Tesla Tower: electrical calculation
I read with great pleasure the topic-study of the Tesla tower .
Of course, the authors set a very attractive goal: the transfer of energy without wires, on a global scale, just a dream of energy.
The analysis carried out in the topic is deep, the formulas are the classics of radio engineering, all calculations are correct.
But after reading the question remains: if everything is done according to the authors, what will we get? What are the transmission characteristics of such a system?
Here is a quote from the source:
Let us allow ourselves to put this statement of the authors into doubt, and to carry out calculations precisely in this direction.
The essence of grounding is in the ability of the earth to accumulate and give a charge almost unlimitedly. Unlimited it should be understood as "very much", given the size of the planet Earth. Below we estimate this "unlimited", but first things first.
Further, calculations are carried out everywhere with simplification (the sum instead of the root of the sum of squares, the amplitude value instead of the current one, the rounding of the values).
Such calculations should be considered as estimates.
Let's first consider the transfer of anything electrical - energy, signals - over a single wire using earth as the second conductor:
')
Will this work? It will, and it works - the authors of the publication noted as confirmation of this tram.
The earth remarkably performs the role of a second conductor, and the resistance of the earth, as the authors rightly noted, does not really depend on the distance between the electrodes that arestuck in the earth.
(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 220 volt network phase, and at the same time, the insulation of the soles leaves much to be desired - (wet floor, etc.), it can well strike with current, the second wire circuit is closed through the ground.
Will this construction work here?
Of course there will be - why not, Earth2 also plays the role of the second conductor in the same way. It should be noted that everything said by the authors about the picture of the distribution of earth's potentials when an alternating current flows through the earth as a conductor, most likely takes place - distribution, standing waves, etc.
Slightly shorter: it plays a role in which points of the surface of the planets to connect the receiver wires.
Confirming such a distribution on a planetary scale would be an enchanting and very beautiful experiment.
And what do the authors offer us? It can be schematically depicted in this way:
Despite the seeming absurdity of such a scheme, it is workable within certain limits. As a concomitant example, radio communication can be given: the ground can be the common wire of a circuit, the human body, etc. There are a lot of situations where neither the transmitter land, nor the receiver earth is connected to the common ground.
An example, of course, is not entirely successful - in radio communications, the transfer of energy is emitted by radiation , we do not consider this situation, and this is simply an illustration of the fact that the planet’s surface may not necessarily be the earth, but just some kind of conductor.
As an illustration of the method of energy transfer using the Tesla tower, we can cite the following experience: if an alternating voltage generator of sufficient magnitude is assembled and any metal object is brought to the generator, an arc lights up between the generator output and this object:
The authors described the mechanism of energy transfer in a similar way: the potential of an isolated metal object with respect to infinity (forgive me, physic ...) 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.
High frequency in such structures is required to maintain the current strength sufficient for the arc to burn (the current through the capacitance of the metal object is proportional to the frequency — see below).
That is, it will still work?
The generator current “flows away” to infinity through the capacitance at the top of the Tesla tower (which plays the role of earth for the generator). Suppose, for simplicity, this will be a ball with a radius of 1 meter (this does not change the essence or the orders of magnitude).
In fact, the current “flows” into the conductor, increasing its charge and, as a result, its potential. On one half-period of the current, the conductor will be charged to one sign, when the current changes the sign - it will be recharged to the other.
Let us estimate to what voltage the conductor will be charged.
Capacity of a single spherical conductor in vacuum:
For a ball with a radius of 1 meter, the capacity will be approximately 110 picoFarads.
The authors mentioned a current of 1 kiloAmper and a frequency of 20 kilohertz
The maximum potential of the sphere with a radius of 1 meter will be
With the above data, we obtain 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 attainable value in the 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 stress on the top of the tower (where the sphericalhorse is a conductor). Suppose that there is no technical difficulty to provide insulation at such a voltage.
Then the current in the generator circuit will be approximately 4 Amps.
At a voltage of one million volts, this corresponds to a transmitted power of 4 megawatts. Cool! No, not cool. The above-mentioned power lines with a voltage of 1150 kiloVolts have a capacity of 5500 megawatts - 1000 times more at the same voltage.
So raise the tension! I'm afraid there is no place - 1000 kV in the power industry is considered to be ultra-high voltage, causing a lot of difficulties. The same transmission line with a voltage of 1000 kV is currently operated at a voltage of 500 kV.
But this is not all 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 * capacitance) = 71 kΩ
In fact, this is the internal resistance of the “power line” using the Tesla tower.
Let a transformer that reduces the voltage to 220 volts is connected to this “line” with a voltage of 1000,000 volts and an internal resistance of 71 kΩ. In this case, the internal resistance of the 220 V circuit will be (71000 * 220) / 1000 000 = 15 Ohm.
15 Ohms in the 220 Volt circuit is a lot, when you turn on the load with a power of 1 kilowatt (current 5 Amps, this is one small iron, or computer + TV + lighting) the voltage drop will be 75 Volts, that is, the actual mains voltage will fall below the level when It can be used for power supply.
