I finally had time to look around for something to explain the shape of the arch formed by forcing the ends of a cattle panel inward. I kept looking because I wanted to know what the arch would look like at different widths, so I could decide how I was going to build. I found that the shape is a catenary, which is the shape of a chain hanging from two equal endpoints. You can illustrate by holding a small chain in both hands and watching as you move the ends in or out.The arch is the mathmatical result of inverting the shape.
The drawing below is a sample of what a 16 foot length (cattle panel or PVC pipe) would look like if bent to the measured endpoints. I've included an approximate height at the peak/center of the arch which results from each shape. The overall height of the structure is then set by changing the height of additional veritical sidewalls under the arch.
Hopefully this is interesting to someone else...I had fun doing it, but I'm a nerd.