Algebra I was about 28 years ago...

I'm sure I learned a formula that would allow me to figure this one out, but I'm getting frustrated trying to remember, so I will leave it to the greater intelligence of the group to find me an answer!

A friend gave me some old hog panels he had out in the weeds and I would like to make an arch (or two, or three, or four...) to grow birdhouse gourds and what-not on. They are 4 feet tall and 16 feet long. If I want the arch 7 feet tall at the center, how wide will the arch be? And when you figure it out, will you show me the darn math, so I can do it myself next time?!

Many thanks!

-- Polly (tigger@moultrie.com), May 17, 2000

Answers

Rats!! I forgot to ask - any suggestions on what I should use to anchor the sides down with? Tent stakes? Metal T posts? Electric fence posts? Landscape timbers?

Do I need something inside to tie it down to?

Thanks again!

-- Polly (tigger@moultrie.com), May 17, 2000.

Polly: On the math, here's what I would do. Assume a circle with a circumference of 32 feet (two 16' panels) and divide by pi (3.14) You'll get 10.2 feet or a circle with a 10.2 foot diameter. Divide that by 2 (semi-circle=1- 16'panel) Divide 10.2' by 2 for the radius of the circle (5.1') and that would be the height of the 10.2' wide arch. I'm guessing the arch would have to be about between 7-8 feet wide to give you a 7' height. If all else fails cut a wire with a little springyness to 16" long, form your arch to give you 7" height and measure the distance between the ends. That will get you in the ballpark.

been thinking along the same lines for a project here. I'm thinking landscape timbers with a hole on each end so a piece of rebar or some kind of long metal stake can be driven thru it to anchor it.

-- john leake (natlivent@pcpros.net), May 17, 2000.

I'm in the process of building these myself. Two 4ft. treated 2x4s, 1/2" holes drilled a few inches from the ends for 24" 3/8" rebar stakes, which are bent 2" (90 degree angle). Hog panel attached with fence staples. I was just going to stake one end then stake the other to form the arch I want! My instructions show that at 6' high, they will be 8' long. Algebra never entered my mind! Not surprising, I know. Hope this helps!

-- Jean (schiszik@tbcnet.com), May 17, 2000.

Just thought I might speculate here. I think you have long passed algebra and entered the world of trigonometry. It could be done much faster by arching it over a 7 foot pole and anchoring the ends at the desired width although IMHO you will have to add to your 16 foot lengh to achieve your desired width. This is aka "hillbilly math"

-- Joel Rosen (Joel681@webtv.net), May 18, 2000.

Polly, I used old dimensional lumber, cut the tops into chevrons to look like pickets, put those in post holes. Then added the arch and secured that with wire, staples, whatever. I also added horizontal wooden slats near the ground to train vines onto. (about a foot apart and three on each side). This was a fun project, and all it cost me was time. My kids painted it white, (and the ground, rocks, part of the sidewalk) and it looks great.

-- Rachel (rldk@hotmail.com), May 18, 2000.

Polly, John's maths as requested is right; but you're also faced with engineering and architectural considerations.

I'm assuming that your hog panels are more or less like our portable sheep-yard panels - stiff, and enough in them to let the animals see them easily, and be convinced they're not worth trying to go through. Even more so with hogs. If that's the case, they wouldn't bend easily.

If that's so (or anyway) maybe you could consider Japanese style arches - square or rectangular; upright posts and horizontal lintels being the visual component. If so, then approximately eight feet high by eight feet wide works out fairly easily with the help of an angle grinder or whatever to chop your panels in half. I'd be inclined to go about that high, and to prefer clearance (i.e. uprights) at the edges as well, because things hang down from arches. An eight-foot overhead could easily have only six feet clearance from the vegetation. Under the same circumstances, a seven foot circular arch would have five feet only in the centre, and a lot less a foot or two either side of centre. I'd have more confidence in myself doing the square construction too, rather than having to rely on engineering I didn't understand at a gut level.

Even if you do use the semi-circular arch, I'd suggest you consider having it on top of vertical sections for the above reasons - four foot vertical sections would work nicely, give you a height in the centre of the semicircle of about nine feet, but as above would become less fairly rapidly away from the centre.

For more revision, class: with [*] meaning [multiplied by] -

circumference (of a circle) = 2 * pi * r(adius)

circumference(semicircle) = pi * r = 22/7 (approx.) * r

r = (circumference of semicircle) * 7/22

All of which says you need a bit more than six radii to go around a circle, and a circle is a bit less than a third as wide as its circumference, which we could have figured out without the complications by looking at a picture of a hexagon inscribed in a circle.

