Calculating Turns In a Spiral

[J.Fildes]

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

[Kool Aid]

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 ever-spinning reel

Your 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 multi-storey car parks??

[islandmon]

"When a wire is bent around a cylinder to make a coil, the end of the wire follows a path corresponding to the involute of a circle."

http://demonstrations.wolfram.com/BendingAWireOnACylinder/

http://demonstrations.wolfram.com/BendingAWireOnACylinder/HTMLImages/index.en/4.gif

[islandmon]

"As a straight line rolls on a circle without slipping, a point on the line moves along a curve called the involute of the circle.

The properties of this curve are often used in mechanical engineering to produce gear profiles."

http://demonstrations.wolfram.com/CircleInvolute/

http://demonstrations.wolfram.com/CircleInvolute/HTMLImages/index.en/4.gif

[islandmon]

Parametric equation with animation of the Involute of The Circle :

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

[J.Fildes]

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.

[islandmon]

Using the VW>Model>Helix: