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Abstract

Concepts for propellantless space propulsion are carefully investigated using high-precision balances in the framework of the SpaceDrive Project. The Mach-Effect-Thruster, an original design from Woodward that relies on the particular vibration of an asymmetric, piezoelectric stack actuator to produce thrust, is one concept that was extensively tested. In an attempt to validate the results published in peer-reviewed literature, several MET devices were tested on two different types of balances in vacuum conditions: a torsion balance and an inverted counterbalanced double pendulum, as well as on a rotating apparatus. The instruments are characterized by background noise lower than 5 nN after averaging and are calibrated using laser interferometry and a voice coil with a high-resolution current source. Encased in grounded mu-metal shielding on the balance, and powered by dedicated amplifiers, the device was swept with a frequency between 20 and 50 kHz in order to identify the operating range with the largest beam deflections. Measurements with the torsion balance from a previous campaign seem to indicate vibration artefacts, thermal noise and changes in the experiment’s centre of mass at specific resonance frequencies. These measurements were repeated with different device orientations on the double-pendulum balance, and deflections of similar magnitude that can be explained by thermal expansion and device resonance were also observed. Recording both balance beam displacements with a sampling rate of up to 25 MHz revealed a significant vibration when exciting the actuator around its longitudinal resonance, regardless of the mounting and isolation. Calculations and simple modelling of the resulting pulsed force from the vibrations confirms the hypotheses made from balance measurements. Additional tests were performed on a rotating apparatus to investigate the presence of mass fluctuations in a centrifugal force field without having to synchronize with a push-pull force. Our tests reveal the presence of mechanical artefacts but no thrust.
1
THE SPACEDRIVE PROJECT MACH-EFFECT-THRUSTER EXPERIMENTS ON
HIGH-PRECISION BALANCES IN VACUUM
SPACE PROPULSION 2020+1
17 18 19 MARCH 2021
Maxime Monette(1), Matthias Kößling(2), Oliver Neunzig(3) and Martin Tajmar(4)
(1) Institute of Aerospace Engineering, Technische Universität Dresden, Marschnerstrasse 32, 01307
Dresden, Germany, maxime.monette@tu-dresden.de
(2) Institute of Aerospace Engineering, Technische Universität Dresden, Marschnerstrasse 32, 01307
Dresden, Germany, matthias.koessling@tu-dresden.de
(3) Institute of Aerospace Engineering, Technische Universität Dresden, Marschnerstrasse 32, 01307
Dresden, Germany, oliver.neunzig@tu-dresden.de
(4) Institute of Aerospace Engineering, Technische Universität Dresden, Marschnerstrasse 32, 01307
Dresden, Germany, martin.tajmar@tu-dresden.de
KEYWORDS: space propulsion, breakthrough
propulsion, torsion balance, double-pendulum
balance, Mach-Effect, Woodward thruster
ABSTRACT:
Concepts for propellantless space propulsion are
carefully investigated using high-precision balances
in the framework of the SpaceDrive Project. The
Mach-Effect-Thruster, an original design from
Woodward that relies on the particular vibration of
an asymmetric, piezoelectric stack actuator to
produce thrust, is one concept that was extensively
tested. In an attempt to validate the results
published in peer-reviewed literature, several MET
devices were tested on two different types of
balances in vacuum conditions: a torsion balance
and an inverted counterbalanced double pendulum,
as well as on a rotating apparatus. The instruments
are characterized by background noise lower than
5 nN after averaging and are calibrated using laser
interferometry and a voice coil with a high-resolution
current source. Encased in grounded mu-metal
shielding on the balance, and powered by dedicated
amplifiers, the device was swept with a frequency
between 20 and 50 kHz in order to identify the
operating range with the largest beam deflections.
Measurements with the torsion balance from a
previous campaign seem to indicate vibration
artefacts, thermal noise and changes in the
experiment’s centre of mass at specific resonance
frequencies. These measurements were repeated
with different device orientations on the double-
pendulum balance, and deflections of similar
magnitude that can be explained by thermal
expansion and device resonance were also
observed. Recording both balance beam
displacements with a sampling rate of up to 25 MHz
revealed a significant vibration when exciting the
actuator around its longitudinal resonance,
regardless of the mounting and isolation.
Calculations and simple modelling of the resulting
pulsed force from the vibrations confirms the
hypotheses made from balance measurements.
Additional tests were performed on a rotating
apparatus to investigate the presence of mass
fluctuations in a centrifugal force field without having
to synchronize with a push-pull force. Our tests
reveal the presence of mechanical artefacts but no
thrust.
1. INTRODUCTION
Woodward’s Mach-Effect theory and experiments
seem to support the claim of a new form of
propellantless space propulsion that could
revolutionize interstellar travel. In theory, the input
of energy into a device through proper acceleration
could create a mass fluctuation proportional to the
rate of change of the power input [1]. That mass
fluctuation could then be coupled to a synchronized
push-pull mechanism to produce unidirectional
thrust. The theory is based on Sciama’s argument,
that inertia is a result of the gravitational influence of
distant matter in our universe [2], and it relies on the
linearization of Einstein’s field equations [3].
However, there are a few opponents to that theory
disputing Woodward’s derivation or proposing
alternate derivations [47].
