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!

Comments

[Tom G.]

This is really well written and should be required reading for every high school student and their parents. It sure would be nice if some of the automotive designers also read it and we started paying more attention to Coefficient of Drag and the weight of vehicles. I am so sick of driving a box on 4 wheels. When will we ever get cars that meet the needs of the urban driver. Cars like the Aptera or MIT city car.

At my current electric rate of .11 cents per kW that means that it would cost me a measly $1.56 for every hour [60 miles] I drove in my all electric vehicle [.11/kW X 14.2]. Of course that assumes I have an electric car which of course I don't.

[resume writing services]

Useful tests. But in 20 years all oil and gas vehicles will be too old and out of date. alternative sources of energy is thing of the future.

[Peter Munro]

Great Description.

I have been looking for some real numbers. I have a KurbWatt. I have been trying to figure out how large a range extender generator I need.

This might be realistic
4 kw might power 25 mph
8 kw might power 40 mph
12 kw might power 50 mph
16 kw might power 60 mph

The VW Jetta diesel might be the max.

My question is why are small diesel engines not very efficient?

[Affordable Insurance]

The numbers might even become more convincingly in favor of the EVs when we arrive at being able to figure in clean renewable energy as an alternative to coal, for example. Thanks again for the numbers. As an engineer, I appreciate that.

[Projector Headlights]

In all sense the calculator is right, for which it is the ideal value. But what we can't control are the resistances that apply to our car when we drive it, practical value.

[Man with the Plan]

200 MPG is good but if you get rid of the combustion engine and put in a motor concisting of really strong magnets for the power source(free energy)with a generator to create electricity to drive electric motors. You would never need gas or have to plug your car in to charge it.

[Silvio]

There are several thnigs you can do to improve your gas situation. You can make sure your tires are always filled properly. Staying off the lead foot goes along way to stretching out that tank of gas for a few more days. Let your torque do the accelerating for you, not the horsepower. I drive a V6, and as long I keep the RPMs between 2000-2500 it gives me a smooth and steady accelration without gunning the engine. (besides, if your town is anything like mine you only speed up to stop at the red light 200 feet away ). And you might also try running your car on 3/4 or 1/2 tank of gas. Especially if you live in LA, (or some equally stop go city) all the extra weight of a full tank can make your engine work that much harder, while using up a little extra gas. (It won't double your mileage, but in times of higher gas prices and empty wallets, the little thnigs can add up.) Oh, and I almost forgot, a good, clean air fliter also helps a bunch. Hope this is of some help to you.

[Manas]

compared to what? the old engine it had? prblaoby not, especially if they used the old external components like the spark plugs, filters and wires. The only time you might notice a tiny significance is when you do a tune-up which is when you replace old spark plugs, engine oil and filters with new ones and transmission oil (change time varies from car to car). Also proper air in the tires helps and not having a ton of extra weight inside the vehicle as well. What also helps is cleaning the fuel injectors with a cleaner every six months.

[Serhat]

Steve,I guess I'm one of those eco-fanatics you complain about. We've only got one plaent earth and if we foul it sufficiently life will get a lot tougher real soon. It seems that the market place, i.e., the price of gas and diesel is only one of the factors that can spur positive change and innovation. Sometimes government, we the people, in order to care for the commons , need to make some behavior illegal, like black and white restrooms or housing or sexual preference discrimination.

[Serhat]

Steve,I guess I'm one of those eco-fanatics you complain about. We've only got one plaent earth and if we foul it sufficiently life will get a lot tougher real soon. It seems that the market place, i.e., the price of gas and diesel is only one of the factors that can spur positive change and innovation. Sometimes government, we the people, in order to care for the commons , need to make some behavior illegal, like black and white restrooms or housing or sexual preference discrimination.

[Andrew]

Yes, it's crazy we don't have diesel here. Too bad the 5 seires has such mediocre safety rating. There is a diesel in all the great safe cars Audi A4, A6, etc. But not in the USA. Very, very strange. And how about let's say a Cadillac CTS diesel, or a Ford Taurus? Lots of duh going on here.

[Nikhil]

fluffy:Death be to the Intrigue!!30 mpg with 3.5 litre engnie = 10535 mpg with 2.2 litre engnie = 77Above numbers represent displacement efficiency score , a measure created by ME to demonstrate the fuel efficiency of a vehicle regardless of engnie size.Chevy Cobalt would have to get 47.73 mpg to equal displacement efficiency score of Oldsmobile Intrigue.Death be to the Intrigue!!

[Yuichi]

trombass08April 28, 2010 I think the 230 mpg is a conservative estitame. Seriously, if you only drive 40 miles or less a day, you could practically eliminate gas consumption for your car. That tank of gas that's used after you finish your 40 miles could sit in there for years.

[Kiara]

in the United States (especially eco-fanatic California) emissions rolegatiuns are about political posturing. Steve- if it wasn't for those eco-fanatics' back in the 60 s, the Clean Air Act might never have passed, and you'd be looking at skylines in the US similar through air like that choking the athletes in Beijing this summer.

[Elie]

That's insane!! When my Lumina got nalied there was way more damage on the front end and it was only 1300 that their insurence paid. Speaking of... have you foung out anything on cell phone chicks insurence?

