45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit
2 - 5 August 2009, Denver, Colorado
AIAA 2009-5070
Null Findings on Electromagnetic Inertia Thruster
Experiments using a Torsion Pendulum
Hector H. Brito,* Ricardo Marini† and Eugenio S. Galian‡
Centro de Investigaciones Aplicadas, Instituto Universitario Aeronautico, Cordoba, Argentina, X5010JMN
New propulsion mechanisms are being investigated which get rid of propellants and/or
conventional external assistance. Experiments performed by independent research teams
and reported in peer-reviewed literature suggest that “reactionless” propulsion effects are
being achieved by means of crossed time harmonic electromagnetic fields in high K
ferroelectrics, as inducing a kind of inertia modification (EMIM) of the generating device.
Given the controversial nature of such a claim, the question is, are these results just
experiment artifacts or genuine propulsive effects? The purpose of this paper is to give a
negative answer concerning the latter, on the basis of recent work by the authors using
torsion pendulum thrust measurement techniques. Nevertheless, “anomalous” effects still
show up when the test device is run on a flex pendulum thrust stand in modulated amplitude
power/thrust mode.
Nomenclature
A
C
c0
d
h
H
I
J
n
p
r
t
T
V
x
δ
ε
ϕ
θ
τ
ω
Ω
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
rotation angle amplitude, radian
electrical capacity, F
velocity of light in vacuum, m/s
width of the annular capacitor, m
distance line of suspension/screen, m
Heavide step function
electric current, A
moment of inertia, m-s2
number of turns of each toroidal coil
damping coefficient
lever arm, m
time, s
thrust intensity, N
voltage, V
laser dot “on screen” location, m
laser dot “on screen” displacement, m
relative permittivity of the medium
relative phase angle of current and voltage, radian
rotation angle, radian
free oscillation period, s
activation frequency, radian/s
voltage modulation frequency, radian/s
*
Program Manager, Space Vehicles Department, Ruta 20, Km. 5.5, Senior Member AIAA.
Research Assistant, Space Vehicles Department, Ruta 20, Km. 5.5.
‡
Research Assistant, Space Vehicles Department, Ruta 20, Km. 5.5.
1
American Institute of Aeronautics and Astronautics
†
Copyright © 2009 by Instituto Universitario Aeronautico. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
I. Introduction
E
ither to go to the stars or, more
pragmatically, to substantially cut down
space transportation costs, new propulsion
mechanisms must be found which get rid of
A. A
propellants and/or conventional external
assistance. Experiments involving crossed
time harmonic electromagnetic fields in
high K ferroelectrics were performed by
independent research teams with results
reported in peer-reviewed literature.1-3 They
suggest that “reactionless” propulsion
effects are being achieved, as if a kind of
inertia modification (EMIM) of the
generating device had taken place. Given
the controversial nature of such a claim, the
question is whether those results are just
experiment artifacts or genuine propulsive
effects. The purpose of this paper is to
describe recent work by the authors using
both, flex pendulum and torsion pendulum
Figure 1. Self-contained RAMA-II thrust unit.
thrust measurement techniques.
Experiment artifacts were in all cases identified as related to different sources of spurious effects, like air motion,
self electromagnetic (EM) interactions and with the surroundings, thermal shifting of center of mass, a. s. o. Given
the alleged thrusts levels around 10 µN, some of those classical effects were found to show up at about that order of
magnitude. Aiming at overcoming most if not all potentially spurious effects, a development effort was conducted at
Instituto Universitario Aeronautico (R.A.) leading to RAMA-II, a 1 mN-class “EMIM” thruster. The thruster, shown
in Fig. 1, is a self-contained unit including the propulsion modules and a battery operated 600W/1MHz power
processing unit (PPU). Each module comprises a 30 turns toroidal coil wrapped around a ceramic housing
containing a 10 nF - 8 mm wide annular capacitor with BaTiO3 ceramic dielectric (εr ≈ 4400). The capacitor-coil
assembly is wired as a tank circuit and mounted in a common acrylic housing filled with a Phase Change Material
(PCM), for limited thermal control of the assembly. The modules are wired in parallel to a common supply of 350 V
- AC @ 1 MHz, which allows for a Minkowski’s EM momentum around 0.08 nN-s (peak) per module when the
supply is tuned to electrical resonance of the assembly.
For parallel plate and toroidal capacitors with fully wounded coils wrapped around, and neglecting fringe effects
and magnetic field variations throughout the capacitor volume, the time-averaged thrust is, according to an
“Extended” Minkowski’s force density empirical formulation,1, 4 given by
T =
ε rω nIV d
2c02
sin ϕ ,
(1)
