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!
Shift car into spot by shifting back and forth according to an algorithm.
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:
Start with car lined up with front of spot (not optimal but easier to understand the algorithm).
Turn wheel right and reverse about half the length of the spot.
Turn wheel left and reverse to the end of the spot. The car should be straightened out.
Turn wheel right and go forward about half the length of the spot.
Turn wheel left and go forward to end.
Repeat until car is close enough to curb.
The car tires draw out concentric circles as the car turns.
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:
Line up car with open spot.
Reverse car into spot while turning steering wheel all the way to the right.
After backing car partially into spot, you need to determine when to turn the wheel to the left to straighten out.
Ideally the car should straighten out when it gets to the end of the spot. I match the turning curves so they just touch and are horizontal at the end of the spot.
Turn the wheel all the way to the left at that point, and continue reversing.
Reverse to end of spot and straighten out. (Oops! I bumped the car behind me.)
Now turn wheel all the way to right and go forward. You can plan out the motion by matching curves again.
About halfway across the spot...
...turn the wheel all the way to the left and continue forward.
Continue to the end of the spot and straighten out.
With these steps, you have just shifted your car to the right!
If you repeat the motion steps...
...then you will shift the car closer to the curb.
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.
The tracks of the back tires make nice symmetric curves if you follow this parallel parking algorithm.
What happens if you turn the wheel too soon? In the green sections of curves the car is rotating clockwise (and the orange parts counter-clockwise).
Starting partway into the spot and then following this uneven path...
...the car ends up rotated clockwise. This makes sense since there was more green (clockwise) tracks.
To fix the car's position do an uneven motion again...
...but this time straighten out by spending more time on the orange (counter-clockwise) tracks.
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!
