of spline and catenary

[Ron Nossaman]

>I've always been a sucker for education.  Took me a while to get around to
>it, this time.  Attached Excel spreadsheet compares center loaded beam,
>distributed loaded beam, catenary, and parabola.  (note, only the first
>half of each curve is shown, saved me some time and mental sweat)   It
>occurred to me, after viewing the graph, that the fixed end, distributed
>loaded beam illustrates the component of string vibration influenced by
>only the string's stiffness, and the catenary illustrates the component
>influenced only by the string's tension.  The two are quite different in
>shape.  An illustration of inharmonicity.  Is this what you were getting at?
>
>regards,
>
>Mike

Hi Mike,
I did something similar here, only without the clamped end and distributed 
load examples. What I was wondering is what curve was described when you 
bent a piece of uniform cross section wood. There doesn't seem to be a name 
for it. The rebuilders who are cutting rib crown in a jig which clamps the 
center of the rib, wedging the ends out to form the curve are obviously not 
cutting a constant radius curve in their ribs. As far as I know, this is 
neither good, nor bad. It just is. But what is this curve?  It's close to a 
catenary, but flatter at the ends. As this rib is cut by the table saw, 
these flatter curves at the end will tend to spring and bend more as wood 
is cut away, changing the saw cut line and producing a crown more nearly 
parabolic or catenary than was the case before the cut was taken. The 
bending response of the rib changing as the cut is made also means that the 
crown profile will be asymmetric because half of the crown will be cut from 
the outside to the center, and half from the center out - unless the cut is 
done in two passes, with a bulk removal pass, and a light final pass.

I'm just trying to figure out approximately what is actually being produced 
here.

Ron N