I get a minimum height of 2.5R. So if the loop is 4 meters high (with a radius of 2 meters), the car would have to start 5 meters above the ground to just make the loop. Of course, this assumes there’s no energy loss due to friction; you’d probably want to start a bit higher to account for that.
But Not Too High …
In fact, why cut it close? Why not just start much higher and eliminate all doubt? The reason is that the faster the car goes, the higher the g-forces experienced by the driver in the loop.
Let’s think about this: If you release a car so that it goes around the loop at minimum speed, there will be zero force from the track (FT). You’d feel weightless—zero g’s—for an instant. If the car is released from a height greater than 2.5R, its velocity would be greater than the minimum at the top of the loop. In order to still move in a circle, the gravitational force would not be enough. The track would also have to push down on the car. This would create a g-force greater than zero.
Let’s go back to the video of the real stunt. By comparing the loop to the bystanders, I’m guessing it has a radius of 2 meters. The car is clearly released from a height above the 5-meter minimum—let’s say it’s 8 meters. The force at the top of the loop (divided by the weight, to get it in g’s) would be 3 g’s. It’s possible for humans to withstand up to 20 g’s, so this should be fine.
But if you go extreme? If you start too high and make the loop too small, bad things can happen. What about a height of 20 meters with a 1.5-meter radius for the loop? This would produce a force of 21 g’s. It might look cool, but it also might kill you. That’s not fun anymore.