Download A study of the Biefeld

SHANGHAI HIGH SCHOOL
An Experimental Study
of Biefeld-Brown Effect
Zhen-li Zhang, Ming Yin
Biefeld-Brown effect refers to the lifting force on an asymmetrical capacitor when it is
applied with high voltage (~10kV). In our research we conducted a series of qualitative and
quantitative experiments, based on which we established a model for the phenomena. We also
studied the features of ‘symmetrical capacitors’, where a series of previously unnoticed
phenomenon are found, in agreement with our model.
I. Introduction
In the 1920s, Thomas Townsend Brown, along with his advisor Prof. Paul Alfred Biefeld
found that when a high voltage (~10kV) was applied to a set of asymmetrical electrodes, a force
trying to move the device emerged. Shortly after, such phenomenon was named as the
Biefeld-Brown effect, and the device was generally referred as an “asymmetrical capacitor (AC)”
Copper wire
Direction
of force
Aluminum foil
Commonly, an AC has one electrode of a copper wire, and another of a sheet of aluminum
foil, as shown in the figure above (left). The direction of the force is not related to the direction of
the applied electric field, and always points to the direction of the copper wire. Over the years, the
Biefeld-Brown effect has always been a fascination. A kind of hovering device “the lifter”, as
shown in the figure above (right) functions based on the effect.
In general, AC, as a “capacitor” and “lifter”, has both electric and mechanical characteristics.
The inter-connection between these characteristics is of major interest in the Biefeld-Brown effect.
However, the research focusing on such connection is insufficient, especially experimental data.
So the mechanism of the Biefeld-Brown effect remains unestablished. The few existing research
papers have proposed following hypothesis
a) The static electricity theory. The strong electric field generated by the AC polarizes the
ground, causing a repelling force on the device.
b) Ablative material theory. The ablation of the electrodes produces ions, which are
accelerated by the electric field and exerts a reaction-force on the device.
Instead of trying testing each of those theories, we decided to establish our own model based
on our experiments. Firstly, we conducted a series of qualitative experiments, which demonstrate
the existence of air flow. Such phenomenon indicates that the air around the AC is a major factor
of the Biefeld-Brown effect. Then we can establish some preliminary ion-thrust model based on
this mechanism to compare with the experiments. For this purpose, we designed a set of simple
test-benches to measure both electric and mechanic characteristics in detail. The data collected
from the experiments only support a small part of our preliminary model. But these data lead us to
a few corrections to the original model, which take into consideration the collision between ions
and air molecules and help to explain some phenomena unmentioned by other researches.
With the modified ion-thrust model, we started to gain a new cognition of the different behavior
of this kind of capacitor in low and high voltage environment, while we also gained a more
complete understanding of process of how the lifting force emerges. Finally, as verification for the
theory above, we conducted further experiments on symmetrical capacitors consisting of two
copper wires, which also produced a lifting force and was qualitatively explained by our model.
The devices we made are shown below. The whole frame is made by light wood, while the
asymmetrical electrodes are made up of a copper wire and a sheet of aluminum foil respectively.
In the single-foil asymmetrical capacitor, the width of the aluminum foil is about several
centimeters, while its length l is about ten centimeters, which is equal to the length of the copper
wire. The distance d between two electrodes is approximately a few centimeters. The single-foil
asymmetrical capacitors can be connected into a multi-foil asymmetrical capacitor, which can
produce greater lifting forces. Experiments show that these two kinds of capacitors are essentially
the same both electrically mechanically. For the sake of convenience in experiments, we use the
multi-foil asymmetrical capacitor in qualitative experiments and the single-foil samples in
quantitative measurements.
Copper wire
d
Light wood
frame
l
Aluminum foil
Multi-foil device
Single-foil device
二、Qualitative experiments
1．Air flow in asymmetrical capacitors
Remarkable air flow can be found in the charged asymmetrical capacitors. A simple
experiment can show that it is due such an air flow that the capacitor is recoiled and thus obtains a
lift. In the picture below, a multi-foil device is laid down with its triangular bottom towards right.
