I am trying to build a hoop house/greenhouse. I will need to bend my poles so that there is enough height but still wide enough at the ground. I cannot figure out how to calculate it.
If I have a 14' wide base, that's the diameter of the circle, radius 7. I also thought the 7 here was a chord for the formulas.
I tried this formula, Sagitta = 7 - sqrt(7^2-7^2). This gives me 7. But I don't know how that helps me because I need a piece of PVC that will give me that Sagitta height, and I do not "see," and maybe this is where I am wrong, that a 14' piece of PVC will bend enough to give me 7' high, if the ground is 14'.
What am I doing wrong (or right)? I thought this would give me the length of the arc necessary and I'm not real sure of the angle I would bend it at to get that arc.
I have looked here,
How do I calculate the height of an arc?
radius = distance? arc length = height?
and I have read various things on calculating the Sagitta, like from here:
https://www.mathopenref.com/sagitta.html
This one might be what I need? I admit I didn't understand how to do the math.
Best Answer
If your hoop house is to be $14$ feet wide and $7$ feet high at the center then it will be a semicircle. Your PVC must be as long as half the circumference of a circle of radius $7$, so $$ 7\pi \approx 22 \text{ feet}. $$
Edit: For an arbitrary height of more than $7$ feet you can't have a circular arc.