Originally Posted by dog8mycode
Ya, I introduce my fair share of error in sewing.
I was very tempted to graph the 2 out to see the difference at that shallow of a depth, or better yet, find a depth and starting point that caused them to nearly overlap. You know, for the geek in me.
If I had time, the geek in me would do the same thing. I don't have time though even to find Ivelph's spreadsheet and hack it to do bridge dimensions.
Wouldn't hanging a chain (preferably one with small links) from 2 level points with the prefered depth give me a perfect cat curve? As I understand it, that's the basis for the physics of the curve and it's value. Ultimately, this is really what I meant by it being easier for me to mark and cut a cat curve vs dealing with graphing out the points.
emphasis mine. Perfect if your chain is really a cable with perfectly uniformly cross-section and density throughout, perfect if the attachment points have perfect freedom of movement in the cable's plane.
You're right, that the catenary curve is what you get from a mathematically perfect abstraction of a hanging cable. (It is also true that if you hang load uniformly on that perfect cable you get a perfect parabola.)
What you figure on doing will work just fine. Me, I'd bump the cable for sure sketching it out....and it still wouldn't matter much to the end result.