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SP2020_268
1
HIGH-ACCURACY THRUST MEASUREMENTS OF THE EMDRIVE AND ELIMINATION OF FALSE-
POSITIVE EFFECTS
SPACE PROPULSION 2020+1
17 – 18 – 19 MARCH 2021
M. Tajmar (1), O. Neunzig (2) and M. Weikert (3)
Institute of Aerospace Engineering, Technische Universität Dresden, Marschnerstrasse 32, 01307
Dresden, Germany,
(1) Institute Director and Head of Space Systems Chair, Email: martin.tajmar@tu-dresden.de
(2) Research Associate, Email: oliver.neunzig@tu-dresden.de
(3) Research Associate, Email: marcel.weikert @tu-dresden.de
KEYWORDS: EMDrive, Propellantless Propulsion,
Thrust Balance
ABSTRACT:
The EMDrive is a proposed propellantless
propulsion concept claiming to be many orders of
magnitude more efficient than classical radiation
pressure forces. It is based on microwaves, which
are injected into a closed tapered cavity, producing
a unidirectional thrust with values of at least one
mN/kW. This was met with high scepticism going
against basic conservation laws and classical
mechanics. However, several tests and theories
appeared in the literature supporting this concept.
Measuring a thruster with a significant thermal and
mechanical load as well as high electric currents,
such as those required to operate a microwave
amplifier, can create numerous artefacts that
produce false-positive thrust values. After many
iterations, we developed an inverted
counterbalanced double pendulum thrust balance,
where the thruster can be mounted on a bearing
below its suspension point to eliminate most
thermal drift effects. In addition, the EMDrive was
self-powered by a battery pack to remove
undesired interactions due to feedthroughs. Using
a geometry and operating conditions close to the
model by White et al that reported positive results
published in the peer-reviewed literature, we found
no thrust values within a wide frequency band
including several resonance frequencies. Our data
limits any anomalous thrust to below the force
equivalent from classical radiation for a given
amount of power. This provides strong limits to all
proposed theories and rules out previous test
results by more than three orders of magnitude.
1. INTRODUCTION
Propulsion systems that emit propellant are not
suitable for reaching even the next star Proxima
Centauri within a human lifetime. The best
available technology for a crewed mission would be
nuclear pulse propulsion like the one developed in
project Orion, that would need 133 years for a
100 m diameter and 400,000 t spacecraft without
considering de-acceleration at the end of the
journey [1]. That leaves only propellantless
propulsion for much smaller robotic probes due to
the low forces of radiation pressure. In principle,
there are two major methods: using a sail to deflect
photons or particles from the solar wind, or to use
an on-board emitter like a laser. The first method
only works near the extrinsic power source like a
terrestrial laser array or the sun whereas the
second method works as long as a power source is
available on the spacecraft. However, on-board
photon rockets produce a very small force F per
input power P given by F/P=1/c=3.3 nN/W, where
c is the speed of light, which increases the trip time
even for a very small spacecraft to thousands of
years.
Already some 20 years ago, a new propellantless
propulsion concept was proposed by R. Shawyer
called the EMDrive [2], which was claimed to use
the difference in radiation pressure from
microwaves inside a tapered cavity bouncing back
and forth between the smaller and larger end to
generate thrust orders of magnitude larger
compared to the classical radiation pressure force.
Although met with high criticism, several
experimental tests and theories appeared
supporting this claim. Most notably, White et al
from NASA Eagleworks published a peer-reviewed
test campaign claiming a force of 1.2 mN/kW for an
input power of 40-80 W on a torsion balance in high
vacuum [3]. This is a factor of 500 higher than pure
photon thrust and would therefore be of high
interest if confirmed.
In our SpaceDrive project, we are designing high-
performance thrust balances with the aim to assess
advanced propulsion concepts and anomalous
thrust claims or theories like the EMDrive and many
others [4], [5]. Previous measurements already
2
revealed one major error source due to partially
shielded cables and their interaction with the
Earth’s magnetic field [6]. After many iterations and
improvements, we developed a setup that allows to
reliably measure forces from an EMDrive similar in
design to the one used by White et al [3] with a
noise level below the photon thrust threshold of
3.3 nN/W, which we are using as a benchmark to
compare against state-of-the-art propellantless
propulsion.
This paper is structured as follows: We will first
briefly review the various experimental claims and
theoretical predictions, summarize the
experimental difficulties and errors that we found
which led to false positives, present our
consolidated final setup as well as measurements
along a wide frequency spectrum including several
resonance frequencies that should have produced
a force. We close this paper with a conclusion and
outlook.