A candle flame is put about 30cm away. When a voltage of 8.2V is applied, one readily observes
that the oblique flame results, which is caused by a distinctive air flow easily felt by hands.
Capacitor
V=0
Foil
V = 8.2kV
Copper wire
Flame
2. The effect is independent of the surroundings’ electrostatic polarization.
Some theories suggest that the Biefeld-Brown effect is
due to the electrostatic polarization of the ground or other
surrounding surfaces, which then repel or attract the capacitor.
Our simple experiments also reject such electrostatic
explanations. As shown is the picture at the right, a multi-foil
2nd
device hangs from the second floor of the building, about
floor
3.5m above the ground. When a suitable voltage is applied
the measured lifting force is of no essential difference with
that measured inside the laboratory. This tells that
electrostatic effects could not play a major part in lifting the
capacitors.
3. Relationship of the force’s direction and the direction of
the electric field
Flame
Device
Ground
floor
Based on our preliminary measurements on the single-foil and multi-foil asymmetrical
capacitors we made. We conclude that the direction of the force is independent of the direction of
electric field applied. The force always directs from the foil to the wire, even though one exchange
the positive and negative ends of the voltage. Actually if the device is turned upside down, with
the wire below the foil, the device is still pushed towards the wire; i.e. it is pushed downward.
According to the above results our qualitative experiments, we conclude that the lift is caused
by the recoil of air flow and not based on electro-static repelling.
III. The electric and mechanic characteristics of asymmetrical capacitors
1. Measuring apparatus
As shown in the figure below, the force-measuring device was essentially a lever. The test
sample of the AC hangs on one end, while on the other end a piece of counter-weight is placed on
an electronic scale. As the lift appears, the reading of the scale gets smaller than normal. The
difference of the reading indicates the lifting force multiplied by a factor of lever-arm-ratio.L1: L2,
which can be adjusted within the range of 2:1 to 5:1. With such an apparatus, the scale can detect
L1
L2
the weight change as little as 0.01 grams, corresponding to the lifting force of 0.00002N.
The electric measurement circuit is shown in the figure below. A current-meter I2 was
connected in series with the test sample to measure the current directly. However, the voltage was
far beyond the range of any of our voltage-meters. So we connected another current-meter with 5
high-voltage resistors with R = (10.0±0.5)Mto make a high-voltage-meter to measure the
voltage V.
R
R
R
R
R = 10M I1
Current-meter
Test sample
I2
V= 0 ~ 20kV
Thus the voltage and current are given by
V = I1(5R)，I = I2
2. The single-foil asymmetrical capacitor
In the experiments on single-foil capacitors, the device was hung about 1 meter above
ground.
Copper wire
Copper
wire
To circuit
Aluminum
foil
Aluminum foil
Single-foil AC
3. Experimental results on the single-foil AC sample
Voltage (V), current (I), distance between the electrodes (d) and force produced (F) was
measured as variables in our experiment. For a fixed d value, V, I, F data are collected to plot the
F-V and I-V curves.
Such I-V curve under different d is shown in the figure below. The curve shows that I is very
small when V < 10kV, and I increases more rapidly as d decreases. When V reaches about 15kV,
the air between the two electrodes starts to break down, causing the AC to discharge. The
breakdown voltage increases with d.
d=2.0cm
d=1.5cm
d=3.0cm
d=2.5cm
I/μA
V/kV
F-V and F-I curves under different d are shown in the figure below. Which shows that when
V < 10kV and I ≈ 0, F is neglectable. As V exceeds 10kV, current I and force F both appears at the
same time increases with V. On the other hand, for the same V, F decreases with d. In general, F
d=2.5cm
d=3.0cm
F/gF
d=1.5cm
d=2.0cm
V/kV
reaches its maximum just before the device breaks down, which was about 0.6 grams in our
experiment.
d=2.5cm
d=3.0cm
F/gF
d=1.5cm
d=2.0cm
I/μA
IV. The ion-thrust model
Such results of our experiment that F appears with current and disappears with the device’s
breakdown can be explained by the ion-thrust model, which suggests that the lift is a reaction
force applied on the electrodes by the accelerating ions in the electric field. With this simplified
model the relationship between V, I, d, and F can be obtained as follows.
