Need to calculate the length of an arc: 16' wide at base, rises 12" in center

Saibaton

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Hello,

I Need to make an arc that is 16' wide at the base, and rises 12" in the center. It'll be a perfectly curved arc. need to know what the length of the beam for the arc should be. looked up formulas online but they all want the degree of the arc, but I won't have that until I build it. Would very much appreciate the help.

 

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Hello,

I Need to make an arc that is 16' wide at the base, and rises 12" in the center. It'll be a perfectly curved arc. need to know what the length of the beam for the arc should be. looked up formulas online but they all want the degree of the arc, but I won't have that until I build it. Would very much appreciate the help.

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What kind of arc do you want - elliptic, circular, hyperbolic, .....?
 
Hello,

I Need to make an arc that is 16' wide at the base, and rises 12" in the center. It'll be a perfectly curved arc. need to know what the length of the beam for the arc should be. looked up formulas online but they all want the degree of the arc, but I won't have that until I build it. Would very much appreciate the help.


I assume you want a circular arc, though that may not be what you get if you bend a "beam" just by exerting pressure rather than deliberately forming it into a circle.

If so, see http://mathforum.org/dr.math/faq/faq.circle.segment.html . Your problem is case 8, with c=16, h=1 (feet). Note that the first formula gives the radius, and the second formula gives the angle of the arc, which you then use in the next. You have to calculate the angle in radians, not degrees.
 
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