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