Tom - You can shoot with a flash. Just use common sense and do not shoot it towards the driver. We all shoot with flash at the major events. I shot with flash 2 weeks back and didn't get one complaint. I just use my SB-800 and shoot it on manual... I do shoot it remote with Pocket Wizards sometimes. When I finally get some nice strobes for studio work they wont come near the track...
Here is a cool shot I got last time out. The track had deteriorated quite a bit and it was near impossible to get it right every time. Talking former World Champions having problems with it. No one likes pics of their cars like this but I made sure to get one of a buddy. Nice reminder of the event for him.
