Published in physic.philica.com
In precedent work, the author presented a method for the theoretical
computation of zero-point-energy converters, called Dynamic
Finite-Element-Method (DFEM). In several articles some examples for the
conversion of zero-point-energy have been demonstrated, which deliver an
output power in the Nanowatt- or in the Microwatt- range, which is a
fundamental proof of the principle, but not sufficient for any technical
The way towards a powerful zero-point-energy converter in the
Kilowatt-range needed some additional investigation, of which the
results are now presented. Different from former fundamental basic
research, the new converter has to be operated magnetically, because the
energy-density of magnetic fields is much larger the energy-density of
electrostatic fields, namely by several orders of magnitude.
In the article here, the author presents step by step the solution of
the theoretical problems, which now allows the theoretical construction
of a zero-point-energy converter in the Kilowatt-range. The result is a
model of a zero-point-energy motor with a diameter of 9 cm and a height
of 6.8 cm producing 1.07 Kilowatts.
Definition of the project
principle proof of the utilization of zero-point-energy was given in [Tur
09]. A basic understanding of the physical fundament how to convert
zero-point-energy was shown in [Tur 10a], but there it was not yet
possible to present a model for a machine with realizable parameters.
The first theoretical model with realizable parameters has been
published in [Tur 10b], but the output power was so small, that only
acoustic noise could be produced, which requires very low power. The
article presented here is the last logical step in this theoretical
train of thoughts, which shows the theory of a powerful
zero-point-energy converter and gives hope for technical utilization.
The Kilowatt zero-point-energy engine presented here, needs less space
then a washing-machine. From the point of zero-point-energy conversion,
the power-density could even be much larger, but the material gives
restrictions to the power-density in order not to be damaged during
operation. Restrictions come for instance from the electrical current in
copper wires, or from the speed of the revolution of a rotation magnet,
which should not damage the bearing.
the model presented here, the theory is developed far enough, that an
experimental verification is desirable now, so that the next step is not
a theoretical one, but an experimental one.
A first approach to the solution
solution is a continuation of the DFEM-model known from [Tur 10b],
working with two coupled oscillations, one is a mechanical oscillation
and the other one an electrical oscillation-circuit. The setup is drawn
LCR (electrical) oscillation-circuit, where a capacitor is
charged (AC-) electrically, but the distance of the capacitor-plates is
variable (by the use of a spring), so that the capacity is not constant.
If a mechanical oscillation is coupled with the electrical oscillation
in appropriate manner, it is possible to convert zero-point-energy into
electrical energy within the electrical circuit and/or mechanical energy
within the mechanical oscillation. By the way: The inductivity of the
coil is enhanced by the use of a coil bobbin.
can for instance be extracted from the mechanical oscillation of the
capacitor plates (as shown in fig.2) as well as from the electrical
oscillation by the use of a load resistor Rload, which is
operating in series with the Ohm’s resistance R of the wire from which
the coil is made.
2: Variable capacitor with
flexible plates, made from thin stretchable plastic-foil, which is
covered with a thin metallic film. It can be stretched on a frame. This
is an imaginable realization of the capacitor in figure 1, which would
be supplied permanently with zero-point-energy so that it can oscillate
permanently without consuming classical energy.
The vibration of the plastic-foil might be noticed if it can be arranged
in a way that it produces acoustic noise, because the sensitivity of the
human ears allows to hear a power of only 10-12 Watt/m2.
The setup should produce noise without any classical power supply.
it can not be extracted more power than only for acoustic noise, which
requires typically some Nanowatts or Microwatts. The example shown here
was computed to produce a power of only P=1.22·10-9Watts,
although all system-parameters have be optimized till the very end, and
the capacitor plates have a cross section area of several square meters.
For a principle proof of the utilization of zero-point-energy this might
be nice, because everybody might feel the effect of zero-point-energy
very directly by hearing it. But a technical application needs a
different setup, which can produce several orders of magnitude more
power. This leads us to the following questions:
- By which means would it be possible to
enhance the power-density within the setup remarkable ?
- By which means would it be possible to
extract remarkable power from the system ?
we face an additional question:
- The converter
according to fig. 1 and fig. 2 requires a very complicated and sensitive
adjustment of the system-parameters. Would it be possible to find a more
stable way to operate the systems ?
the way it should be noticed, that we first want to begin with some
thoughts, which can not be regarded as the solution to the
power-extraction problem. A possible solution is presented not earlier
than in section 6. Nevertheless, we want to regard all the steps which
leads us to section 6, because otherwise nobody would understand section
6 on its own. Besides, the steps towards the solution help colleagues to
avoid tiresome trying and solving the same problems as me. But for the
sake of overview, we will not look into all preliminary blind alleys
with all details. The very details are written only for the final
solution in section 6.
the three above questions we want to start out with the last one first.
Stabilizing the operation of the zero-point-energy converter by pulsed
problem with the adjustment of all system-parameters of the
zero-point-energy converter results from the time-drift of the both
resonances (the mechanical and the electrical one), which have to be
adjusted exactly to each other. If both resonance-frequencies are not
identical, which is normally the case due to practical reasons (for
instance such as tolerances), the phase-difference between the both
oscillations increases as a function of time. The consequence is that
the oscillations run away from each other, and the adjustment of the
propagation-speed of the forces of the interaction will become worse
within a certain time of operation. This causes a limit of the
conversion of zero-point-energy only due to the apparatus in use, as can
be understood as following:
adjustment of the propagation-time of the forces of interaction also
decreases the amount of energy converted per time, which is the
converted power. Finally the system comes into a state, where it can no
longer be accelerated (or even supported) by zero-point-energy. This
means, the system might run into a stable state of operation, which is
kept by zero-point-energy, but in this state of operation the system can
not give away any energy-output. If some energy should be extracted, the
adjustment of all system-parameters should be renewed. Perhaps the
system might even come to standstill, because the support with
zero-point-energy is even missing completely. From there we come to the
idea, which engineers call "phase lock":
we want to extract power continuously, we have to solve the problem of
adjustment of both resonances to each other. Periodic input pulsed
signals could be the way for renewing this adjustment periodically.
