Race car insurance
I had done a lot of searching on different forums. The impression I got was that the companies that did offer coverage would not cover the car once it was running unless you paid for on track coverage.
Just last weekend I saw a car with it's door open in the staging lanes get hit by a dragster rear tire. Luckily the guy in the dragster was paying attention and stopped realizing he had hit something even though he could not see it.