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Need Math Help From The Gurus ;)

 
 
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Old 12-06-2015, 02:23 PM  
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Need Math Help From The Gurus ;)


So I'm building a 10,000 sq ft monster with a spiral staircase in a 3 story cylindrical turret with pinnacle roof (witches tit is what I've always called it but anyway...)
Here's my math question:
What is the formula for finding the arc length of a segment starting from only having the radius and chord length known?

Especially when the angles aren't 90,45,45?

For instance with a circle with a radius of 6' and a chord length of 7' what is the arc length?

And remember- I haven't got any formal math education so keep it simple- I have a basic understanding of trig functions but I'll need to be walked through

By the way- havnt seen yall in awhile just been swamped. I went from a 2-3 man show doing a few homes a year to doing over a dozen a year and being president of the local HBA. It's been a ride Name:  ImageUploadedByContractorTalk1449429786.419484.jpg
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Last edited by Ninjaframer; 12-06-2015 at 02:42 PM.
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Old 12-06-2015, 02:26 PM  
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Re: Need Math Help From The Gurus ;)


Don't have your answer but good to hear from ya! Awesome that things are going well for you!!

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Old 12-06-2015, 02:50 PM  
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Re: Need Math Help From The Gurus ;)


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Originally Posted by Ninjaframer View Post
What is the formula for finding the arc length of a segment starting from only having the radius and chord length known?

Especially when the angles aren't 90,45,45?

For instance with a circle with a radius of 6' and a chord length of 7' what is the arc length?
Will this help you?

http://planetcalc.com/1421/
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Old 12-06-2015, 02:57 PM  
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Re: Need Math Help From The Gurus ;)


I looked at that and played with my trig master calculator till 4am last night. I'd need some one to walk me through it.
Once I learn a formula I'm good but I don't have any formal education so I can't read equation very well.
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Old 12-06-2015, 03:01 PM  
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Re: Need Math Help From The Gurus ;)


?
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Old 12-06-2015, 03:09 PM  
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Originally Posted by Ninjaframer View Post
I looked at that and played with my trig master calculated till 4am last night. I'd need some one to walk me through it.
Once I learn a formula I'm good but I don't have any formal education so I can't read equation very well.

I'm not a very good teacher, but I'll try -

In the meantime, here's an even better calculator -

In the example you have in your OP, the "width of arc" in the formula is a chord.

So just punch in radius (72)

width of arc (84)

set the output of arc length to inches

push calculate.

I'll work on the formulaic explanation if someone doesn't beat me to it.

http://www.handymath.com/cgi-bin/arc...ss=1&decimal=5
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Old 12-06-2015, 03:28 PM  
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Re: Need Math Help From The Gurus ;)


Ya an explanation of formula is what I'm after. I keep a black book of all this kind of stuff so once I get it it goes in there
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Old 12-06-2015, 03:49 PM  
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Re: Need Math Help From The Gurus ;)


You have a piece of pie. The chord cuts across the curve, making a triangle with the two radii.
split that triangle down the middle, and you have two right triangles, each with hypotenuse equal to the radius of the circle (6’ in your example) and one side equal to the chord divided by two (or 3.5 in your example).

The “central” angle of each right triangle has a sine (opposite over hypotenuse) of 3.5/6.0 in your example. In other words, that angle (half of the pie piece) is arcsin(3.5/6.0), or sin^-1(3.5/6.0), or 35.685 degrees in your example. Since the original pie piece had two of the halves, the total angle is 35.685*2 = 71.371. The length of the arc (a string laid around the edge of the circle, is (71.371/360) * 2*pi*r, or (71.371/360) * 2 * pi * 6.0 = 7.474, in your example.

Given the radius r and chord c, the formula is

((2 * arcsin((c/2)/r))/360)*2*pi*r

Simplified, and if arcsin will answer in radians rather than degrees (as Excel does), that is arcsin((c/2/r)*2*r

or in Excel, for your example, “=ASIN((7/2)/6)*2*6"

Probably someone else should check all that. It's important to get the parenthesis right, or if you're doing it with a calculator, the order of operations, which is:

If your calculator operates in radians (rather than degrees). Again, Excel by default operates in radians.
chord/2
Then that divided by radius.
Then arcsine that.
Then that times 2.
Then that times the radius.

If your calculator operates in degrees
chord/2
Then that divided by radius.
Then arcsine that.
Then that * pi
Then that divided by 180
Then that times 2.
Then that times the radius.
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Last edited by CarpenterSFO; 12-06-2015 at 04:27 PM. Reason: Needed to account for radians v degrees.
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Old 12-06-2015, 03:55 PM  
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Re: Need Math Help From The Gurus ;)


Much better explanation than what I was writing!