These signals shall act similar like a trigger, which resets the
adjustment of all system-parameters from time to time, bringing back the
system into a well defined initial state with optimal adjustment of the
resonances to each other. From this moment of "triggering",
the resonances begin to drift again, but the next trigger-pulse will be
given much earlier than the adjustment becomes seriously bad. Thus we
investigated the DFEM-Simulation of a triggered operation.
electrical triggering is much easier than mechanical triggering, it was
decided to try the following: The mechanical position shall be the
orientation for the moment, at which the electrical trigger-pulse shall
be given into the system. The electrical trigger-pulses shall be given
into the circuit as a voltage as shown in fig.3, which can be understood
as an upgrading of fig.1.
Insertion of trigger-pulses to our zero-point-energy converter,
with the purpose to make the adjustment between the mechanical resonance
and the electrical resonance stable in time (phase lock).
trigger-pulses can be given as shown in fig.4. They are actuated at a
well defined geometrical position of the mechanical part of the sytem.
Of course the trigger-pulses themselves shall consume as low power as
possible, otherwise they would feed the engine instead of the
4: Red: Mechanical
oscillation, at which thetrigger-pulses are orientated.
Blue: Trigger-pulses with very low power.
differential equation on which the electrical oscillation is based, can
be derived from the use of Kirchhoff’s voltage rule [Ger 95]:
is an inhomogeneous differential equation of 2nd order, with
a disturbance function according to fig.4.
mechanical oscillation follows the differential equation:
capacitor plates are mounted symmetrically with regard to the origin of
coordinates, so that their positions are –x(ti) and +x(ti).
Thus we write Coulomb’s force between the capacitor-plate as
because the distance between the capacitor plates is 2·x(ti).
the computation of the force of the helical spring, we have to use a
totally different length, namely the alteration of the spring length
relatively to the spring without load. If CD = length of the unloaded
spring, the alteration of its length relatively to CD can be written as
CD-2·x(ti), not forgetting the algebraic sign of x(ti).
If we regard the motion of the capacitor-plates a symmetrically with
regard to the origin of coordinates, (where the coordinate-system is
fixed in the middle of the capacitor, each half of the spring follows
exactly half of CD-2·x(ti), so that the force of the spring,
acting on each of the capacitor plates is FF=-D·(x(ti)-CD/2)
, as written in equation (5).
coupling between the mechanical oscillation and the electrical
oscillation can be recognized when regarding the last summand of
equation (5), where the electrical part of the apparatus carries out its
influence onto the mechanical part of the apparatus. But we also
recognize it in equation (1), where the capacity C is influenced by the
this concept allows a stable operation of the zero-point-energy
converter, as can be seen in fig.5 and fig.6.
5: The electrical charge
in the capacitor oscillates with a sine.
6: If we observe the
oscillation over long time, the graphics display does not dissolve all
pixels of the sine, but it becomes very clear, that the operation runs
we want to extract energy from the system, we can try to insert a load
resistor as a consumer of energy. This load resistor has to be inserted
into equation (1) in series with the resistance of the wire from which
the coil is made, following equations (6) and (7).
the extraction of power, we optimize the load resistor in such way, that
it extracts just the amount of energy coming from the zero-point-energy.
A larger load resistor would decrease the oscillation and a smaller load
resistor would have the consequence that the oscillation would increase
the result of these DFEM-simulations was, that the triggered
zero-point-energy converter allowed only few microwatts to be extracted.
This is more than the acoustic power to be extracted from the setup
without triggering and phase lock, but it is not really satisfactory.
Besides, the capacitor had plates of 6 m2 up to 20 m2 (for
different trials) with power-output between Nanowatts and few ten
the gained power is very low, the result is encouraging, because the
gained power is by several orders of magnitude larger than the
input-power of the trigger-pulses. Obviously the trigger-pulses are only
needed for the adjustment of the system and not as an energy-supply.
There have been examples of simulation with a mechanical power-gain
which is more than a factor of 106 larger than the
energy-supply of the input trigger-pulses.
it was observed, that the mechanical oscillation of the capacitor plates
acquires much more energy than the electrical oscillation in the LCR-circuit.
This leads us to the question, whether a mechanical extraction of energy
is more efficient than the electrical extraction of energy. In order to
try this, a constant mechanical friction was included into the DFEM-algorithm,
not thinking about the question how this constant mechanical friction
could be realized in praxis (especially with regard to the capacitor
plates of several m2).
this purpose we expand differential equation (5) by a constant load
force Fload and thus come to the differential equation (8) of
a damped oscillation.
constant load force acts in counter-direction with regard to the
acceleration (thus the negative algebraic sign), and it can be switched
on at an arbitrary moment of time. By this means a converter has been
input-power (trigger) of Pinput,electr =
an electrical output-power of Poutput,electr =
mechanical output Poutput,mechan = 2.611·10-5
if the extracted power exceeds the input-power of the electrical
trigger-pulses by a factor of 194, the total power gain is only few more
than 260 microwatts (see fig. 7), although the capacitor had plates of 6m2
(difficult to realize, and thus not satisfactory).
