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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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    In fact, in Japan, where space is at a premium and parking lots are quite small, everyone parks backing in, nearly 100% of the time, for the reasons you mentioned.2013-08-19

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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:
             enter image description here

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    these kinds of curves appear in **contact geometry**. See [What is a Legendrian Knot?](http://www.ams.org/notices/200910/tx091001282p.pdf)2015-10-18