"CNNMoney took a Tesla Model S on a test drive from Washington D.C. to Boston. The all-electric car drove 450 miles with two stops to recharge at Tesla's Supercharger stations in Delaware and Connecticut"
A second problem is that unlike conventional gasoline cars that can be refueled very quickly, charging can take a relatively long time, and adds significantly to your total travel time. In the near future, as the number of Teslas increase, the number of charging stations is likely to go up too. However, it will remain a sparse resource for some time. A future Tesla trip from New York to California will require many recharging stops, reminiscent of the old stagecoach problem during the Gold Rush era, which is used to illustrate the principles of Dynamic Programming.
Update: May30, 2013
Popular Mechanics reports:
"...the California-based EV automaker plans to expand its fast-charging "supercharger" network across the continental U.S. During today's announcement, Musk said New York to Los Angeles trips would be viable as soon as this winter.
"When you get in a car you have the ability to go almost anywhere," Musk said. "That's what the supercharger network will do."
The rollout will begin as soon as this summer, with the number of stations tripling to 27 nationwide by the end of June. In addition to increasing supercharger density along the already-established California and Mid-Atlantic coasts, Tesla will debut chargers in a handful of new metropolitan areas within the next few weeks, including Austin/Houston, Portland/Seattle, Boulder/Denver, and Chicago/Milwaukee. By the end of the year, Musk expects to to have "a couple hundred" superchargers spread across the U.S. and southern Canada, with as little as 80 to 90 miles between stations along the Altantic and Pacific coasts..."
Tesla Routing Problem
Given a road network G having a limited number of charging stations located at specific nodes, the Tesla Routing Problem (TRP) will have to:
Find the shortest feasible time path from origin O to Destination D in network G.
Feasibility requires the car to visit enough charging stations in a timely manner. Optimality requires that the sequence of visits be carefully selected such that the total time spent is kept to a minimum.
Total travel time = driving time + recharge time
D1. Which recharging stations to visit en-route?
D2. How long to recharge at every pit stop?
A1. The longer you recharge, the longer your available range (to a limit).
A2. All recharging stations are similar, and infinite capacity (no queuing!)
A3. Range is deterministic
Update on A2: The Tesla can charge on any outlet, but the time to recharge can vary depending on the source.
Clearly, optimally solving TRP involves the finding a solution to a Traveling Salesman Problem even in the special case of instantaneous recharge (Y=0).
(Updated September 2013: As mentioned in the comments, the general case is not a TSP in the network of charging stations. Here, the assumption is that stations are sparsely located and we visit each one along the way. The title is changed to reflect this distinction).
This is no different from the (milder) challenge faced by conventional car drivers in unfamiliar areas where gas stations may be hard to come by (see this old post). Charge cannot be carried in Jerry-cans. The shortage of charging stations does make every long Tesla trip a non-trivial problem to manage. Tesla owners have to deal with a NP-Hard Optimization Problem (Heh) on every such trip, but in practice, it should not be difficult to find good quality, feasible TRP solutions.
The recharge time makes the TRP a bit more interesting. If two stations are close to each other, we don't have to recharge fully, and just need the minimum to reach the next stop - or perhaps we recharge fully, which allows us to reach a station that is further away but turns out to be more time-effective, overall. Clearly, these two decisions appear to be interlinked and may need to be jointly optimized. D1 is a binary decision variable X(i) - we either visit or don't visit a station at node X(i), whereas D2 is a semi-continuous variable Y(i) conditional on D1:
Y(i) ≤ U.X(i)
where U = maximum recharge time.
Another interesting and maybe even useful problem for Tesla-makers to solve is where to add new charging stations on the network G over time. What is the minimum number and location of stations required to guarantee feasible solutions to any TRP in the 48 states of continental US? How will stations deal with congestion in the future? and so on ...
I haven't driven a Tesla yet but I wouldn't mind relocating my office to inside one and telecommute.