#129422  09/18/09 04:22 PM
Calculating Turns In a Spiral

Greenhorn
Registered: 09/16/09
Posts: 21
Loc: Ohio

Does anybody know how to calculate the number of turns in a spiral if we know the length, the thickness of the material, and the core diameter?
I've been searching the internet for a formula but nothing seems to fit or there is heated debate over the subject.
Imagine a roll and we know the entire length of the "tape" and how thick it is. And we wrap it around a core. How many turns that is in the final roll is what i'm looking for.
For illustration sake lets make the length of the tape = L the thickness of the material = t the core diameter = d the final diameter = D the number of turns = N
L= 125" t= .125" d= .5"
we've thrown some equations around here at the office that perhaps it should look something like this
Assuming that the area = (PI/4)(D?d?) and area also = Lt Lt= (PI/4)(D?d?) where D = d+2Nt Lt = (PI/4)[(d+2Nt)?d?] or N= SQRT[((4Lt)/(PI))+d?]/(2t)
Any corrections or incite would be appreciated and welcome
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J. Fildes Mechanical Designer _____________________________________________________ Windows XP, VW2008 SP3 Fundamentals/Machine Design Intel Core 2 Duo E4600 @ 2.40GHz, 2GB Memory

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#129434  09/18/09 07:02 PM
Re: Calculating Turns In a Spiral
[Re: J.Fildes]

500 Club
Registered: 08/01/09
Posts: 575
Loc: Llareggub

Signing out for the day, but thus sang Dusty Springfield: Round, Like a circle in a spiral Like a wheel within a wheel, Never ending on beginning, On an everspinning reel http://www.youtube.com/watch?v=Wl8fKAYQuPkYour formulae look promising in a dilettante's eye and the issue is intriguing. Sort of: some of us have to deal with spiral ramps of multistorey car parks??
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#129437  09/18/09 07:28 PM
Re: Calculating Turns In a Spiral
[Re: islandmon]

Vectorworks Addict
Registered: 02/02/04
Posts: 3375
Loc: California

Parametric equation with animation of the Involute of The Circle : http://en.wikipedia.org/wiki/Involutel
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Architect, Civil & Geodesic Engineer ( retired ) User since Minicad v1.0 Bunch of stuff...iMac27,2.66 Core i5,8GB RAM

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#129438  09/18/09 08:04 PM
Re: Calculating Turns In a Spiral
[Re: J.Fildes]

Greenhorn
Registered: 09/16/09
Posts: 21
Loc: Ohio

We looked back over the original formula.
It reads N= SQRT[((4Lt)/(PI))+d?]/(2t)
It should read N= SQRT[((4Lt)/(PI))+d?]d/(2t)
that revised formula actually solves the problem. so if anyone is curious you can use that equation to solve for how many turns the length of some object would make when creating a spiral. so long as you know the core diameter, the length and the thickness of the material you can derive the number of turns from the solution. likewise you can use Lt= (PI/4)(D?d?) to find D.
Thanks to all who contributed to this post. Thanks to Bill here at the office for the equations.
_________________________
J. Fildes Mechanical Designer _____________________________________________________ Windows XP, VW2008 SP3 Fundamentals/Machine Design Intel Core 2 Duo E4600 @ 2.40GHz, 2GB Memory

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#129445  09/18/09 11:26 PM
Re: Calculating Turns In a Spiral
[Re: J.Fildes]

Vectorworks Addict
Registered: 02/02/04
Posts: 3375
Loc: California

Using the VW>Model>Helix:
Attachments
SpiralTape.JPG (258 downloads)
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Architect, Civil & Geodesic Engineer ( retired ) User since Minicad v1.0 Bunch of stuff...iMac27,2.66 Core i5,8GB RAM

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