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In article <112@telesoft.UUCP>, roger@telesoft.UUCP (Roger Arnold @prodigal) writes:
> > > 	I have heard a similar story about farmers in the Midwest using
> > > long stretches of barbed wire fence near long distance power lines for the
> > > same "free" power gambit.
> > 
> > 	The above situations sound like rural (as opposed to urban) legends
> > to me. [..]
> > 	Now, let's look at this situation and apply a bit of electrical
> > engineering.
> > [back-of-envelope analysis omitted]
> > 	The above assumes an iron core in the "receiving coil", which at
> > 4 x 40 feet in dimensions is pretty impracticable.  Without actually doing
> > the calculations, an air core would be at least an order of magnitude less
> > efficient.

> I don't immediately see what iron core vs. air core has to with the amount
> of power that can be extracted in this situation.

	Hmmm...  You pose a good question!  I will try to answer it as best
I can.
	The first issue to be decided is what mathematical/physical model
to use for explanations and calculations.  As I see it, we have no choice
but to consider this as a "transformer" situation, and we have at least
two models to choose from:

1.	We can use an "iron core" transformer model, with the power line
	as a single-turn primary, and an "air gap" (damn big one! :-)
	between the primary and secondary windings.  This model is the
	one that I used because it was the most simple, and I know the
	equations from memory.  While the "air gap" is admittedly large,
	the results still seem reasonable to me.

2.	We can use an "air core" transformer model.  Since we don't
	exactly have tight-coupled (i.e., bifilar) windings that have
	a relatively simple solution, the only method available is to
	use the mutual inductance method.  This is much more complex
	than the "iron core" calculations above.  It's been a while
	since I have done an air core transformer calculation by the
	mutual inductance method, but I believe it is essential that
	an incremental length of power line be chosen, along with a
	calculated voltage differential and inductance of such incremental
	length; this is starting to get esoteric and complex since we
	now have to speculate on power line characteristics beyond that
	of current flow.

	So my first point is: I chose an iron core because it was required
for the calculation which I used.

	In general, the following are reasons why an iron core should
RESULT in greater efficiency than an air core in this, uh, application:

1.	The general objective of ferromagnetic cores is to confine the
	magnetic flux within the transformer windings.  An iron core has
	a much lower reluctance than an air core; therefore less primary
	current is required to establish a given magnetic flux in an iron
	core than in an air core.  In addition, when current flows through
	the secondary winding of a transformer, a secondary flux is created,
	and the presence of the iron core confines this secondary flux and
	thereby minimizes the transformation loss.

2.	Consider the self-inductance of the "transformer" windings.  The
	emf of self-inductance is (L)di/dt.  The self-inductance is obviously
	much larger with an iron core, and therefore di/dt need not be as
	large to produce a given emf.

3.	Consider that an iron core extending beyond the "secondary" winding
	will capture and direct more lines of flux to the winding itself.
	Consider also that the presence of such an iron core will make
	"alignment" of the "secondary" winding with respect to the "primary"
	winding less critical for optimum power transfer. 

> But if you were serious about extracting power by
> this method, wouldn't you use a resonant circuit, or something that gave a
> high current in the pickup coil, properly phased against the induced EMF?

	Creating a resonant secondary circuit only has the effect of making
secondary impedance approach Rs at the point of resonance.  The secondary
impedance is probably not going to be much greater than Rs anyhow, so
the use of a resonant circuit may be of marginal benefit.
	Also, a problem develops in that as the impedance of the "load"
on the tuned secondary winding changes, so does the resonance of the
secondary winding; as a result, this arrangement would have to be retuned
each time the load changes - which is not such a great idea.

	I don't want to talk about the polyphase implications of three
"primary" windings with one "secondary" winding in this application. :-)

<>  Larry Lippman @ Recognition Research Corp., Clarence, New York
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