Nikola Tesla: Colorado Springs Notes, 1899-1900 Page 61

July 3

The distributed capacitance of the secondary windings is difficult to determine. It depends on the coil diameter, the dimensions of the wire and the insulation and the winding pattern. In a single-layer coil it is due mostly to the capacity between neigh boring turns, and this is the way Tesla calculated it. He considers a greatly simplified model in which it is taken that the parasitic capacity per turn is equal to A/4πd, where A = rπl, half the surface area of the wire in one turn, and d is the distance between turns. The capacitance is calculated as that of a plate condenser of area A and gap d with air between the plates. This model is open to a good many criticisms, but it must not be forgotten that Tesla had to find some solution, whatever its shortcomings. It is also not correct that the total inductance and capacitance of the secondary circuit with the “additional coil” are additive, but Tesla was himself aware that this was guesswork, and often mentions the words “roughly”, “estimate”, etc.

In an earlier calculation (see June 20th) he had started from the primary circuit and worked out the values for the secondary, whereas here he attacks it from the other end: from the resonant frequency of the secondary circuit and the known primary inductance (one turn) he finds the required capacity of the primary circuit. He then checks whether this capacity can be used with an LF transformer of the given power. The formula is approximate, but gives a good rough guide for the power in the mains transformer. The peak power rating of the transformer must be even greater than the value found because the condenser is not charging all the time but only in short pulses.

July 3

Secondary distributed capacitance is one of the Tesla oscillator elements which cannot be determined easily. This magnitude depends on coil diameter, wire size and its insulation and coil winding method. At one layer coils it originates mainly due to influence of adjacent windings and Tesla calculates it so. He ultimately simplifies the model and takes that parasitic capacitance per turn is equal A/4πd, where A=rπl - ½ of one turn wire area, and 'd' is distance between turns. According to this model, capacitance is calculated as for a plate type capacitor of area A and distanced between plates with air insulation. There are a number of disadvantages of such a model, but it should not be forgotten that Tesla is looking for the solution. It is not correct also that he considers in the secondary circuit with "additional coil" all inductances and capacitances added together, but Tesla is aware that all this is just guessing and he frequently mentions words as "approximately", "estimate" and "similar".

Contrary to one previous calculation (please see June 20) when Tesla started with primary circuit and calculated the secondary, now he does the opposite; on the basis of secondary circuit resonant frequency and known primary inductance (one turn) he determines the primary circuit capacitance. After that he checks whether the found capacitance is allowed to be used with regards to the transformer power of low frequency. The applied equation is approximate, but it is good for orientational analysis of network transformer energy balance. Maximum transformer power has to be larger than the found one, because the capacitor in the primary is not charged all the time, and then only in short impulses.

July 4

Discovery of "standing waves" created by natural discharges Tesla described and commented on in articles "The Problem of Increasing Human Energy" in 1900⁽⁴¹⁾, and "Electrical Energy Transmission Without Wires" in 1904⁽¹⁾. He didn't write about these waves in patents he submitted approximately one month later^(9,10). With most details and numerous data, the phenomenon of "standing waves" is described in patent "Electrical Energy Transmission Method Through Natural Media" submitted on May 16, 1900⁽⁴²⁾. There Tesla says that on the basis of numerous data found that one wavelength was, approximately, between 25 and 70 km. On the basis of these results and some theoretical deductions he concluded that the waves of this kind could propagate in all directions on the earth globe and could be of some other wavelengths which in the final case depends on the earth globe, its dimension and characteristics. Tesla described the earth globe as a "perfectly smooth conductor, of negligible resistance with evenly distributed capacitance and inductance along the symetrical axis of a propagating wave". In order to get such conductor i.e. earth globe in resonance according to Tesla the following conditions should be met:

1. 1. The radius of the earth globe has to be an odd multiple of one quarter of the wavelength.
2. 2. The oscillations applied have to be such that the energy radiation in the shape of Hertz electromagnetic waves is small. Further orientation, Tesla says that frequencies have to be below 20 kHz, and that minimal frequency at which the effect of standing waves appears is 6 Hz.
3. 3. The most important condition is that oscillations last a certain period of time - not less than .08484 second, which time is necessary for the wave to leave and return back from the point on opposite side of earth globe from the place where the receiver is. Briefly described, the patent request, based on discovery of standing waves consists in improvement of method for obtaining and use of standing waves on the earth globe of various wavelengths, with free choice of moving the locations of nodes and amplitudes.

According to Tesla's writing in 1904⁽¹⁾, the event which he described on July 4 in the notes took place on July 3. Tesla was obviously very impressed with this discovery therefore he devoted much attention to it. It appears, however, that others didn't have as enthusiastic impressions but, it is certain that his ideas had impact. According to Eccles⁽¹²⁾, in summer 1899 there was a rumor that "one American company will construct radio stations in New York and Ireland for the purpose of communication across the Atlantic. These stories were probably based on Tesla's preparations in the U. S. for communications over long distances by means of continuous waves instead of sparks. On one side that caused the drop of cable dividend values on stock market, and on the other side it stimulated the discussion on the waves propagation along the ground." Eccles writes about experiments which Tesla performed in 1899: "Tesla's attempt in 1899 to send the signal over a long distance with very long continuous waves was not successful, although his method for producing the waves and wavelengths choice, approximately 20,000 m, proved to be extraordinary for ocean distances later on, when more sensitive receiving devices than his were invented. But his work helped in efforts to use long waves and next step in improvement of arcing telegraphy was directed in that direction". As far as electrical discharges and waves created by them, however large, before Hertz' research on electrical waves were published pointed to the possibility that discharge of lightning is oscillating in nature similar as a discharge of Leyden's Jar. In 1895 Popov detected remote disturbances with his receiver⁽³²⁾ and showed that they were due to electrical discharge which follows them, and created natural electromagnetic waves which the antenna receives. Feriyi registered discharges at distances of approximately 150 km in 1901, and Turpain on the basis of numerous observations showed in 1903 that notes on discharges could be used for weather forecast.

Later, the natural electrical discharges were used for determining some parameters on waves propagation in the range of extremely low (6 to 3,000 Hz) and very low frequencies (3 to 30 kHz), as well as for determining so called Schwnann resonances. In wave propagation analysis from the mentioned fields it is assumed that the entire earth globe is ideally conductive as well as the ionosphere. On borderline surfaces of sphere wave conductor, which creates the earth globe and ionosphere, currents appear which could be with some reservations considered as Tesla's "conductive currents". Tesla's assumption on the earth globe resonances is proved by Konig measurements and others in 60's of this century. The resonances were found at approximately 8, 14, 20 Hz and at high frequencies⁽³⁴⁾. The measurements of fading at propagation of extremely low frequencies (1 to 2 dB at 1000 km at approximately 50 Hz.) showed that Tesla was right when he was talking about small fading. Standing waves about which Tesla talks are confirmed by measurements, but they are emphasized around anti-poles and not everywhere around the earth globe because the ground is not ideal conductor except at frequencies in the range of 1 Hz. It has to be mentioned however that disregarding the obvious similarity of Tesla's ideas and experiments. Tesla's name, it appears, was not related to modern researches until 1974, when Wait⁽²¹⁾ wrote about it.