The embodiment of the theory is a multi-layered,
piezoelectric stack pre-stressed between two
different masses using a multiple screws
connection, and is tested on a torsion balance in
vacuum. The device is connected to the measuring
apparatus by a bracket attached to its heavier end,
and power is transferred to its electrodes using an
amplifier. Precise torsion balance test results from
Woodward have shown the presence of a particular
force trace amounting up to 100 µN when the device
is driven at a system resonance of 36 kHz and a
power of about 30 W [8]. Allegedly, this effect was
SP2020_00278
2
consistently observed for the forward and reverse
thrust-producing orientations, and was not observed
when placing the thrust axis parallel to the torsion
balance beam [1]. Other research teams, notably
Buldrini et al. [9] and ourselves [1013], have
observed a similar effect in the forward runs at a
much lower force level. The force trace is
characterized by larger switching transients when
turning the device on or off and by a smaller force,
if any, during the pulse. In order to maximize the
force and target the right operating conditions, we
then performed different fixed frequency as well as
swept frequency tests using separate sets of
electronics. The results did not show much variation
in amplitude [12]. Furthermore, force traces with the
same magnitude were observed in all orientations,
notably in the no-thrust producing axis. Also, the
beam was shown to vibrate at lower frequencies
when powering the test object and the effect was
attributed to vibrational and thermal artefacts
[12,13].
In order to better explain the origin of the effects
observed, a different force measuring apparatus
was conceived and tested. The inverted
counterbalanced double-pendulum, or double-
pendulum balance (DPB), was constructed to
reduce the pseudo-forces observed coming from
centre-of-mass shifts on the thruster plane. Indeed,
thermal expansion of different parts of the test
object can lead to a detectable beam displacement
on the torsion balance that can be mistaken for
thrust. The double-pendulum balance is composed
of two horizontal planes resting on three aluminium
beams and the thruster is placed on the top plane.
The linear deflection of the frame due to a thrust
force is supported by nine linear torsional springs.
Due to the particular configuration and increased
stability of the structure, centre-of-mass shifts
occurring on one horizontal plane itself should not
lead to any detectable frame displacement. In
section 2, the measuring apparatus and test devices
will be described in detail and characterized. The
test results on the different balances will be
examined and compared in order to draw our
conclusions in section 3.
Lastly, a different concept for detecting mass
fluctuations that does not require the generation of
thrust, or a sensitive thrust balance, was examined.
A similar pre-stressed, piezoelectric actuator with
an embedded passive piezo-disk was attached to
an arm and spun at varying angular frequency. The
goal was to observe the influence of the energy
input on the centrifugal force measurement by the
passive gauge. This experiment, also conceived by
Woodward [14], was meant to simplify the detection
of mass fluctuations at twice the driving signal
frequency. This concept will be thoroughly
investigated in section 4.
2. EXPERIMENTAL SETUP
2.1. Thrust balances
Understanding the functioning of the measuring
instrument is a crucial part of the investigation. The
mechanism of the well-known torsion balance is
described in Figure 1. A force in the balance plane,
perpendicular to the balance beam, will generate a
displacement that will be detected at the other end
by a laser interferometer (attocube, IDS3010). The
laser has a resolution of 1 pm and a noise of 2 nm
at room temperature in medium vacuum where the
experiments are performed. Power to the test object
is transmitted through liquid metal contacts in the
pivot axis, as can be seen in the CAD model, to
allow the free rotation of the beam and exclude
forces from rigid cables. The balance is calibrated
with small pulses in a range of 1 to 100 µN using a
voice coil mounted in the thrust axis. The balance
was also calibrated by voice coils mounted in the
two other axes and the tests showed no important
force [10]. However, centre of mass shifts in any
axis could create some balance beam zeroing,
which hasn’t been characterized yet.
The double-pendulum balance relies on the
unstable equilibrium of the upper platform with
respect to the balance’s centre of gravity and its
connection to the bottom platform, where the
displacement is measured. The upper platform,
where the test device is mounted, is supported by
three axes and the whole frame is supported by a
total of nine C-flex torsional springs. The balance’s
frame and parallelogram deflection can be seen in
Figure 2. This balance also uses the laser
interferometer from attocube and the voice coil for
calibration. Sorbothane pads separate the test
device from the support platform to damp vibration.
The sensitivity of the balance can be changed by
adding weights on the lower platform, or by shifting
weights on the platform’s supporting. Twisting the
frame seen in the picture would result in a
displacement of the upper platform as well.
However, the frame is resistant to the centre-of-
mass shifts occurring on one horizontal plane. Both
balances use passive eddy current damping: a
permanent magnet is moved between two
adjustable copper plates. Damping is used to limit
excessive and transient displacements in order to
measure steady thrust. Whereas the torsion
balance (TB) has the magnet on the moving beam
to limit the effects of electromagnetic interaction
with the device, the double-pendulum balance has
its permanent magnet connected to the supporting
structure across the lower platform, since the
electronics are located far from it. This balance also
features liquid contacts for power transmission,
aligned along one side of the structure and featuring
pins dipped in Galinstan cups, to remove any force
from connecting rigid cables.
