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

Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>

At 06:58 AM 7/19/2005, you wrote: 
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.

-- overtones, to me, means exact harmonics or close to it, in the sense of higher order modes in a resonant structure (for instance, a string fixed at each end can vibrate at any of a series of frequencies all harmonically related). However, the string fixed at each end or a simple narrow band cavity resonator are just examples of *simple* harmonic motion/oscillation. I put the emphasis on simple, because the system is simple. It's not dispersive, it's frequency and time invariant, etc., which is a pretty far cry from the earth's surface.

It's even not a particularly good model of a tesla coil, since the capacitance of the streamers changes the equivalent lumped model in a time varying way. Although, I will say that for construction purposes and for conceptual understanding, simple lumped models of whatever order have great utility in tesla coiling: e.g. Antonio's models of magnifiers basically modeled as 3 coupled resonators.

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.


-- Except that the propagation speed varies, depending on the path. AND, the attenuation over the various paths changes (many orders of magnitude difference). This tends to distort and spread the resonance, exactly as if you had a bell with a big dent in it, or a crack. Neither has a very pure note.

As you note, at higher frequencies, the differential path length (in electrical terms) is a bigger problem.


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


I would venture to guess that there's no line spectrum visible even for a fundamental mode. My recollection is that the peaking of atmospheric noise at around 7-8 Hz is quite broad.



> >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.


However, previous comments on the list have implied that the "receiver" of the transmitted power would be physically small (compared to wavelength), which implies high Q (if you have high efficiency), which in turn implies very narrow band.

For the purposes of illustration, and to put some numbers on it...

I have an antenna with a physical extent of about 1 meter, and it has a bandwidth on the 75 meter band (3.8 MHz) of about 2 kHz, which corresponds to a Q of around 2000. This antenna is roughly 0.01 wavelength in extent I also note that it's pretty inefficient (<<1%). If I were to magically eliminate the resistive losses, the Q would increase to about 200,000 (and be impractically narrow band, but that's another story)

Now, let's look at 10 Hz. The wavelength is 30,000 km. That 0.01 wavelength is now 300 km, which is still quite a large structure. But, no matter, let's assume we're happy with this. Further, assume we have somehow removed all the losses (not only superconducting antennas, but also some way to eliminate the ground losses, since this antenna is going to be close to the earth's surface, and will interact). Scaling (which I think is valid here), the Q will still need to be 200,000. This would imply that the path delays for all paths by which the power is being transmitted must match to that degree (i.e. one part in 200,000). This is substantially closer than the differential distance of the sphereoid (one part in 300).

Sure, one could surmise some sort of adaptive equalizer, but, so far, all the adaptive equalizers I've seen tend to be inefficient (in a watts into the equalizer compared to watts out of the equalizer). On the other hand, I don't know that there's been much work on high power adaptive equalizers at this frequency. (I've personally been involved in a similar scheme at 32 GHz though..http://ipnpr.jpl.nasa.gov/tmo/progress_report/42-158/158D.pdf)



> > > 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.)


You are right if you're talking about a frequency invariant time delay. However, EM propagation over the earth's surface (a dielectric boundary, with varying properties) is hardly frequency invariant.




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.


Yes, this is true. However, I maintain that to be a viable method of transmitting power, with reasonable sized receiving antennas, the Q of those receiving antennas must be so high that even the very small variations we're talking about would be excessive.