2. REVIEW OF EMDRIVE THEORY AND
EXPERIMENTS
The EMDrive is a tapered cone shaped resonant
cavity fed with electromagnetic power in the
microwave regime. Shawyer based his design and
theory on the observation of Cullen [7], that the
radiation force depends on the shape of the
waveguide and therefore the group velocity. His
thought then was that if microwaves are bouncing
back and forth between a smaller and larger end
cap, a significant net force is generated. Some
designs use a dielectric disc at the smaller end to
even further reduce the microwave’s group velocity
and increase the effect. He proposed an equation
[2] for the produced force as
𝐹 = 2 ∙ 𝑃 ∙ 𝑄𝑢∙ 𝐷𝑓
𝑐
Eq. 1
where P is the input power to the cavity, Qu the
unloaded quality factor (=stored energy divided by
energy lost per cycle) and Df the design factor
which depends on the used frequency and
geometry of the tapered cavity. He lists typical Qu
values as several thousands for first generation up
to several ten-thousands for optimized second
generation designs. The Df factor varies from 0.56
for a NASA-type geometry to 0.91 for further
optimized designs [8]. From this equation, it
appears that the produced thrust shall be
approximately given by the standard radiation
pressure force multiplied by the cavity’s quality
factor. This immediately raises questions on
momentum and energy conservation as well as
Newton’s action-reaction principle. Obviously, from
a textbook physics point of view, radiation bouncing
back and forth will only produce heat and oscillation
of the cavity, but no thrust. Shawyer claims that the
conservation laws are conserved due to pre-
tension in his setups, which is necessary in order
to obtain thrust [9]. For example, this can be done
with a counter-weight on a weight balance or with
two EMDrives pointing in opposite directions.
Alternatively, no pre-tension is necessary if the
EMDrive is operated with amplitude modulation or
essentially in pulsed mode with frequencies at 50
and 300 Hz, which showed good results.
Some theories have appeared that support
Shawyer’s claim. For example, McCulloch
proposed a theory [10] based on inertial
modification due to Unruh radiation giving a similar
force prediction as Eq. 1 with a design factor close
to unity. However, in his definition Qu is not the
quality factor but the number of reflections within
the cavity (which is typically much less). He later
refined his model taking the dielectric into account
[11]. White et al [3] proposed that the EMDrive
directly interacts with the background zero-point-
fluctuations of the vacuum to create propellantless
thrust. Smolyaninov [12] suggested that the
electromagnetic fields in the cavity may create
Axion-like particles as an optical analog of the
Schwinger effect that could be responsible for the
observed forces. Last but not least, Grahn et al [13]
assumes that photons may in fact leave the closed
cavity in the form of phase-opposing and thus E-
field-free photon pairs.
Of course, all these theories are highly
controversial [14] as any observation of forces
higher than photon thrust is outside mainstream
physics. They rely on the fact that the claimed
thrusts are real, therefore we will concentrate on
the best experimental evidence as the baseline for
our investigation.
Shawyer published three detailed test reports on
his webpage, which used electronic balances at
ambient pressure as the force transducer. The first
one conducted several experiments with a thruster
operating at a power of 850 W and a resonance
frequency of about 2.45 GHz with a dielectric at the
smaller end [15]. The microwaves were generated
from a magnetron powered by a half wave rectified
high voltage power supply at 50 Hz resulting in
pulsed operation. Three different balance
configurations were used including a beam balance
with counterweight, an electronic balance at the
bottom with the EMDrive on top and a spring that
connected it to a fixed top structure, as well as a
horizontal variant with a pivot that converted
horizontal movement into a force again pushing on
an electronic balance. Qu values were ranging from
3
2,500-5,900 and the forces measured were in the
range of 10 mN in line with the prediction of Eq. 1.
Different orientations seemed to be consistent with
a real thrust such that the thruster pointing upwards
and downwards produced thrusts with changing
signs, and pointing perpendicular with respect to
the force measurement direction produced zero
thrust. Moreover, various spurious effects were
analyzed and dismissed such as buoyancy, any
influence from the Earth’s magnetic field or the
cooling fans from the magnetron.
The second test report [16] details a more efficient
thruster without dielectric powered again by a
magnetron and without pulsed operation. With an
unloaded Qu factor of 19,521, a thrust of 82 mN
was measured for an input power of 744 W. This
was verified again in a vertical and horizontal
measurement with different thruster orientations.
