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Charging in the Electric Robocar World
I've suggested that robocars enable the electric car by solving the battery problem. People today demand long range from their cars, and that requires a large, expensive and often heavy battery pack. They also are bothered by the idea that once an electric car runs out its range, it must sit for hours charging before you can use it. They are scared of losing the effectively "infinite" range of a gasoline car that just refuels at a gas station in 5 minutes.
The first step to enabling the electric car through robocars is to realize that when taking most robocar trips, you will know in advance how far you're going. If you are taking a series of trips you will specify that. You can then be sent a robocar that has enough range to make that trip. You don't care that after it's done it will have to limp off to a charging station for 4 hours. That's not your problem. Even if it's your car.
If you do need a car again soon, and your car is low on juice, you might hire a robotaxi, possibly arranging for your personal stuff locker to be exchanged first. That taxi will handle your needs.
And if you do need to go cross-country, or have not settled on your destination, then you'll get a liquid fuel (perhaps gasoline) car that works the old fashioned way, and can just refuel quickly and go.
The charging downtime of an electric car does remain a problem. There are a few ways it can be dealt with:
When you charge depends on your own economic valuation of how much cheaper night electricity is, how much extra battery packs cost or indeed how much extra robocars cost. Some robocars may be so cheap that it's simpler just to leave discharged ones idle while fresh ones go into service.
While the ideal is to use a vehicle that has no more battery in it than a given trip needs, in reality this will not always make sense. So vehicles will come with capacity for 2 or 3 trips if that's what people need. Adding battery capacity adds cost and weight, but delays charging and makes the vehicle more flexible.
With swappable cartridges, it's also possible to swap in cartridges of different capacity. So a car being sent for a 10 mile trip might swap in just enough juice for that, to reduce the weight.
In an electric car world, a charging station is nothing fancy. In fact, it will just be a pole in some parking spot. The robocar will drive up to the pole (very accurately) and then extend a robot arm to plug into it. It will send some data over the line to authorize payment for the power, and start getting juice. Such poles could be found all over the city.
(Actually, it need not even be a pole. It could be recessed in the ground, so that the car's arm reaches down while over it to remove the plate and plug in. So these could sit at the side of streets, or be embedded in street parking spaces.)
Robocars could also plug into ordinary power plus for very slow charging. This might create a bit of power theft, but the charging is so slow I think this will mostly be done in garages.
Rapid high current charging will require special stations. So will battery depots. As gas stations close, I suspect we'll find a place for them.
As noted, nuclear and coal plants don't alter their output very quickly. They prefer to run constantly, but power demand is much lower at night. Power at night can be much cheaper than power in the daytime. People charging batteries, be they car owners or battery swap depots, will decide what makes the most sense -- own more batteries/cars and charge them all at night, or own fewer, and do some daytime charging. The market will figure this out.