You’re driving in a parking lot. As you turn into a space you realize that you’re going to hit something–perhaps the curb or a lamp post. Maybe you’re just going to park over the line. You back up a bit, do a little S-turn to redirect the car, and get into the space.
This works because real cars are capable of accelerating very slowly. Part (2) is the key, and it’s quite difficult if you’re doing more than about five mph. After all, parking spaces aren’t very wide; you’ll overshoot if you back up at speed. Substantially redirecting the car in a small area requires the ability to accelerate gently, and use that slight velocity to get into a carefully-chosen position.
Arcade-style driving games generally have strong acceleration, and that means the little maneuvers necessary to correct a missed turn are quite difficult. By the time one is ready to put the “S” in the s-turn, part (2) in the diagram above, one is already back at the starting point. The effort to get off the obstacle ends up looking like this:
This can go on for quite some time.
Assuming slowing the car’s acceleration isn’t an option, the solution is to change the turning radii when the car is moving forward and backward:
This isn’t realistic–but that hardly matters. Arcade racers are all going fast, about keeping control at the edge of the performance envelope, about doing unreasonable, death-defying, exciting things. Struggling to get back on track doesn’t check any of those boxes. Make turns behave unrealistically so that I can back to them when my terribleness slows the game down. 😉