We assumed that the air molecules around the electrodes are ionized, and exert a force on the
AC as they accelerate. So the number of ions produced per second is
n = I/q
(1),
where q is the charge of an ion.
After accelerated, an ion gains the kinetic energy
Ek = mv2/2 = qV
So the velocity when the ion arrives at the opposite electrode is
v = (2qV/m)1/2
(2)
So the reaction force F on the device can be given as
F = nmv
(3)
Combine (1), (2) and (3), so the relationship between V, I, d, and F can be given as
F = (2mI2V/q)1/2。
Based on this model, the following conclusions can be readily drawn. Unfortunately, we
found some of them did not quite agree the experimental data.
Firstly, the direction of the force on the device should have depended solely on the direction
of the applied voltage, since the acceleration of ions only depends on the direction of the electric
field, and nothing to do with the shape of the electrodes (wire or foil). On the contrary,
experiments showed that the electrode’s shape, rather than direction of voltage, determines the
direction of force.
Secondly, F is directly proportional to I√V，the constant of proportionality depending only on
the nature of ions and not on the geometry of the device at all. As a comparison, the F-I√V given
by the experiments is shown in the figure below, where no obvious linear relation is seen over the
whole range of voltage V (0 ~ 20kV). Furthermore, experiments imply clearly a remarkable role
played by the device geometry, namely the distance d between the electrodes. In fact, it is seen
that the force F increases dramatically with d, a fact not included in the ion-thrust model.
Finally, the most serious problem with ion-thrust model is the estimate of order of magnitude
of the lifting force. If the mass and charge of the accelerating ions is estimated to be of the same
magnitude of air molecules and e (electron charge), then with V = 15kV and I = 24A (typical in
our experiments), a simple calculation gives the force F ~ 2*10-3mN, while our measurement
gives 3.09mN.
Some phenomena in the qualitative experiments cannot be easily explained either, including
the strong air flow coming out of the base of the device, which means a remarkable number
uncharged molecules may also be accelerated and pushed out of the capacitor, without being
absorbed by the electrodes. Actually, the qualitative experiments made the process more like the
acceleration of air molecules, rather than the acceleration of ions!
d=1.5cm
d=2.0cm
F/gF
d=2.5cm
d=3.0cm
IV1/2/μA·kV1/2
The above disagreement shows that the ion-thrust model is somewhat over-simplified. It did
not take into account the effect of asymmetrical electrodes, which could result in an ‘asymmetrical’
electrical field. This leads us to the assumption that ions may not be produced and accelerated
everywhere in the capacitor. Also, it is unlikely that ions may accelerate to the electrode without
stop. It may lose some kinetic energy during the collision with the surrounding air molecules.
Hence the ion-thrust need to be modified to include such effects.
V. Analysis of the experiments of asymmetrical capacitors; modified ion-thrust
model
1．Production of ions at low voltages
Air molecules are ionized in strong electric fields. Due to the smaller radius of curvature
compared with aluminum foils, copper wires have stronger fields around and ions are first
produced near the copper wire when voltage V increases from 0. Obviously only one species of
ions (namely those repelled by the coppor wire) are then accelerated toward the aluminum foil; the
others are absorbed by the copper wire. Therefore the acceleration is always from copper wire to
aluminum foil, no matter the copper wire is the positive or negative electrode of the capacitor.
This explains why the force invariantly directs from foil to wire.
When one increases the voltage, the force increases because more ions are produced and
accelerated. But when the voltage V increases to point close to the breakdown of capacitor, Air
molecules are ionized near the aluminum foil. The produced ions are then acceleratd towards the
copper wire and therefore produces a force in the opposite direction. The net force would then be
weaker than that predicted by the ion-thrust model. Therefore, the above ion-thrust model is more
likely to work in the low voltage region. This region (V = 10 ~ 15kV) is then measured in more
detail. The data is shown in figures below.
