## Nikola Tesla Books

Books written by or about Nikola Tesla

# Nikola Tesla: Colorado Springs Notes, 1899-1900Page 65

July 6-7, 1899

This gives C in microfarad per 1 km., according to the authority. Here the length of wire total is 5280 feet roughly or 5280 x 12 x 2.54 = 160,934 cm. Taken as a pair of conductors this would give length $! {160,934 \over 2}$! = 80,467 cm.

Now $! {d \over r}$! = $! {4.23 \over 0.127}$! = $! {4230 \over 124}$! = 33.3   d = $! {10" \over 6}$! = 4.23 cm.

log $! {d \over r}$! = 1.522444   r = $! {0.1" \over 2}$! = 0.127 cm.

from these data we would have per 1 km. in microfarad.

C1 = $! {0.01206 \over 1.522444}$! = 0.00792 mfd. per km.

Now the length of the pair of parallel wires as supposed would be 80,467 cm. or 0.80467 km. or for the secondary the capacity would be C = 0.80467 x C1 x 2, double since both sides must be counted, or C = 0.00792 x 2 x 0.80467 = 0.01584 x 0.80467 = 0.012746 mfd. or 9 x 105 x 0.012746 = 1274.6 x 9 = 11,471.4 cm. Evidently this is not applicable, the capacity could be at the utmost 3000 - 4000 cm. judging from the vibration of the secondary.

July 7, 1899

General conclusions arrived at after all these and previous experiences with electrical oscillators of this kind. It is important as a rule and sometimes imperative to overcome distributed capacity. In large machines it also becomes necessary to overcome the too great self-induction since it prevents obtaining a very high frequency which is generally of great advantage. The high e.m.f. being for the chief purposes aimed at - that is power transmission and transmission of intelligible messages to any point of the globe - essentially necessary, it is important to ascertain the best manner to obtain it. As has been already stated this result may be reached in two ways radically different - either by a high ratio of transformation or by resonant rise. For power transmission it seems that ultimately the former method must prevail, but where a small amount of energy is needed the latter method is unquestionably the better and simpler of the two. By placing the secondary in a very close inductive relation to the primary, the self-induction is diminished so that the self-induction in a highly economical machine of this kind would not seem to be an impediment in the way of obtaining a very high frequency, at least not one which could not be more or less overcome by scientific design of the machine. But the distributed capacity is a troublesome element in such a machine and all the more so as the e.m.f. increases. When the pressure reaches a few million volts almost all the energy is taken in

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65

July 6

Returning back to the problem of coil-form capacitance, he attempted to calculate by means of equation for the capacitance of two parallel symmetrical conductors, so that he takes half of the coil length as feeder length, and the distance between the conductors centers he takes it as equal to distance between centers of two adjacent coil turns. Calculated value for one coil convinced him that this method is not applicable because the difference between calculated and by indirect method determined distributed capacitance is too large.

July 7

For the “resonance method” Tesla envisaged two possible types of resonant transformer: one with loose coupling between the primary and secondary, and the other with tight coupling but only with part of the secondary inductance*. This latter type he protected under the patent “Apparatus for transmitting electrical energy”, for which he applied on 18 January 1902(44); a good deal of his time at Colorado Springs was spent in developing it.

His conclusions about various parameters of the oscillator indicate that he had by then gained sufficient experience to be able to design such devices with improved performance in the parameters he wanted. As the experiments proceeded he gradually increased the voltage of the LF power supply. On June 20th he had calculated with an excitation voltage of 20 kV, but he had assumed a much higher rate of charging of the condenser, so that he obtained then a greater power than now with 40kV. The difference in the number of chargings per second is nowhere explained, nor had he ever previously described how it was calculated. The first time he had probably taken it as being equal to the number of breaks on the rotary discharger, and the second time as double the mains frequency. In this light the accuracy of “the capacity of condenser which the transformer will be able to charge” is dubious. However, Tesla did not take the value he calculated as limiting the capacitance in the primary, noting that it did not take into account resonance and other factors which might enable the transformer to charge a much larger condenser.

* It is easily demonstrated that these two methods are similar. If in the second case a part L’2 of the secondary capacitance is coupled to the primary with a coupling coefficient of k2, while in the first case the entire secondary inductance L2 is coupled with a coefficient of k1, then the response of the secondary to the primary will be the same if $!{k_{1} = k_{2} \sqrt{L'_{2}/L_{2}} < k_{2}}$!.

