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Old 07-10-2008, 06:44 AM   #1 (permalink)
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Math help: how do you calculate the length of a spiral?

Say you had a wire spiraling around a 30" pipe at a 6" pitch. How would you go about calculating the length of that wire per foot of the pipe?

I have an equation for doing such but it makes no sense to me and I wanna make sure it's right.
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Old 07-10-2008, 06:45 AM   #2 (permalink)
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cut wire off... flatten out on floor, measure.
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Old 07-10-2008, 06:59 AM   #3 (permalink)
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cut wire off... flatten out on floor, measure.
godamnitmothfuckle this is hypothetical...gimme the mathematical way of solving it
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Old 07-10-2008, 07:00 AM   #4 (permalink)
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What is your level of math...I can give it to you is terms of calculus...
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Old 07-10-2008, 07:08 AM   #5 (permalink)
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What is your level of math...I can give it to you is terms of calculus...

I went to clemson too.....so please use small words and speak slowly!



The formula they used is:

length (per foot) = circumference+(pitch^2)^.5/pitch

however, the (pitch^2)^.5/pitch really equals one so it comes out to:

length = circumference + 1


I understand this is probably a close approximation of the actual length and not as accurate as a calculus method would get it, but I still don't fully understand where it's coming from.
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Old 07-10-2008, 07:14 AM   #6 (permalink)
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Originally Posted by bgaidan View Post

however, the (pitch^2)^.5/pitch really equals one so it comes out to:

length = circumference + 1
Not if the exponent is .5/pitch since pitch is variable.

EDIT
Your talking about a helix, here is a link.
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Old 07-10-2008, 07:16 AM   #7 (permalink)
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Not if the exponent is .5/pitch since pitch is variable.
If it's a spiral, isn't the pitch constantly changing?

Sounds like it would require the utilization of calculus concepts.
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Old 07-10-2008, 07:23 AM   #8 (permalink)
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I get 96.94 inches per wrap with that formula...2 wraps = 193.28 inches


EDIT: With Calculus I get 191.727 Inches

For the calc...

Parametric equations :

x= r*cos(t)
y= r*sin(t)
z= ct

to make z=6 inches when t= 2*pi c= 3pi

SO the length of that helix over 1 foot (4pi)=

Integral from 0 to 4pi of (sqrt(x^2 +y^2 + z^2)dt

sub the parametric equations in and you get

(sqrt((r*cos(t))^2 +(r*sin(t))^2 + 3pi(t)^2)dt from 0 to 4pi...


any way all that shit = 191.7272

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Old 07-10-2008, 07:27 AM   #9 (permalink)
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If it's a spiral, isn't the pitch constantly changing?
If it was installed poorly, yes

This sounds just like an auger. The flights (or wire) can have an exact, constant pitch along the rotation of the shaft.

Kinda like when you look at an auger in one spot and rotate it, that spot will appear to move down the length of the shaft. That is the pitch, or gap remaining constant.
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Old 07-10-2008, 07:28 AM   #10 (permalink)
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Originally Posted by PTSchram View Post
If it's a spiral, isn't the pitch constantly changing?
Pitch is defined as change/revolution. If it is revolving around a pipe with a constant OD then the pitch will be constant. I meant variable as the pitch is a variable in the equation, not the application.

EDIT
Drew this up quick, this is 6" pitch, 30" OD. This is the segment he would be calculating.
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Old 07-10-2008, 07:30 AM   #11 (permalink)
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If it was installed poorly, yes

This sounds just like an auger. The flights (or wire) can have an exact, constant pitch along the rotation of the shaft.

Kinda like when you look at an auger in one spot and rotate it, that spot will appear to move down the length of the shaft. That is the pitch, or gap remaining constant.
We are discussing two different things. A spiral starts in the center and moves outward (or at least, that's how I was visualizing it), thus the radius is constantly changing. What you've described is not a spiral, but a fixed diameter pitch.
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Old 07-10-2008, 07:33 AM   #12 (permalink)
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Originally Posted by PTSchram View Post
We are discussing two different things. A spiral starts in the center and moves outward (or at least, that's how I was visualizing it), thus the radius is constantly changing. What you've described is not a spiral, but a fixed diameter pitch.

Right, but a wire wrapped around a pipe is not a spiral in that sense. It's more like a spring spiral with a fixed ID and OD. The pitch will remain constant (if it was built, and installed correctly).

What you are describing only holds true if the OD of the pipe changes diameter throughout its length. Edit: and even if the pipe size changed, the pitch could still remain constant. The length of wire per foot would change though.
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Old 07-10-2008, 07:35 AM   #13 (permalink)
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Originally Posted by PTSchram View Post
We are discussing two different things. A spiral starts in the center and moves outward (or at least, that's how I was visualizing it), thus the radius is constantly changing. What you've described is not a spiral, but a fixed diameter pitch.
I think they just had poor wording on the problem. Spiral is a rather broad term. It states "pipe" in the problem which would have a fixed OD.

We're discussing a "helix" here:

he·lix Audio Help /ˈhilɪks/ Pronunciation Key - Show Spelled Pronunciation[hee-liks] Pronunciation Key - Show IPA Pronunciation
–noun, plural hel·i·ces Audio Help /ˈhɛləˌsiz/ Pronunciation Key - Show Spelled Pronunciation[hel-uh-seez] Pronunciation Key - Show IPA Pronunciation, he·lix·es. 1. a spiral.
2. Geometry. the curve formed by a straight line drawn on a plane when that plane is wrapped around a cylindrical surface of any kind, esp. a right circular cylinder, as the curve of a screw. Equation: x = a sinθ, y = a cosθ, z = b θ.
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Old 07-10-2008, 07:35 AM   #14 (permalink)
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It's basically a helix, as described a couple posts ago. If you read the original question, it is basically a wire wrapping around a pipe. An auger flight is a good example.


We did just find an error in the way we were looking at the equation, it should be:
(circumference+(pitch^2))^.5/pitch

I was missing a set of parenthesis.


I foung this little explanation about calculating the railing length around a spiral staircase, which is ultimately the same thing:
http://www.newton.dep.anl.gov/askasc.../math99080.htm
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Old 07-10-2008, 07:36 AM   #15 (permalink)
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Right, but a wire wrapped around a pipe is not a spiral in that sense. It's more like a spring spiral with a fixed ID and OD. The pitch will remain constant (if it was built, and installed correctly).

What you are describing only holds true if the OD of the pipe changes diameter throughout its length.
OK, I read the original post and now I see that it isn't that difficult of a calculation.
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Old 07-10-2008, 08:07 AM   #16 (permalink)
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Using this formula, I come up with 188.495" wire length per foot.

This is using 0" as a diameter of wire, which is unknown at this point, and will have an effect.



Formula is shown on this web page with the online calculator.

http://deepfriedneon.com/tesla_f_calchelix.html
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