Solved!
After further research, I've discovered a more accurate answer to this problem, and I also put together some VB.NET code that will find the form of this curve (well, a bunch of {x, y} points along the curve). I found a new paper that was one of the keys to figuring this out: "An...
I don't believe that formula was in his book...he only posted it to his blog today after I had posed the question to him (the book came out last June). He had figured out the circle relation earlier though (here), so that was likely in his book.
Oh wow: http://thegeometryofbending.blogspot.se/2014/01/these-saw-blade-curves-seen-in-two.html
I had e-mailed the guy, Mårten, about my inquiry, and he wrote me back with the above formula, h=\sqrt{(\frac{2L}{5})^2-(\frac{d-\frac{L}{5}}{2})^2} with d being the distance between the two...
I did look into elastica, but again, I haven't been able to find a straightforward way to derive or numerically solve for height yet, let alone plot the actual shape of the curve. I did find a few more relevant resources though:
http://myweb.lsbu.ac.uk/~gossga/thesisFinal.pdf...
Hi all,
I'm trying to do something that might be impossible, but seems to me should have a solution: Finding the height (or displacement) of a long, thin rod or wire under horizontal compression forces at the ends (pinned, not clamped) causing it to bend into a stable arch-like shape given...