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# Mathmatical problem. Need help

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I run into this quite a bit at work. I'll find some kind of arched header or circular wall that I have to shore up or whatever and need to contour plywood or steel to fit.

I can obviously get the x and y dimension, but I dont know if there is a formula that can give me the radius or diameter of the arch with just these 2 dimensions assuming it's a portion of a circle.

The y dimension could be as small as 2'-0" or as big as 50'-0"

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I think this is what you're looking for.

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i would take a picture from a position as square to the arc as possible and measurements and play with them in Google sketchup that way i could get all the numbers i would need and be able to see if the curve holds close to the mathematical arc.
I once had to order doors for some curved cabinetry and template and trial and error with a 6 foot compass was all i could figure out. This method adjust for the places where the arc was off

have you tried googling radius of an arc?

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Hello Twoply.
If you have got physical access to said arc, and so, in addition to x and y, you can take also the measurement of s, where s is the length of the arc (see atteached pciture), beyond the web sites suggested by our friends, there is the following (approximate) formula allowing you to easily calculate the radius R:

R = s / sqrt(24 · (1 - y/s))
Stay safe out there
Blue Skies and Soft Walls
BASE #689 - base_689AT_NO_123_SPAMyahoo.com

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If you're still looking for help, could you please upload an illustration in a more universally accessible format (no MS Paint here)?
Math tutoring available. Only \$6! per hour! First lesson: Factorials!

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Because you don't really want a section of a circle with a constant radius. You really want a parabola. At least I would.

http://en.wikipedia.org/wiki/Parabola

The advantage being the parabola is more structurally sound.
The World's Most Boring Skydiver

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Quote

The advantage being the parabola is more structurally sound.

Why? Cycloids are sexy.

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Given the lengths you have you can calculate the radius (double for diameter) of the circle as followed:

r = (4x² + y²) / (8x)

See the attachment for an explanation (sorry for the bad image quality).
Nice words are not always true - and true words are not always nice.

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Math Mike? Really? You're not fooling anyone...we know you can't count past potato

Fiend

I am about to take my last voyage, a great leap in the dark. - Thomas Hobbes.

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Because you don't really want a section of a circle with a constant radius. You really want a parabola. At least I would.

http://en.wikipedia.org/wiki/Parabola

The advantage being the parabola is more structurally sound.

Not if he's fitting his reinforcing material to an existing CIRCULAR structure, as his post suggests.
...

The only sure way to survive a canopy collision is not to have one.

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My suggestion: String Theory will solve the problem.

...get a long string and....
My reality and yours are quite different.
I think we're all Bozos on this bus.
Falcon5232, SCS8170, SCSA353, POPS9398, DS239

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Quote

Quote

Because you don't really want a section of a circle with a constant radius. You really want a parabola. At least I would.

http://en.wikipedia.org/wiki/Parabola

The advantage being the parabola is more structurally sound.

Not if he's fitting his reinforcing material to an existing CIRCULAR structure, as his post suggests.

Except that many arches only appear to be circular or parabolic when in reality they're some form of inverted catenary.

A parabola is at least a close approximation to a catenary and easier to work with

http://en.m.wikipedia.org/wiki/Catenary#section_2

ZMC

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Quote

Quote

Quote

Because you don't really want a section of a circle with a constant radius. You really want a parabola. At least I would.

http://en.wikipedia.org/wiki/Parabola

The advantage being the parabola is more structurally sound.

Not if he's fitting his reinforcing material to an existing CIRCULAR structure, as his post suggests.

Except that many arches only appear to be circular or parabolic when in reality they're some form of inverted catenary.

A parabola is at least a close approximation to a catenary and easier to work with

http://en.m.wikipedia.org/wiki/Catenary#section_2

ZMC

He said (among other things) "...circular wall " (emphasis mine).

As far as arches are concerned, Norman and Saxon arches are circular, Gothic consist of 2 circular arcs, Roman and Greek arches are circular or flattened circular. I doubt he's shoring up the gateway arch in St. Louis, which is a catenary.
...

The only sure way to survive a canopy collision is not to have one.

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Mathmatical problem

Once you solve your mathmatical problem, we'll get cracking on your spelling.

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Ha! And I beat up ironworkers on their grammer! Good catch!

Grammar.

lisa
WSCR 594
FB 1023
CBDB 9

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nice sig when you highlight it

x2 now!

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