Thursday, September 15, 2011

Not quite 22 megawatts

Jonathan/Yoni's insightful post on Sunday highlighted a limitation of electric cars. He calculated that a gasoline pump transfers energy to your car at a rate of around 22 megawatts. According to Wolfram|Alpha, this is around 3667-7333 average households' power consumption, or just over half the total power output of the largest US photovoltaic power plant.

This would be amazing if cars utilized 100% of the thermal energy output of gasoline combustion. But, automobile engines (like all heat engines) can not operate at 100% efficiency. According to Wikipedia, car engines operate at 15-20% efficiency.[wiki quoted source] This means that before anything else is taken into consideration, it's an order of magnitude less useful energy transferred. Electric motors, on the other hand, have efficiencies which approach 100%![source] So, even if the rate of energy transfer to the car is slow, the real question is what is the effective (useful) power.

So, I've come up with what I think is a good measure for this, which incorporates all the losses of energy inherent in the system: How long does it take to load the energy into the car required to travel a particular distance. Or, what is the (miles per energy)*(energy transfer rate), alternatively [and equivalently] (miles traveled)/(car energy transfer time). This value has units of [distance]/[time] and can be expressed in miles/min or miles/hr (or kph, for our metric friends). This is a great way to compare all cars in terms of usefullness and efficiency using a familiar unit.

For example, our Ford Focus gets 40mpg on the highway.[source] So, it's "usefulness speed" is: (40 miles/gallon)*(10 gallons/min) = 400 miles/minute, which works out to 24,000mph! A Ferrari 599 GTB Fiorano "usefulness speed" is (15 mpg)*(10 gpm) = 150 miles/minute, or 9,000 mph [source]  The Prius, at 48mpg is 480 miles/minute, or 28,800 mph. [source]

The Nissan Leaf, with a range of 100 miles/charge and a greater than seven hour home charge time (under ideal circumstances), has a useful speed of 0.23 miles/minutes, which is only 14 miles/hour. That makes it 0.05% as useful as my car, and 0.16% as useful as a Ferarri!

So, instead of focusing on top speed when buying a car, you can focus on top usefullness speed! You can even go one step further and look at top usefullness speed/cost. And, I agree with Jonathan/Yoni's conclusions: Until batteries and their charging methods improve drastically, gasoline wins by a landslide.

Note: I was trying to do these calculations with the Chevy Volt, but it requires a few too many assumptions.
Also Note: If anyone wants to estimate what a bicycle's useful speed is, the comments are open!

1 comment:

  1. Re "a bicycle's useful speed," that depends... Are you eating soybeans or beef?