i need to know how to find length of varies arch?

Question

please keep it as watered down as possible haved been in a math class in almost ten years but thought i remember there being something i could use. its so i know how much trim ill need for some openings none are the same and i have bet with a friend that my way is faster. he cuts long fits cuts asgian fit cuts agian .... till it fits right ... for this we'll say opening is 16 feet long 18 inches high at center of arch

its goes across opening of the garage that help any. basicly makes top panel look good

Answer 1

You need to specify the SHAPE of the arch--is it circular? Ok . . . stay tuned . . . Alright. If you have a piece of bendy moulding say, or anything that sags under its own weight and can be tied down at the ends, the resulting shape is a catenary. For the catenary you describe, 18 inches at the center for a garage from -8 to 8 ft, the form is y=21.57ft/2(e^(x/21.57ft) +e^(-x/21.57ft))+23.07ft. If you want the arc length of this curve; int(sqrt((y')^2+1))x=-8 to 8. It happens to be 24.8 ft long if an arch is to do what you describe. This doesn't take into account distortion if the thing is really springy and under high tension. This way is going to be faster only if you have access to some quality math software, or at least excel and an online numerical integrator. If you are not constructing something supporting itself under gravity, then make it a section of a perfect circle, and finding the length will be cake.

Answer 2

sory