3
Calibration using a set of known forces from the
voice-coil reveals a linear correlation on the left of
Figure 3 for both balances. The slope of the
interpolation represents the calibration factor of the
balances, indicating the slightly higher sensitivity of
the torsion balance in this configuration. Shorter
calibrations are performed before and after each
thruster test sequence. Then, the balance response
to a 1 µN, 20 s pulse from the voice coil, illustrated
on the right-hand side of Figure 3, shows a slightly
underdamped curve and a very similar damping
ratio for both balances. This response is known to
represent the simple harmonic oscillator response.
The force of the voice coil is accurately measured
using our previously measured calibration factor
and the time response is around 6 s for both
balances. Thus, the test pulses were selected to be
slightly longer.
2.2. MET and electronics
The embodiment of the Mach-effect theory is
illustrated in Figure 4, showing the screw
connection, the bracket, the piezoelectric stack
actuator sandwiched between an aluminium and a
brass mass. Energy input to the piezoelectric
actuator is performed using a dedicated amplifier
(PA04 in bridge-mode, APEX). The whole system is
shown in the diagram of Figure 5. The amplifier was
chosen to deliver the desired voltage, by-passing
the need for a transformer and audio amplifier as
used by Woodward [15]. Not only was it shown that
the piezo-amplifier is less subjected to noise, the
force trace observed was also similar to using the
audio amplifier and transformer [12].
The piezoelectric device was characterized using
its embedded, passive strain gauge as well as the
impedance by sweeping the driving frequency and
examining the signals. In Figure 6, left, the
impedance spectra were obtained for the two
devices at different times of the campaign and
indicate the resonances (peaks) and the anti-
resonances (troughs). The second curve of the
WT3 device indicates the influence of a
depolarization event that occurred sometime during
our campaign. This suggests that the mechanical
properties of some of the piezo-discs were modified,
probably due to mechanical stresses during
repeated testing under harsh conditions or an
inaccurate retightening of the bolt. In Figure 6, right,
the gauge signal to the input voltage reveal the
same resonances as illustrated in the previous
graph: an important realization is that the passive
gauge shows the same resonances as in the
impedance spectrum. The two devices tested, NS5
on the torsion balance and WT3 after depolarization
event, on the double-pendulum balance, were
obtained from Woodward and show different
resonances. The balance test runs were performed
by paying attention to the properties of the devices
as detected by spectral analysis. Fixed frequency
pulses of 16 s, where the driving frequency is held
constant, as well as 24 s forward driving frequency
sweeps, and a minimum of 5 runs in each
orientation were performed on each balance. The
operation included a reasonable cool-down period
to limit device overheating.
2.3. Rotary device
This apparatus relies on a simpler principle to
detect the mass fluctuation than a torsion balance.
As the piezoelectric stack is rotated, the centrifugal
force acting on the embedded strain gauge will vary
if the mass of the stack varies due to the Mach-
effect. The strain gauge is simply a thin, passive
PZT disk. The challenge of this setup is to reduce
electromagnetic interaction, and noise in the strain
gauge signal. As portrayed in Figure 7, the stack is
connected to a 8.4 cm long arm and can be rotated
to 60 Hz by a DC brush motor (Johnson Electric,
HCP877-011P). This rotation speed, measured
using a photoelectric barrier and oscilloscope,
results in a stack acceleration of 1100 g. The power
is transmitted using a slip-ring (Senring, G012-12)
with a maximal voltage capacity of 440 VAC. The
same amplifier electronics are used as for the
balance tests and are assembled as shown on the
right side of Figure 7. The spectrum and calibration
of the embedded gauge for an accurate
determination of the centrifugal force are discussed
in section 4. Lastly, since the mass fluctuations are
expected at twice the driving frequency, an 8th order
Butterworth high-pass filter was used to filter the first
harmonic component of the gauge signal and
extract the second harmonic component.
3. BALANCE TESTS
Characterization of the balance started with
running DC current over a resistor to analyse
electromagnetic interaction and thermal effects.
Figure 8, left, shows the results of both balances
when driving a 15Ω resistor with 1.5 A for the
double-pendulum balance and 0.8 A for the torsion
balance. In the latter case, the test resulted in a
small but noticeable thermal drift of about 30 nN
between the start and end of the pulse. This kind of
linear thermal drift can be filtered and is not a thrust
force. However, one notices a major discrepancy
between the two tests that cannot be simply
explained by the difference in the currents. In the
case of the double-pendulum balance, the overall
force response was significantly larger, with a drift
of around 1.5 µN and a superposed, steady force of
around 1 µN. This effect was investigated after the
MET test campaign, and was attributed to the
repulsion force between the Galinstan liquid and the
immersed pin contacts. However, since the
experiments conducted with the MET are
exclusively performed using AC signals, these DC
current effects can be ignored.
Then, the sinusoidal pulse test with the voice coil
resulted in comparable force responses for both
4
balances, as seen on the right-hand side of
Figure 8. With a repetition rate of 0.5 Hz, switching
transients just below 100 nN in magnitude can be
observed, as well as a low amplitude 0.5 Hz
oscillation. The amplitude of the oscillation is
expected to go down with increasing excitation
frequency, however, the current source
(Keithley 2450) could not be driven at higher
frequencies. Moreover, the noise seen in the torsion
balance profile is greater than on the double-
pendulum balance, which correlates with the latter’s
higher force-displacement conversion factor, given
similar background building noise. This test shows
that both balances can be considered to behave like
a simple harmonic oscillator, and that larger
switching transients may appear due to low
frequency excitation.