Best wishes.

-- Don Armstrong (darmst@yahoo.com.au), May 18, 2000.

OK - answer from a mathematician.

Square arch - gives only 2ft width: 7' up + 2' over + 7' down = 16'

Triangle (8' on each edge, 7' in center) -> slightly under 8' wide (use pythagoras and two back to back triangles /|\: SqRt(8 squared - 7 squared) = SqRt(15) about = 4)

Semi circle has already been discussed (10' wide x 5' tall).

So a typical rounded arch (semi circle on top of rectangle): Let r = radius of rectangle (= 1/2 width of arch). Let h = height of rectangle. Formulas are 2h + (pi)r = 16 h + r = 7 Solve for h, r: h = (7pi - 16)/(pi - 2) = 5'3" r = 1'9" width = 2r = 3'6"

-- Deborah (ActuaryMom@hotmail.com), May 18, 2000.

I made a couple of these after seeing them in the magazine. I used wire to tie the end of the panel to a couple of cinder blocks, then bend the panel down and do the other end the same way. ( I read that suggestion on this forum). I found that the curve was lopsided, though, and that bugged me, so I ended up actually folding my panels (they'll fold, just stomp on 'em) and now they are more "A" shaped than curved. I've got peas growing on mine. At least, I did before this hail storm began 5 minutes ago...

-- Shannon (Grateful Acres Animal Sanctuary) (gratacres@aol.com), May 18, 2000.

Thanks, everyone, for all the answers. I read all the suggestions, but then I gave up and reverted to the "hillbilly math". (Sorry, but the only pi's at our house R round, cobblers R square. snicker!) I cut a length of clothesline wire to 16 inches, using a 1 inch to 1 foot scale, then bent it to a 7 inch center height and measured the distance between the ends, which came out to 6 inches. I did a little more finageling and came up with 6 1/2 feet tall and 6 1/2 feet wide also. I'd like to be able to walk under them, but at slightly less than 5 feet tall, I want whatever I'm growing on them to be within my reach (about 6 1/2 to 7 feet, depending on the stretch factor). I wanted to know how big it was going to be before I set it up so I could figure out exactly where it was going to go - saves time and labor and the Dad/Hubby aggravation factor! I had a boss in the factory one time who always put me on any new installation (equipment) that came into our department - he said "Now, I'm not saying that you're lazy..., I'm just saying that you always manage to figure out the easiest way to get things done." I informed him that the word he was looking for was efficient!!

Thanks again to all who answered!

-- Polly (tigger@moultrie.com), May 19, 2000.

How did all your garden arch making go? The children & I made 2 of these this year and they turned out very nice! We are pleased. We've got pole beans on one and sugar snap peas on the other. I would have made more, but my husband was getting possessive of the remaining hog panels. Probably thinking of using them for...hogs! Oh, well. Maybe I'll actually buy a couple of new panels next year. Are you all going to take them down for winter and store them or leave 'em up??

-- Jean (schiszik@tbcnet.com), June 22, 2000.

They're working out great, Jean! He gave me two tall ones (cattle panels?) and one short one. They look pretty neat in the garden. The really great thing is that the "bug patrol" (birds) uses them for an observatory tower, then they swoop down un theior unsuspecting lunch! I'll take them down in the fall, because right now, they are where the grape arbor will go next spring. Not real sure where I will put them next year - but I know that they will go somewhere!! I may spead them out a little so they are wider than they are tall and put them all in a row to make a play tunnel for kids...

-- Polly (tigger@moultrie.com), June 22, 2000.

The tunnel sounds like fun! My children would love that, too! I was thinking how pretty they would be with something like morning glories, sweet peas or scarlet runner beans growing on them for next year. Of course, I'd need to build more...

-- Jean (schiszik@tbcnet.com), June 22, 2000.

I made one after I saw one in the magazine,we went to the wreckers and bought a 4x12...or was it 16???{I dunno} hog panel and we put it in between our two raised bed boxes,intending to secure it at the bottom...but you know before we could get to that everything had grown up and held it in place >IT IS GORGEOUS!!!next year we will add three more to that and have a looong tunnel.I,ts probably only about 4 1/2- 5 foot high though,and could easily have been secured to the raised beds.

-- teri murphy (mrs_smurf2000@yahoo.com), September 26, 2000.