# Parallel Parking optimization (US customary units)

- Author:
- mathcare, jeromeawhite

- Topic:
- Trigonometry

In my brief moment of semi-fame, my exploration of parallel parking ended up in the New York Times 10th Annual Year In Ideas magazine http://www.nytimes.com/interactive/2010/12/19/magazine/ideas2010.html#Perfect_Parallel_Parking.
Shortly after there was a front page article in the local New Orleans Times-Picayune http://www.nola.com/education/index.ssf/2011/01/offbeat_lusher_charter_school.html
I certainly have to credit Professor Simon Blackburn, University of London, for his original work which sparked my interest in the subject.
https://www.ma.rhul.ac.uk/SRBparking
Even though Geogebra was never mentioned by name in any of the news articles, it was central to my being able to visualize the problem better and test/confirm my equations.
This Geogebra model is in US customary units. I've also posted a metric model at http://www.geogebratube.org/material/show/id/3023

This exercise is intended to find the minimal distance required for a parallel parking spot (beyond the length of the car itself). Adjust the sliders to see how the various parameters affect the outcome. Note that d_c is the distance you're allowing to exist between the parked car and the parallel curb. Setting d_c to zero would have the car positioned flush against the curb at the end of its backward motion. Setting d_c to a positive value allows the car to pull forward in order to straighten out after initially backing up. Intuitively, the larger you set d_c to be, the less distance you need to fit between the parked cars.
Note that the angle alpha is also critical to a good parallel parking job. Check the "optimize" box to use the value of alpha that will minimize the required parking space.
Note: Setting both d_c and alpha to zero reduces my model to Professor Blackburn's model, but I find this to be overly conservative.