For the fixed frequency test with the MET, care was
taken to pick the frequency with the highest
potential effect, chosen to be at the loaded system’s
resonance, in our case, the device’s resonance. In
the torsion balance’s case, this occurred at 34.0 kHz
with the NS5 device and for the double-pendulum
balance at around 21.8 kHz for the partially
depolarized WT3 device (see Figure 6). The force
traces are examined without first going into the
detail of the potential electromechanical
phenomena that depend on the health of the
piezoelectric devices between the tests. Starting
with the 0°, or forward, orientation in Figure 9, left, it
is obvious that the electromechanical behaviour is
different between the two sets of runs, as seen from
the current traces. Whereas the current amplitude
during the double-pendulum test is constant at
0.45 A, the amplitude for the torsion balance test
has a 0.65 A spike at the beginning before dropping
rapidly to 0.48 A, and experiences a slow rise until
the end of the profile. In both cases, though, both
currents can be turned on and off almost
instantaneously. Interestingly, the force traces are
almost identical, even if offset by about 50 nN,
despite the difference in devices, current and
frequency. Both force traces show the same
behaviour: low noise before turn-on, a positive
switch-on transient, a recoil of the balance in the
opposite direction during the pulse, then a slow
return to the zero-line and finally a sharp negative
switch-off transient. In the 90° case, on the right of
Figure 9, the device is parallel to the balance beam.
Again, the current behaviour is slightly different,
even though the same respective frequencies were
selected. This time, the current is higher, with a
starting current of 1.1 A for NS5 on the torsion
balance, and device WT3 stays at 0.45 A on the
double-pendulum balance.
In the torsion balance profile, one observes the
same force trace as for the 0° orientation, only with
the now smaller switching transients in the opposite
direction. The double-pendulum profile also shows
a small switching transient at turn-on but the force
shoots up and reaches 80 nN and does not show an
important switch-off transient. This result does not
seem consistent with the theory of unidirectional
thrust.
In the sweep frequency tests, the force traces for
the 0° and 90° orientations are plotted for each
balance alongside the driving frequency and the
current against time. Here, the sweeps were
conducted with the partially depolarized WT3 device
on both balances. Figure 10, left, shows the force
profiles for both orientations for the double-
pendulum, with linear correction for thermal drift. In
the 0° case, there is a sharp force peak which
occurs at the first resonance around 22 kHz,
demonstrated by the current peak. In the 90° case,
the behaviour is very similar, only the transient force
is smaller and occurs at a slightly higher frequency.
Notice that there are no switching transients at the
beginning or end of the sweeps, but rather slower
drifts. Figure 10, right, shows the same graph for the
torsion balance with linear thermal drift correction,
where sharp force peaks of a few 100 nN can be
seen. The transient force seems to occur at the first
resonance, for the orientation, and it is exactly
reversed for the 90°, at the second resonance.
Since the magnitude of the effects is similar for both
orientations, these observations hint at something
other than thrust.
Hence, the displacement of the beam of both
balances was observed using the laser
interferometer with high sampling frequency.
Figure 11, left, depicts the result of a single
waveform, discrete Fourier transform (DFT) when
driving the device around the same frequency as for
the previous, respective fixed frequency tests. In the
frequency spectrum, the driving frequencies are not
to be seen, however, two obvious peaks are
present: 500 Hz for the torsion balance and close to
900 Hz for the double-pendulum, along with other
lower frequency peaks. These vibrations were only
observed around the resonances of the system
when powering the device, as can be seen in
Figure 11, right, where the amplitude of these lower
range frequency vibrations is plotted. In the case of
the double-pendulum, the amplitude of the vibration
is lower and consistent so far with the other balance
tests and higher force-displacement conversion
factor. Although the exact cause of these sub-
harmonic vibrations is unknown, it’s reasonable to
assume that one or more components of the
complex assembly are excited by the device’s
amplified oscillations at resonance. How oscillating
forces can cause either balance to show switching
transients has already been extensively examined
by us using the voice coil [13].
5
4. ROTARY DEVICE TESTS
The rotary device has the advantage of looking at
the mass fluctuation without the need of a complex
thrust balance, and also without having to
synchronize the device’s first harmonic oscillations
with electrostriction to produce thrust, required
according to Woodward and Fearn [15]. Knowing
the voltage-force conversion constant of the passive
gauge embedded in the stack allows one to
determine the change in the forces from the gauge
signal. Using the piezoelectric voltage coefficient
(g33) of about 25 Vm/N for hard PZT materials, the
conversion factor for the 0.3 mm thick piezodisk
should be 26.5 mV/N [16]. However, this will be
different when placed in a pre-stressed multi-
layered stack with screw connection. Thus, the
stack was put to test using an electromechanical,
universal testing machine (ElectroPuls, E3000). The
results of the calibration using a 100 N pulling force
at varying forcing frequency, and a constant pre-
stress of 200 N in addition to the pre-stress of the
bolts, are shown in Figure 12. The curve shows a
stabilization around 22 mV/N, which is close to the
prediction and means that the external force is well
transmitted to the strain gauge and the stack is
stiffer than the parallel screw connection. Below a
forcing frequency of 50 Hz, the conversion factor is
lower since the small piezoelectric charge has time
to dissipate before the next pulse. On one hand, it
seems that the conversion factor reaches a steady
value at higher frequencies, and it is assumed that
it will not change for high frequencies in the kHz
range. Also, an internal force generated in the pre-
stressed assembly by charging the piezoelectric
stack could result in different dynamics compared to
the external pulling force used in the calibration
method. Therefore, an additional calibration method
will be developed in the future to verify these
assumptions.
