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Re: 7.1Hz, how the heck did Tesla succeed?

Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>




Yes, but think about it:  his claims were originally dismissed because
radio waves don't go around the earth, so resonance is impossible, Tesla's
objections to the contrary.  Then science advanced, soon finding that
radio waves do go over the horizon.  Then fifty years later Schumann
rediscovered the resonances Tesla was always talking about.  Is Tesla
vindicated?  No, his claims were STILL dismissed.  After all, if you're
sending out high power VLF (at hundreds of HZ?), you can't receive it,
since you'd need a quarter-wave antenna 100 kilometers long in order to
intercept significant energy from the fields.  But this objection turns
out to be wrong too.  An ideal short antenna can absorb the same energy
flux as a full size quarter-wave antenna.  That's assuming ideal zero-ohm
inductors with infinite Q tank circuits.  Real inductors make short
antennas behave much larger than their physical length, but not 1000KM
large.  But received power depends on receiver Q, and isn't fixed by
antenna length.


Ahem. the earth is not a sphere (eccentricity is about 1 part in 300), particularly for an EM wave, and it is quite lossy. If you send an impulse out from a point on the earth, and you sit at the antipodes, it will not be a nice narrow pulse. This makes the Schumann resonance quite broad.

As for the tradeoff between size, efficiency, and bandwidth (Q) etc. of antennas, you need to look at the work of Chu in 1948 ("Physical Limitations of Omni Directional ANtennas" Journ. App. Phys., v19 Dec 1948), as well as the dozens of folks following him, although they are mostly refining the theory. If you take the Chu limit as a order of magnitude, you won't be far off. Essentially, all physically small antennas (i.e. small compared to a wavelength) have a narrow bandwidth OR low efficiency.

> > Or could he even have made a 60Hz extra coil? With such low 
>  > frequencies a non-resonant air-core transformer could easily be driven
>  > by mechanical AC generators, and only the "extra coil" would need to
>  > be resonant.  But the wandering Earth-resonance frequency would still
>  > be a problem.
>
> Why should it wander?

Why should it remain fixed?  The real question is *how much* does it
wander (a tiny percentage, or a significant amount?)  I've seen papers
that mention significant frequency changes over spans of months, so these
changes are possible.  If there were significant random changes over a
span of seconds, then this would appear on spectrum measurements as an
artifact: a falsely wide resonance band, and a falsely low Q.  See
http://www.pupman.com/listarchives/1995/january/msg00002.html

The propagation speed of an EM wave over the surface varies quite a bit, over land and sea, for instance, because of the different dielectric constants and conductivity.

There's also the variability of the height of the ionosphere to consider. Before it was decommissioned, Omega navigation relied on the relatively stable propagation of waves at around 10-13 kHz, but even there, the nav solution needed to take into account the difference in prop delay along a night path and a day path. But even there, you're looking at uncertainties on the order of 1 part in 20,000 (which, I grant you, is a fairly high Q)