If you live in a big city, this scenario is all too familiar: Traffic is bad. You're late for work. And, of course, the parking garage is now full. So you're forced to parallel park on the street. You finally find a spot between two hulking SUVs, but it looks pretty tight. Do you go for it or move on?
Not to worry; geometry can save you. Run a simple calculation and — voila! — you'll know just what to do.
Ignore the car that's sneaking into your space as you do the calculation. You'll need a few pieces of information:
- Your car's turning radius, r
- The distance between the front and rear wheels, l
- The distance from your front wheel to the corner of the front bumper, k
- The width of the car you're trying to park behind, w
Now it's simply a matter of plugging those variables into the handy formula (see our illustration), and you'll know if that spot could have been yours.
The Formula
Source: The Geometry of Perfect Parking by Simon R. Blackburn
The formula for the perfect parking job was recently worked out by mathematician Simon Blackburn, professor at the University of London. Stanford mathematics professor Keith Devlin tells NPR's Audie Cornish "it's actually a very clever use of simple mathematics."
The most complicated part, Devlin says, is our good old friend the Pythagorean theorem. That's a squared plus b squared equals c squared, as you'll remember from your high school geometry class, no doubt.
"The formula tells you exactly how much extra space you need, beyond the length of your vehicle, in order to park it in a simple, reverse-in, straighten-the-wheels, switch-the-engine-off move," Devlin explains. In other words, no back-and-forth, no see-sawing — the perfect parallel parking job.
Blackburn's formula does this by sketching the arc of your car's turning capability into a full circle, then using the center of the circle to create the right-angle triangles Pythagoras loved.
That's a lot of work just to tell you if you have enough space for an easy park. And it doesn't tell you how to do the parking. That's something you have to learn by doing, which is how most people figure out whether they have enough space to park in the first place. Devlin says that behind all that guessing, math is at work.
"Mathematics gives you a way of understanding in detail what people have learned to do simply by practice and expertise," he says.
"In fact, when we practice something, be it on the athletic field or in an automobile, we are becoming very good mathematicians at doing a particular kind of operation," Devlin says. "But usually we don't call it mathematics — and we certainly don't give people a pass on the math test because they can park their car."