In Figure 13, the graph on the left illustrates a
frequency spectrum of the gauge signal amplitude
against the driving frequency for a constant AC
voltage input of 180V amplitude applied to the stack
in a range of 10 to 45 kHz. The values are obtained
by extracting the main component from a DFT of the
unfiltered gauge signal waveforms in response to
each excitation frequency. Furthermore, the three
curves are obtained at different rotation rates of the
apparatus. If the voltage-force conversion factor of
the passive gauge remains constant over the
frequency range, one can accurately determine the
internal force acting on the gauge at any frequency.
In addition, the centrifugal force can be ignored
since it is a constant force if the rotation rate is held
fixed throughout the test run during which the AC
signal is applied. Hence, the 0 rpm curve strictly
shows the internal forces, varying with the driving
frequency around resonances, as expected.
In the event that the frequency response of the
stack does not depend on the rotation rate, the
mass fluctuation could be obtained as the difference
in the second harmonic amplitudes extracted from
the gauge signal, since the mass fluctuation is
expected to occur at twice the driving frequency.
However, Figure 13, left, shows that the internal
forces do vary with the rotation rate, especially in
the neighbourhood of the resonance and anti-
resonance peaks. The analysis could focus on the
minimal difference between the 1800 and 3600 rpm
curves, but the discrepancy is still too large
compared to the predicted mass fluctuation.
Figure 13, right, shows the second harmonic
component of the gauge signal during the driving
frequency sweep, at various rotation rates, obtained
this time from a DFT analysis of the filtered gauge
signal. This figure shows that there is an important
non-linearity present around the resonances, even
without rotation, as detected from the 0 rpm curve.
Moreover, there is an important difference in the
second harmonic component for the varying rotation
rates. Is this difference due to the Machian mass
fluctuation? Not necessarily. Since the first
harmonic component of the internal forces do vary
with the rotation rate, so could the second harmonic
component vary as well. Since the exact nature and
distribution of the nonlinearity present in the stack
cannot be accurately determined, the mass
fluctuation, if present, is hidden in the second
harmonic content of the piezoelectric oscillation.
The solution to this problem requires a re-design of
the test object to remove even the smallest
nonlinearity, and an accurate quantitative analysis
demands a re-evaluation of the calibration method,
which are both on-going.
5. CONCLUSION
The exciting perspective of a new form of
propellantless thrust has led to a thorough
investigation of the claim for Mach-Effects. The
results obtained for MET tests with a sub-µN torsion
balance in the framework of the SpaceDrive project
have been corroborated by the results obtained with
the double-pendulum thrust balance. Both balances
seem to suffer the same weakness in measuring the
force transmitted by a piezoelectric stack: they rely
on mechanical connections susceptible to vibration.
Since effects of the same magnitude were observed
for both thrust-producing (0°) and non-thrust
producing (90°) orientations of the device, an
investigation of possible artefacts was undertaken.
Examining the movement of balance beams using a
laser interferometer with high sampling frequency
led to the discovery of vibrations at frequency lower
than the driving frequency, especially at resonant
excitation. Comparing the results with the known
and tested response of harmonic oscillators to a
sinusoidal excitation provides an explanation for the
switching transients observed. Lastly, the nature
and magnitude of the force traces observed seem
to be relatively indifferent to the change in the thrust
balances, electronics, devices, currents and driving
6
frequencies. Thus, it is concluded that the claimed
thrusts using an MET or MEGA thruster device
consist in vibrational artefacts.
Furthermore, first tests with a rotary device to
detect Machian- or mass fluctuations of other nature
have been performed. Our results have been limited
by the nonlinearity present in the piezoelectric
stacks, which will be improved in future tests
6. ACKNOWLEDGEMENTS
We gratefully acknowledge the support for the
SpaceDrive Project by the German National Space
Agency DLR (Deutsches Zentrum fuer Luft- und
Raumfahrttechnik) and funding from the Federal
Ministry of Economic Affairs and Energy (BMWi) by
approval from German Parliament (50RS1704). Our
sincere thanks go to the colleagues of the Friedrich-
Siemens Laboratory for their help with the
ElectroPuls machine. We would also like to
acknowledge the support from J. Heisig, J.
Woodward and H. Fearn for their contributions to
the ongoing experiments.
7. REFERENCES
1. Woodward, J.F. Making Starships and
Stargates: The Science of Interstellar
Transport and Absurdly Benign Wormholes;
Springer: New York, 2013; ISBN
9781461456223.
2. Sciama, D. On the Origin of Inertia;
Cambridge, 1953.
3. Woodward, J.F. Flux capacitors and the
origin of inertia. Found. Phys. 2004, 34,
14751514.
4. Rodal, J.J.A. A Machian wave effect in
conformal , scalar tensor gravitational
theory. Gen. Relativ. Gravit. 2019, 51, 123.
