From: lytle@noao.edu (Dyer Lytle  CCS)
Newsgroups: rec.autos
Subject: Re: ANGLED LINES YIELDING SMALLER SPACES???
Date: 9 Sep 92 16:04:19 GMT
Organization: National Optical Astronomy Observatories, Tucson, AZ, USA

In article <BuBF9u.Ctq@wpi.WPI.EDU> beuf@wpi.WPI.EDU (Richard J Fuller) writes:
>
>
>
>This may be obviously wrong but here goes anyway....
>I TOTALLY DISAGREE THAT ANGLED SPACES ARE narrower than
>straight ones...
>
>A picture is worth a thousand words.....
>
> ____ ____ ____ ____ ____
>|    |    |    |    |    |
>|    |    |    |    |    |
>|    |    |    |    |    |
>|    |    |    |    |    |
>
>
>is the same thickness as an angled set
>
> ____ ____ ____ ____ ____
>\    \    \    \    \    \
> \    \    \    \    \    \
>  \    \    \    \    \    \
>   \    \    \    \    \    \
>
>CORRECT ME IF I AM WRONG BUT In both cases the width
>of any one spot is 4 characters..... so the narrowness is not changed by angling the spots...
>
>
>I hate to disagree but if I do not understand geometry somebody please let me know
>because last time I checked 4 was equal to 4....
>If that changed let me know quick (my bank statement came in yesterday...!!!!)



    I can't believe I'm doing this...

    This is obviously wrong, just consider the case where the angle above
    approaches 0 degrees.  The lines get very close together and the width
    of the parking space approaches zero.


    Example:

    Lets call theta the angle between the curb and the lines seperating the
    parking spaces.

    Angle = theta = 90 degrees
    separation between lines at curb = 8 units

    -------- -------- -------- -------- --------
   *        *        *        *        *        *
   *        *        *        *        *        *
   *        *        *        *        *        *
   *        *        *        *        *        *
   *        *        *        *        *        *
   *        *        *        *        *        *
   *        *        *        *        *        *
   *        *        *        *        *        *
   *        *        *        *        *        *
   *        *        *        *        *        *
   *        *        *        *        *        *



    Angle = theta = ~30 degrees
    separation between lines at curb = 8 units

    -------- -------- -------- -------- --------
   *        *        *        *        *        *
      *        *        *        *        *        *
         *        *        *        *        *        *
            *        *        *        *        *        *
               *        *        *        *        *        *
                  *        *        *        *        *        *
                     *        *        *        *        *        *
                        *        *        *        *        *        *
                           *        *        *        *        *        *
                              *        *        *        *        *        *
                                 *        *        *        *        *        *

    notice that the distance between the lines is about half of what it was
    above.  (if you don't believe this, get out your ruler and measure!)
    separation between lines = ~4 units  (angle ~30 degrees)

    please notice that the width of the parking space is not the distance
    between the lines along a line parallel to the curb but is, in fact, the
    distance between the lines perpendicular to those lines.


             |<---------------- R1 ----------------->|
                                      |<--- R2 ----->|

	      ---------------------------------------------------------------
             *   theta                * theta       /
                *                        *        /
                   *                        * 90/
                      *                       /*
                         *                  /     *
                            *             / AA       *
                               *        /               *
                                  * 90/                    *
                                     *                        *
                                        *                        *
                                           *                        *

    length of AA = R1 sin (theta) - R2 sin (theta)

    = (R1 - R2) * sin (theta)

    = (spacing between lines at curb) * sin (theta)

    That is:

    (width of parking space) = (spacing between heads of lines) * sin (theta)

    where theta is the angle of the lines from the curb.


         Have fun, be happy, do more geometry problems!
 -Dyer


-- 
Dyer Lytle, National Optical Astronomy Observatories, Tucson, AZ, 602-323-4136
Internet: lytle@noao.edu        SPAN: NOAO::LYTLE (NOAO=5355) 
Newsgroups: rec.autos