# Geometry of nose in and nose out parking in parking lots

I would like some computational evidence in favor of my observation that one can park a car in tighter (parking lot) spaces by backing in rather than nose in. I have been doing this successfully for some 15 years, but see few others trying this.

So, the model is a rectangular parking space, orthogonal to the side of the lot, and a second row of cars blocking the way, opposite the space. A car has fixed wheels in back, maybe at 1/4 the length, and turning wheels in front, maybe also 1/4 the length, I don't know. I see people going in and out trying to get into spaces (nose in) that I would have gotten first try. If there were no second row of cars narrowing things, of course they could, essentially make a turn and then simply drive in a straight line into the space. But that is not how parking lots are made. A given car has a minimum turning radius, but the main point is that the center of the circle may not be where one expects.

In the long run, I would love to have something I can show to Berkeley Bowl West and Trader Joe's suggesting that they put up signs "Consider parking by backing In."

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Is ask-orourke a real tag? –  lhf Dec 23 '11 at 0:36
For the moment it is. It wasn't a real tag until I typed it in as such. –  Will Jagy Dec 23 '11 at 0:43
This is half of the reason that fork-lifts always put the steering wheels at the rear (opposite the forks). –  Carl Brannen Dec 23 '11 at 2:24
@CarlBrannen What is the other half of the reason? –  Will Jagy Dec 23 '11 at 4:24
The front wheels of a fork-lift have to carry the heavier load. So it's an easier design if you make the load-bearing wheels not able to turn. –  Carl Brannen Dec 23 '11 at 11:13

Sorry to disappoint despite the (now removed) eponymous tag :-), but in fact I don't have a precise answer. Here are three possible sources, the second two mathematical.

(1) "You're Parking Wrong: Why it's almost always better to back into a space than pull into it head-on." Tom Vanderbilt, Slate, Feb. 2011. (Article link.)

(2) "Mathematical Analysis of the Parallel Parking Problem," William A. Allen, Mathematics Magazine, Vol. 34, No. 2 (Nov.-Dec., 1960), pp. 63-66. (JSTOR link.)

(3) "The Geometry of Perfect Parking," Simon R. Blackburn, 2009. (Web link leading to PDF link.)

The two math papers concentrate on parallel parking, which is not your question, but is nevertheless quite interesting. Here is a nice figure from Allen's paper:

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Thanks, Joseph. Just so you do not feel you are the only one summoned unfairly, or the first, see mathoverflow.net/questions/69542/uniformly-convex-spaces –  Will Jagy Dec 23 '11 at 1:45