5. Williams, L.L.; Inan, N. Maxwellian mirages
in general relativity Available online:
http://arxiv.org/abs/2012.08077.
6. Brans, C.H. Absence of inertial induction in
general relativity. Phys. Rev. Lett. 1977, 39,
856857.
7. Fearn, H.; Rossum, N. van; Wanser, K.;
Woodward, J.F. Theory of a Mach Effect
Thruster II. J. Mod. Phys. 2015, 06, 1868
1880.
8. Woodward, J.F.; Kennifick, D.; Broyles, M.;
Akins, C.; Fearn, H.; Rodal, J.; March, P.
Mach Effects for In-Space Propulsion:
Interstellar Mission - NIAC Phase II Final
Report; Los Angeles, 2020;
9. Buldrini, N.; Tajmar, M.; Marhold, K.; Seifert,
B. Experimental Results of the Woodward
Effect on a uN Thrust Balance. In
Proceedings of the AIAA/ASME/SAE/ASEE
Joint Propulsion Conference & Exhibit;
2006; Vol. 42, pp. 112.
10. Kößling, M.; Monette, M.; Weikert, M.;
Tajmar, M. The SpaceDrive project - Thrust
balance development and new
measurements of the Mach-Effect and
EMDrive Thrusters. Acta Astronaut. 2019,
161, 139152.
11. Tajmar, M.; Kößling, M.; Weikert, M.;
Monette, M. The SpaceDrive Project - First
Results on EMDrive and Mach-Effect
Thrusters. 2018.
12. Monette, M.; Kößling, M.; Tajmar, M. The
SpaceDrive Project - Progress in the
Investigation of the Mach-Effect-Thruster
Experiment. In Proceedings of the 36th
International Electric Propulsion
Conference; 2019; pp. 1520.
13. Monette, M.; Kößling, M.; Neunzig, O.;
Tajmar, K. Experimental Investigation of
Mach-Effect Thrusters on Torsion Balances.
Acta Astronaut. Submitted: 2021.
14. Woodward, J.F. A Test for the Existence of
Mach Effects With a Rotary Device. In
Proceedings of the AIP Conference
Proceedings 1208; 2010; pp. 227236.
15. Fearn, H.; Woodward, J.F. New
Experimental Results of the Mach Effect
Gravitational Assist (MEGA) Drive. In
Proceedings of the AIAA Propulsion and
Energy Forum NNF; Indianapolis, 2019; pp.
112.
16. PI Ceramic GmbH Material Data Available
online:
https://www.piceramic.com/en/products/pie
zoelectric-materials/#c15193.
7
Figure 1: sketch (top) and CAD (bottom) of the torsion balance
Figure 2: sketch (left) and CAD (right) of the double-pendulum balance
8
-60 -40 -20 0 20 40 60
-100
-80
-60
-40
-20
0
20
40
60
80
100
Balance Calibration Comparison
Voice Coil Pulses
Commanded Force [µN]
Measured Beam Displacement [µm]
Torsion Balance (TB)
Double-Pendulum Balance (DPB)
010 20 30 40 50 60
-1
0
1
2
3
4
5
6
7
Balance Comparison
5 µN Voice Coil Pulse
Force [µN]
Time [s]
Commanded
Observed (TB)
Observed (DPB)
Figure 3: calibration comparison
Left: full calibration, both balances, right: single pulse calibration, both balances
Figure 4: picture of the MET
Figure 5: electronics diagram
9
Figure 6: spectrum of devices, at different times
Left: impedance spectrum, right: gauge signal spectrum
Figure 7: rotary apparatus setup
Left: CAD model, right: electronics diagram
010 20 30 40 50 60 70 80
-0.12
-0.09
-0.06
-0.03
0.00
0.03
0.06
0.09
0.12
Balance Comparison, Voice Coil Test
1 µN, 0.5 Hz, Sine
Force [µN]
Time [s]
Observed (TB)
Observed (DPB)
Commanded
-1.0
-0.5
0.0
0.5
1.0
Voice Coil [µN]
Figure 8: zero tests
Left: DC current test, right: voice coil sine test
20 25 30 35 40 45 50
-10
-5
0
5
10
15
20
25
30
35
40
Loaded Impedance Spectrum
60V, Devices NS5 and WT3
Impedance [dB, @50]
Frequency [kHz]
WT3
WT3 - dep.
NS5
20 25 30 35 40 45 50 55 60
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Gauge Signal Ratio, Unloaded Spectrum
2V, Devices NS5 and WT3
Gauge Signal/Input Voltage Ratio
Frequency [kHz]
WT3 - dep.
