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 a loop. Of course, this assumes that there is no energy loss due to friction; you’d probably want to start a little higher to account for this.
But not too high…
Actually, why cut it down? Why not just start A lot above and dispel any doubts? The reason is that the faster the car goes, the greater the g-forces the driver experiences on the loop.
Let’s think about it: if you ponderous your car down to go around the loop at a minimum speed, this will happen zero force from track (FT). For a moment you will feel weightless – zero g. If the car is released from a height greater than 2.5 R, its speed will be greater than the minimum at the top of the loop. To continue moving in a circle, gravity would not be enough. The track would also have to put pressure on the car. This would produce a g-force greater than zero.
Let’s get back to video of a real stunt. Comparing the loop with random people, I guess it has a radius of 2 meters. The car clearly releases itself from a height above a minimum of 5 meters – say 8 meters. The force at the top of the loop (divided by the weight to express it by) will be 3 g. Its it is possible that a person can withstand a load of up to 20 gso it should be ok.
But what if you go extreme? If you start too high and make the loop too tiny, bad things can happen. What about a height of 20 meters and a loop radius of 1.5 meters? This would create a force of 21 g. It may look frigid, but it could also kill you. This isn’t entertaining anymore.