[Edu-sig] Even more re: catenaries vs. parabolas

[Kirby Urner]

Earlier today I wrote:
>Note: especially important is the pantograph, which maintains 
>contact with the wire to maintain contact with the line, which 
>is only very shallowly catenary (i.e. dips up and down with 
>far less amplitude than an overhead telephone line).

Even aside from the garbled sentence, I was a bit confused
about the overhead caternary design.  

There's an upper wire with a pronounced dip, the true catenary, 
suspended from which is the actual high voltage line, which 
is in theory parallel to the track at all times (although 
the spring-loaded pantograph will accommodate some deviations, 
no?).

So it's more like having a lot of miniature suspension bridges 
between the poles.

So I'd like to do another graphic, with the catenary on top 
(not as deep-dipping as before -- bigger 'a'), and a horizontal 
line (different color) below.  Then I'll add some vertical rods, 
evenly spaced, to indicate that my lower line is suspended 
from the upper one.

The old + new pictures, with some Python-colorized Python code, 
is at:

  http://www.inetarena.com/~pdx4d/ocn/catenary.html

You may wonder why I'm putting so much time into this 
rather obscure topic (cued my posts by Martha Haehl,
Abraham S. Mantell et al on the MATHEDCC listserv).[1] 

Well, finding all those train links under "overhead
catenary systems" made my little heart go pitter pat,
given all the train metaphors already operative at
one of my websites (Design Science Central):

  http://www.inetarena.com/~pdx4d/  [2]

I guess I just couldn't resist!

Kirby
Curriculum writer
Oregon Curriculum Network
http://www.inetarena.com/~pdx4d/ocn/
 
[1] http://archives.math.utk.edu/hypermail/mathedcc/
[2] this site still very much under construction.  I got the
    idea of using trains to link websites from the people
    behind The Rail:  see "track link" at the bottom of 
    my http://www.teleport.com/~pdx4d/hypertoon.html --
    one of the original "great circles" (good use of 
    metaphor).