NS5
Piezo-gauge
z
x
Device
10
010 20 30 40 50 60 70 80
-0.05
-0.03
0.00
0.03
0.05
0.08
0.10
0.13
0.15
0.17
0.20
Balance Comparison
Fixed Frequency Test, 90°
Force [µN]
Time [s]
Force (TB)
Force (DPB)
Current (TB)
Current (DPB)
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
Current [A]
Figure 9: MET fixed frequency balance tests
Left: 0° orientation, right: 90° orientation
025 50 75 100 125 150
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Force (0°)
Force (90°)
Frequency
Current
Torsion Balance
Swept Frequency Test
Force [µN]
Time [s]
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
Commanded Frequency [kHz]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Current [A]
Figure 10: MET sweep balance tests
Left: torsion balance sweep, right: double pendulum balance sweep
102103104
10-7
10-6
10-5
10-4
10-3
10-2
10-1
Beam Vibration DFT
Balance Comparison
DPB, 900 Hz
Vibration Amplitude [µm]
Frequency [Hz]
Torsion Balance
Double-Pendulum Balance
TB, 500 Hz
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
DPB Current
TB Current
DPB Vibration
TB Vibration
Balance Comparison
Frequency Sweep and Beam Vibration Analysis
Current [A]
Frequency [kHz]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Double Pendulum Beam Vibration [nm]
0
10
20
30
40
50
Torsion Balance Beam Vibration [nm]
Figure 11: MET beam vibration analysis
Left: DFT, one waveform, both balances, right: 90° sweep, both balances
010 20 30 40 50 60 70 80
-0.05
-0.03
0.00
0.03
0.05
0.08
0.10
0.13
0.15
0.17
0.20
Balance Comparison
Fixed Frequency Test, 0°
Force [µN]
Time [s]
Force (TB)
Force (DPB)
Current (TB)
Current (DPB)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Current [A]
025 50 75 100 125 150
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20 Force (0°)
Force (90°)
Frequency
Current
Double Pendulum Balance
Swept Frequency Test
Force [µN]
Time [s]
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
Commanded Frequency [kHz]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Current [A]
11
020 40 60 80 100 120
0
5
10
15
20
25
ePuls Calibration Test
Conversion Factor vs Forcing Frequency
Conversion Factor [mV/N]
Frequency [Hz]
Figure 12: ElectroPuls calibration
10 15 20 25 30 35 40 45
0
5
10
15
20
25
30
35 3600 rpm
1800 rpm
0 rpm
Rotary Device Frequency Sweep
First Harmonic Spectrum
Gauge Signal [mV]
Frequency [kHz]
30 31 32 33 34 35 36
0
5
10
15
20
25
30 3600 rpm
1800 rpm
0 rpm
Rotary Device Frequency Sweep
Second Harmonic Spectrum
Filtered Gauge Signal [mV]
Driving Frequency [kHz]
Figure 13: S03 device spectra vs rotation rate
Left: first harmonic spectrum, right: second harmonic spectrum.
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
Successful interstellar venture depends on the development of propellantless propulsion with a thrust-to-power ratio much greater than a photon rocket and without the limitations of solar sails. Claims of μN thrust for Woodward's MEGA Drive, along with predicted mass fluctuations as a consequence of the Mach-Effect have initiated a few decades of table-top experiments seeking to observe variable mass and using it to generate significant propellantless thrust efficiency. However, using different thrust balances with increasing measurement sensitivity to characterize these effects resulted in a decrease in the claimed effect's magnitude. Large second harmonics begin to appear in the pre-stressed piezoelectric stack's integrated strain gauge signal, showing the vibration present at system resonances, as well as significant nonlinearity. Observation of the balance beam's oscillations reveal sub-harmonic vibration coupling and amplified vibration around electromechanical resonances of the system that can explain the transients observed in the force trace. Different piezo-actuator driving conditions are explored and an account for the different behaviors observed is made. The varying driving conditions do not significantly affect the forces observed, contrary to the theory. It is concluded that the observed effect is a result of coupled vibrations on the torsion balance.
Conference Paper
Full-text available
An innovative concept for propellantless space propulsion, originally proposed by Woodward using the so-called 'Mach Effect' and supported by peer-reviewed, experimental evidence, was investigated at TU Dresden in the framework of the SpaceDrive Project. The Mach-Effect-Thruster is a pre-stressed, multilayer piezoelectric stack driven by a sinusoidal voltage at an optimal frequency producing propellantless thrust, orders of magnitude more efficient than a photon rocket. As a follow-up to the previous test campaign, in which no significant thrust could be systematically detected above the noise range of the torsion balance in vacuum, the tests are repeated on a torsion balance with increased sensitivity. Equipped with two A-20 C-Flex pivot bearings, the background noise measured as a standard deviation of the beam displacement was reduced from 200 nN to around 5 nN. In this recent experimental campaign, Woodward's original equipment, which includes a Carvin audio amplifier and a 1:4 transformer in the driving electronics, was used. A force signal qualitatively similar to the effect described by Woodward could be observed. The switching on-off transients of 30 nN were, however, were significantly smaller than the force previously claimed at a similar voltage. Furthermore, the force signal was also observed when orienting the MET's theoretical 'thrust' vector parallel to the balance beam which should show zero thrust. In addition to these experiments, the mutual influence of the driving electronics and its piezoelectric load is carefully analyzed in a range of 24 to 48 kHz, the balance is fully characterized with a purely resistive dummy load, and is calibrated along its three principal axes using a voice coil. Finally, this paper presents an investigation of the thermal, vibration and electromagnetic artefacts that can occur in such torsion balance measurements.
