I came up with a pretty insane for a new kind of motor sport a few years ago that simply doesn't exist.
The series is call Brake Drag Racing.
Your car has no motor, and the tracks are specially designed with steam catapults in them, same as an aircraft carrier.
The two vehicles are locked into the catapult in their respective lanes, and then launched at the same time (or different times for bracket drag racing).
After the release from the catapult, the cars roll unpowered towards a white line, at say, 200 feet or something from the start line. Any deceleration within a certain limit before the line, or actual braking, and you are disqualified.
The moment you hit that line, you engage the brakes on the vehicle, and whoever comes to a stop first, wins.
Different classes of cars, from 'stock' cars that only have brakes in the wheels, moving up to cars with chutes, all the way up to the top tier, where the cars would open like an aerodynamic swiss army knives, with air brakes, chutes, etc.
You would want the car to be as slick as possible to quickly get to that line first, then open up into the least slick shape possible to stop first.
All in all I think it would be a very interesting engineering challenge that would produce some unique vehicles unlike anything ever seen before.