In the third test [17], a so-called C-Band flight
thruster without dielectric operated at 3.85 GHz,
and with approximately 300 W as well as an
unloaded Qu factor of 55,172 produced a force of
around 100 mN. A travelling wave tube amplifier
(TWTA) was used instead of the magnetron without
any mentioning of pulsed outputs, so we can also
assume continuous operation. In addition, a
contactless connection between amplifier and
cavity was used without further details. In the test
report, no information was given on force
measurements for different thruster orientations or
discussions on possible spurious effects, only a
vertical measurement was described with the
thruster hanging down from a spring and touching
the balance on the bottom. Another test is only
briefly described, where a 100 kg test rig consisting
of the EMDrive and all associated electronics is
mounted on an air bearing with flexible cables
providing power [18]. It is claimed that 334 W
produced a force of 96 mN and a corresponding
rotary motion on the air bearing, but unfortunately,
no test data or analysis with different thruster
orientations was made available.
Yang et al [19] initially reported very high thrust
measurements for an EMDrive on a force-feedback
thrust stand powered by a magnetron at 2.45 GHz
with a power ranging from 80-2,500 W and
corresponding forces of 70-720 mN. However, later
measurements with a different wire torsion
pendulum did not show any thrust higher than their
measurement uncertainty of 0.7 mN at a power of
230 W [20]. Fetta [21] reported thrust generated
from a pancake-shaped cavity at 937 MHz with
very high Q values of 107 just below liquid helium
temperatures of around 10 mN for an input power
of 10.5 W. However, his setup and measurement is
poorly described. Brady et al [22] further tested
Fetta’s design on a torsion balance obtaining
22.5 µN with an input power of 28 W at room
temperature using a standard solid-state amplifier
and a PTFE dielectric at one end.
White et al [3] performed an extensive test
campaign in high vacuum on a torsion balance test
stand with an EMDrive using a tapered cavity with
a dielectric at the smaller end, a frequency of
1,937 MHz, power levels ranging from 40-80 W, a
loaded quality factor of 7,123 and thrusts ranging
from 30-130 µN, which is around an order of
magnitude below Eq. 1. Considering that an
unloaded Q factor (direct measurement of cavity) is
usually higher than the loaded one (including
losses from all electronic components), the fit
should be even better. Tests were done in forward,
reverse and perpendicular (=null-thrust) orientation
with corresponding thrust measurements
consistent with a real thrust. All electronic
components including a solid-state amplifier were
mounted on the balance powered through liquid
metal contacts. Resonance frequency tracking was
implemented using a digital closed-loop control.
The observed thrust slopes were superimposed on
thermal drifts of similar magnitude. At the end, the
paper lists a number of possible error sources
which were analyzed and dismissed including air
currents, radiofrequency (RF) and electromagnetic
interactions, thermal issues and outgassing.
McDonald [23] published a test setup using also
White’s cavity geometry and a frictionless finger-
joint/RF coupling technique to further reduce
electromagnetic interactions. Due to the depth of
their assessments, we will concentrate our own
experimental assessment on the White cavity
design.
Sokoloff et al [24] recently published a test of two
identical EMDrives in opposite directions on top of
an electronic balance that can be alternatively
operated in order to check for corresponding
upwards and downwards forces without modifying
the setup. Due to the high weight and stiff coaxial
cable from the amplifier, no force was measured for
a thruster operating with 2.45 GHz, a Qu factor of
3,550 and a power of 200 W within their
measurement resolution of 5 mN. Shortly
afterwards, an update was published by Peyre et al
[25] with a contactless microwave connection and
an increased Qu factor of up to 18,500, where no
force was measured down to 0.1 mN for a power of
150 W into the cavity.
Our own tests started with an EMDrive using a
2.45 GHz microwave oven magnetron at 700 W
with a Qu factor of 50 on a beam-balance at
4
ambient pressure [26], which showed a difference
between upwards, downwards and horizontal
orientation but large thermal drifts in the order of
hundreds of µN. The same thruster was then
mounted on a torsion balance in high vacuum and
did not show thrusts higher than our error bar of
20 µN.
Next, we replicated the geometry used by White et
al [3] including the dielectric end plate and
significantly upgraded our balance and electronics
[6]. Using a much larger vacuum chamber, a higher
sensitivity torsion balance and a solid-state
amplifier, we obtained similar values as others
such as a Qu factor of 20,000 and a thrust that
changed sign depending on its orientation in the
range of 3-6 µN for an input power of 2 W. This is
an order of magnitude less compared to what we
would expect from Eq. 1, however, the unloaded Qu
factor might have been too high. The force-to-
power ratio of around 1 µN/W or 1 mN/kW was
similar to the one reported by White et al [3].