[Susy]

system streamlines the chgnairg of electric vehicles and extended-range hybrids by eliminating the nuisance of the cord and the plug. For those that have been hesitant to purchase

[Kalpesh]

Sorry if this answer is too long but its the only way to dsircebe it My guess is that when things start to get tight there will be two options for aircraft and they will utilize both First is ethanol farm high sugar content crops ferment them to convert to ethanol a few additives and you've got some pretty good avgas. (Of course biofuel could work good for jet fuel too!)Second is solar energy planes that have demonstrated this have been light in weight, with the majority of their weight actually being solar cells Also because the cells are rigid and straight the wings on the plane were more rigid on top. They didn't have that nice curve that generates the most lift. Solar companies are now developing solar cells that weigh up to 10 times less then their silicon predecessors, and they are flexible! These new cells have been demonstrated to work but are still in the development stage. Also the efficiency of solar cells in general is on the rise meaning they can pull more energy out of the sun. By the time were running out of fossil fuels this technology will be much cheaper and powerful.So you'll end up with a kind of hybrid plane, covered in cheap solar cells that flex to fit the streamline shape of the plane. For take off (when the most power is needed) it will use ethanol for fuel to power the engine, (by then our engines will be very efficient too!) and then after your above the clouds and in cruise the solar takes over, providing free unlimited energy to keep the plane aloft. Imagine the endurance on that plane! You could stay up there indefinitely!

[Bobby]

There are currently 6 jeeps in the line up. Two are crovsoser that are not technically Jeeps but re branded Mitsubishi's (compass and patriot). They get great gas mileage (up wards of 30mpg highway). However they do poorly offroad since they are actually cars that resemble an SUVs, conversely they are excellent on road. Those two are the only ones that come with a 4 cylinder engines and before that only the wrangler, liberty and cherokee had them and they weren't that much better than the six cylinder when it comes to gas mileage (low 20's) added to that they were extremely underpowered. Jeeps or any real offroad vehicle are not good with gas mileage and you should not expect it to be otherwise since offroad ability and gas mileage are exclusive to one another.

[Said]

Yes what a milestone our car maeufacturnrs have reached. I saw a commercial a week or so ago where GM was hailing a new era of cars with good MPG. They claimed they had like 19 cars that get over 20MPGs.1) how many of them are actually from foreign companies GM bought?2) how many total cars do they make? Like 100. So 19% of their cars get over 20MPGs?3) Didn't we have cars that get over 30MPGs 50 years ago? How is this some huge big thing to celebrate?

[Caro]

I thought it was. Stuff like this is only pslsiboe because we can make engines that think now. Of course, they only think about combustion, but still that's pretty cool. Friend of mine is a diesel mechanic. His nickname is Diesel Dick . And that is the name of his shop.

[Travis]

Here's your proof. Before the car is turned on the only engrey in the system is in the gas and in the battery. Fill up does not provide ANY ENERGY to the system. The scammer in the video drives with better power (maybe) because the battery is making hydrogen. The battery is therefore tired, and must be replenished by the charging system, that draws power from the engine, that runs on GAS. Making HHO is not perfectly well-organized. They only get about 70% of the engrey it takes to make it back.

[Lagrimas]

The injectors need to be aehacttd. The fuel pressure alone is enough to shoot the injectors out of the fuel rail at least 40psi, many of the modern return-less systems have a base fuel pressure of 58psi.There are a few ways this can be accomplished, but in all applications the fuel rail(s) must be bolted down.A majority of the manifolds have a tapered bore that the business end of the injector sets in, it gets smaller going into the manifold like this: \ / . Others have a straight bore with a stop at the end like this I_ _I . There are a few applications that have a straight bore through to the inside of the manifold, this style needs clips that hold the injector to the rail and the injectors have a pintle cap designed to hold the lower o-ring/seal on the injector.

[Nemanja]

I have a 90 GMC suburban. That rtnlceey broke down. Engine shut off and would not start. Fuel pump is working fine, fuel filter etc. Throttle linkage is also fine. My guess is something electronic, maybe a safety feature is causing the fuel injectors not to release fuel. All fuses have been checked.Any ideas for things to check? It is an electronic fuel injected throttle body.

[Desal]

These will all help but some are more practical than otrehs1.Maintain constant speed, avoid accelerating and braking 2.Slipstream another vehicle 3.Have your engine service to ensure you are running rich (greater fuel air ratio than required) 4.Close windows 5.AirCon off 6.Correct Tyre pressure 7.Remove excess weight, spare type, passenger seats 8.On downhill sections, press the clutch down to coast. 9.Although this is not great for the clutch if are running on fumes and it's still a few miles to the petrol station, it helps 10.If you're trying to go as far as possible on a single tank, fill up in the morning when it's colder. Fuel is denser when it's colder so you can fit more in. 11.have your ECU reprogrammed. Manufacturers program them to get a balance of performance and economy. In the same way you can get them remapped for performance, you can have them remapped to improve economy.

[Mata]

Make sure you get the lubricants chagned after a fixed time period, keep your car tuned and drive at low speed in high gears if it is manual. I mean change gears quickly instead of reving it up in every gear. Lastly make sure your injector nosels are clean as a whistle, deposits can lead to poor fuel economy. Cheers.