## Numbers: Electric Car Energy

It is hard to get decent numbers from electric car enthusiasts. Maybe this is a problem in transferring from gallons of gasoline to a proper energy measure. Maybe something else. David Nolan does put up some numbers in his item on Life With Tesla Model S: Battery Degradation Update. Culling the piece, here are some of the tidbits:

after a 210-mile trip, the car’s data readout told me I had used 63.5 kilowatt-hours and 93 percent of my battery capacity

Those numbers implied a 100-percent capacity of only 68.3 kWh—6 percent below the 72 kWh I’d measured just three months previously

The apparent 68-kWh capacity was 12 percent less than the nominal 76 kWh that Tesla guru Nick J. Howe estimates as the usable capacity of a brand new 85-kWh battery

A study last year of Model S batteries in the Netherlands showed an average capacity loss of 6 percent after 50,000 miles

A 2014 study of the Nissan Leaf showed a three-percent range loss after 40,000 miles in Leafs that used 50-kW DC fast charging compared to those using the standard 6.6-kW AC charge rate.

Now figure that a gallon of gas is [carstuff] 33.7 kWh and you realize that the Tesla energy storage is about the same as a two gallon gas tank. The 210 mile trip used the equivalent of 2 gallons of gas or 105 mpg. A gas based car like this might get 40 mpg on such a trip so the ‘burn efficiency’ of the electric is about three times that of the gas. This makes sense as electric motors are much more efficient than thermal motors. As wikipedia notes, the gas engine efficiency is around 25% to 30% (which is why you need a radiator and a good cooling system). Toolbox lists electric motor efficiency in the 80% to 90% range. So a 3:1 efficiency difference sounds about right. What this efficiency measure does not take into account, though, is the losses in the battery and control systems. A better measure would be to look at how much electricity was used to charge the battery versus miles driven rather than just look at the electricity used by the drive motors.

The other item of interest in the piece is battery degradation over time. Lead acid batteries are generally expected to loose about 20% of their capacity over 5 to 7 years. A lithium battery might last a bit longer than this but 6% in three months seems a bit heavy. Even being an optimist, consider the cost of replacing a 80 kWh lithium battery every ten years.

Finally, think about the charging station. Do you have any 7 kW appliances in your home? That’s 30 amps at 240 volts. An electric range or clothes drier might have such a circuit. An 80 kWh battery is going to need 10 hours or more of that circuit to charge. At typical electric rates, that \$1/hour and you better make sure that your wiring is up to snuff and all the connections tight. So it’s about \$10 to do the equivalent of filling a 2 gallon gas tank that delivers the equivalent of about 5 or 6  gallons of gas.