7a: Extracted mechanical
power staying in the oscillator. The electrical power is negligible.
example is for sure not the solution of the power-extraction problem,
even if the trigger-pulses help us to come into the upper
tests with a load-force of friction proportional to the velocity of the
capacitor plates Fload=-β·dx/dt allow us to
enter the milliwatt-range, but I even regard this not as the solution of
the power-extraction problem. Fig.8 is based on a load-force of friction
proportional to the velocity and comes to a power-gain of a bit more
than 4.5 milliwatts. The trigger-pulses are orientated with their phase
relatively to the mechanical oscillation. At the beginning of the
operation, there is not yet any mechanical power in the system, and the
trigger-pulses initiate the oscillation at all. At this time, the
amplitude of the oscillation is growing permanently. At the moment
t=100sec., the mechanical load-force is switched on with a friction
keeping the amplitude constant from there on. From t=100sec. up to
t=200sec., a mechanical power-extraction of a bit more than 4.5
milliwatts is observed as stated above. Obviously the mechanical damping
reduces the frequency of the oscillation, which is rather typical for
damped oscillations. But this does not disturb our system, because the
trigger-pulses are orientated relatively to the mechanical deflection.
Mechanical deflection of the capacitor-plates in meters. The position of
rest is located at 1.0 Millimeters = 0.001 Meter. The deflection is to
be understood relatively to the rest position. purple:
Electrical power-supply of the trigger-pulses. They have an amplitude of
0.1 Volt and are rather short.
the capacitor-plates in the simulation example have a mass of 440 kg per
each, the stiffness of the springs is rather high, with a Hooke’s
spring constant of 86487 N/m. This means that the converter has no
practical sense at all, even if it appears realizable by principle. But
– how to extract few milliwatts from such large capacitor-plates ? The
question will remain unsolved, because we will soon see a better design.
Power extraction from the coil
we found out, that the capacitor is almost incapable to release its
energy, we want to try, whether the coil is capable to release its
energy. This requires some impedance-transforming, so that we come to a
design as seen in fig.9.
9: Suggestion for making the extraction of energy from the
zero-point energy converter better.
the coil bobbin from fig.1 is extended to be yoke of a transformer now,
so that coil in the LRC-oscillation circuit will be the primary-coil of
a transformer, from whose secondary-coil we can extract energy. This
arises the hope, that the impedance of the coil can now be transformed
in such way, that we can gain more energy and/or power than before.
primary-coil produces a magnetic field due to its current [Stö 07],
we put the equations into each other, assuming a homogeneous magnetic
field, we come to a magnetic flux in the yoke, which has the same value
in the secondary-coil as in the primary-coil:
notation has been adapted to the use in the differential equations of
the coupled oscillations. From there we come to the relation of the
electrical currents in the secondary-coil relatively to the
allows us to convert the values of the primary sizes Q1, dQ1/dt,
dQ12/dt2 into the values of
the secondary sizes Q2, dQ2/dt, dQ22/dt2
(see index), so that we can calculate the power-extraction of the
system. This is the way, how we include the secondary-coil into the
differential equations of the oscillation. The load resistor can be
translated into a resistor in parallel to the primary-coil, which can
then be inserted into the differential equations of the oscillation.
translating computation requires a longsome derivation, finally
resulting in the differential equations (14), which shall not be derived
here explicitly, because we will soon observe, that this way is also not
the very solution of out power-extraction problem.
this construction it was possible to enhance the extracted power to 63
milliwatts, but still using the unrealistic large capacitor-plates as
have been used for the simulation-examples of fig.8. The extracted power
is low enough not the justify the enumeration of the more than 20
parameters of the system, which have been necessary for the DFEM-simulation
of the differential equations containing equation (14). The situation is
not advanced by the suggestion of fig. 9 very much. We will have to try
Variability of the coil
all we found, we come back to our questions at the end of section 2,
which should guide us towards the solution of out power-extraction
problem. We now see, that the pulse-operation is not the only way.
of all, we remark, that an enhancement of the power-density within the
system is absolutely necessary. If there is low energy and power within
the system, there is not much to be extracted. The weak point in the
design is the capacitor with only two massive (thick) parallel plates.
This type of capacitor is known for its low capacity. The capacitor on
which fig.8 is based had a capacity of only 79.7 nF with a
surface of the plates of 6m2. It should be mounted like a
we want to enhance the power-density of the system, we should respect
equations (15) and (16) and come to the point to make the energy within
the capacitor about the same large as the energy within the coil. This
means that we have to use a capacitor much larger than what we did up to
now. This should help us to have the same amount of energy in the
electric circuit as in the mechanical oscillation.
enhancement of the capacity can be realized rather easily with a
standard commercial capacitor. But this means that we lose the
possibility to have an oscillation of the capacitor-plates. So we have
to go back to the very beginning and look again to fig.1. The
variability of the electric LC- oscillation circuit can be achieved not
only by the capacitor but also by the coil. We need this variability in
order to control the speed of propagation of the field of the
interacting forces, but this control can be realized either by the
capacitor or by the coil. So we come to an alternative design as shown
in fig.10. There we have a coil with the coil bobbin moving inside the
windings, which gives rise to an alteration of the inductivity of the
coil, as soon as the coil bobbin has a permeability different from 1,
this is µr≠1.
