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

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: William Beaty <billb@xxxxxxxxxx>

On Sat, 16 Jul 2005, Tesla list wrote:

> Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>
>
> >Doesn't it affect narrow pulses and high frequencies?   Supposedly the
> >resonance overtones vanish above 10 to 20 KHz, and Earth eccentricity
> >would be a good explanation for this.  The low overtones, where wavelength
> >is nearly the size of the earth, those would essentially ignore the
> >geographic features which are far smaller than the wavelength.  But I
> >don't know how to figure the frequency above which these effects start to
> >ruin the resonance.
>
> It's not really an overtone kind of thing,

It's exactly an overtone thing.   The Earth is like a tesla coil
secondary: it has different Qs depending on which overtone you use.

When I visualize the bands of EM standing waves on the Earth, I see that
the different transit times will have very little effect if we drive the
Earth at the lowest frequency (it would just cause line broadening at that
frequency.)  But if we drive it at a high overtone, the bullseye pattern
of EM waves on the Earth is distorted, and depending on the path taken by
the waves, their relative phase could be shifted an entire 180 degrees.

Which suggests that the line spectrum for high overtones would have
enormous broadening, perhaps with no lines even detectable.


> >Yep, and Tesla's high-power system would have to be very narrowband, like
> >single-freq 60Hz power lines, and unlike voice transmissions with big
> >sidebands.  The challenge is how to design small high-Q receiving
> >antennas, and how to keep the narrowband tuning from missing the
> >narrowband transmissions.
>
> The problem would be that the transmission medium is temporally dispersive
> and so, cannot support a narrow band transmission.

ALL narrowband transmissions everywhere are impossible, since no
transmission line has zero dispersion?  :)  It's obviously a question of
how much dispersion is tolerable and how narrow a spectral line is useful
for power transmission.

I recall that Tesla found that he couldn't even detect the earth
resonances above 20KHz, and he considered them useless.  This suggests
that those on this list who assume that Tesla used his 40KHz Colorado
Springs coils to *directly* excite the Earth at 40KHz ...don't know much
about Tesla's work.



> > > 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)
> >
> >Aha, some numerical values!  The uncertainties for lower resonances would
> >be proportionally smaller, no?
>
> Not necessarily, it depends on the physics causing the uncertainty,

I drew some sketches, and I see that you're wrong.  Path-dependent
uncertainty in propagation speed *must* have a much larger effect on Earth
resonances at higher frequencies, since a time delay would shift the phase
of shorter wavelengths proportionally more ("phase" meaning the phase of
the wave after one pass around the earth.)

An uncertainty which changes the phase of one section of a 7Hz 3D
travelling wave by a nearly insignificant amount (say 0.1%) will shift the
phase of a 3.5KHz wave by 180 degrees.  If half of the Earth had that 0.1%
time delay and half did not, then the differing path delay would totally
distort the resonances above 3500Hz, yet it would have nearly
insignificant effect on the 7Hz resonance.



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