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

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>

At 12:22 PM 7/16/2005, you wrote:
> Original poster: William Beaty <billb@xxxxxxxxxx>
>
> On Thu, 14 Jul 2005, Tesla list wrote:
>
> > Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx>
> >
> > 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.
>
> 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, although, Fourier series (or any 
set of orthogonal functions) can be used to represent any function or 
waveform. It's more a broadening  of a spectral line. The non-spherical 
nature is a much smaller effect than the land sea difference.25km or so out 
of 20,000 for the oblateness which is about part in 1000.So, this alone 
could limit the Q.


> > 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.
>
> 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.The problem is similar to 
a tuning fork or quartz crystal in a vibration environment.




> > 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,

>  But the lower we go, the smaller the
> antennas behave, and the higher the Q needed in order to receive
> signficant power.  The system probably won't work at all at 7Hz or at
> 100KHz. Somewhere in between it might become a feasible proposition, or
> might not.