10: Suggestion for an
improvement of the zero-point energy motor namely by improving the
energy inside the system, which allows to improve the energy-coupling
between the mechanical part of the system and the electrical part of the
system. The variation of the inductivity of the coil is due to an
oscillation of the coil bobbin, which has a permeability different from
permeability of the coil bobbin can be very large (depending on
appropriate material), so that the variation of the inductivity of the
coil is very large. The coil bobbin is fixed to a spring which makes the
bobbin oscillate mechanically, so that we now do not alter the capacity
but we alter the inductivity in the LC-circuit. Thereby the electrical
energy-density of the system can be enhance so much, that the electrical
circuit contains about the same amount of energy as the mechanical
oscillation. This helps us to get rid of the weak link in the system,
which has been the electrical part.
disadvantage of the procedure is the rather large mathematical effort
for the DFEM-calculations, because we now have to calculate the
inductivity of the coil as a function of the position of the coil
bobbin. This causes that we can not use any standard-formulas from any
formulary tables. This brings us into the necessity to derive the
behaviour of each winding individually, and to derive the behaviour of
the whole coil as a summation of the behaviour of each winding.
Therefore we chose a setup as shown in fig 11.
11: Characterization of the parameters of a coil bobbin (blue),
which is emulated as a cylindrical coil (red), and which is oscillating
inside a real cylindrical coil (black). On the one hand, the coil bobbin
takes up Coulomb-forces from the magnetic field of the outside
cylindrical coil, but on the other hand, the coil bobbin induces a
voltage into the outside cylindrical coil due to its movement relatively
to the outside cylindrical coil. The crucial point is, that the coil
bobbin influences the inductivity of the coil.
ls = length of the coil body
bs = latitude of the coil body
di = inner diameter of the coil body
da = outer diameter of the coil body
Dd = diameter of the coil’s wire
n = number of windings in radial direction
m = number of windings in axial direction
dk = diameter of the coil bobbin
lk = length of the coil bobbin
x = deflection of the coil bobbin
relatively to the rest position
ls-x = retrection depth of
the coil bobbin into the outside cylindrical coil
theoretical simulation now goes as following:
magnetic field of a cylindrical permanent magnet has the same structure
as the magnetic field of a cylindrical coil, thus we can calculate both
fields in the same way. Therefore we use the law of Biot-Savart and
calculate the magnetic field of each single conductor loop (as shown in
fig.12). The magnetic field of one conductor loop of the coil causes a
Lorentz-force onto each single conductor loop of the coil simulating the
coil bobbin. If we calculate in such way the interaction between each
pairs of all single conductor loops (in combination), we can sum up all
forces of interaction until we get the total force between the coil
bobbin and the cylindrical outside coil. This calculation was done for
each arbitrary position of the coil bobbin relatively to the cylindrical
outside coil, so that a force-deflection curve was computed.
12: Illustration of the parameters of two single conductor
loops interacting with each other. The parameters are used for the
application of Biot-Savart’s law and for the calculation of the
Lorentz-forces between the conductor loops.
field produced by a finite conductor element of loop 1 at the position
of a finite conductor element of loop 2 is (see [Jac 81])
the magnetic field of a cylindrical permanent magnet has the same
structure as the magnetic field of a cylindrical coil, we can use this
consideration for the calculation of the magnetic field of both
components in the same way. The Lorentz-force acting onto the conductor
loop elements of loop 2 are then calculated in the usual way:
we conduct the outer vector product within the integrals, then perform
the integration, and finally sum up all the forces between all finite
conductor loop elements (using the cylindrical symmetry of the setup),
we come to the following result:
field of the permanent magnet (loop 2) can be separated into two
components, a radial and an axial component. A motion of the magnet will
cause Lorentz-forces. The Lorentz-forces due to the radial component of
the field want to move the electrons in the coil (loop 1) perpendicular
to the direction of the wires, which is a direction, in which electrical
current is not possible. This means that the whole wires take mechanical
forces, which we know in every day’s life to be the magnetic forces
between a magnet and a coil. Their calculation has been demonstrated
above. On the other hand, the Lorentz-forces due to the axial component
of the magnetic field of the permanent magnet (with its motion) want to
move the electrons in the coil (loop 1) into the direction of the wires,
where they can flow easily. This gives rise to induction, as we know it
in every day’s life from the induced voltage in the coil.
magnetic flux, which the coil bobbin causes in the coil can be derived
after some calculation to be
current I2 in coil no.2 (which represents the permanent
magnet, loop 2) is to be understood as the current which is necessary to
emulate the permanent magnet by a coil.
derivative of the magnetic flux is the induced voltage in the coil, by
which the mechanical motion of the permanent magnet acts into the coil
and thus into the electric circuit. Its formula can be developed as
these formula we are now able to calculate
the magnetic forces, which the coil with electrical current
causes onto a permanent magnet, and
the induced voltage, which a permanent magnet in motion brings
into a coil.
this basis we can now perform the DFEM-simulation of the system shown in
this simulation we learn a technical problem, which still prevents us
from extracting noteworthy power from the zero-point-energy converter
system. The difficulty consists of two aspects, which conflict each
other. They are explained as following:
first aspect results from the mass of the permanent magnet. If we
activate the converter system by a mechanical motion of the permanent
magnet, the geometrical oscillation of the permanent magnet causes the
induction of some voltage-pulses into the coil, but this electrical
energy is not enough to excite the electrical oscillation of the LCR-circuit
(at least due to the damping of the Ohm’s resistance of the wire of
the coil). Because of the mass inertia of the permanent magnet, which
has to be accelerated and decelerated all the time due to its
oscillation, it is impossible to enhance the velocity of motion of the
permanent magnet enough, that it will bring a voltage into the coil,
which is sufficient to arise a permanent oscillation of the electrical
charge in the LCR-circuit. The energetical coupling between the two
oscillations (the mechanical and the electrical oscillation) is
constrained seriously by the mass inertia of the permanent magnet. We
can also regard this aspect from the point of view of the spring (which
moves the permanent magnet): If the spring is not very strong (low
Hooke’s constant), the permanent magnet oscillates rather slow, and
the low velocity of the magnet is responsible for the problem, that the
induced voltage in the coil is very low. But on the other hand, if the
spring is strong (large Hooke’s constant), the mechanical amplitude of
the magnet is rather low, which also results in the problem, that the
induced voltage in the coil is very low. In any case, the electrical
oscillation can not be properly coupled with the mechanical oscillation.
