is currently the highest mileage car in the US with a Highway MPG of 48. It achieves this primarily by having a Coefficient of drag of .25, and an estimated engine efficiency of 30% at 65 mph. Try putting these numbers in the calculator and then changing them. Getting the picture?

But, wait, it’s a hybrid. Isn’t that why?

Well, I’m glad you asked. Remember we are talking steady speed. The Hybrid function recovers energy lost through braking. That energy recovered was only the energy we used to accelerate the vehicle. At a steady speed, the hybrid has no advantage over a non-hybrid.  In fact, you will notice the city mileage (stop and go) is actually higher at 51mpg. That is where the Hybrid does it’s work recovering energy.

And, that brings us to our last topic for now – acceleration. My Malibu weighs 3,460 pounds Every time we accelerate that mass to 65 mph it uses approximately 650 BTU’s of energy to do so. Per the laws of physics, that energy is then stored in the mass of the car as kinetic energy until we decelerate (slow down). When we apply the brakes, we convert that kinetic energy to heat which is then lost to the air. This is why stop and go driving normally has much lower MPG numbers.

My Malibu achieves a real world highway mileage of 26 MPG. That means we use a total of 4,384 BTU’s for each mile driven (Remember 75% - 3288 BTUs - are wasted). If we accelerate twice each mile to 65 (using an additional 1300 BTUs), then stop, that consumption will rise to 5,684 BTU’s per mile. Doing the math again puts our resulting mileage at 20 MPG.

I hope I have shed some light on this topic, and on the impossibility of some of the snake oil. While there are various other factors that will change these results in the real world – air temperature, hills, tires, road surface, and specific engine configuration to name just a few, they will not vary by much. And the results for the “perfect” engine will still set a maximum limit on what is achievable.

Ain’t science wonderful!

US Energy consumption.

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I was trying to follow a lecture about energy needs the other day, and make sense of the speaker's numbers. I know most energy statistics, but his numbers were not adding up. I started wishing I had an energy "crib sheet" with simply the big numbers to help me understand. So, I made one. Here it is. This is the amount of energy the US used in October of 2009. I did not make any correlations between units or types, these are the raw figures. Here is this country's overall energy use:

U.S. Energy use for the month of October 2009.

Type of energy	Trillions of BTU's	Millions of Megawatt Hours	Amount
Electricity	1,200	351	Not Applicable
Natural Gas	1,800	527	1.8 Trillion Cubic Feet
Gasoline	1,364	399	11 Billion Gallons
Diesel Fuel	700	205	6.2 Billion Gallons
Totals	5,064	1,482

 (The amount column is the amount of the fossil fuel we used. Electricity is generated by various means. It is an energy carrier, not a fuel.)

Those are BIG numbers. To clarify the units, the totals equal:

5,064,000,000,000,000 BTUs. and 1,482,000,000,000 Kilowatt hours.

If that were YOUR electric bill for October, at ten cents per kWh, the amount due would be: $148,200,000,000.00! That is 148 Billion dollars. Your electric rate may vary.

According to the EIA, on a BTU Basis, the US uses 21% of the worlds energy. So, multiply those numbers by five and you know (roughly) how much the world uses.

One final note on electrical generation.

This country has slightly more than 1,000,000 megawatts (1,000 GigaWatts) of nameplate generation capacity installed. Of that total, about 550,000 megawatts is available at any one time. The rest is down for maintenance, repairs or other factors. There are 720 hours in a month. So we can actually generate about 396 Million Megawatt Hours each month.

Watts, joules & BTUs - What energy terms mean and why.

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Watts, BTUs, joules – oh my. It is easy to get confused with all the different acronyms, and units, being bandied about. Well, In a spirit of pure public service, I am going to try to explain what the different energy terms mean. Hey, I said try…

Although this is not meant to be a first year physics text (there would be much more “between the lines”), before we can understand the units, we must somewhat understand the concepts of work, and force. And how the two are inter-related. We also have to understand what energy is.

Energy:

While energy can be an abstract concept, in our particular context energy means the potential (or ability) to do work. Work is what shifts energy from one system to another. Energy can exist in two general forms potential (stored) or kinetic (in motion). Gasoline contains potential energy. It is just “sitting there” taking up space. Once that energy is shifted to the mass of your car, by doing work – acceleration - the mass of your car then contains energy in the form of kinetic energy. It will contain exactly the amount of energy that was transferred to it.

“It is important to realize that in physics today, we have no knowledge what energy is. We do not have a picture that energy comes in little blobs of a definite amount. — Richard Feynman”

• So, Energy is the ability to do work.

Work:

Now, work seems a simple concept, and it is, sort of. Work, in physics, is of course mechanical work, The moving of something over a distance. If you push your car up the driveway, it is obvious you have done work. Obviously! You have done that work by transferring your bodies’ potential energy into the mass of the car, accelerating the car up the driveway.

But, Interestingly, if you push and push, and the car does not move, according to the laws of physics, you have not done any work. Your energy was expended as waste heat and was not transferred to the car. Physics demands that something be moved for work to happen. Hence no work. Unfair, I know, but that’s the way it is.

