You also seem to misunderstand the laws of physics a bit. Under almost no conditions would a following distance of "one inch" be safe, even for the fastest computer. Not even at a of couple feet, most likely. The Model S weighs over two tons. If the car in front has a better stopping time then you're going to rear-end them. The car has no way to know the braking power of the car ahead, so the gap between vehicles has to be far enough so that if the car in front hits an invisible brick wall and comes to a dead stop almost instantly you still have enough room to stop safely. The car can calculate this safe distance based on speed and other factors pretty easily.
Hmm...
Assumptions:
The Tesla can stop as quickly as the car in front.
(Not 100% true - the Model S can manage 60-0 in 108 feet in testing
here - one of the better sedan results but not the fastest; Motortrend came up with 22 high performance sports cars that can do less than one hundred feet, the best at 93 feet
here. More important, this assumption guarantees that if the car in front is abruptly decelerated by hitting something, the Tesla will plow into the back of it.)
Tesla is using the Delphi ESR or a comparable unit, which measures the speed of all objects within the field of view every 50 ms.
(No idea, but the Delphi looks similar to the Tesla pictures I've seen and seems to be the best of the current supplier batch.)
The car can make a decision in 20 ms.
(Pulled from thin air, but I think conservative.)
Bosch iBooster in the Tesla application can develop full braking force in 120 ms.
(vendor certified for the general case.)
The car in front starts braking instantly immediately after a radar ping.
(worst case, almost certainly unrealistic - I don't think any car can switch instantly to full braking without a buildup period.)
This means that the minimum distance where the Tesla can match the braking of the worst case car in front is the distance it covers in 190 ms. At 60 mph (88 feet per second,) that would be (.19*88)
16.72 feet.
Actually, that's quite a bit further than I was thinking it would be before I started pulling numbers together. There is obviously a big hunk of conservatism in the assumption that the other car can slam on the brakes that fast, but it would still be dangerous for Tesla to program anywhere near that close because of the discussion in the first assumption about running over cars that hit things.
Even with the iBooster (3x faster than past systems, they say,) ~2/3rds of this delay is applying the brakes, which implies that a train of communicating cars can benefit substantially over a train of cars that don't talk and just rely on their own sensors (because the communicating cars can start their brake delay before they see the car in front braking.)
Not advocating anything in particular wrt TACC here, just saw a couple folks throwing swags at an interesting technical question.
Walter