It's a pretty simple calculation to calculate
roughly how many stalls have to be built per car produced. This is in addition to those needed for geographical coverage. Let's make some assumptions. Feel free to modify them as you see fit.
- PTS = Percent of Tesla Charging on Superchargers. Assume 5%.
- AM = Average Miles driven per year by Teslas. I assume 12,000 miles per year.
- BDF = Busy Day Factor. The ratio of use on busy days vs average days. AKA, the Mother's Day factor for phone lines. Assume 2x.
- ACR = Average Charge Rate while using a Supercharger. Assume 200 mph.
- EQE = Erlang Queueing Efficiency to avoid queues at Superchargers. For a 10 Stall Supercharger it is 51%. Let's take that for big city, lots of Teslas, calculations.
- EBH = Equivalent Busy Hours of Supercharger use per day. If all the use per day were at the busy hour rate, then this times the busy hour rate would give you the charging per day. Assume 5.
The number of Supercharger miles charged per busy day per car is AM/365*PTS*BDF. That is the Average Miles per year divided my 365 days per year times the percentage of miles that are Supercharger miles times the Busy Day Factor.
A single stall at a supercharger can provide so many miles per day with minimal queues. That is ACR*EBH*EQE or the Average Charge Rate times the Equivalent Busy Hours per day time the Erlang Queueing Efficiency.
The number of Teslas that can be supported by each stall is then the Miles per Day per Stall divided by the average Supercharger Miles per day per car or
ACR*EBH*EQE/(AM/365*PTS*BDF)
= 200 mph per Stall * 5 hours * 51% / (12,000 miles per year per Tesla / 365 days per year * 5% * 2
= 155 Teslas per Stall
We assumed 10 Stall Superchargers, so that means that Tesla needs to build about
one 10-Stall Supercharger per 1,550 Teslas. Because they are now making about 600 Teslas a day, then that means
another Supercharger every 2.5 days now or about two per week. Counting world wide, they have been doing a little better than that. This does not seem to be a problem to me. Of course, as the production rate of cars goes up, so will the installation rate of Superchargers.
My assumptions are WAGs (Wild Ass Guesses), but probably within reason, and better than SWAGs (Stupid Wild Ass Guesses). Tesla has all the monitoring tools needed to track actual usage, Superchargers nearing capacity, etc. It should be pretty easy for them to stay ahead of this. It's not rocket science. Telecommunications engineers have been doing these calculations and monitoring to stay ahead of demand and avoid the dreaded busy signal for over a century. With a little care and planning, Tesla should do fine.
I also like the Green/Yellow/Red signaling that has been suggested. If this coding could be put on the car's map for Superchargers, that would be great. Green means no waiting, Yellow means some power sharing and Supercharger approaching capacity, and Red means queues happening regularly. This would allow drivers to plan stops, especially when, with greater Supercharger density, there are multiple choices of where to charge.