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perpendicular parallel parking

Puzzle

It is a fun (and rarely appreciated) moment when basic math and engineering can help one solve a non-technical problem.  Recently, I witnessed such an occasion where a non-standard solution was the only one that would work.  Warning: This is a geeky post, but hopefully entertaining nonetheless.

Here's a visualization of the problem...

Namely, car 1 and car 2 were parked on a curb and car 3 (a police car) was double-parked, but at a position such that our car could not easily be parked in the desired spot.  Yes, four-wheel steering and its interesting fuzzy-logic research is now available on some  trucks and I am aware of other cars that have even used it for parallel parking, but it was not available on the car I was in.  Other alternatives like this creative parking solution also were not on hand.

Crash Scenarios

If you think about traditional ways of getting into the spot, you will inevitably have collisions because the dimensions of the various cars are just out of the range compared to what's needed, as animated below.  Drawn as close to scale as presentation software allows, a mulit-point turn and park was also infeasible because of curb proximity.

Solution

The solution? As the title indicates, it was to approach the problem from a different angle.  In this case, that angle was perpendicular and then a multi-turn technique was applied.  As part of the entertainment promised, below is a coarse animation of the process.

Of course, this weird problem may be solved by four-wheel turning quite easily because then the car has an augmented set of physical movements.  It is also fun, but much less feasible, to imagine these weird techniques being applied to more competitive parallel parking records.

Yay for Mili and Eric.

Update: Yes, the car in question was a bit smaller than the others because it was a VW Bug.  There's no reason that a larger vehicle couldn't pull off the same physics feat, but I wanted to draw the operation to scale for more dramatic effect. Thanks for the gotcha, Carl!

3 Comments

  1. Jessie wrote:

    Great blog & this is a geeky post indeed, hahaha. I wonder though, is there any way to assess the feasibility of the perpendicular parallel parking before actually doing it? Coz it involves many times of fine steering.

    Wednesday, February 18, 2009 at 6:58 pm | Permalink
  2. Eric wrote:

    Thanks for the interest and interesting question. Yes, you can compute a solution ahead of time -- at least you can assess *if* your car will fit. Just make sure that the diameter of your car (from your rear left tail-light to front right head-light -- reverse if you're somewhere British) is smaller or equal to the distance between all points between car 1 front bumber and car 3 rear bumper (i.e. the front left of car 1 and back right of car 3). As for the number of moves, that depends on how aggressive you are and how many dents you can tolerate !

    Thursday, March 5, 2009 at 1:46 pm | Permalink
  3. Slinky wrote:

    Hi, thanks for the patch, released v1.1 now. I couldn't find a way to prevent pinging from going off automatically. No idea if it's possible per-post in current WPs, even.

    Nice post btw!

    Friday, June 5, 2009 at 6:01 am | Permalink

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