other aspect of the difficulty can be seen, if we try to activate the
converter system from the electrical side, putting electrical
input-pulses into the LCR-circuit. Due to the Ohm’s resistance of the
wire of the coil, the electrical oscillation is damped. And the energy
of the electrical oscillation is absorbed by the resistance of the wire
of the coil so fast, that it is impossible to activate the mechanical
oscillation of the permanent magnet via Lorentz-forces. Very low
amplitudes are possible, which do not allow satisfactory
power-conversion from the zero-point energy.
we would like to adjust the mechanical oscillation of the permanent
magnet to the electrical oscillation of the LCR-circuit, we have to
adjust the resonance-frequencies of both oscillations to each other.
Therefore we should decrease the mass (inertia) of the permanent magnet
(together with Hooke’s spring constant) so far, that the mass density
of the permanent magnet is lower then the mass density of air. Obviously
this is not realistic, but our aim was the theoretical development of a
realizable zero-point-energy converter. This means that the setup
according to fig.10 is not even capable for a sensible operation of a
zero-point-energy converter at all. To say it in clear words: The setup
according to fig.10 is not a zero-point-energy motor. It can not convert
zero-point-energy by principle.
this setup helps us mentally to find a way towards a good design for an
appropriate zero-point-energy motor. With other words: From the setup in
fig.10, we now come to the solution of our energy-extracting problem,
namely as following:
found that the only problem in our design was the mass inertia of the
permanent magnet in combination with the fact, that the permanent magnet
has to change its direction of motion all the time (twice per period).
If we would find a possibility to avoid, that the permanent magnet has
to go back and forth all the time, its mass inertia would no longer be a
problem. A continuous periodic motion – this would be the solution of
our problem. And it is not very complicated. It is a circular motion, a
rotation. That’s all we need to add into our concept. A circular
motion does not need oscillating acceleration and deceleration, but it
repeats its position periodically nevertheless. Thus we can enhance the
speed of the motion without needing the strong spring-force at all. Mass
inertia does not disturb our possibility to enhance the speed of the
circular motion. The periodicity of the rotation can be easily
understood, if we regard the Cartesian components of this motion. This
approach will indeed be our solution of the energy conversion problem as
well as of the energy extraction problem.
The solution: A zero-point-energy motor with a rotating magnet
the mechanical rotation, we want to use a magnet with cylindrical shape,
but for the electrical induction of voltage into the coil, a magnet with
a homogeneous field is preferable. (And besides, that calculation is
easier with a homogeneous magnetic field, which is indeed important for
the elapsed time to run the DFEM-algorithm), so that we decide to use a
magnet according to fig.13.
13: A cylindrical magnet,
which produces a homogeneous magnetic field. Such magnets are available
in commercial magnet shops.
magnet has to rotate inside a coil with "n" windings. All
windings can be located at the same position in good approximation.
Other then in section 5, this is a good approximation here, because the
magnet interacts with the coil not by translation but by rotation.
due to the rotation we now have to deal with a torque acting onto the
magnet (and not with linear forces as it was the case in section 5).
This means that we want to take the motion as a pure rotation in the
DFEM-simulation. Consequently we have to calculate the torque between a
magnetic dipole and the magnetic field of the coil. Because of
Newton’s axiom "actio = reactio", the magnet gets the same
torque as the coil, so that we can calculate the torque of the magnet in
the field of the coil or on the other hand the torque of the coil in the
field of the magnet as well. Due to the fact that the magnetic field of
the permanent magnet is homogeneous, the calculation of the torque onto
the coil inside the field of the permanent magnet is the more efficient
variant, so that we will follow this way.
magnetic dipole moment "m" of a coil is given in equation
(21), the torque of the coil in the magnetic field is
given in equation (22) [Tip 03].
calculation of the torque represents the mechanical influence of the
coil onto the magnet. This allows us to calculate, how the electrical
circuit acts onto the mechanical motion.
opposite direction of the coupling of the two motion, namely the
influence which the rotation of the magnet brings into to the electrical
circuit has to be calculated via the induced voltage, which the rotating
permanent magnet brings into the coil. This can be performed via the
magnetic flux Φ, which the permanent magnet brings into the coil.
illustration can be seen in fig.14.
