### parking geometry

###### Fri 25 October 2013

Cars parallel parked in Washington, D.C., USA. (Photo credit: Wikipedia)

When I was a child, I wonder how cars could be parked in a parallel way.

Later, I passed my driving license , so I learn how to do but not why it works. Now, I think I can explain how to park a car in parallel parking and illustrate why it works

## a word about steering

Ackermann steering geometry when turning. (Photo credit: Wikipedia)

A wheel ‘s trajectory is parallel to the wheel (otherwise it looks like a drift). Usually, the rear wheel cannot move, so when turning, the center of the circle is on the rear’s wheel axe. This geometry is described on the wikimedia image . I will simplify it by only drawing a rectangle for the car, the center of turning circle , and the trajectory of the outer front wheel.

## steps of parallel parking

My drawing is not as beautiful as I hoped, but it is normal, I’m not an infographist. Look at all the dotted lines to see wheels’ trajectory.

Parallel geometry

The (light) red cars are the one you must avoid when parking between. The front is on the left (remember the rear wheel are on the turning circle diameter). The steps are the following:

1. blue: while being parallel to the car next to yours, turn the steering wheel .
2. light blue: move backward
3. go to light green position (backward and straight)
4. turn on the opposite direction to go to green position
5. you can move ahead a little to be right in the middle of your place (not drawn)

When going from green to green position, you almost hit the car in front of you. In real life, there is only few centimeters (one or two are OK). Don’t forget to go as slowly as you want to avoid car crash .

Look at the alignment of your car when going from light blue to light green position. I don’t remember much of my driving lessons but there you should look at

• the center line of your car alignment (longitudinal) with the front wheel of the red car behind
• the driver’s head alignment (left to right axis) with the rear wheel of the red car on the front when starting to turn (light green position)
• all the drawings are made using only 3 steering wheel positions: all-right (blue to light blue), straight (light blue to light green) and all-left (light green to green). In real life, you should use this extreme positions and there is no need to use others (except if you want to park into an extremely long place)

## extension to other parking

Bataille geometry

I would like to speak about what we call “stationnement en bataille” in french (I don’t know the English name). As rear wheel are fixed, you just need to put them in the right place and go straight ahead (…straight back). this is mainly done by looking (all) the rear-view mirrors , especially the ones on the outside (left and right comparison to let the same empty place on both side).

Bataille (Photo credit: Wikipedia)

I hope this help you to see why you must do as you learned to park a car. This is not magic, just steering geometry.

(Non-)related articles

Category: maths Tagged: Parallel parking Park