July 7

From his writings on experiences with high frequency oscillator it can be seen how deeply Tesla got into the operation optimization of this device. He wanted to construct the oscillator of high power and very high voltage, but he had to make a compromise as far as dimensions are concerned because they are in direct relation with the voltage and in reciprocal ratio with the operating frequency. From already mentioned patented and written works (please see comment June 4) it is known why Tesla considers that it is necessary to achieve very high voltages. Explaining Tesla's ideas on wireless transmission, Fleming wrote in 1944: "It appears that Tesla considers that transmission mechanisms will be different if powers of sufficiently high level are achieved and he started the production of high frequency power of very high level, probably hoping to cause by means of it the disturbances comparable in magnitude with cosmic disturbances. Other experiments of that time were satisfied with power of several watts and they didn't want anything else then to produce very weak signals at the distance.... Tesla's vision was focused on an attempt to produce some important efforts at long distances, and he didn't succeed. In his efforts he produced almost incidently the series of devices which were successfully used by other researchers with less ambitious goals"(20).

From the viewpoint of high voltages production method Tesla makes a distinction between transformation method in transformer with a good link (similar as at transformer of low frequency) and the method with resonant transformer. For the method with strong link it is considered that it is applicable when power transmission at a distance is in and for method with resonant transformer that it is much better at low level powers. The assumption that along with application of first method due to strong link between primary and secondary the reduction of primary inductance will occur (which would according to Tesla enable the primary circuit oscillation at high frequency) is not in general case correct. As far as the influence of the secondary self capacitance is concerned Tesla is correct when he considers it is an obstacle in achieving high voltage levels, because the transformation ratio of the resonant transformer is proportional to ratio of primary and secondary capacitance (please see appendix: Tesla's Oscillator).

For "resonant method" he foresees two methods of operation of resonant transformer: one with a poor link between primary and secondary and the other with strong link, but only with a portion of the total secondary inductance*. This latter method Tesla protected by patent "Apparatus for Electrical Energy Transmission" submitted on Jan. 18, 1902(44), and he worked a great deal of the time developing it in Colorado Springs.

The conclusions on various oscillator parameters show that Tesla's experience reached such levels that he was able to design devices with improved performance characteristics on the basis of some system parameters. As experiments progress, he gradually increases the source voltage of low frequency. On June 20th, he performed the calculations for an excitation voltage of 20 kv, but he assumed a considerably higher number of capacitor charges per second, and obtained higher power than now at a voltage of 40 kv. The difference in the capacitor number of charges is not explained, and even today it is not known how it is calculated. First time it probably was assumed that the number of discharges is equal to the number of spark interruptions of the rotating arcing device (spark gap), and at another time that number is equal to double the frequency of the network voltage. On the basis of this it is not possible to rely on the accuracy of "maximum capacitance which the transformer can charge." However, by this calculation Tesla did not limit the magnitude of capacitance in the primary because he mentioned that the value so determined does not take in account the resonant and other conditions which would perhaps enable the transformer to charge much larger capacitor.

* It is easy to show that these two methods are similar. If in the second case the portion of the secondary inductance L'2 is linked to its primary so the the link coefficient is k2, and in the first case the entire secondary inductance L2 is linked with primary so that link coefficient is k1, then, for the same secondary reaction to the primary $! {k_{1} = k_{2} \sqrt{L' / L_{2}} < k_{2}}$!

## Glossary

Lowercase tau - an irrational constant defined as the ratio of the circumference of a circle to its radius, equal to the radian measure of a full turn; approximately 6.283185307 (equal to 2π, or twice the value of π).
A natural rubber material obtained from Palaquium trees, native to South-east Asia. Gutta-percha made possible practical submarine telegraph cables because it was both waterproof and resistant to seawater as well as being thermoplastic. Gutta-percha's use as an electrical insulator was first suggested by Michael Faraday.
The Habirshaw Electric Cable Company, founded in 1886 by William M. Habirshaw in New York City, New York.
The Brown &amp; Sharpe (B &amp; S) Gauge, also known as the American Wire Gauge (AWG), is the American standard for making/ordering metal sheet and wire sizes.
A traditional general-purpose dry cell battery. Invented by the French engineer Georges Leclanché in 1866.
Refers to Manitou Springs, a small town just six miles west of Colorado Springs, and during Tesla's time there, producer of world-renown bottled water from its natural springs.
A French mineral water bottler.
Lowercase delta letter - used to denote: A change in the value of a variable in calculus. A functional derivative in functional calculus. An auxiliary function in calculus, used to rigorously define the limit or continuity of a given function.
America's oldest existing independent manufacturer of wire and cable, founded in 1878.
Lowercase lambda letter which, in physics and engineering, normally represents wavelength.
The lowercase omega letter, which represents&nbsp;angular velocity in physics.&nbsp;