Parallel parking is hard. Many of us avoid parallel parking if we can help it, and yet there are a select few that seem to be able to parallel park with ease. How do they do it? Over the past three years, I’ve been forced to parallel park a lot since our apartment doesn’t have enough parking in the lot. All the practice has helped me get a lot more comfortable about parallel parking, but it has also got me thinking. Parallel parking is an iterative process; somehow by going backwards and forwards and turning the steering wheel back and forth you can shift your car into a spot. I realized there must be an algorithm, a simple set of rules, that will always move the car smoothly into the spot. So I figured out a way to do it, and want to share it with you today. Maybe knowing the rules will help our parallel parking!

The basic problem with parallel parking is to shift your car into the spot, as shown in the sketch above. It would be easy if the front and back wheels could rotate 90 degrees, but with a normal car you have to deal with only the front wheels able to turn. Here is an algorithm I found for parallel parking:

1. Start with car lined up with front of spot (not optimal but easier to understand the algorithm).
2. Turn wheel right and reverse about half the length of the spot.
3. Turn wheel left and reverse to the end of the spot. The car should be straightened out.
4. Turn wheel right and go forward about half the length of the spot.
5. Turn wheel left and go forward to end.
6. Repeat until car is close enough to curb.

As I was figuring out how to sketch the process of a car parallel parking, I actually learned something about car steering. It turns out that the front wheels do not point exactly in the same direction during a turn. Instead they follow the Ackermann condition so that every wheel draws out a circle with the same center point, as shown in the sketch above. With this insight, I was able to trace out the motion of the car as it parallel parks. The images below break down the process:

So if you trust my drawings, following these steps solves the parallel parking problem. Give it a shot! It is a little unnatural at first following a series of steps, but is nice once you get the hang of it. I like knowing that I can always shift the car where I want it just by going forwards and backwards.

To really learn something, I think it’s important to mess around and try things. I played around with making the turns uneven and found that this can cause the car to be crooked or straighten it out after I make a mistake. The slides below explore how this works.

Thanks for reading my thoughts into how parallel parking works. I hope it was helpful and interesting. Part of my inspiration was a nice article I read about visualizing algorithms. Please let me know if you have and questions or comments!