RE: Need Formula for length of spiral

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

Original poster: "Steve Greenfield by way of Terry Fritz <twftesla-at-qwest-dot-net>" <alienrelics-at-yahoo-dot-com>

This fits right in with my r^2 theory.

Mmmm... universal donut...

Steve Greenfield

--- Tesla list <tesla-at-pupman-dot-com> wrote:
> Original poster: "Pete Komen by way of Terry Fritz
> <twftesla-at-qwest-dot-net>" <pkomen-at-zianet-dot-com>
> 
> Sorry Jim, but the r^2 doesn't make sense to me.  I
> suggested that the
> length of the wire is PI * Average diameter * number
> of turns.  Take the
> case of three turns: the center turn length is PI *
> Diam., the outer turn is
> PI * (diam + delta); the inner turn is PI * (diam -
> delta).  Add them all
> together and the + and - PI * delta terms cancel
> leaving 3 * Diam * PI.
> 
> R^2 gives units of area (a unit of length squared). 
> For a close wound coil
> the area of the windings divided by the width of the
> wire would give a close
> approximation of the length but not r^2.  Note that
> the width is arbitrary.
> 
> You said, "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."
> 
> I agree with the first part, but the conclusion is
> wrong.  Consider your
> painting with three wide rings of constant width. 
> The total length of the
> rings is proportional to r^2/width (of the ring). 
> Since the width term is
> not fixed your conclusion is invalid.  In any circle
> of radius R, any
> arbitrary number of rings could fit, thus making the
> total length (or
> average circumference) of the rings arbitrarily
> different from R^2.
> 
> Regards,
> 
> Peter Komen


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