0.5
0.4
0.3
slope = 0.0023
0.4
Slope = 0.0018
0.3
0.2
0.2
0.1
d=1.5cm
d=2.0cm
0.1
0
0
0
50
100
150
0
200
0.2
50
100
150
200
250
0.4
slope = 0.0029
0.15
slope = 0.0034
0.3
0.1
0.2
d=2.5cm
0.05
0
d=3.0cm
0.1
0
0
20
40
60
80
0
20
40
60
80
100
The experiments show that for small values of V, F is roughly proportional to I√V, in
agreement with the ion-thrust model. But the constant of proportionality increases with d, the
distance between the electrodes. Actually, the relation may be written as
F ∝ IdV1/2.
This relation, along with the discrepancy in the order of magnitude of the force, should then be a
result of the collision of ions and the surrounding air molecules. To this end, we proposed the
‘life-time’ description of this process.
2．Modified ion-thrust model: The ‘life-time’ description
Let the mass and charge of ions be m and q. At any instant, the number of all ions in the
capacitor is denoted by N. The force on the device equals the force on all the ions:
F = NEq = NVq/d.
At low voltage, since all ions are ‘born’ near the copper wire and ‘dies’ at the aluminum foil, we
may think of each ion as having a life-time T. Now the number of ions born per unit time is I/q;
according to the relation between population and life-time,
N = (number of born ions per unit time)(life-time) = IT/q.
So
F = (IT/q)(Vq/d) = TIV/d
(4)
Thus the lifting force depends on the life-time of ions. Now the effect of ions’colision with air
molecules on the lifting force F can be studied by considering how the lifetime T changes with the
collisions.
Let’s first look at the ion-thrust model again, namely the model with no collisions. The
life-time T equals the time of acceleration
T = (2d/a)1/2
where
a = qE/m = qV/dm.
So
T = (2d/a)1/2= (2d2m/qV)1/2∝dV1/2
(5)
and substitution in to (4) one gets
F =(2mI2V/q)1/2.
This is the same result as that obtained in the ion-thrust model, which shows the equivalence of
life-time description and ion-thrust model in the collion-free case.
3. Modified ion-thrust model
If the collisions of ions and air molecules are not strong enough to ionize the air molecule,
then the result of collision is to decelerate the ions, thus enlongating its life-time and enhanceing
the lifting force. According the experimental results mentioned above
F ∝ IdV1/2.
Compard with (4)，one gets the life-time
T ∝ d2V1/2.
(5’)
Equations (5) and (5’) shows a major difference between ion-thrust model (T∝dV1/2) and
experiment (T∝dV1/2) at low voltages.
To get a more quantative picture of the accelerating process with collisions, we may assume
the ions lose all its kinetic energy on a collision and are accelerated from rest over again. If we
denote by t the time between two successive collisions, and by Nc the number of collisions an ion
experiences in her ‘life’, then her life-time is
T = N ct
(6).
Since the ion moves a mean free path  in two collisions, we have
Nc = d/
t = (2/a)1/2
If the acceleration a = qE/m = Vq/dm is substituted in to (6) and (4), we get the life-time and
lifting force
T = (2md3/Vq)1/2 ∝ d3/2V1/2
F = (2mdI2V/q)1/2 ∝ d1/2IV1/2.
(7)
Compared with the no-collision case, this ‘lose-all-re-accelerate’ assumption gives a better
prediction of life-time and force, as shown in the following table.
Model
assumption
lifetime
Lifting force
ion-thrust model
No-collision
T ∝ d
F independent of
d
Modified ion-thrust model
‘lose-all-re-accelerate’
T ∝ d3/2
F ∝ d3/2
T ∝ d2
F ∝ d
Experimental result
The mean free path of particles in air is known to be approximately ≈ 60nm and the mass of
an ion (which is estimated to be equal to the mass of an air molecule) is m ≈4.9*10-26kg. With (7)
one can calculate F ≈ 1.6mN, of the same magnitude as that measured in experiment.
Compared with the ion-thrust model, it is seen that the lifting force is enhanced by a factor of
(d/)1/2~103. F increases if the mean free path  is shorter. Collisions, which hinder the
acceleration process in the first place, actually enhance the recoil of the capacitor - a really
interesting phenomenon. Nevertheless, there is still discrepancy between the modified ion-thrust
model(T ∝ d3/2V1/2, F ∝ d1/2IV1/2) and experiment(T ∝ d2V1/2, F ∝ dIV1/2). This means this
‘lose-all-re-accelerate’ model still remains to be improved. The comparison in the above table
shows that the actual collision process must result in an even longer life-time of ions. But as to a
more realistic collision model, we are still at loss.