However, our test setup included an optional 40 dB
attenuator that basically eliminated all microwaves
going into the cavity while leaving the rest of the
setup identical to the previous measurement. Tests
with the 40 dB attenuator showed similar thrust
values compared to without it, indicating that these
forces must be due to something else than the
microwaves in the cavity. Our best estimate was an
interaction of just a few centimeters of unshielded
cables with the Earth’s magnetic field that
produced similar forces. Further work concentrated
on trying out liquid-metal RF feedthroughs, which
placed the amplifier with its high DC currents and
thermal load outside the chamber [5], as well as the
development of a continuously rotating thrust stand
using superconducting levitation [27] to investigate
the reality of the observed forces.
Last but not least, Taylor predicted that an EMDrive
operating at optical frequencies instead of
microwaves might be more compact and efficient
[28]. This was experimentally investigated by
ourselves in a separate paper [29]. The continuous
development of the various setups provided us with
a good understanding of different experimental
artefacts and led to the development of a reliable
setup that eliminated spurious interactions and
drastically boosted our sensitivity to below the
photon pressure force, which is our design
benchmark for propellantless propulsion. Given the
power levels involved, this required sub-µN
resolution for hundreds of Watts to just a few nN for
a few Watts of input power.
A summary of all published measurements and a
comparison to the data obtained in this paper is
shown in Table 1.
3. EXPERIMENTAL DIFFICULTIES
So far, we have seen two different measurement
principles: an electronic balance using weight
changes or a torsion balance that uses deflection
and a spring constant to calculate the force
generated by the EMDrive. There are many
thruster-induced and environmental interactions
that can easily generate false-positive thrust
signatures similar to the ones reported above. Here
is a list of the most important ones that we
observed:
1. Buoyancy, atmospheric interactions and
outgassing: Apart from the fact that an ambient
atmosphere causes noise and therefore may
prohibit any balance to reach the sensitivity
required, buoyancy is a significant factor for the
forces involved. Injecting tens to hundreds of
Watts into a cavity causes the thruster and its
electronics to heat up significantly. If we
consider a typical cavity volume of
15x15x15 cm³, a temperature change of only
one degree Celsius creates a lifting force of
150 µN! This severely affects all weight
measurements in ambient conditions. In
vacuum, gases can cause problems too. For
example, some residual gas or other
components that can easily evaporate may be
trapped. Heating up the thruster can cause
outgassing in one direction that can create
forces which mimic a real force, which even
changes signs correctly with different thruster
orientations.
2. Magnetic interactions: The amplifiers on the
EMDrive need high currents of at least several
Amperes. Cables going to the electronics can
be twisted in order to reduce external magnetic
fields. However, no shielding is perfect and
there are always little paths without twisting
that add up to non-negligible fields. This can
then interact with the Earth’s magnetic field or
with permanent magnets in close vicinity.
Examples are magnets used for eddy-current
damping of the balance or magnets in vacuum
gauges or turbo pumps, which are mounted on
the chamber walls. Reorientating the thruster
can also change the direction of the force if
those external magnets are mounted off-axis.
It is therefore very important to map the
magnetic environment close to the balance to
remove such obstacles. In White et al’s setup
[3], the damping magnet was mounted on the
5
external supporting structure and not on the
balance arm, which can very well cause
orientation-dependent magnetic interaction
forces of similar magnitude compared to their
claimed thrusts. Another non-intuitive magnetic
interaction is that high-frequency fields can
induce currents in voice-coils, which are
frequently used to calibrate balances. A DC
power supply connected to the coil can rectify
the signal causing a real force [30].
3. Feedthrough interactions: So far, three
different feedthroughs were used to provide
power to the thruster or read back monitoring
signals: flexible cables, liquid-metal pin
contacts and contactless RF joints which
require very precise alignments. The first
method is obviously the worst choice as it
introduces an additional spring constant that
can create large forces. They can have a
strong temperature dependence, which in turn
can lead to false positives rendering sub-µN
measurements impossible. Liquid-metal
contacts seem like a good choice on first sight
and were used on many of the previous tests
as the liquid removes the cable’s stiffness.
However, we found out that surface tension
forces between the pin and the liquid exist that
depend on the current passing through. This
can lead to several µN for currents required to
power the amplifier. In addition, careful
positioning of the feedthrough is required in
order to limit their interaction with the overall
thrust measurement.
4. Thermal interactions: This is one of the most
important interactions, which may explain a
majority of the claimed thrust measurements.
