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!
How much fuel is carried on an alinrape? I saw a movie once where an alinrape landed on a building and it did not burn up or the building fall down but with 911 alinrapes the building went down. Is there enough fuel in an alinrape for it to be use like a bomb? I really do not buy in to conspiratory theories. But I have been worring if it was more to it then this. So how much fuel is carried on a alinrape? And could this be real?
Posted by: Shoosh | August 6, 2012 at 11:12 PM
Cars have options of bio fuels and elteirccity.. Ships have nuclear options But what fuel option does an airplane have?We hear of airline fleets expanding and newer, better and bigger airports being built all the time, but is there an eternal source of jet fuel?
Posted by: Ilyas | August 7, 2012 at 12:06 AM