4. Conjecture about the lift in asymmetrical capacitors over the whole voltage range
Based on the modified ion-thrust model, we make the following conjecture about the lift
effect of asymmetrical device for all low as well high voltages.
At very low voltage (V < 10kV), no air is ionized and no lifting force is produced.
When some threshold is reached (V = 10~15kV), the air near the copper wire begins to ionize
and a current builds up (I > 0). Half of the produced ions accelerate toward the aluminum foil and
collide with the neutral air molecules (the other half of the ions being absorbed by the copper
wire). In this process ions transfer its momentum to the neutral molecules and an air flow is
produced and pushed out of the device from the aluminum end. Since the ions lose most of the
momentum and energy it obtains from the electric field, the whole thing looks as if the capacitor
and air flow obtain momentum in opposite directions. This process gives rise to a lifting force in
the form F∝ IV1/2, as shown in region I of the figure below.
At a large voltage (V > 15kV)，the air near the aluminum foil also begins to ionize. The
resultant ions are driven towards the copper wire by the same electric field. This causes a force
opposite to that caused by the ionization near copper wire. As a result, though the lift still
increases with I, the F-IV1/2 cannot follow the linear relationship any more, as shown in region II.
The lift force disappears as the discharge causes the electric field to breakdown.
Copper wire
air
ion
0.6
𝑭
0.4
II
I
0.2
Force direction
I·V1/2
0
Aluminum foil
0
100
200
300
Recoil
Since the ions produced near the copper wire are different from those near the aluminum foil
(cations and anions), their motion may give lifting forces of different magnitude, namely by (7)
F∝I(m/q)1/2
where I is the current caused by the ions near different electrodes. Because these opposite forces
may not identically counter-balance each other, there may still be a net lift even though the
electrodes are identical. This leads us to the study of Biefeld-Brown effect in symmetrical
capacitors (SC).
VI. A preliminary study of lift in symmetrical capacitors (SC).
1. The lift phenomena in symmetrical capacitors.
In a symmetrical capacitor both electrodes are made of parallel copper wires. The samples we
made are shown in the figure below. The geometry of the devices is similar to asymmetrical ones,
including the width and distance of electrodes.
Copper wire
Copper wire
To circuit
Symmetrical device
Although we have not found relevant report about the lift in SC, our experiments show that
such symmetrical capacitors do produce lift as well as the asymmetrical ones. When the electrodes
are spaced at a distance d = 2cm and a voltage of V = 14kV is applied, the direction and magnitude
of the lifting force is shown in the following table.
Positive
end of
voltage
Lift
Averaged
force
I(A)
Force (gram)
(gram)
not inverted
335
0.22
Upper
Negative
0.295
copper wire
inverted
320
0.37
end to
14
positive end
not inverted
330
0.27
Bottom
0.290
of
capacitor
copper wire
inverted
340
0.31
Here the device is inverted (upside down) and the force F is re-measured. Since the change in
F caused by such inversion is due to the slight difference between the two copper wires, the
averge of F before and after inversion reflects the force caused by ion-acceleration.
In contrast to asymmetrical capacitors, in symmetrical devices the direction of F does depend
on the electric field direction; i.e. the lifting force always directs from the negative to the positive
electrode of the capacitor. This implies that although the electrical field is symmetric, the
contributions of anions and cations do not cancel off. The positive ions produce more recoil.
Another feature of symmetrical capacitors is that the maximal lift (V ~ breakdown voltage) is
in the same order of magnitude (though weaker) with that of the asymmetric ones. We think this is
due to fact that for the same voltage, symmetric devices can produce much larger current. For
example, at V = 14kV and d = 2cm, I = 330A for symmetrical structure while it’s only 60A for
asymmetrical ones. In other words, if both electrodes are copper wires, much more ions are
produced and accelerated. It has weaker lift just because much of the recoil effect are
cancelled off.
