GetOffYourGas said:
Simplistically speaking, we drive our cars on the 2-dimensional surface of the earth. If the distance between chargers doubles, the number of chargers necessary to cover the same area decreases by a factor of 4.
On the other hand, for a driver on an infinitely long trip, you are driving in one dimension, and will need half as many chargers. Of course, the first charge is "free" since it is from home, so you do need slightly less than 1/2 the chargers.
This really isn't correct.
You might need to take only half the stops with double the battery, but you have to wait twice as long to charge. So, overall, the
time on chargers is not a function of the battery capacity but a function of the miles you do, and the limitation in a scenario where there is a large population of EV drivers is how many charging sessions you can get out of a charger in a day.
One driver with 2.N.kWh battery on an infinite trip would, numerically speaking, use a half of the chargers that another driver with N.kWh battery, but he'd be sitting on each for twice as long, so the total number of chargers that a large population of drivers need would be exactly the same, assuming the same mi/kWh, because the limitation is time-on-chargers not whether there is a charger there.
(And there has to be a large population of drivers else there is no point in putting up a charging network!)
So-many chargers have so-many charge-minutes per day between them, and whether a population of cars with small batteries use them in twice as many charge sessions as large battery cars, there are only so-many kWh they can put out in the day, and therefore only so-many EV miles.
But in fact carrying around an extra N.kWh would probably hit your mi/kWh figure, so it is possible that the folks with larger battery capacities might actually need MORE chargers, not less.
In practice they would need less because they can get further on their first 'leg' of the journey and that cuts out 'one charge', and such lengths of journeys occur more often than longer journeys. It is the elimination of 'the first charge' that is the main benefit. The whole calculation is dependent on some integer maths and how many miles the cars are actually expected to be used.
Put it another way. Say there are two chargers on a route and all these N.kWh cars are using them. All of the drivers move to 2.N.kWh cars and say between themselves 'hey, we have twice the capacity, we can get rid of one of the chargers'. Now you have all the drivers turning up to the one charge point instead of being split between the two, hence you will need to double the number of chargers at this, new, singular location. Outcome, yeah, half the number of charger
locations, but still the same number of chargers.
Your logic only works if you are going on the basis that the chargers will not be saturated in use, and that most people only need one charge between their origin and destination. That might well be true in a majority of cases, but there is nothing certain about it.