Article
Full-text available
A frequency-dependent Machian effect previously put forward by Woodward (that for a body undergoing mass–energy fluctuations, the second time derivative of the mass–energy density is a source of a gravitational field) is discussed within Einstein’s theory and justified using Hoyle–Narlikar’s conformal gravitational theory. It is shown that Einstein’s theory has a similar term that is 3rd order post-Newtonian, but besides the issue of coordinate-dependence, the Machian significance of any field term in Einstein’s equation depends on the (universe’s) cosmological solution to the field equations. Therefore, Woodward’s theory is examined within Hoyle–Narlikar’s scalar–tensor theory of gravitation (a theory that was expressly developed with the intent to incorporate Mach’s principle) for a universe undergoing accelerating expansion (hereby accounted for by a positive cosmological constant). It is shown under gauge invariant expressions that the conformal, scalar–tensor gravitational theory of Hoyle and Narlikar has a similar term of first order when the mass–energy fluctuation is due to distant objects but that it effectively becomes a higher order effect when the mass–energy fluctuations arise from fluctuation of the (local) mass–energy (as is necessarily the case in Woodward’s experimental results, since the only mass that can be purposively fluctuated in energy, monochromatically, is the local mass, instead of the distant masses responsible for most of the inertia according to Mach’s principle). Therefore this effect appears too small for practical space travel application (unless the spaceship is near a black hole or a neutron star). Present cosmological measurements of the possible time variation of G are shown to occur at much lower frequencies and therefore cannot be used to rule out Woodward’s effect if G exhibits significant time-dependence at higher frequencies than observed in these cosmological measurements.
Conference Paper
Full-text available
Propellantless propulsion is believed to be the best option for interstellar travel. However, photon rockets or solar sails have thrusts so low that maybe only nano-scaled spacecraft may reach the next star within our lifetime using very high-power laser beams. Following into the footsteps of earlier breakthrough propulsion programs, we are investigating different concepts based on non-classical/revolutionary propulsion ideas that claim to be at least an order of magnitude more efficient in producing thrust compared to photon rockets. Our intention is to develop an excellent research infrastructure to test new ideas and measure thrusts and/or artefacts with high confidence to determine if a concept works and if it does how to scale it up. At present, we are focusing on two possible revolutionary concepts: The EMDrive and the Mach-Effect Thruster. The first concept uses microwaves in a truncated cone-shaped cavity that is claimed to produce thrust. Although it is not clear on which theoretical basis this can work, several experimental tests have been reported in the literature, which warrants a closer examination. The second concept is believed to generate mass fluctuations in a piezo-crystal stack that creates non-zero time-averaged thrusts. Here we are reporting first results of our improved thrust balance as well as EMDrive and Mach-Effect thruster models. Special attention is given to the investigation and identification of error sources that cause false thrust signals. Our results show that the magnetic interaction from not sufficiently shielded cables or thrusters are a major factor that needs to be taken into account for proper µN thrust measurements for these type of devices.
Article
Full-text available
I review arguments indicating that there is no real, physically detectable, local inertial-induction effect in general relativity, contrary to recent comments by Tittle.
Article
Forces claimed by potential propellantless propulsion systems like the Mach-Effect-Thruster or the EMDrive are in the μN or even sub-μN range. In this paper, an automated thrust balance design capable of measuring forces of 100 nN for devices with a maximum mass of 10 kg is described to test these claims. The torsion balance features an electromagnetic calibration method, adjustable magnetic damping and tilt control as well as electromagnetic shielding. All onboard electronics can be controlled wirelessly via an infrared module for serial communication. Power is supplied to the balance using three separate liquid metal feedthroughs: one for voltages up to 500 V and frequencies up to 200 kHz, one for high voltage up to 30 kV DC or AC, and one for high frequency signals up to 3 GHz. The device can be rotated by 180° to measure three different thrust directions without breaking the vacuum and changing the setup in order to gain confidence and refute e.g. thermal drifts. The whole balance is controlled via a script language implemented in LabVIEW. We tested Mach-Effect-Thrusters provided by Woodward and our self-built model exploring higher frequencies and mixed-signals that are believed to create significantly higher forces. Also a magnetostrictive version was built and tested. For the EMDrive, several different frequencies and setups (with/without dielectric insert, flat/spherical end caps) were tested. Results of the tests performed between August and September 2018 are presented, but no final conclusions can be drawn.
Article
The explanation of inertia based on Mach's principle is briefly revisited and an experiment whereby the gravitational origin of inertia can be tested is described. The test consists of detecting a small stationary force with a sensitive force sensor. The force is presumably induced when a periodic transient Mach effect mass fluctuation is driven in high voltage, high energy density capacitors that are subjected to 50 kHz, 1.3 kV amplitude voltage signal, and threaded by an alternating magnetic flux of the same frequency. An effect of the sort predicted is shown to be present in the device tested. It has the expected magnitude and depends on the relative phase of the Mach effect mass fluctuation and the alternating magnetic flux as expected. The observed effect also displays scaling behaviors that are unique to Mach effects. Other tests for spurious signals suggest that the observed effect is real.
Making Starships and Stargates: The Science of Interstellar Transport and Absurdly Benign Wormholes
  • J F Woodward
Woodward, J.F. Making Starships and Stargates: The Science of Interstellar Transport and Absurdly Benign Wormholes; Springer: New York, 2013; ISBN 9781461456223.
On the Origin of Inertia; Cambridge
  • D Sciama
Sciama, D. On the Origin of Inertia; Cambridge, 1953.