Thus, it is difficult to power one apartment from such a receiver of energy, and then without powerful energy consumers.
How is it that where the energy goes, the authors wrote about a very high efficiency?
Nowhere does not go away. These resistances are reactive, but the voltage drop on them will be observed in all its glory.
But what about resonances?
Calculate the parameters of the resulting contour.
Capacity = 110 picoFarads (see above), frequency = 20 kHz (from the authors).
The characteristic impedance of the circuit will be 750 kΩ.
When a load is connected to such a circuit, which introduces a resistance of 71 kΩ into the circuit (i.e., if one apartment is connected to the energy receiver, see above), the Q factor of the circuit drops to 10 (roughly), and when 10 apartments are connected, the Q will drop to 1, resonance phenomena will disappear and the system will completely stop working.
What does it mean at all? When the Q-factor falls, the output voltage of the receiver will also proportionally fall. That is, without a load - well, as the load increases, the voltage drops to zero.
As an optimistic finale, let's count everything too, but for real grounding, that is, the Tesla tower is a separate planet the size of Earth.
Capacity = 700 microfarad.
The maximum voltage at a current of 1 kA and a frequency of 20 kHz = 78 Volts, that is, it is possible to repeatedly and safely increase the operating voltage, thereby increasing the transmitted power.
Internal resistance of the system in the high voltage circuit at the same frequency = 0.011 Ohm
The reduced resistance in the circuit is 220 Volt = 2 micro ohms, which is orders of magnitude less than the resistances in any power supply lines.
Here it is - a real ground!
The above disadvantages of such a system cannot be eliminated by changing the design, using special materials, etc. — these are the disadvantages of the very method of energy transfer (well, except to make the Tesla tower with dimensions comparable at least to asteroids).
Note that the actual design was calculated - without any losses, without taking into account the influence of current / voltage distributions on a planetary scale.
In fact, a calculation was made of an ideal generator and an ideal receiver, connected at one end and each with its own grounding.
The problem of energy transfer using Tesla towers is that the tower itself is an extremely inefficient ground.
Demonstration of the effects of energy transfer is possible, but from the standpoint of electrical engineering such a transmission line, to put it mildly, is inexpedient:
- huge voltages at “stations”
- at the same time the small transmitted power
- large internal resistance
- low load capacity
- Strong dependence of voltage on the load due to resonance phenomena.
Of course, the authors set a very attractive goal: the transfer of energy without wires, on a global scale, just a dream of energy.
The analysis carried out in the topic is deep, the formulas are the classics of radio engineering, all calculations are correct.
But after reading the question remains: if everything is done according to the authors, what will we get? What are the transmission characteristics of such a system?
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 figure above?
... for the generator the tower is “grounding” through resistance equal to the resistance of the tower
Let us allow ourselves to put this statement of the authors into doubt, and to carry out calculations precisely in this direction.
The essence of grounding is in the ability of the earth to accumulate and give a charge almost unlimitedly. Unlimited it should be understood as "very much", given the size of the planet Earth. Below we estimate this "unlimited", but first things first.
Further, calculations are carried out everywhere with simplification (the sum instead of the root of the sum of squares, the amplitude value instead of the current one, the rounding of the values).
Such calculations should be considered as estimates.
Earth as a conductor
Let's first consider the transfer of anything electrical - energy, signals - over a single wire using earth as the second conductor:
')
Will this work? It will, and it works - the authors of the publication noted as confirmation of this tram.
The earth remarkably performs the role of a second conductor, and the resistance of the earth, as the authors rightly noted, does not really depend on the distance between the electrodes that are
(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 220 volt network phase, and at the same time, the insulation of the soles leaves much to be desired - (wet floor, etc.), it can well strike with current, the second wire circuit is closed through the ground.
Will this construction work here?
Of course there will be - why not, Earth2 also plays the role of the second conductor in the same way. It should be noted that everything said by the authors about the picture of the distribution of earth's potentials when an alternating current flows through the earth as a conductor, most likely takes place - distribution, standing waves, etc.
Slightly shorter: it plays a role in which points of the surface of the planets to connect the receiver wires.
Confirming such a distribution on a planetary scale would be an enchanting and very beautiful experiment.
Isolated "land"
And what do the authors offer us? It can be schematically depicted in this way:
Despite the seeming absurdity of such a scheme, it is workable within certain limits. As a concomitant example, radio communication can be given: the ground can be the common wire of a circuit, the human body, etc. There are a lot of situations where neither the transmitter land, nor the receiver earth is connected to the common ground.
An example, of course, is not entirely successful - in radio communications, the transfer of energy is emitted by radiation , we do not consider this situation, and this is simply an illustration of the fact that the planet’s surface may not necessarily be the earth, but just some kind of conductor.
As an illustration of the method of energy transfer using the Tesla tower, we can cite the following experience: if an alternating voltage generator of sufficient magnitude is assembled and any metal object is brought to the generator, an arc lights up between the generator output and this object:
The authors described the mechanism of energy transfer in a similar way: the potential of an isolated metal object with respect to infinity (forgive me, physic ...) 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.
