Friday, February 13, 2009

Equating "fuel" efficiency between electric, hybrid, and gasoline vehicles

An earlier posting about Miles per gallon ratings with plug-in hybrid vehicles begs an interesting question. Just how does one measure "fuel efficiency" in a vehicle that runs on electricity and hence doesn't consume a fuel? The miles/gallon figure is what our society is accustomed to from over a hundred years of gasoline vehicle usage. An electric vehicle doesn't burn a fuel, it consumes electricity. Electricity has no weight and does not take up space in a container. Electricity is held in a battery but neither the size nor weight of the battery changes as the battery discharges. Yet a given battery can contain a given quantity of electricity, which determines the vehicle range and speed.

Electricity quantities are measured in kilowatt-hours. One watt is the electricity equal to one volt and one amp (watts = volts * amps). For example most handheld hair dryers use 750-1500 watts, and on a 120 volt circuit 750 watts requires 6.25 amps of current whereas 1500 watts requires 12.5 amps. Outside the U.S. where 220 volt circuits are more common the same 750 watt hair dryer requires 3.4 amps of current and at 1500 watts requires 6.8 amps. A kilowatt-hour is 1000 watts consumed over an hour of time. This is covered in more depth in: Overview of batteries and electric vehicles, Electrical Basics covering batteries in electric vehicles and Power Density in Batteries and Electric Vehicles

Why is this important? We are being asked to believe large miles/gallon efficiency claims for plug-in hybrid vehicles and we need to understand how to interpret those claims. If those claims are bogus then our society will have been fooled into a false solution to our transportation problems.

Miles/gallon to miles/kilowatt-hour are not directly comparable. My mind echo's with my high school science teachers yelling from across the room that you're comparing apples and oranges. What's going on is driving the vehicle down the road consumes energy. The different forms of energy are not directly comparable because one is gallons of gasoline, the other is kilowatt-hours of electricity, and the units are all different. In science class however the practice is to convert from one unit to another, leading my fellow classmates to convert all speeds to furlongs per fortnight. The U.S. Department of Energy has published a chart giving conversion factors and says that: Every fuel has different energy density. The most common way to measure how much petroleum is displaced through the use an alternative fuel is to convert the energy density of an alternative fuel unit to the energy density in a gasoline gallon. (Converting Alternative Fuel Units to Gasoline Gallon Equivalents (GGE))

Said chart shows one kilowatt-hour is convertible to .03 gallons of gasoline. Or 33.56 kilowatt-hours is convertible to 1 gallon of gasoline. Hence miles / 33.56 kilowatt-hours is equal to miles/gallon in this conversionary math system.

For example Tesla Motors publishes a chart showing Well-to-Wheel efficiency where they claim an energy efficiency of 177 W·h/mi. After a bit of calculation wikipedia converts this to 190 miles/gallon equivalent. Another interesting conversion is the cost per mile, assuming $.10 / kilowatt-hour to buy electricity, .177 kilowatt-hours consumed per mile is $.0177 per mile for the electricity.

I have a couple examples closer to home and more affordable than the Tesla Roadster (ahem). I talk of my electric motorcycle and electric bicycle. Last year I observed the electricity usage for my daily commute - 10 miles over very flat terrain in Silicon Valley. The motorcycle routinely consumed 3 kilowatt hours for the 10 mile trip while the bicycle routinely consumed 0.3 kilowatt hours for the same trip. Of course being a bicycle I pedaled to provide part of the power, meaning there is unmeasured energy input from my leg muscles, also meaning that it provided personal exercise benefits. In any case let's crunch these numbers a bit.

The motorcycle consumed 300 watt hours per mile (.3 kwh/mi), less efficient than the Tesla Roadster. However applying the same conversion derived by the wikipedia page, (1/300)*33705=112.35 meaning my motorcycle gives over 112 miles/gallon equivalent fuel efficiency.

The bicycle however consumed 30 watt hours per mile (.03 kwh/mi). Applying the same conversion, (1/30)*33705=1123.5, meaning my bicycle gives over 1120 miles per gallon fuel efficiency.

Getting back to my high school science teacher and apples and oranges. Saying my bicycle gets 1120 miles / gallon can be misleading, since it doesn't burn gasoline. Or putting it another way, to say a Tesla Roadster gets 190 miles/gallon fuel efficiency may keep the mind focused on improving miles/gallon and lead one to continue looking for high miles/gallon efficiency.

The problem here is not to achieve the most efficient burning of gasoline, instead the problem here is our need to transport our butts around town. The chosen popular transportation technology requires liquid fuels which are due to become in short supply soon, leaving us potentially unable to transport our butts around town. If we look at the problem purely through the lens of miles/gallon efficiency of burning gasoline, we remain stuck in the mindset of burning gasoline to solve the problem of transporting our butts around town. We need to focus on the energy efficiency of different forms of transportation, and we need to remain unattached to specific solutions of the need to transport our butts around town. This mathematical conversion technique simply helps us compare energy efficiency across different units of measurement.

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