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.
I found this not only very interesting but helpful. I want to build a hoop house over a couple of raised veggie beds for this winter. This will help me to know what to expect in height for the size of the bed.
WOW!!! David...The catenary is a GREAT answer to the Rion complaint!! I am at this time shopping for a GH kit but am delaying commitment because I am reading about the missing pieces and non fitting parts. Now I have read your post and seen your diagram. I have several cattle and hog panels waiting to find a use. I'm not sure that the Planning and Zoning for Pima County will accept the idea...but if I work out the other dimensions perhaps the catenary will "fly". Long live the Nerds of this world. I think my panels may be 20'. I'll measure this morning. Thanks for the priceless input. BTW,,,is there a formula for 20' long catenary? Thanks again.
There isn't a simple plug-in the number formula. There are lots of descriptions on the internet, but the math is not easy. You can Google "catenary formula" to get some idea. Here's a link to the description on Wikipedia
A very good way to experiment is with a foam-board from a craft store (the kind with 1/2-inch squares), a couple of push pins, and a chain necklace of the interesting length. I tested my approximations in the graph above like that. The only difference in what I drew is that I made the endpoints stiffer (like a cattle panel would be) rather than a completely flexible chain.
David...Thanks again...especially for the lead to Wikipedia. I never entered there before...It's a nerd paradise!!...more information than I can even think to ask!! I knew it was "out there"...but never bothered to find out where "there" really is. The catenary math is a tad beyond me..at this time...but perhaps I can learn. Looks like a worthwhile endeavor to me and for me. The foam board replication of that curve over a graph like background will help a lot...I can use my quilter's cutting pad which is already calibrated in inches and metric measure (and will accept pins) instead of the foam board.
Hello again David. I am at last starting my cattle panel hoop greenhouse. I am perhaps a "slow bloomer". Five cattle panels are ready to set up but I'm concerned about the wind gusts in Tucson Mountain area; they can be 50-60 miles per hour. Do you have any information about what the best angle to the prevailing winds might be for the inverted catenary hoop?
I tried an 8' x 8' kit:: EZ2 Build greenhouse...but have been replacing several roof panels every few months. I'm not very happy with the small square design or the polycarbonate panels. I'm hoping that the hoop design will serve better. BTW I'm using Wikipedia regularly since your suggested link several years ago.
So Thanks again
Good idea David, I'll try a second layer ..bubble wrap on the inside to hold the heat inside in winter and outside in summer. Right now we are between hot and cold...Snow predicted for Tucson in a few days...AFTER our heat wave of about 86 today. I'm going to try a cross of two of the panels for the shape and the strength. I'll post after it's up...Hope that will be in days and weeks instead of months and years.
Thanks for your reply.