Perfect Parallel Parking the Mathematical Way

January 20, 2010

Simon Blackburn (University of London) has come up with a bit of mathematics to make the trickiest parallel parking a snap.

Blackburn's mathematics centers on the radius of a car's curb-to-turning circle and its wheel base and length. Guided, moreover, by the length of the car's nose and the width of an adjacent car, the formula then calculates how big a space has to be for any vehicle to fit into it. Having worked out when to turn the steering wheel, the driver easily does the rest.

Blackburn's paper, "The Geometry of Pertfect Parking," was commissioned by Vauxhall Motors, which, in a survey, had found that about 3 out of 5 drivers lacked confidence in their parking ability, and that about 3 of every 10 drivers would rather avoid trying to park in a tight spot.

Blackburn said, "This was the perfect opportunity to show how we can apply mathematics to understanding something that we all share...If you understand the angles and the dimensions of your own car then you can work out how to park in a nice, confident way."

If you're still unconvinced, the following references from Blackburn's 10-page paper ought to turn you around:"Ackermann Steering Geometry"; John Baylis, "The Mathematics of a Driving Hazard" (Mathematical Gazette 57 [1973], 23–26); Edward J. Bender, "A Driving Hazard Revisited" ( SIAM Review 21 [1979], 136–1380; John Bryant and Chris Sangwin, "How Round is your Circle? Where Engineering and Mathematics Meet" (Princeton University Press, 2008); H.I. Freedman and S.D. Riemenschneider, "Determining the Path of the Rear Wheels of a Bus" (SIAM Review 25 [1983] 561–567);  E.H. Lockwood, "A Book of Curves" (Cambridge University Press, 1961); and J.Y. Wong, "The Theory of Ground Vehicles" (John Wiley & Sons, 2008).

Source: FOX News (December 14, 2009); Vauxhall Motors (doc).