so that an average thrust of 0.25 mN per “resonant” module should accordingly be obtained.
Four modules are mounted onto a bed rigidly fixed to the PPU “electronic box”, on which a five lead-acid cells
battery pack is fixed, too. A coaxial cable assures the connection between the PPU and the propulsion modules.
II. RAMA-II Testing on a Flex Pendulum Thrust Stand
The thruster was tested on TS-2; a flex pendulum thrust stand using a high sensitivity piezoceramic strain
transducer (PST). The experimental setup basically consists of mounting the thruster as a seismic mass atop a thin
vertical cantilever beam, sitting on a vibration-free platform in a vibration isolated working place, as shown in Fig.
2. By using sine modulation of the supply (“carrier”) AC voltage, a modulated average thrust is theoretically
achieved, at the modulation and twice the modulation frequencies, with amplitudes 1/2 and 1/8, respectively, of the
non-modulated average thrust. By detecting this alternate force, the geomagnetic influence becomes averaged out;
direct detection in frequency domain also permits to get rid of numerical artifacts since advanced numerical filtering
2
American Institute of Aeronautics and Astronautics
is no longer required. If the voltage amplitude
modulating frequency is different from the
setup natural frequencies, ground noise
becomes less significant. Air motion, being
related to the power supply frequency, averages
out to vanishing contribution, too. Uncertainties
were expected to remain regarding power
supply induced EMI, but were shown to
amount to a small fraction of the observed
effect by locking the beam motion.1
As a result, enhanced 5σ responses of TS-2
were found when the power modulation
frequency closely matched the first (1.1 Hz) or
the second natural frequency of the setup (24.8
Hz), as shown in Fig. 3. Moreover, the response
for arbitrary modulation frequencies bears the
right spectral signature, thus precluding the
existence of spurious effects due to inner
masses resonances at those modulation Figure 2. EMIM thruster on the flex pendulum thrust stand.
frequencies. All other typical sources of
spurious effects were previously found to contribute with levels several orders of magnitude below the measured
thrust.
This uncertaintities analysis clearly point to 5σ evidence of an anomalous force effect in the 0.01 – 0.1mN range,
requiring further investigation since the energy-momentum of the setup as a whole (“closed system”) does not seem
to be conserved.1, 4 Unless presently unidentified spurious effects are found to explain it, the effect has space
propulsion application as the underlying
mechanism of a propellantless thruster. The
theoretical framework is, in the classical sense,
against this possibility, however it is important
to point out that positive experimental results
do not necessarily mean that the law of linear
momentum conservation is not satisfied. In
other words, the fact linear momentum of the
system {thruster + its EM field} does not
remain constant is not in contradiction with
Newton’s Second Law since such a system,
which can be viewed as a closed one in the
classical sense, could not be so according to
new theoretical developments about the origin
of inertia,5-7 and the behavior of vacuum
fluctuations in “crossed” EM fields.8, 9 Given
the power levels involved in the experiments,
any real deviation from the classical framework Figure 3. PST sensing device output with the thruster
could only show up through small observable activated in modulated power mode (raw and filtered signals).
effects, close to the sensitivity limits of the
measurement instrumentation.
III. RAMA-II Testing on a Torsion Pendulum Setup
The use of power thus thrust amplitude modulation was dictated by the need of taking advantage of the flex
pendulum dynamic characteristics. On the other hand, PST vibration-sensing devices are unsuitable for detecting
thrusts under non-modulated operating mode, which is required as a definite test of the device ability as a true
propellantless thruster. For direct assessment of propulsive forces, a Cavendish-Coulomb method of detection based
on a very sensitive single fiber torsion pendulum was implemented, together with a Kelvin laser measurement
technique (see Fig. 4). The setup was intended to be run in dynamic mode. In the dynamic mode, the test device and
3
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its counterweight suspended by the torsion fiber
are allowed to swing free and to undergo small
angular oscillations about the vertical fiber axis.
This system behaves as a linear torsion
pendulum. This oscillatory behavior result from
propulsive, boundary, or random torques acting
against the restoring torque of the fiber, and the
oscillations are typically damped by the
frictional forces. If the pendulum is shielded so
the random torques due to air motion are
negligible, the pendulum motion can be
