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

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Ed Phillips <evp@xxxxxxxxxxx>

Here's a note I put together some time back giving some of my thoughts
on the design of a Tesla world power system; it starts with Tesla's own
description with quotes from his patents and then goes on to show some
of the factors which would come up in the design of the transmitting
station.  Will some of the "true believers" run through the calculations
and pass along their refutation?

Ed

EXCERPTS FROM PATENT #645,576
 ("Dr. Nicola Tesla, Complete Patents")

"Expressed briefly, my present invention, based on these discoveries,
consists then in producing at one plint an electrical pressure of such
character and magnitude as to cause thereby a current to traverse
elevated strata of air between the points of generation and a distant
point at which the energy is to be received and utilized."  Lines
114-121, page 313.

"In the transmitting apparatus the Coil A constitutes the high-tension
secondary and the coil C the primary of much lower tension of a
transformer.  - - - One terminal of the secondary is . . . led by a
conductor B to a terminal D ... maintained . . . at an elevation
suitable for the purposes of transmission, as described."  Lines 2-13,
page 314.

	This is clearly and undeniably the description of a system for
transmitting power by producing a high voltage between a ground terminal
and the conducting elevated strata, and transmitting it by means of a
conducting path through the earth and a path throw the "elevated
strata".  No mention of "longitudinal waves" or ground waves.

"From my experiments and observations I conclude that with electromotive
impulses not greatly exceeding fifteen or twenty million volts the
energy of many thousands of horsepower may be transmitted over vast
distances..."  Lines 129-134, page 315

	This states the order of magnitude of the voltage he felt would be
required.

"What I now claim is-
1.
The method herinbefore described of transmissing electrical energy
through the natural media, which consists in producing at a
generating-station a very high electrical pressure, causing thereby a
flow of electrical energy, BY CONDUCTION , THROUGH THE EARTH AND THE AIR
STRATA, and collecting or receiving at a distant point the electrical
energy so propagated or caused to flow." [Emphasis mine} Lines 77-86,
page 316

	This further reinforces the prior statement as to the method of
transmission.

	In summary, my interpretation of all of this is that he intended to
create a very high voltage (or the order of fifteen or twenty million
volts) between two CONDUCTORS - the earth and the ionized upper
atmosphere -  and through them to CONDUCT energy to a "distant point".
Is any other interpretation possible?  If so, what is it?

	Let's pretend that we're the engineer assigned the task of building a
small "industrial" transmitting station.  Start with the electrical
design of the transmitter,  ignore for the moment the fact that resonant
circuits are used to generate the high voltage required, and calculate
the properties of the transmission line comprised of the earth and the
upper strata.  The first step in the design process is to calculate the
power involved in maintaining the upper strata at a voltage of 15
million with respect to earth.  Let's start a series of calculations.

1. The conductors are two spherical shells separated by a distance of a
number of miles.  These dimensions produce the capacitance at the
transmitting terminal across which the high voltage is to be generated
can be calculated as follows:

To simplify the calculation assume that, instead of the two spherical
shells, we have two flat plates of the same area as the average of that
of the two spherical shells.   Again, to simplify, let the radius of the
earth be taken at 4000 statute miles or 6.44 x 10^6 centimeters.  The
area turns out to be 1.3 x 10^18 cm^2,

The capacitance of a flat plate capacitor with air dielectric is

	C = 0.0885 A/t, where A is the area in cm^2 and t is the separation in
cm.

Assume the upper strata are at an elevation of 50 miles, or 8.05 x 10^6
cm.  A/t is then about 1.62 x 10^11 cm and the capacitance turns out to
be 1.432 x 10^10 uufd or 0.01432 farad.

2. Next calculate the reactance of this capacitor at a frequency of 925
Hz, the lowest I can find in the patent.

	X = 1/(2 x pi x f x C) = 1/(2 x 3.1415926 x 925 x 0.01432) = 0.012 ohms

3. Next calculate the charging current which must flow in this capacitor
to maintain a voltage difference of only 1,000,000 volts.

 I = V/X = 10^6/0.012 = 8.33 x 10^7 amperes = 833 MILLION amperes!

4. Calculate the loss in the effective resistance of the ground circuit,
assuming it to be the unattainably low value of 0.001 ohms.  (The lowest
ground resistance for which I can find a resistance is that of the old
VLF station at Cutler, Maine.  It employed 2500 miles of buried wire and
the resistance was about 0.02 ohms, or 20 times higher than the assumed
value.  The loss is

	P = i^2 x R = (8.33 x 10^7)^2 x 0.001 = 6.93 x 10^12 watts = 9.3
BILLION horsepower!

This is the power which must be provided to keep the upper conducting
strata at a voltage of only 1 million, about 1/15 of that which Tesla
estimated.  The loss at 15 million would be 10^2 or 225 times as high.
This is the power power would have to be supplied even if there were no
load being drawn from the system.

	I'll stop here and invite everyone to check these calculations and then
go on with the design of the real system.  Even if the calculations are
off by a factor of a thousand or so I think there are still prodigious
obstacles to be overcome.  Among these are the problems of:

a. Conducting the high voltage from the transmitting station to the
upper atmosphere by means of a transmission line which doesn't lose
power due to breakdown of the air through which it passes.

b. Figuring out how to hold that transmission line in place.  Anyone who
has ever attempted to hold a balloon on a long tether will have
encountered problems with the winds.

c. Figure out how to keep both the transmitter and the receivers "in
synchronism" as the height of the upper atmosphere (and hence the
capacitance of the transmission line) varies with fluctuations in the
height due to variations in the intensity of solar radiation.  Based on
observations of changes in propatation due to changes in the effective
height of the ionosphere, I'd expect changes of at least 50%.

d. Figure out how to keep the power output of any one receiver fixed as
the load on the system fluctuated.

e. Figure out where the transmitted power is to come from.

f. Figure out how to bill correctly and how to disconnect non-paying
customers.  This one item alone could make the difference between a
practical system and one that was useless.

	I'll leave all of this for you readers.  Comments solicited.

Ed