Re: Need Formula for length of spiral

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jimlux-at-earthlink-dot-net>

A further aspect which occurred when driving to work this morning..

Consider the length of each turn (spiral or not, but concentric circles, in
any case).  They're going to be some form of 1+2+3+4+5+.... which is a
N^2+N kind of thing...

Another analogy (due to Leibniz, and the Chinese, much earlier). Imagine
you are painting in a circle with concentric rings of constant width.  The
area (or circumference, since it is constant width) of a given ring is
proportional to its radius. 

You know that the sum of all areas of the rings is the area of the circle,
which is proportional to r^2, so therefore, the sum of the circumferences
must also be proportional to r^2.

A spiral winding typically doesn't start at the center of the circle, so
you're really working on an annulus (a circle with a circular hole in the
middle), but the idea of dependence on r^2 still holds.

And, just to beat this into the ground somewhat more, I considered the case
of the spiral where r = k * theta.  There are other spiral forms, which may
have different relations (because the assumption of equally spaced rings,
as above, doesn't hold). (examples: r = r0*k^theta (equiangular/log spirals))

For those more analytically inclined..

consider a small length of the winding ds.  ds = r*dtheta where r =
r0+k*theta, so, the total length is

integral[theta start, theta end] of (r0+k*theta)*dtheta



Tesla list wrote:
> 
> Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<jimlux-at-earthlink-dot-net>
> 
> since the length is essentially integrating a linearly varying function
> (radius) there will need to be some squared term in the equation. Granted,
> for small enough ranges of parameters, a linear approximation will probably
> work.
> 
> ----- Original Message -----
> From: "Tesla list" <tesla-at-pupman-dot-com>
> To: <tesla-at-pupman-dot-com>
> Sent: Wednesday, February 13, 2002 8:37 PM
> Subject: Re: Need Formula for length of spiral
> 
> > Original poster: "Steve Stuart by way of Terry Fritz <twftesla-at-qwest-dot-net>"
> <sstuart-at-glasscity-dot-net>
> >
> > Try:
> >        L = (Do - Di) / 2 * 1.6 * pi * T
> >
> > Where:
> >        L  = conductor length
> >        Do = outside diameter
> >        Di = inside diameter
> >        T  = number of turns
> >
> > It will give you a pretty close approximation
> >
> > 73 de Steve
> > ·¸¸·´¯`·¸¸·´¯`·¸¸·´¯`·¸¸·´¯`·¸¸·´¯`·¸¸·
> > w8an-at-w8an-dot-net
> > http://www.w8an-dot-net
> >
> > Tesla list wrote:
> > >
> > > Original poster: "John Tomacic by way of Terry Fritz
> > <twftesla-at-qwest-dot-net>" <tesla_ownz_u-at-hotmail-dot-com>
> > >
> > > Hi everyone,
> > >
> > > Does anyone have a formula that I can use to calculate the length of
> wire
> > > required in a flat spiral coil? I have the formula for inductance,
> however,
> > > I really need the wire length.
> > >
> > > Thanks,
> > >
> > > John
> > > SST coiling in Ottawa.
> > >
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