Yes, CAB, there are rules of thumb for the amount of angular change between the street and the driveway to prevent cars from scraping. I believe these are in Architectural Graphic Standards. I got a heck of a lot of work to do right now, but when I get a chance, I'll try to look this up for you. When the angle is too much, you can put in a sag vertical curve to make a more gentle transition, although that will require a steeper driveway. That said, I will ask our survey forum members to whip up a parabolic curve equation to help you out.
Kate, that photo is cool.
Bob G.