You have, however, transferred energy from one system (you) to another (the air) via heat. Well, in thermodynamics, there is another, broader, definition of work. Work can also be defined as the transfer of energy from one system to another. Both definitions are important to the understanding of the terms below.

So work is either the movement of a mass (stuff) over a distance in physics, or, the transfer of energy from one system to another in thermodynamics. The distinction is that in Physics we are dealing with the transfer of energy by mechanical means. In Thermodynamics, energy is transferred, not mechanically, but via heat.
At the risk of being overly simplistic, these are two of the four primary ways that energy is transferred. The other two are electromagnetic waves and gravity. Note there are many defined FORMS of energy – as I stated, energy as a concept is elusive – but it is transferred between systems mainly in these four ways.

But, back to work:

• Work is the movement of a mass over distance, or the transfer of energy from one system to another.

Force:

Force is the influence (or applied energy) that causes work to be performed. When a force acts to move an object, we say that work was done on the object by the force. That force can be electricity, and the object a motor shaft. The force can be chemical energy, and the object a piston or turbine. The force can be gravity, and the object a skydiver falling out of an airplane. Force when applied to a mass (thing) to cause a displacement over a period of time is causing work to be done. In physics, force is mass times acceleration. (F=ma).

• So, force is an influence that causes an object to speed up or slow down (i.e. accelerate or decelerate), or that causes work to be performed.

Power:

And, finally, there’s power. Power is a measurement of how fast that object is speeding up or slowing down, or how fast energy is being transferred between systems. In other words, how much work is being done?  As we all know, the more power we have, the faster the work is done.  Conversely, the faster a certain amount of work is done, the more power is required, and the more power has been used. Power equals work divided by time (P=W/T). Power is an aggregate of all the former terms. It is the measurement of the final result, so to speak, of using energy to apply a force to do work.

• So, if work is defined as moving (accelerating or decelerating)  something, then force is what causes it to happen. Energy is the push behind the force, and power measures how much work has been done.

But, you came here to learn about the units we measure this stuff with, right? Well, if you are still here, we are about done!

“For those who want some proof that physicists are human, the proof is in the idiocy of all the different units which they use for measuring energy. — Richard Feynman.”

We measure the quantity of energy (or force) with the units Kilowatt hour, BTU, or Joule. These are all measurements of “units of energy”.  Conversely, the same units can be used to measure how much energy a process has used. We used so many BTU’s of fuel, so many Kilowatt-hours of electricity, or so many Joules of energy. If energy were water, the equivalent unit would be the gallon.

There are 1055 Joules in a BTU, and there are 3414 BTU’s in a Kilowatt-Hour.

We measure the amount of work that is done with units of power. The Horsepower, the Watt, or the BTU per hour (BTU/Hr). In our water example, these would be equivalent to Gallons Per Hour.

A horsepower is a unit of power sufficient to raise 550 pounds One foot in 1 second. Equivalent to roughly 745.7 Watts, or 2,546.6 BTU/Hr.

There you go! So much background. Well, the concepts I briefly explained (and it was brief) before defining those terms, are extremely important to all fields of energy. They are the foundation principles. The above explanation only scratched the surface.

I will finish this up with a couple of examples.

First with water. The garden needs to be watered with a gallon of water every hour (big garden). This is the amount of energy (water) we need. SO we will be doing work at the rate of one gallon per hour. At the end of ten hours we will have used ten gallons (units) of our energy.

Now lets make the garden a 100-watt light bulb. We need 100 watts of energy every hour to light our room. So we will be doing work at the rate of 100 watts of electrical energy every hour. At the end of ten hours we will have consumed 1 Kilowatt hour (1 unit) of electrical energy.

Our Furnace needs 50,000 BTUs of energy every hour to keep our toes toasty. So we will be doing work at the rate of 50,000 BTUs per hour. At the end of ten hours, we will have consumed 500,000 BTU’s (units) of energy.

Our car needs two gallons of gas (248,000 BTUs) every hour to go a steady sixty MPH. So, we are doing work at the rate of 248,000 BTUs per hour. At the end of ten hours, we will have consumed 2,480,000 BTUs (units) of energy. Of course we ran out of gas 6 hours ago…

I am going to elaborate on that last example, lest you think this is all academic. Simple math tells us that car is getting 30 MPG on the highway. So, how much horsepower did we need from the engine? Well, if you have been attentive, you would realize you divide that 248,000 BTUs by the amount of BTUs in one horsepower and get 97 Horsepower. Right? Well, sort of, but wrong.  In the average gasoline internal combustion engined car, 75% of those BTUs were wasted, they did not make any horsepower. The went out the tailpipe, and kept your radiator warm. SO, the correct way to do it is to take 25% of those BTUs, 62,000 (which is what was actually used to make Power), and divide by 2,546.6.  Which gives us 24 Horsepower. And, that indeed, as a rule of thumb, is what the average 30 mpg car needs to go down the road at 60 MPH.