analyzed in terms of the propulsive, boundary,
and frictional forces, and can be used in a
general way to characterize the nature of simple
forms of propulsive forces. In particular, a
propulsive force pulse can be applied to the
oscillating pendulum during a time less than
half a period of oscillation and the resulting Figure 4. EMIM thruster on the torsion pendulum setup,
amplitude change of the pendulum swing with including counterweight and oil damper.
respect to the initial value is directly
proportional to the applied force. The test unit being a self-contained one, spurious effects like inner motions, selfelectromagnetic couplings, piezoelectric, electro/magnetostriction, and thermal shifts of center of mass, are deemed
to have a negligible influence on the setup dynamics.
The thruster and its counterweight are fixed to a hollow cylindrical bar 0.4-m length, the whole fixture vertically
suspended by a steel wire 0.8-mm dia., 2.45-m
x’
x
Screen
δ
length. The suspension point was located 0.22 m
from the thruster center of mass, and 0.15 m from
the counterweight attachment point. The
x
suspended fixture had a moment of inertia with
h
respect to the wire axis of 0.937 kg-m2, and a free
oscillation period of 168 s. A laser beam is
α
reflected by a mirror fixed to the suspension wire
Laser
2θ
onto a screen located 5.02 m from the suspension.
The successive peak locations of the laser dot are
marked on the screen following visual recording
of the dot motion (see Figs. 5, 6), thus performing
a Kelvin laser measurement technique.
Given the measured free oscillation period and
Rot. θ
the estimated moment of inertia, the rotation
Counterweight
angle dynamics as affected by the EMIM thrust
Thruster
acting between instants t1 and t2 can be assessed
by means of the following differential equation of Figure 5. Torsion pendulum setup schematics.
motion:
T  H ( t − t1 ) − H ( t − t2 )  r
d 2θ
dθ 4π 2
+
2
p
+
=
θ
dt 2
dt
J
τ
(2)
From Fig. 5 it can be seen that, taking into account the rotation angle amplitude and a reference laser dot “on
screen” location, the laser dot “on screen” excursion, is given by
x′ =
x + h tan 2 A
1 − ( x h ) tan 2 A
4
American Institute of Aeronautics and Astronautics
(3)
x [mm]
After conducting setup dynamics
simulations involving varied initial
RAMA 2
conditions as well as activation times
350
(t2 – t1), the setup was found to be
able of discriminating thrusts in the
300
µN range, when the forces were
applied according to the above250
mentioned procedure. However,
200
under activation of the RAMA-II
thruster in non-modulated power
150
mode, no propulsive effect above
that sensitivity range was observed,
100
as shown in Table 1 where three
successive peak locations are
50
presented for each test, with the
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
thruster activation occurring between
n
peaks #2 and #3. In all tests two
propulsive modules of four were Figure 6. Laser dot peak locations during a test run of the torsion
activated to avoid PPU overheating pendulum setup.
and the measured supply voltage was
280 V, which yields an expected thrust around 320 µN, according to Eq. (1). Lower than nominal PPU output
voltages were reported as related to poor current delivery capabilities of the employed lead-acid batteries, and builtin current and temperature limitations to avoid propulsion modules and PPU overheating.
Table 1. Test results of the RAMA-II thruster on the torsion pendulum setup.
Test #
Damping
Factor
x
[mm]
x*
[mm]
x**
[mm]
1
2
0.0010
0.0010
177
227
229
190
177
226
Estimated amplitude [mm]
Thrust ON
Thrust OFF
405
389
51
34
Real
Amplitude
[mm]
55
36
IV. Analysis of the Torsion Pendulum Results
The observed negative results for RAMA-II activation in non-modulated power mode, imply that the following
theoretical approaches are wholly or partially falsified:
-
“Extended” Minkowski’s force density.1, 4 Since harmonic EM fields in phase quadrature are involved, time
averaged electromagnetic forces being vanishing small, polarization currents should not be considered in force
density calculations, i.e. the “standard” formulation holds.
-
Minkowski’s energy-momentum tensor + mass tensor 2nd conjecture.1, 11 This formulation relates to the
motion of extended systems when represented by “solidification” points other than their center of mass, and the
conjecture that the translational motion of those systems is not affected by tensor mass rotations. Therefore,
either the system behaves as bearing a tensor mass and global electromagnetic momentum in the matter rest
frame of the thruster subsystem is being generated, in which case the 2nd Conjecture is false if rotation of the
EM momentum carriers is assumed, or mass tensor behavior is not being observed.
-
Transient mass fluctuation.2, 12 Thrust predicted according to Woodward’s formulation is around 3.4 mN, thus