14: Placement of the
permanent magnet in the coil. The permanent magnet rotates around the
x-axis, so that the angle φ(t) between the magnetic field flux
lines of the permanent magnet and the normal vector of the area of the
coil’s conductor loops is to be measured relatively to the y-axis.
induced voltage is now
one component of the torque, which is responsible for the acceleration
and the deceleration of the rotation of the magnet is the x-component,
namely Mx . For the vector calculus in equation (22) can be
done most easy in Cartesian coordinates, we write (leaving away the
arrow over a vector-size means a calculation of its absolute value):
the rotation always goes back into its starting-point without any
restoring spring-force, we do not have a spring at all, and thus no
oscillation in our calculation. Therefore a spring-term in the
mechanical differential equation is not to be applied any more here.
electrical part of system of two coupled differential equations can be
used identically as in our former consideration (see for instance
section 5) and also follows the equations (1), (2), (3), (4). But we now
want to set the input voltage identically to zero, i.e. Uin(t)=0,
because we do not need any input voltage at all. We will soon see, that
the machine is self-running, i.e. it works without any classical energy
input. And we will also see, that the machine operates stable, so that
it does not need any triggering.
mechanical part of the differential equations is based on the rotation:
is indeed the differential equation to describe a rotation.
coupling between the differential equations (1), (2), (3), (4) and the
differential equation (32) is given via the magnetic (Lorentz-) forces
and via the induced voltage.
coupled system of inhomogeneous differential equations of 2nd
order contains nonlinear disturbance functions. Thus it is sensible to
solve it numerically with our DFEM-algorithm. The Sorce-code of the
algorithm is printed in the appendix of the article. The central part of
the solver can be seen in the body of the main program [Bor 99]. The
coupling of the differential equations is explained in the following
equations (33) and (34). The Sorce-code of the algorithm has to take
additionally constants of integration into account, which are taken from
the initial conditions of the system [Bro 08].
first the algorithm has to be verified. Therefore a torque-computation
was checked with a constant electrical current in the coil. The rotation
of the permanent magnet has been started with constant angular velocity,
and the rotation was observed as a function of time (see fig.15).
Obviously the angular velocity is modulated by the magnetic forces as
15: Display of the angle
of the rotation, which shows the modulation of the angular velocity, due
to the magnetic forces between the magnet and the coil.
the way, the angular acceleration does not follow a sine shape, as can
be seen in fig.16.
16: This is the angular
acceleration, which leads the motion shown in fig.15.
we start the rotation with a constant angular velocity, and allow the
coil to take induced voltage, but also produce a magnetic field due to
the induced current, we can find very different behaviour of the
magnetic forces (as well as very different behaviour of the angle of
rotation), depending on the choice of the system-parameters. An example
therefore is shown in fig.17 (angle of rotation) and in fig.18
(electrical current in the coil). If we analyse the total energy of the
system (with normal classical adjustment of the parameters), we find
perfectly the conservation of classical energy, this is the energy-sum
of the kinetic energy (of the rotation of the magnet), the electric
energy in the coil and the electric energy in the capacitor, because the
potential energy of the magnet in the coil is converted immediately into
electrical energy going into the coil (and later also into the
the purpose of illustration: During the rotation of the magnet, a
voltage is induced into the coil, which converts mechanical energy (in
the rotation) into electrical energy in the LCR-circuit. But the
Lorentz-forces convert electrical energy in the opposite way back from
the LCR-circuit into energy of the mechanical rotation. This causes a
rather complicated type of motion of the magnet, as can be seen in
17: Angle of rotation of
the magnet inside the coil.
Electrical current (Amperes) in the coil, which is caused by induction
due to the rotation of the magnet.
now introduce the Ohm’s resistance of the wire, from which the coil is
made (and later additionally also some additional load resistance for
the purpose of the extraction of energy from the system). By this means
we come to the following test of verification:
start the rotation with a constant angular velocity (as initial
condition), but without any electrical charge or energy in the LCR-circuit.
The rotation of the magnet induces a voltage into the coil, which then
causes some energy-loss at the resistor. This absorbs some energy from
the system as can be see in fig.19 (the kinetic energy of the rotation
is decreasing as a function of time) and in fig.20 (the electric current
in the coil is decreasing also as a function of time).
Angular velocity as a function of time.
Electrical current in the coil as a function of time.
we reduce the Ohm’s resistance to zero (the wire of the coil as well
as the load resistor), for the purpose of verification, we can verify
the conservation of classical energy accurately: Fig.24 shows the total
energy of the system as the sum of the coil’s energy (fig.21), the
capacitor’s energy (fig.22) and the rotation-energy of the magnet
(fig.23) [Bec 73] – as long as the system’s parameters are not
adjusted for the conversion of zero-point energy.
21: Energy in the coil Ecoil=1/2
22: Energy in the
capacitor Ecapa=1/2 C U2
23: Energy of rotation in
the magnet Erot=1/2 J omega2
Total energy-sum Etotal=ES+EC+ER.
Except for numerical noise, the total energy-sum is constant (when
solving the differential equation without adjustment to
now begin the adjustment of the system parameters for the conversion of
zero-point-energy. Therefore we have to align the resonance frequency of
the electric LCR-oscillation-circuit with the frequency of rotation of
the permanent magnet. But they can not be identical, because the
power-extraction from the electric circuit acts like a damping of the
oscillation-circuit, which de-tunes its characteristic resonance
approach to the adjustment of the system parameters with all resistors
being switched of (Ohm’s resistor and load resistor both being zero).
Then we start the rotation of the magnet with a well defined number of
revolutions per minute. Under these conditions, we start to adjust the
electric LCR-oscillation-circuit to the same frequency as the
rotation of the magnet has. At the beginning, the electrical circuit did
not contain any energy. When the adjustment of the electrical
oscillation-circuit is close enough to the frequency of the initial
rotation, we have a state of the system, which can be understood as the
double-resonance of the electrical and the mechanical parts. In this
state, the system begins to build up classical energy by alone, and the
new classical energy is coming from the zero-point reservoir.
soon as we have found this point of operation, we can slowly introduce
the Ohm’s resistance of the coil’s wire, in tiny steps, step by
step, into the differential equations. But we have to perform very small
steps for the enhancement of this Ohm’s resistance, and always to
renew the adjustment the parameters of the electrical circuit (capacity,
inductivity, number of coil’s windings) step by step, in order not to
lose the state of operation, in which zero-point energy is gained. This
procedure has to be done very carefully; otherwise we would lose the
information about the good operation of the system. Step by step we
learn how to operate the system in a way, that the power-gain from the
zero-point-energy is large enough to support the complete coil (with its
whole Ohm’s resistance) with power. Very carefully we give attention
to the double-resonance in order not to lose it.
this mode of operation is found, the rotor runs safe and reproducible
with the system parameters we have found, to be a self-running engine.