And I cheated and checked it with the calculator, it agrees.
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Old 12-06-2015, 04:10 PM  
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Re: Need Math Help From The Gurus ;)


I imagine either one of these guys can help.

Try the SBE website, lots of info there.

Nice to see you back & that you are doing well....

https://www.contractortalk.com/members/birch-50235

http://www.sbebuilders.com/
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Old 12-06-2015, 05:05 PM  
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Re: Need Math Help From The Gurus ;)


Both Sim and Birch have helped me before- I hope one of them pop in. Birch has been good about writing out keystrokes for the type of calc I use and explaining formula in a way I can grasp both awesome guys!
Thanks for the responses so far- it's good to poke back in here every so often- see a ton of new names for sure
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Old 12-06-2015, 05:16 PM  
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Re: Need Math Help From The Gurus ;)


Or:
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Old 12-06-2015, 05:28 PM  
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Re: Need Math Help From The Gurus ;)


Wish it was explained to me in school that this stuff could be remotely useful in the future.
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Old 12-06-2015, 05:31 PM  
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Wish it was explained to me in school that this stuff could be remotely useful in the future.

That's the freekin truth.
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Old 12-06-2015, 05:31 PM  
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Re: Need Math Help From The Gurus ;)


You must have some really crappy prints to not have this info at your fingertips. I don't hesitate to call on the archy when something is missing that I need to do my job. Shouldn't have to be that complicated.
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Old 12-06-2015, 05:39 PM  
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Wish it was explained to me in school that this stuff could be remotely useful in the future.
Pretty tough for a kid in high school to accept that. My older son accepted it on faith that math would help him succeed in life. My younger son doesn't accept it, and though he's an outstanding math student, there hasn't been a lot of his free will involved in getting there and staying there. He'll thank me when he's 50, or not.
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Old 12-06-2015, 05:40 PM  
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Re: Need Math Help From The Gurus ;)


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So I'm building a 10,000 sq ft monster with a spiral staircase in a 3 story cylindrical turret with pinnacle roof

Sure would like to see the construction of the spiral staircase, if you can take a few pictures during....
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Old 12-06-2015, 06:27 PM  
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Re: Need Math Help From The Gurus ;)


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Originally Posted by Warren View Post
You must have some really crappy prints to not have this info at your fingertips. I don't hesitate to call on the archy when something is missing that I need to do my job. Shouldn't have to be that complicated.

They are so bad I had to call the architect because there was not even dimensions to the radius point for the turret anywhere- on any page. I couldn't even lay out the foundation.

I'd want to know how to do this math anyway though just me
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Old 12-06-2015, 06:34 PM  
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Re: Need Math Help From The Gurus ;)


Quote:
Originally Posted by CarpenterSFO View Post
You have a piece of pie. The chord cuts across the curve, making a triangle with the two radii.
split that triangle down the middle, and you have two right triangles, each with hypotenuse equal to the radius of the circle (6’ in your example) and one side equal to the chord divided by two (or 3.5 in your example).

The “central” angle of each right triangle has a sine (opposite over hypotenuse) of 3.5/6.0 in your example. In other words, that angle (half of the pie piece) is arcsin(3.5/6.0), or sin^-1(3.5/6.0), or 35.685 degrees in your example. Since the original pie piece had two of the halves, the total angle is 35.685*2 = 71.371. The length of the arc (a string laid around the edge of the circle, is (71.371/360) * 2*pi*r, or (71.371/360) * 2 * pi * 6.0 = 7.474, in your example.

Given the radius r and chord c, the formula is

((2 * arcsin((c/2)/r))/360)*2*pi*r

Simplified, and if arcsin will answer in radians rather than degrees (as Excel does), that is arcsin((c/2/r)*2*r

or in Excel, for your example, “=ASIN((7/2)/6)*2*6"

Probably someone else should check all that. It's important to get the parenthesis right, or if you're doing it with a calculator, the order of operations, which is:

If your calculator operates in radians (rather than degrees). Again, Excel by default operates in radians.
chord/2
Then that divided by radius.
Then arcsine that.
Then that times 2.
Then that times the radius.

If your calculator operates in degrees
chord/2
Then that divided by radius.
Then arcsine that.
Then that * pi
Then that divided by 180
Then that times 2.
Then that times the radius.

Perfect- thanks for dumbing it down for me it didn't occur to me to split the triangle and create 2 with right angles- duh.
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Old 12-06-2015, 06:50 PM  
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Re: Need Math Help From The Gurus ;)


Quote:
Originally Posted by aptpupil View Post
Wish it was explained to me in school that this stuff could be remotely useful in the future.

That was me because the math seemed stupid. Go figure that now I'm bad with math and need to use it.

I only did geometry I believe, never did calculus. I've toyed with taking some online math class or something to see if I can improve my skills.

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