Our experiments also show that although F and I also increase with V (and I is larger for
symmetrical capacitors), no obvious linear relation between F and IV1/2 can be identified.
2. Glow discharge at electrodes
An interesting phenomenon in symmetrical capacitors is the glow at electrodes. After the
ionization begins (i.e. I > 0), purple glow starts to appear at both copper wires as V increases.
There are also bright dots distributed regularly on the negative electrode.
The same device, placed non-inverted and inverted, is shown in the following picture. Both
electrodes are copper wires of length l = 30cm, displaces at a distance d = 2.5cm. Experiments
showed that purple appeared on both wires while the bright dots appear only at the negative wire.
On the negative electrode, glow and dots occur alternatively along the wire, forming a regular,
‘periodic’ pattern.
Device inverted
or not
V(kV)
Direction of
force
Air flow
Air flow
Force
Force
Positive copper wire
Negative copper wire
Positive copper wire
Negative copper wire
By a closer (and dangerous) observation of the wires, we found the glow and dots are closely
related to the vibration of copper wires. When the ions are accelerated, air flow (caused by
collisions) drives the positive copper wire to vibrate violently; meanwhile a clear standing wave
pattern can be seen on the positive copper wire. The negative wire also vibrates but in much more
gentle way. It is then seen that bright dots are located exactly at the antinodes of the standing wave,
in the form of a spark between the endpoints of vibration, as shown in the following figure. On the
sample in the above picture, the standing wave has a wavelength of about 3cm and amplitude of
2~3cm. In addition, by directing a laser beam across the vibrating wires, we used a photo-detector
to measure the vibrational frequency to be 170Hz.
Negative electrode
Bright spot
The glow on both wires verifies our conjecture that air ionization does take place at both
electrodes. The similarity in the distribution of glow patterns on two wires show that similar
standing waves form on both; the bright dots appear only on the negative wire just because it
vibrates more violently. In other words, ionization, vibration and recoil behavior are not identical
in the symmetrical capacitor. It is this asymmetrical effect in the symmetrical device that produces
a lift.
However, a quantitative model of the glow phenomena here as well as its relationship with
the lift is not yet available to us. Actually by very careful observation, glow phenomena (though
not distinct) can also be identified in the asymmetrical capacitors. Although a spectroscopic
analysis of the glow may help to identify the species of accelerating ions, till the end this project,
we have not started to investigate this phenomenon in more detail.
VII. Conclusion
We made samples of asymmetrical and symmetrical capacitors to test the Biefeld-Brown
effect. Qualitative experiments confirm that the lift is accompanied by a strong air flow in the
opposite direction. Based on the quantitative experiments on the asymmetrical capacitors, the
elementary ion-thrust model is used to explain the phenomena. The effect of collisions between air
molecules and ions proves to be important and is included in the model via the life-time
description of ion acceleration process. The theory agrees with experiment in (1) order of
magnitude of force, (2) quantitative relation between lift F and V, I and (3) semi-quantitative
relation between F and electrode distance d at low voltage. This leads us to make a plausible
conjecture of the whole process of Biefeld-Brown effect.
We also found lift in symmetrical capacitors, where the direction of lifting force is essentially
different, in qualitative agreement with the ion-acceleration process. The observation of glow and
vibration of electrodes verifies the relation between ionization and lift, but remains further
investigation and modeling.
Acknowledgement
We acknowledge the great help and encouragement of our physics teacher and supervisor Mr.
ZHAO Qiwei. Also we are grateful to the technical support from the physics lab of Shanghai High
School, especially Mr. TIAN Zhou and Mr. LU Shisong in helping set up the testing bench.
References
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measured in horizontal and vertical configurations, Hawai’i space grant consortium
undergraduate fellowship reports.
2. Thomas B. Bahder, Christian Fazi, Force on an Asymmetric Capacitor, ARL-TR-XXX
3. Francis X. Canning, Cory Melcher, Edwin Winet, Asymmetrical Capacitors for Propulsion,
NASA/CR—2004-213312
4.江兴流，易立志，刘锐，乐小云. 电晕放电飘升机研究.《航空学报》2005 年第六期