# 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.)

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
these kinds of curves appear in contact geometry. See What is a Legendrian Knot? – cactus314 Oct 18 '15 at 12:34