07102008, 07:44 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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07102008, 07:45 AM  #2 (permalink)  
thhhpptthh!

cut wire off... flatten out on floor, measure.
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07102008, 07:59 AM  #3 (permalink)  
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godamnitmothfuckle this is hypothetical...gimme the mathematical way of solving it
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07102008, 08:08 AM  #5 (permalink)  
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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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07102008, 08:14 AM  #6 (permalink)  
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EDIT Your talking about a helix, here is a link.
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07102008, 08:23 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 Last edited by Schmozilla; 07102008 at 08:46 AM. 
07102008, 08:27 AM  #9 (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.
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07102008, 08:28 AM  #10 (permalink) 
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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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07102008, 08:30 AM  #11 (permalink)  
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07102008, 08:33 AM  #12 (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. 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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07102008, 08:35 AM  #13 (permalink)  
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We're discussing a "helix" here: he·lix Audio Help /ˈhilɪks/ Pronunciation Key  Show Spelled Pronunciation[heeliks] Pronunciation Key  Show IPA Pronunciation –noun, plural hel·i·ces Audio Help /ˈhɛləˌsiz/ Pronunciation Key  Show Spelled Pronunciation[heluhseez] 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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07102008, 08:35 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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07102008, 08:36 AM  #15 (permalink)  
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07102008, 09:07 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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