With these parameters, the motor can be started with a given initial
number of revolutions per minute. Therefore it is started once by hand,
and then the rotation continues by alone, being supplied from the
zero-point energy of the quantum-vacuum. We now can measure the angular
velocity of the rotor (see fig.25) und the electrical current in the
coil (see fig.26). Now it is clear, that the total sum of the classical
energy within the system is not constant, because the system is
connected to the zero-point energy of the quantum-vacuum (fig.27).
the way, it should be mentioned, that an improper adjustment of the
system parameters can have the consequence, that classical energy is
converted into zero-point energy of the quantum-vacuum. In this case,
the engine has to be feeded with more classical mechanical energy, than
the Ohm’s resistances consume. This means, that under such operation,
the total energy sum, including the Ohm’s losses and the load is not
constant, but decreasing during time. The lack of classical energy,
which can not be explained from classical energy conservation, has its
reason in the conversion of classical energy into some zero-point energy
of the quantum-vacuum. This means that the machine can be used in both
directions: As a converter of classical energy into zero-point energy as
well as a converter of zero-point energy into classical energy.
Angular velocity of the rotation. Due to the high revolution speed, the
resolution of the graphics does not allow to see the single
Electrical current in the coil. Due to the high
revolution speed, the resolution of the graphics does not allow to see
the single oscillations.
27: Total energy-sum of
the system. Due to the high revolution speed, the
resolution of the graphics does not allow to see the single
the system is started with a given angular velocity at the very
beginning. From there on, it gains classical energy from the zero-point
energy, which it converts completely into the energy of rotation. This
is done until the angular velocity of the rotation reaches a certain
value. The restriction to this value has its reason in the fact, that a
further additional enhancement of the angular velocity would decrease
the adjustment of the system parameters, with the consequence that from
there on less zero-point energy could be converted. This point is
reached at a time of about 1700 Skt. (see fig.25).
this point on, where the mechanical energy due to the angular velocity
must be constant, the energy gain from the zero-point energy is pumped
into the electrical circuit, so that from time of about 1700 Skt. up to
about 1900 Skt., the electrical oscillation gains energy (see fig.26).
both parts of the system are filled up with enough energy, so that the
system itself can not take more energy inside than it already has. In
this state, every enhancement of the amount of energy inside would
decrease the adjustment of the parameters, so that energy will be given
away, until the system comes back into its good state of operation. From
there we see, that the system runs into a stable operation by alone, so
that is not necessary to support trigger-pulses to control the
operation. The system can now run (as long as nobody will stop or damage
it) being supported by zero-point energy. This state of stable operation
can be called as "energetically saturated".
now want to introduce an additional load resistor (additional to the
Ohm’s resistance of the coil’s wire) in order to extract energy from
the system (see fig.28). This load resistor will extract permanently
energy, which is the energy-output and power- output of the zero-point
energy machine. In the differential equations, we have to introduce an
additional load resistor in series with the Ohm’s resistance of the
coil’s wire, see equation 35. The calculation of the extracted power
is shown in equation 36.
This setup now shows the results of the present publication: It
is a powerful zero-point energy motor with realizable dimensions.
crucial point is, that the converter has to be driven in a state short
below the "energetical saturation", so that the energy-gain
from the zero-point energy is maximal. This state of operation can be
found in theory quite well, because in theoretical calculations it is
easily possible to control the behaviour of the system with very
different values of the system parameters very efficiently and very
exactly. Under this control it is possible to adjust the system
parameters, such as the capacity, the inductivity, the number of
windings, and so on… The parameters which have been found for good
operation can be seen in the Source-code of the DFEM-algorithm in the
practical experiment to build up such a zero-point-energy converter is
only sensible on the basis of a well understood theory, from which we
can learn how to adjust the system parameters. The adjustment of the
system parameters appears difficult enough, that it is not very likely,
that anybody might manage to find this adjustment without theoretical
understanding: From theory we must learn how adjust the
zero-point-energy converter, and in experiment we will have to build up,
what we learned from theory.
soon as the system is adjusted, the motor will run stable, as long as we
do not try to extract more energy then the motor can deliver. (For more
energy we should use a larger motor.) Our Motor has a diameter of
9 cm and a height of 6.8 cm – so this is not
very much – and we will soon see that it produces a power of 1.07
Kilowatt. On the other hand, if the load is decreased, the power
production will be decreased. This is a feature of the system, because
the system never can overtake the state of “energetic saturation”.
This feature is a great advantage of the zero-point energy converter
presented here, because it never can run away (as it is known from other
systems reported in literature, see for instance [Har 10]). This makes
our system safe in operation and avoids accidents.
Can the power-density of 1.07 Kilowatts in a cylinder of 9 cm x
6.8 cm be enhanced even more ?
reality the optimization of the system parameters can be developed much
further, so that even such a small zero-point-energy converter as in our
example could be brought into the Megawatt-range, because the energy-
density of the zero-point-energy is tremendously large. But in the
example shown here, the further optimization of the system parameters
has been withdrawn in order to restrict the converted power to 1kW,
because there we reach the limit of the strength of the material. The
magnet rotates with 6000 rpm, which should not be a problem for a good
commercial bearing, and the copper wire from which the coil is made has
a cross section area of 1.0 mm2 , which is not too much for
an electric alternating current of Imax =
18 Ampere in the peak (the effective values are smaller of course). This
is the reason, why I decided not to demonstrate even more power-density,
because this would be not realizable due to the stability of the
us now have a look into few details of the DFEM-model of the zero-point
electrical current in the coil (see fig.29) is AC, same as in fig.26.
