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I'm wanting to bend 3/4" PVC pipe into a roughly 7ft tall elliptical shape using a 4ft wide base. Can anyone tell me the length of pipe I will need to bend? Basically I am going to drive 1/2" rebar in the ground spaced 4 ft apart leaving 2 ft above ground. I'll slip the two ends of the pipe over the rebar to hold the structure. Thanks

Kenny Sale
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  • This structure sounds quite practical. Your upper limit is of course the semi-circle of radius $7$ giving $7\pi\lt 22$ in feet. The actual arc length of an ellipse in general may be quite difficult... Note that since $2$ feet of each side are straight with the rebar, your upper limit moves to $5\pi+4\lt 19.8$ in feet. – abiessu Feb 17 '21 at 18:50
  • Thanks for the reply. I basically just want the peak in the middle (walkway) to be 6.5-7ft tall. This will be a cucumber trellis. The rebar height isn't set in stone. I could go 1ft or 1.5 ft even. It's just there to hold the pipe. I was hoping somewhere around 15-16 ft was doable. – Kenny Sale Feb 17 '21 at 19:03
  • The rebar height is helping make the length shorter (in a very small way), but the difference is not very much. The real difference is the height at the top, and there's not much that will change the length of pipe required aside from reducing that height, or reducing the depth of pipe along the rebar. If you want to get to $16$ feet, you'll have to reduce the overall height to slightly less than $6$ feet (we have $4\pi+4\gt 16.5$ and this is no longer an overestimate), or else reduce the amount of overlap between rebar and pipe by not letting the pipe go all the way to the ground. – abiessu Feb 17 '21 at 20:23
  • If you take the approach of "don't let the pipe go all the way to the ground" you can make a simple $4$-foot semicircle with equal remainders on both sides and just work with the rebar and the height you want the top to be at and fix that as the stopping point for where the pipe covers the rebar. For this approach, $16$ feet would be sufficient. – abiessu Feb 17 '21 at 20:28
  • You've been a big help. Let me ask for one more calculation please. It was the wire mesh length that was kinda restricting me to 16 ft but I found a roll I can cut to size. I have 10ft PVC on hand that I can connect for up to 20 ft lengths. So Lets settle on a 6.5 ft height with the pipe covering the rebar to the ground. What length of pipe am I looking at? Thanks again for taking the time to help me out. I'm not a math guy. – Kenny Sale Feb 17 '21 at 22:30
  • In terms of raw pipe length you are looking at somewhere between $4\pi+5$ and $\frac 92\pi+4$ which in feet is in the interval $[17.5,18.2]$. This puts you within about $4$ inches of your target height on either side, so I would suggest starting with $18$' $6$" and cutting it down to size as needed. – abiessu Feb 18 '21 at 00:03

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