At 02:51 AM 2/3/2003, Loren A. Busch wrote: >Let's close this subject, go to: >http://www.2dcurves.com/exponential/exponentialhc.html > >Notice no mention of 1::1 ratio in the dimensions. Eyeballing the curve >suggests that that could be a characteristic, but not requirement. I'm >not going to try to figure it out right now. Nice one, Loren. Catenary with 1:1 ratio is a single case among infinite possibilites. A cable stretched so tight there is no visible deflection will still form a catenary in a uniform gravity or acceleration field, although you wouldn't ordinarily notice it (and of course to be accurate it has to be infinitely flexible and totally inextensible). Likewise taking a mile of this theoretical cable and suspending the ends two feet apart will result in a catenary, though again almost unrecognizable. Like the surface of a soap bubble, it's a minimum-energy configuration, in this case potential energy -- every part is as low as it can be given the physical constraints of the system. Suspension bridges ordinarily use some close approximation to a catenary for the main cables, naturally enough since that's how they will hang anyway if left alone. I haven't read this thread so maybe it's all been said, if so sorry. :) david
-- David Beierl -- dbeierl@attglobal.net |
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