# Tesla Tower: Electrical Engineering

It was with great pleasure that I read the topic study of the Tesla Tower .
Of course, the authors set a very tempting goal: the transfer of energy without wires, on a planetary scale, is simply a dream of energy.
The analysis carried out in the topic is deep, the formulas are classics of radio engineering, all calculations are correct.
But after reading the question remained: if everything is done according to the authors, then what will we get? What characteristics of energy transfer will such a system have?

Here is a quote from the source:
Where do we get the “grounding” to which the generator is connected to pump such a resonator in the previously shown figure?
... for the tower generator, this is the “grounding” through the resistance equal to the active resistance of the tower

Let us challenge this statement of the authors, and make calculations in this direction.
The essence of grounding is the ability of the earth to accumulate and give charge almost unlimitedly. Unlimited should be understood as "very much", given the size of planet Earth. Below we will evaluate this "unlimited", but first things first.

Further, everywhere the calculations were carried out with simplification (the sum instead of the root of the sum of squares, the amplitude value instead of the current one, rounding values).
Such calculations should be considered as estimates.

##### Earth as a conductor

Let us first consider the transmission of anything electrical - energy, signals - over a single wire using the earth as a second conductor: Will this work? Will, and it works - the authors of the publication noted as confirmation of this tram.
Earth remarkably plays the role of a second conductor, and the resistance of the earth, as the authors rightly noted, really does not depend on the distance between the electrodes that are stuck placed in the ground.
(There is even a problem on this topic in the second year of the physics department).

The side effect of this method of energy transfer is well known to many - if you pick up the phase of the 220 Volt network, and at the same time the insulation of the soles leaves much to be desired (wet floor etc.), it can well be shocked, the circuit of the second wire closes through the ground.

Whether such a construction will work: Of course it will be - why not, Earth2 just as accurately performs the role of a second conductor. It should be noted that everything the authors said about the picture of the distribution of earth potentials during the flow of alternating current through the earth as a conductor, most likely, there is a place to be - distribution, standing waves, etc.
Slightly shorter: it plays a role in which points on the surface of the planets connect the receiver wires.

Confirmation of such a distribution on a planetary scale would be an enchanting and very beautiful experiment.

##### Isolated "lands"

And what do the authors offer us? This can be schematically depicted in this way: Despite the seeming absurdity of such a scheme, it is operational in a certain framework. As a concomitant example, one can cite radio communications: the ground can be a common circuit wire, a human body, etc. There are many situations where neither the transmitter’s ground nor the receiver’s ground are connected to the common ground.
The example, of course, is not entirely successful - in radio communications, energy is transmitted by radiation , we do not consider such a situation, and this is just an illustration of the fact that the "earth" may not necessarily be the surface of the planet itself, but just some kind of conductor.

To illustrate the method of energy transfer using the Tesla tower, one can cite the following experience: if you assemble an alternating voltage generator of sufficient magnitude and bring any metal object to the generator, an arc lights up between the generator output and this object:

The authors described the mechanism of energy transfer in this way: the potential of an isolated metal object with respect to infinity (forgive me physical faculty ...) is zero. The generator constantly recharges this piece of iron, changing its potential, and a current flows between the output of the generator and the object.
A high frequency in such designs is required to maintain a current strength sufficient for arc burning (the current through the capacity of a metal object is proportional to the frequency - see below).

That is, will it still work?

#### Calculation of an isolated “earth” and related parameters

##### Transmitter

The generator current "flows" to infinity through the capacitance at the top of the Tesla tower (which plays the role of earth for the generator). For simplicity, let it be a ball with a radius of 1 meter (this does not change the essence or order of magnitude).

In fact, the current "flows" into the conductor, increasing its charge and, as a consequence, the potential. On one half-period of the current, the conductor will be charged to one sign, when the current changes sign - it will recharge to another. Let’s estimate to what voltage the conductor will be charged.

Single spherical conductor capacity in vacuum:

C wire = 4 * pi * (electric constant) * (ball radius)

For a ball with a radius of 1 meter, the capacity is approximately 110 picoFarad.

The authors mentioned a current of 1 kiloAmpere and a frequency of 20 kilohertz. The

maximum potential of a sphere with a radius of 1 meter will be

Potential = charge / capacitance = (current * time) / capacitance = (current * half oscillation period) / (capacitance)

With the above data, we get that the maximum potential of the upper part of the Tesla tower will be approximately 225 million volts .

