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.

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

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