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  #1  
Old 02-12-2013, 06:50 AM
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Default calculate the height of an arch

I have a 16' panel that I would like to bend it and attach each end to the ground to form an arch (basically I am making a garden trellis). I am trying to figure out for how wide it might be at the base, how high it would be at the peak. For example if the ends are 5' apart (making it 5' wide) how tall would it be. I have tried to find some kind of formula, but have only come up with formulas for circles in my search, which it is not. Thank you!
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Old 02-12-2013, 09:37 AM
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Default Re: calculate the height of an arch

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I have a 16' panel that I would like to bend it and attach each end to the ground to form an arch (basically I am making a garden trellis). I am trying to figure out for how wide it might be at the base, how high it would be at the peak. For example if the ends are 5' apart (making it 5' wide) how tall would it be. I have tried to find some kind of formula, but have only come up with formulas for circles in my search, which it is not. Thank you!
You will probably need some bracing to hold this shape. I think what you want is a semicircle at the top to form the arch and two equal straight sides. If ends are d apart, d is also the diameter of the semi circle, and the arc length of the semicircle is d*pi/2.

Subtract that from total length L, and divide by 2 for the height of the two straight sides.

h = (L - d*pi/2)/ 2

For L = 16 ft, d = 5, the arc is 7.85 ft curve, and each side height 4.07 ft.
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Old 02-12-2013, 10:18 AM
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Default Re: calculate the height of an arch

Thank you so much! I was thinking of it more in terms of a parabola, as opposed to part of a circle with straight sides. You're right, I'll be using T-posts in the ground on the corners to anchor it. So if I am understanding correctly, the apex of my arch would be 7.85'?
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Old 02-12-2013, 10:26 AM
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Default Re: calculate the height of an arch

Ok, I think I got it! The apex of arch would be the height: h=(L-d*pi/2)/2 plus the diameter?
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Old 02-12-2013, 04:35 PM
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Default Re: calculate the height of an arch

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Ok, I think I got it! The apex of arch would be the height: h=(L-d*pi/2)/2 plus the diameter?
It would be h plus the radius (which is half the diameter) so 4.07 + 2.5 = 6.57
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