"scott" <sco### [at] spamcom> wrote:
> PM 2Ring wrote:
> > The catenary is the curve formed by a homogeneous chain suspended
> > between two points in a uniform gravity field. It looks like a
> > parabola, but it's mathematically quite different. The equation of a
> >  parabola is just y = a*x*x, a simple quadratic, whereas a catenary is
> >  y = a*cosh(x/a), a transcendental equation.
> >
> > I had occasion to look at Chris Colefax's chain building code in
> > "Linc.inc", after referring a new user to it, and was dismayed to
> > discover that Chris used quadratics to build his chains. :(
>
> IIRC the "quadratic" chain assumes even weight distribution in the
> horizontal direction, whereas the catenary takes account of the fact that a
> chain at a steep angle will be heavier per unit horizontal distance.
> Clearly the steeper the chain the more of an "error" the quadratic one has.

Yes, the parabola is the curve of a suspension bridge with uniform
horizontal load.

> How about a comparison between the two for different length chains between
> two points?

I've been thinking about doing this, so I'll put something together over the
next day or so. It may be a little bit tricky ensuring both chains are
identical in length... it should be ok if I use very small links, though.
I also want to see the difference between the parabola & catenary with
connection points at unequal heights.

Thanks for your feedback, scott.

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