We will not consider this as a technically achievable value in the electric power industry. In Russia, there are power lines with a voltage of 1000 kilovolts ( 1150 if exactly ), that is, one million volts (in Ukraine there are none). Let this be the maximum voltage on the top of the tower (where the spherical horse is the conductor). Assume that there is no technical difficulty in providing insulation at such a voltage.

Then the current in the generator circuit will be approximately 4 amperes.
At a voltage of one million volts, this corresponds to a transmitted power of 4 megawatts. Cool! No, not cool. The power line mentioned above with a voltage of 1150 kilovolts has a throughput of 5500 megawatts - 1000 times more at the same voltage.

So raise the tension! I'm afraid there is nowhere - 1000 kV in the electric power industry is considered an ultra-high voltage, causing a lot of difficulties. The same transmission line with a voltage of 1000 kV is currently operating at a voltage of 500 kV.

But these are not all the problems.

The resistance of the upper part of the tower, that is, the ball-infinity system, at a frequency of 20 kHz will be

R = 1 / (2 * pi * frequency * capacity) = 71 kOhm

In fact, this is the internal resistance of the power line using the Tesla tower.
Let a transformer connected to this “line” with a voltage of 1,000,000 volts and an internal resistance of 71 kOhm reduce the voltage to 220 volts. In this case, the internal resistance of the 220 V circuit will be (71000 * 220) / 1000 000 = 15 Ohms.

15 Ohms in a 220 Volt circuit is a lot, when a load of 1 kilowatt is turned on (current is 5 Amperes, this is one small iron, or a computer + TV + lighting) the voltage drop will be 75 Volts, that is, in fact the voltage in the network will drop below the level when It can be used for power supply.
Thus, it is difficult to power one apartment from such an energy receiver, and even without powerful energy consumers.

How so, where does the energy go, the authors wrote about a very high efficiency?
It’s not going anywhere. These resistances are reactive, but the voltage drop on them will be observed in all its glory.

We calculate the parameters of the resulting contour.
Capacitance = 110 picoFarad (see above), frequency = 20 kHz (for the authors).

Then the inductance should be equal to 1 / ((2 * pi * frequency) (2 * pi * frequency) * capacitance) = 63 Henry

The impedance of the circuit will be 750 kOhm.
When a load is connected to such a circuit, introducing a resistance of 71 kOhm into the circuit (i.e., if you connect one apartment to the energy receiver - see above), the quality factor of the circuit drops to 10 (roughly), and when 10 apartments are connected, the quality factor drops to 1, resonance phenomena will disappear and the system will completely stop working.

What does it mean at all? With a drop in the quality factor, the output voltage of the receiver will also proportionally drop. That is, no load is good, with increasing load, the voltage drops down to zero.

##### Real earth

As an optimistic ending, let's count everything too, but for real grounding, that is, the Tesla Tower is a separate planet the size of the Earth.

The maximum voltage at a current of 1 kA and a frequency of 20 kHz = 78 Volts, that is, you can repeatedly and safely increase the operating voltage, thereby increasing the transmitted power.
The internal resistance of the system in the high voltage circuit at the same frequency = 0.011 Ohms
The reduced resistance in the circuit is 220 Volts = 2 micro Ohms, which is orders of magnitude lower than the resistances in any power supply lines.

Here it is - real grounding!

##### Conclusion

The listed drawbacks of such a system cannot be eliminated by a change in design, the use of special materials, etc. - these are the drawbacks of the method of energy transfer itself (well, except to make the Tesla Tower dimensions comparable, at least, with asteroids).
Please note that the practically perfect design was calculated - without any losses, without taking into account the influence of current / voltage distributions on a planetary scale.
In fact, the calculation of the ideal generator and the ideal receiver was carried out, connected at one end and each with its own ground.

The problem of energy transfer using Tesla towers is that the tower itself is an exceptionally inefficient grounding.

Demonstration of the effects of energy transfer is possible, but from the point of view of electrical engineering, such a transmission line is, to put it mildly, impractical:
- huge voltages at the “stations”
- at the same time low transmitted power
- high internal resistance