according to the results reported here no Mach induced mass fluctuation is taking place up to the sensitivity of
the experimental apparatus.
In general terms, the torsion pendulum negative results falsify all theoretical formulations predicting
unidirectional thrusts due to crossed harmonic EM fields in phase quadrature, e.g., the nonlinear magnetoelectric
5
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media and the Chameleon field models.13 More specifically (see Appendix), calling V the voltage across capacitor
plates and I the current flowing through coils, formulations predicting thrusts proportional to V2, I2, V(dI/dt), or
(dI/dt)2 are all falsified since they also predict non-zero time averaged thrusts. Instead, formulations predicting
thrusts proportional to I(dI/dt), VI or its time derivative are not falsified, since they yield zero time averaged thrusts.
Torsion pendulum results do not preclude thus alternate thrusts under these formulations. It is readily shown that
modulation of the electrical power at a frequency different from the supply (carrier) frequency allows to eventually
obtaining an alternate modulated thrust at the power modulation frequency and twice this frequency.
Flex pendulum observed results are entirely consistent with the last group of formulations, in particular those
depending on d(VI)/dt, as that based upon Minkowski’s EM momentum. However, the predicted mechanical effects
are several orders of magnitude below those reported here, due to the smallness of the modulation frequency with
respect to the activation or “carrier” frequency.
V. Conclusion
Tests of alleged EMIM effects by means of crossed time harmonic EM fields in phase quadrature, in high K
ferroelectrics, were performed by activating the RAMA-II device in modulated power mode on a flex pendulum
thrust stand, using a high sensitivity piezoceramic strain transducer. Enhanced 5σ responses of the thrust stand were
found when the power modulation frequency closely matched the first or the second natural frequency of the setup.
The vibration-sensing device being found unsuitable for detecting thrust under non-modulated operating mode,
direct assessment of propulsive forces was sought after via a Cavendish-Coulomb method of detection based on a
very sensitive single fiber torsion pendulum, together with a Kelvin laser measurement technique. As a result, no
propulsive effect was observed under activation of the RAMA-II thruster in non-modulated power operating mode.
Several proposed theoretical approaches have thus been wholly or partially falsified. Specifically, the torsion
pendulum experiment is a crucial one regarding propellantless propulsive effects using RAMA-II type devices as
employed in the above-described setup. It can not be seen as a conclusive one regarding the Abraham’s –
Minkowski’s Controversy under the conventional Electromagnetics interpretation, so further experimentation, very
likely in modulated power mode, shall accordingly be needed. The experiment is inconclusive under the mass tensor
and the 2nd Conjecture interpretation, since rotation of the EM momentum carriers (dielectric dipoles) must be
assumed to falsify the latter, unless the total EM momentum in matter is shown to be zero. Reciprocally, further
experimentation aimed to elucidate the Abraham’s – Minkowski’s Controversy will be crucial in respect of the mass
tensor and the 2nd Conjecture validity. Work is presently underway to interpret these seemingly contradictory results
between modulated and non-modulated operating modes. Intensive testing is planned to assess the influence of
potentially spurious effects, and to establish the dependence of the flex pendulum amplitudes on the modulation
frequency in order to identify the force producing mechanism as related to electrical quantities.
Appendix
The PPU output voltage in amplitude modulated power operation mode, which is applied on capacitors and coils
of the parallel wired propulsive modules, can be represented by
V=
V0
(1 − cos Ω t ) sin ω t
2
(A.1)
The current flowing through the capacitor-coil assembly in each propulsive module is proportional to the voltage
first time derivative, that is
I =C
d V CV0
ω (1 − cos Ω t ) cos ω t + Ω sin Ω t sin ω t 
=
dt
2 
(A.2)
Accordingly, the current first time derivative is given by
d I C V0
 − ω 2 (1 − cos Ω t ) sin ω t + 2 ω Ω sin Ω t cos ω t + Ω 2 cos Ω t sin ω t 
=
dt
2 
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American Institute of Aeronautics and Astronautics
(A.3)
Equations (A.1) to (A.3) define harmonic quantities all bearing a spectral signature consisting of the central
frequency ω and the side frequencies ( ω + Ω) and ( ω − Ω). Now, binary products between these quantities as related
to other electrical characteristics, yields the following expressions when collecting the terms not depending on the
carrier voltage first and second harmonics
2
V
2
1
V   3

