The size of the contiguous US is 3,000,000 square miles. Using the metric of 60 cars/15,000 sqmi as our break even point, as long as we plan on having more than 12000 electric cars in this country (WE ALREADY DO), CARPET BOMBING the entire nation in Level 3 chargers is just a NO BRAINER.

**Introduction:**

The results are in: if you love freedom, you hate infrastructure. Why spend money populating the earth with charging stations when you can simply demand the individuals pay for extra batteries in their cars?

This paper is an investigation into the economics of having public charging stations. By the end of this study, I will find out whether charging stations are a good alternative to having tons of batteries in a car, as well as the economies of scale break even point of car density where infrastructure becomes more cost effective than large battery cars.

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**Method:**

This study will compare 2 combinations:

- Lots of charging stations + 80 mile evs
- Fewer charging stations + 200 mile evs

Assumptions:

One public level 3 charging station costs up to $100,000 to install.

One 200 mile ev is $35,000. A 200 mile ev will have 140mi of safe range and require 1 station/15400sqmi

One 80 mile ev is $20,000. A 80 mile ev will have 44mi of safe range and require 1 station/1520sqmi

There must be at least 1 public charging station within the car’s safe range.

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Assumptions:

Level 3 charging stations cost is based on this article which states costs can range from $50k-100k:

http://cleantechnica.com/2014/05/03/ev-charging-station-infrastructure-costs/

the 200 mile ev is based on the Tesla Model 3’s expected price

the 80 mile ev is based on a reduction in price of low range evs when the Model 3 comes to market. The reason it is not proportionate is because while battery cost is variable, there is still the base cost of the car’s frame, body, equipment etc

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the method of determining the max area 1 service station can cover is as follows:

First the car’s straight line range (range * 80% – 20) is determined. The 80% is the usual fast charging goal, and 20 miles is an acceptable margin of safety to account for all the conditions.

Then, the straight line range is used in the circle equation of *A*=*πr*^{2} with (straight line range/2)=r to determine service area.

The service area can then be converted into square grid edges by being rooted.

So the process for 200mile ev is: 140mi range, 15393sqmi, 124mi grid

The process for 80 mile ev is: 44mi range, 1520sqmi, 39mi grid

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Since 15393/1520=10.13, therefore for the same given area, a 200mi car will require 9 less charging stations than an 80mi car.

The efficiency index I will use is cost-per-sqmi, calculated as (cost of all chargers in area + cost of all cars in area)/area.

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**Results:**

I constructed an excel spreadsheet to help with calculations, and the results of the $/sqmi are as follows:

Cars/15000sqmi | 1 | 10 | 25 | 40 | 50 | 60 | 70 | 80 | 90 | 1000 |

200mi cars | 9 | 30 | 65 | 100 | 123.33 | 146.67 | 170 | 193.33 | 216.67 | 2340 |

80mi cars | 68 | 80 | 100 | 120 | 133.33 | 146.67 | 160 | 173.33 | 186.67 | 1400 |

As you can see, when you have only 1 car per 15393sqmi/124mile grid, the 200mile EV will cost $9/sqmi while the 80mile EV will cost $68/sqmi. But more importantly, the break even point is a fairly low number of 60 cars, as in – as long as there are 60 80mile ev car owners per 15000 square miles, or rather, one 80mile ev owner per 250square miles, as in, one 80 mile ev owner for every 15 mile grid, the cost of chargers+cars equalize, as in: if the density of evs increase beyond that, the cost of installing extra chargers as an alternative to having super long range will be worth it.

Of course, the above calculation has the flaw that there really are only so many cars a charging station can service, so using a bare minimum amount of fast chargers may be underestimating.

Assuming on average every car charges 20 minutes per day and assuming you really want to keep utilization at around 25% or 6 hours so that people don’t have to wait too long to charge, that’s 3 cars per cumulative hour, and 18 cars per charger. Taking the increase of chargers to meet demand into account, I changed the bare minimum figure of 1 charger for 200mile cars and 10 chargers for 80 mile cars to a dynamic number of cars/18 which would be more appropriate in situations where the chargers are in constant demand. However, while this kept the cars per charger constant, the method is only accurate above 180 cars (producing the minimum of 10 chargers required for 80mi evs), so for under 180 cars the amount of chargers for 80mi evs is kept at 10, producing quite different results.

