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PA2RHB > INFO 12.07.02 22:07l 34 Lines 1286 Bytes #999 (0) @ WW
BID : EC0014PA2RHB
Read: DB0FHN GUEST
Subj: Re: Catenaries
Path: DB0FHN<DB0ZWI<DB0CHZ<OK0PKL<OK0PHL<OK0PCC<OK0NAG<9A0BBS<LZ1KIS<HR2PAQ<
WB0TAX<PI8WFL
Sent: 020712/1947Z @:PI8WFL.#NH1.NLD.EU #:52242 [Enkhuizen] $:EC0014PA2RHB
From: PA2RHB@PI8WFL.#NH1.NLD.EU
To : INFO@WW
Barry, VK2AAB, wrote:-
> Cantenaries are the overhead wires for the trains to pick up their
> power. Usually here, anyway, with a heavy cable which droops in a curve
> between supports and has hangers which hold in a straight line the
> actual wire against which the pantogragh on the train presses.
In math, 'catenary' is the name for the drooping curve itself.
In some languages, the name translates as "chain line" (Dutch
'kettinglijn') because that is what a drooping chain looks like.
It is not a parabola. That is what you get if a line, itself of no
considerable mass, is supporting a mass proportional to horizontal length.
Think of the Golden Gate bridge. Equation: y= a* x^2 + b.
A catenary (mathematically speaking) is what you get if it is the other
way around: the line itself heavy, and supporting next to nothing. So the
weight is proportional to the length measured along the line.
The classical equation would be y = (2a)^-1 * (e^ax + e^-ax).
A fun fact (for a mathematician) is that the square of the slope, in any
point, is the square of the height of that point minus a constant (the
constant being, of course, the minimum height of the curve).
Boy, I am _really_ of topic now.
Best regards,
Rudolf
Heemskerk
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