=  0   − 2 cos Ω t + cos 2 Ω t + L 
2
2
2

 

V I =
V
d I C V 02
=
dt
16
I2 =
I
2
(A.4)
 

1

 Ω  sin Ω t − 2 sin 2 Ω t  + L 

 

C V 02
8
(A.5)
1


2
2
2
2
2
2
 − 3 ω + Ω + 4 ω + 2 Ω cos Ω t − 2 ω + Ω cos 2 Ω t + L 
(A.6)
C 2 V 02  2
Ω + 3 ω 2 − 4 ω 2 cos Ω t + ω 2 − Ω 2 cos 2 Ω t + L 
16 
(A.7)
d I C 2 V 02 
=
2 ω 2 Ω sin Ω t + Ω Ω 2 − ω 2 sin 2 Ω t + L 
dt
16 
(A.8)
(
) (
(
)
(
)
(
(
)
)
)
dI
C 2 V 02 
3 ω 4 + 6 ω 2 Ω 2 + Ω 4 − 4 ω 2 ω 2 + Ω 2 cos Ω t + ω 2 − Ω 2

 =


16
 dt 
(
)
(
)
(
d
CV 2
(V I ) = 0  Ω 2 ( cos Ω t − cos 2 Ω t ) + L 
dt
8
)
2
cos 2 Ω t + L  (A.9)

(A.10)
For Ω << ω, as it is the case of RAMA-II modulation frequency as compared with its carrier frequency, given
the mechanical filtering properties of the flex pendulum setup, Eqs. (A.4) to (A.10) show that any force producing
mechanism related to the above electrical quantities will necessarily excite the setup at the modulation frequency
and twice its value.
Acknowledgments
This work was supported by “Instituto Universitario Aeronautico” and by the National Agency for the Support
of Science and Technology (Argentina) - ANPCyT (Grant FONCYT- PICT-2002-10-10592). H. H Brito thanks
Enrique Calcagni for his support in signal processing activities, Roque De Alessandro and Felix Chiaretta for their
commitment to the readiness of the test device power electronics.
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American Institute of Aeronautics and Astronautics
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