In the table below, the bracketed number next to all figures below 180 is the whole number of charging stations for 200mi cars.

Cars/15000sqmi | 37(2) | 47(3) | 54(3) | 90(5) | 135 | 180 | 200 | 500 | 1000 |

200mi cars | 100 | 129.67 | 146 | 243 | 365 | 486 | 540 | 1352 | 2703 |

80mi cars | 11 | 129.33 | 138 | 187 | 246.67 | 306 | 340 | 852 | 1703 |

As you can see, above 180 cars there is a proportionate, more or less linear relationship between 200mi cars and 80mi cars where 80mi cars are always 1.58x cheaper per sqmi as a whole.

In terms of cost to the owner, the numbers aren’t bad as well. At 60 cars, the bare minimum break-even point, the cost per car is at $36666.67. At 67 cars for the 80mi the cost per car drops to $34925. And at 200 cars 80mi evs for a 15000 sqmi area, the cost per car drops to $25000. 1000 cars = $21000/car. You can’t get that in a 200 mile EV.

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**Conclusion:**

The facts:

- If you only provide the bare minimum of charging stations, the break-even point in collective spending between 80 mile evs and 200 mile evs is to have 60 of the short range evs in a 15000 square mile area. For reference, the state of Maryland is 12406 square miles, to accumulate 60 nissan leafs there, or even an area of that size within in the state of fucking Wyoming or the middle of the desert, is not that difficult. If you have more than 60 electric cars in an area the size of Maryland, building charging stations simply makes more sense than adding batteries to cars.
- If you try to maintain a charger to vehicle ratio of 1/18 for frequently used chargers, the break-even point drops to 47 short range evs per 15000 square mile.
- If you try to maintain a proportionate charger-to-vehicle ratio, the cost per square mile will just become increasingly linear and directly in favor of 80 mile electric cars

Not only is the act of installing charging stations much cheaper to us collectively than tacking on an extra 120 miles of battery, but the break-even point is ultra-low as well: you only need to have 60 short range electric cars in a given Maryland-sized region for 10 charging stations to make more sense than buying 200mile evs in terms of the bare minimum of enabling an electric car owner to go anywhere within the network.

Now detractors can point out that hey, 200mile evs are a lot more convenient, you don’t have to stop as often. Now that’s true, but this paper is about cost.

At 75 mph, 180 miles takes 2.4 hours. Factor in a 40min/0.66hr of recharging, your average mph in a 200mile ev is** 59mph.**

At 75mph, 60 miles takes 0.8 hours. Factor in a 40 min/0.66 hr of recharging, your average mph in an 80 mile ev is **41mph.**

Now these road trip figures may seem slow, but its far from undoable and for penny pinchers on even a moderate budget, the cost savings of 80 mile EVs is extremely significant, especially those in the used car market where the cost is the difference between getting and not getting an EV, and many people would prefer an extra $10k in their pocket if that means their road trips are 50% longer while remaining 100% green.

And in your day-to-day travels that are shorter than 60 miles, all that extra battery, or a range extender is just dead weight.

Bottom line is the numbers don’t lie, and infrastructure is the obvious, overlooked answer to the manufactured question of battery chemistry and expensive range. Any cost issues with funding infrastructure are decidedly miniscule compared to the cost of 200 mi batteries, and I know that because for the numbers used in this paper, I did everything to skew the data in favor of 200mi evs aside from outright lying.

### The size of the contiguous US is 3,000,000 square miles. Using the metric of 60 cars/15000 sqmi as our break even point, as long as we plan on having more than 12000 electric cars in this country (WE ALREADY DO), CARPET BOMBING the entire nation in Level 3 chargers is just a NO BRAINER.

By building more level 3 (or equivalent) stations, electric cars can truly become **every person’s car** instead of exclusively being the tools of the brave, the rich, and the financially unsound.