And, now you know.

Our Natural Gas supply – The numbers game.

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It does not take long to realize that there are more varied predictions on how much Natural Gas this country has, than there are flavors in your local store’s Ice Cream freezer. And, unlike that Ice-Cream, many of the natural gas numbers leave a sour taste in the mouth. Which numbers are correct, which are biased towards an agenda, and which are just plain old pie in the sky – (a-la-mode)?

Now, I am not a geologist so I cannot offer my own independent conclusions, although that does not seem to inhibit many others. What I can do, is to look at those numbers, compare them, and attempt to derive some sensible compromises based on reality, technical awareness, and just plain common sense.

First, lets look at the numbers reported by what are considered by most to be credible and reliable sources. Unlike some, these sources also have facts and figures to back up their analysis.

The United States Geological Survey in their latest report ( Dec 2008) says we have 742 Trillion cubic feet of proved conventional reserves, 378 Trillion Cubic feet of Unproved reserves, and  743 Trillion Cubic Feet of technically recoverable Unconventional resources (Shale and tight gas).
Ref: http://certmapper.cr.usgs.gov/data/noga00/natl/tabular/2008/summary_08.pdf

The Energy Information Administration in Jan 2007 puts US total recoverable conventional reserves at 211 proved  and 373 unproved,  and technically recoverable unconventional reserves (Proved and unproved)  at 1,366 Trillion Cubic feet.  Ref: http://www.eia.doe.gov/oiaf/aeo/assumption/pdf/oil_gas.pdf

Already we have some serious disagreement, although both sources agree on Unproved Conventional gas. The difference in the unconventional reserves likely centers around the definition of  “Technically recoverable”.

The big difference comes in the proven reserves. For some reason the EIA comes up with a very low figure for this, (I did the math 3 times).  Yet, both sources add up to roughly the same total of 1,800 Trillion Cubic feet of reserves.

Now, lets turn to the Natural Gas Association. First of all, they agree with me that there is a wide disparity in these assessments. I feel so good!  They base their own assessment on EIA data as above with total proven reserves at 211 Trillion Cubic Feet, and a total of  1,536 Trillion Cubic feet of unproven reserves.

http://www.naturalgas.org/overview/resources.asp (Very useful page!).

OK. The above references, ignoring what they consider to be technically recoverable, all predicate that we have a total of about 1,800 Trillion Cubic Feet of Natural gas reserves in the  US. Now, I could fill a few pages with references to other reports that “grow” this estimate in leaps and bounds. It all culminated for me in a purported report from JP Morgan Chase that our reserves are NOW 8,000 Trillion Cubic Feet. I have not been able to find the actual report, only references to it. It does strike me that  many of these inflated numbers are coming, not from geologists, or even energy companies, but  from institutions with a financial stake in the trading of Natural Gas. Hmmmm.

I would like to point out also, that there is wide disparity on how much of that gas can be recovered. Certainly not all. According to the Natural Gas association, about 10% of the unconventional. Many sources put it closer to 30 percent. So far shale gas production in the Barnett shale has not lived up to expectations, and they are recovering about maybe 35% of what they thought they would. http://www.aspousa.org/index.php/2009/08/lessons-from-the-barnett-shale-suggest-caution-in-other-shale-plays/

One final issue I would like to address. A common talking point is how many years this supply of Natural Gas will last us. First some baseline numbers. We used 22 Trillion Cubic Feet of Natural Gas last year. That is 1.8 TCF per month, or 60 Billion Cubic Feet a Day!  In the same month we will use about 11 Billion gallons of gasoline,  5 billion gallons of diesel fuel and 342 Million-Megawatt hours of electricity.

Well, if we change nothing, and manage to recover all 1,800 TCF of our natural gas, we are good for 81 years. If we manage to only recover  35%, then about  28 years worth.

But, what if we try to replace our gasoline use with natural gas? That 11 Billion Gallons of gasoline a month is about 1,364 trillion BTUs. Equivalent to 1.3 trillion Cubic Feet of Natural Gas, increasing our consumption by 72%.  If we add in the diesel, that would equal  .65 Trillion more Cubic feet. So replacing our transportation fuel would more than double our consumption of Natural Gas, and reduce our remaining supply to 14 or 40 years, depending on your optimism level. http://www.theoildrum.com/node/5615.

Let’s replace electricity from coal instead. Coal supplies 48% of our electricity, or  164 Million-Megawatt hours a month. Each one has 3.414 BTUs of energy. So, that is 560 Trillion BTU’s. (I checked the decimal point). It would require .6 trillion Cubic Feet of Natural gas to replace our coal. About a 33% increase, assuming the power plant  efficiency is the same – it is close. That would make our natural gas last anywhere from 19 years to 54 years, again depending on how much natural gas we can actually recover.

Finally, I would recommend reading this report on The Oil Drum. It addresses some of these points, and also makes the point that the whole natural gas reserves picture is steeped in unfounded numbers and hype.

http://www.theoildrum.com/node/5676

As for me, I think I will have some Ice Cream.