High frequency in such structures is required to maintain the current strength sufficient for the arc to burn (the current through the capacitance of the metal object is proportional to the frequency — see below).
That is, it will still work?
Calculation of isolated "land" and related parameters
Transmitter
The generator current “flows away” to infinity through the capacitance at the top of the Tesla tower (which plays the role of earth for the generator). Suppose, for simplicity, this will be a ball with a radius of 1 meter (this does not change the essence or the orders of magnitude).
In fact, the current “flows” into the conductor, increasing its charge and, as a result, its potential. On one half-period of the current, the conductor will be charged to one sign, when the current changes the sign - it will be recharged to the other.
Let us estimate to what voltage the conductor will be charged.
Capacity of a single spherical conductor in vacuum:
C_wire = 4 * pi * (Electric constant) * (radius of the ball)
For a ball with a radius of 1 meter, the capacity will be approximately 110 picoFarads.
The authors mentioned a current of 1 kiloAmper and a frequency of 20 kilohertz
The maximum potential of the sphere with a radius of 1 meter will be
Potential = charge / capacity = (current * time) / capacity = (current * half of the oscillation period) / (capacity)
With the above data, we obtain 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 attainable value in the 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 stress on the top of the tower (where the spherical
Then the current in the generator circuit will be approximately 4 Amps.
At a voltage of one million volts, this corresponds to a transmitted power of 4 megawatts. Cool! No, not cool. The above-mentioned power lines with a voltage of 1150 kiloVolts have a capacity of 5500 megawatts - 1000 times more at the same voltage.
So raise the tension! I'm afraid there is no place - 1000 kV in the power industry is considered to be ultra-high voltage, causing a lot of difficulties. The same transmission line with a voltage of 1000 kV is currently operated at a voltage of 500 kV.
But this is not all problems.
Receiver
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 * capacitance) = 71 kΩ
In fact, this is the internal resistance of the “power line” using the Tesla tower.
Let a transformer that reduces the voltage to 220 volts is connected to this “line” with a voltage of 1000,000 volts and an internal resistance of 71 kΩ. In this case, the internal resistance of the 220 V circuit will be (71000 * 220) / 1000 000 = 15 Ohm.
15 Ohms in the 220 Volt circuit is a lot, when you turn on the load with a power of 1 kilowatt (current 5 Amps, this is one small iron, or computer + TV + lighting) the voltage drop will be 75 Volts, that is, the actual mains voltage will fall below the level when It can be used for power supply.
Thus, it is difficult to power one apartment from such a receiver of energy, and then without powerful energy consumers.
How is it that where the energy goes, the authors wrote about a very high efficiency?
Nowhere does not go away. These resistances are reactive, but the voltage drop on them will be observed in all its glory.
But what about resonances?
Calculate the parameters of the resulting contour.
Capacity = 110 picoFarads (see above), frequency = 20 kHz (from the authors).
Then the inductance must be 1 / ((2 * pi * frequency) (2 * pi * frequency) * capacitance) = 63 Henry
The characteristic impedance of the circuit will be 750 kΩ.
When a load is connected to such a circuit, which introduces a resistance of 71 kΩ into the circuit (i.e., if one apartment is connected to the energy receiver, see above), the Q factor of the circuit drops to 10 (roughly), and when 10 apartments are connected, the Q will drop to 1, resonance phenomena will disappear and the system will completely stop working.
What does it mean at all? When the Q-factor falls, the output voltage of the receiver will also proportionally fall. That is, without a load - well, as the load increases, the voltage drops to zero.
Real Earth
As an optimistic finale, let's count everything too, but for real grounding, that is, the Tesla tower is a separate planet the size of Earth.
Capacity = 700 microfarad.
The maximum voltage at a current of 1 kA and a frequency of 20 kHz = 78 Volts, that is, it is possible to repeatedly and safely increase the operating voltage, thereby increasing the transmitted power.
Internal resistance of the system in the high voltage circuit at the same frequency = 0.011 Ohm
The reduced resistance in the circuit is 220 Volt = 2 micro ohms, which is orders of magnitude less than the resistances in any power supply lines.
Here it is - a real ground!
Conclusion
The above disadvantages of such a system cannot be eliminated by changing the design, using special materials, etc. — these are the disadvantages of the very method of energy transfer (well, except to make the Tesla tower with dimensions comparable at least to asteroids).
Note that the actual design was calculated - without any losses, without taking into account the influence of current / voltage distributions on a planetary scale.
In fact, a calculation was made of an ideal generator and an ideal receiver, connected at one end and each with its own grounding.
The problem of energy transfer using Tesla towers is that the tower itself is an extremely inefficient ground.
Demonstration of the effects of energy transfer is possible, but from the standpoint of electrical engineering such a transmission line, to put it mildly, is inexpedient:
- huge voltages at “stations”
- at the same time the small transmitted power
- large internal resistance
- low load capacity
- Strong dependence of voltage on the load due to resonance phenomena.
Source: https://habr.com/ru/post/206290/
All Articles