But please have in mind, that the time scale in fig.29 is different from
the time scale in fig.26, so that the oscillations can be seen now.
Please notice, that the energy in the coil (see fig.32) must go back to
zero within every revolution, because there has to be a moment in every
turn of the magnet, during which the coil does not produce any magnetic
field. This is necessary, because the magnetic field has to be switched
on and off periodically, otherwise it would not be possible to convert
zero-point energy. During each turn of the magnet, there are two moments
in time, at which the coil produces a magnetic field, which accelerates
the magnet. But there must be intermediate time-intervals between these
field-moments, where the magnet has an orientation, that the field would
decelerate its rotation. During this intermediate time-intervals, the
electrical charge is stored in the capacitor, so that the coil has no
current, so that the magnetic field is absent, so that the magnet is not
decelerated. The fact that this procedure accelerates the magnet can be
seen in fig.30, where the magnet become faster and faster (up to a
certain point as stated above). This can be seen in fig.31 very clearly,
when we look to the angular velocity. There we see, that the angular
velocity is increasing until the motor finally comes into its "energetical
fact that the angular velocity contains a small part of an oscillation
is also clear, because the rotating magnet is accelerated twice per each
turn, and in between there is a time-interval without acceleration. In
the intermediate time-intervals between the acceleration, there is even
some deceleration, because the flux of the electrical charges, which
causes the acceleration needs some time to leave the coil and go into
the capacitor. Nevertheless it is clear, that the system is optimized
for energy-conversion from the zero-point energy, so that the
acceleration and deceleration and the electrical AC-current are adjusted
to each other. The result can be seen in fig.32, where we see the total
energy-sum of the classical energy in the system. (The saturation is due
to the extraction of energy by the load resistor.)
Electrical current in the coil
Angle of rotation
Energy in the coil
Total energy-sum in the system.
we have a listing of the 11 system parameters in the algorithm in the
appendix, everybody can understand the presented example and optimize
his or her own system and adjust it to the available materials. This
means that the theoretical conception is developed far enough, that
experimentalists are invited to verify the zero-point-energy converter
system in the laboratory. Everybody is welcome to build up his or her
own zero-point-energy motor.
result of the present work is, that the available theory not only
explains the theoretical fundament of the conversion of
zero-point-energy, but it also allows to construct a machine with
practicable dimensions and powerful operation. It is a self-running
zero-point-energy motor in the Kilowatt-range, which is now
theoretically understood. On this basis it should be possible to develop
a practical setup.
from practical experiments reported in literature, this is the first
complete theory and a basic understanding of zero-point-energy motors.
This arises hope for a reproducible practical machine.
[Bec 73] Becker, R. and Sauter, F. (1973), Theorie der Elektrizität,
Teubner Verlag. ISBN 3-519-23006-2
[Bor 99] Borland Pascal (Delphi 5 from 1999 or newer version)
[Bro 08] Bronstein, I. N., Semendjajew, K. A. , Musiol, G. , Mühlig, H.
(2008), Taschenbuch der Mathematik, Verlag Harri Deutsch, 7.Auflage,
[Dub 90] Beitz, W., Küttner, K.-H. et. al. (1990), Dubbel - Taschenbuch
für den Maschinenbau , 17.Auflage, Springer-Verlag. ISBN 3-540-52381-2
[Ger 95] Vogel, H. (1995), Gerthsen Physik, Springer Verlag. ISBN
[Har 10] Hary, G. (2009/10), Practical experiments by Guy Hary, private
[Jac 81] Jackson, J. D. (1981), Klassische Elektrodynamik, Walter de
Gruyter Verlag, ISBN 3-11-007415-X
[Stö 07] Stöcker, H. (2007), Taschenbuch der Physik, Verlag Harri
Deutsch. ISBN-13: 987-3-8171-1720-8
[Tip 03] Tipler, P. A. and Llewellyn, R. A. (2003), Moderne Physik,
Oldenbourg Verlag. ISBN 3-486-25564-9
[Tur 09] Turtur, C.W. (2009), Conversion of the Zero-point Energy of the
Quantum Vacuum into Classical Mechanical Energy, 1. Auflage, ISBN:
[Tur 10a] Turtur, C.W. (2010), Fundamental Basics of Vacuum-energy and
the Principle of the Construction of Zero-point-energy motors, The
General Science Journal, ISSN 1916-5382, http://wbabin.net/weuro/turtur2e.pdf
[Tur 10b] Turtur, C.W. (2010), DFEM-Computation of a Zero-point-energy
Converter with realistic Parameters for a practical Setup, PHILICA.COM,
ISSN 1751-3030, Article number 213
Adress of the Author:
Prof. Dr. Claus W. Turtur
University of Applied Sciences Braunschweig-Wolfenbüttel
Salzdahlumer Strasse 46 / 4
Germany – 38302 Wolfenbüttel
Tel.: (+49) 5331 / 939 – 42220
Sorce-Code of the DFEM-algorithm
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|The full citation for this Article is:
Turtur, C. (2011). DFEM-Simulation of a Zero-point-energy
Converter with realisable Dimensions and a Power-output in the
Kilowatt-range. PHILICA.COM Article number 219.