Heating up of the cavity or the electronics
during operation causes thermal expansion
which in turn shifts the center of gravity.
Torsion balances are very sensitive to such
shifts causing motion of the balance to its new
zero position. This can easily be misinterpreted
as a real thrust with the correct signature as
changing thruster orientations can lead to a
change in the new zero position direction too.
Also, weight balances show changes if the
center of gravity moves above their suspension
point because it creates a torque. That is why
most electronic balances feature a hook to
weigh samples below it connected to a single
point in the middle to remove this artefact.
However, all tests using this method so far like
the ones from Shawyer [15]–[17], positioned
the EMDrive on top of the balance. Tests
performed by us with samples that can heat up
show a significant difference if weighted above
or below on a hook due to this effect [31].
Specifically, the EMDrive with its large volume
usually made from copper or steel acting as a
heat sink is very sensitive to this. In addition,
heating up of the cavity is linked to the
thruster’s resonance frequencies, which can
produce very convincing thrust signatures. Not
only the thruster itself is susceptible to thermal
drifts, also the balance itself consisting of its
arms and spring can be influenced by varying
temperatures. A change in the spring constant
directly translates into deflections that are
interpreted as forces. This can be even
amplified by mechanical fixation of some parts
of the thruster to the balance arm, which results
in large false-positive forces. In addition to real
thrust-mimicking plateaus, thermal drifts are
always present and are usually superimposed
on any measurement. McDonald tried to
remove them by heating up the whole balance-
thruster assembly to a constant temperature
[23]. Software tools are necessary to
automatically detect such drifts and
systematically remove them in order to achieve
high resolution.
In addition to taking care of such thruster-
environment interactions, it is very important to
have a reliable null-measurement, e.g. by having
the thruster pointing in a direction perpendicular to
the measurement axis. Many iterations in the setup
both on the thruster and the balance are necessary
in order to determine if a signal is real or an
artefact.
4. EXPERIMENTAL SETUP
Here we describe our final configuration, which
addressed all the artefacts that we observed in
order to achieve a reliable and high sensitivity
measurement to assess, if the EMDrive produces
any force higher than a pure photon thruster. In
short, our key components are as follows:
1. A new type of thrust balance was designed that
was much less sensitive to center of gravity
shifts.
2. The thruster was mounted on a bearing below
its suspension point to further reduce thermal
induced expansion shifts or mechanical stress
on the balance and its pivots.
3. Magnetic components were removed or
relocated as much as possible like the eddy-
current damping magnet or vacuum chamber
components until the magnetic environment
did not cause any measurable effect.
4. The EMDrive was mounted as a “black box” on
the thrust balance. Using a battery-pack to
6
power the amplifier and required electronics,
we eliminated all feedthrough (high currents,
RF) issues. Only data monitoring and
commanding signal connections used a liquid-
metal pin contact but at such low power that the
influence was below our resolution. This
complete assembly should also represent a
real application like operating a thruster on a
satellite as close as possible.
A detailed description is summarized as follows.
5.1 Inverted Counterbalanced Double
Pendulum
Considering the weight of the whole EMDrive
assembly of 9 kilograms, a weight balance is not
an option to reach radiation pressure resolution. On
the other hand, a classical torsion balance as used
by White, McDonald and ourselves, which consists
of a single arm and a torsion spring in the middle,
turned out far too sensitive to center of gravity shifts
due to thermal expansion. We therefore developed
an inverted counterbalanced double pendulum [32]
as illustrated in Fig. 1. Instead of a single arm, it
consists of two platforms, which drastically reduces
the influence of the actual position of the center of
gravity. The top square hosts the thruster and the
counterweights are located at the bottom. A tripod
connects the two platforms with a total of nine
frictionless flexural pivots. The deflection is
measured using an attocube IDS3010 laser
interferometer with a 10 Hz low-pass filter.
Calibration of the balance is performed using a
voice-coil, which is commanded using a
Keithley 2450 precision current source. This
converts the observed deflection into force. The
voice-coil itself was calibrated and compared
against its datasheet force constant using a
Sartorius AX224 balance. The resulting calibration
constant was highly linear within our measurement
range as shown in Fig. 2. In order to remove any
permanent magnet in the vicinity of the thruster, we
decided to implement damping as a closed-loop
software solution using the voice-coil instead of the
usual eddy-current permanent-magnet-copper
plate assembly. Proper counterweights and the
selection of a critical damping constant resulted in
a reaction time of about 15 seconds and an
exceptional low noise as shown in Fig. 3, while the
whole setup was mounted but non-operational.
Using data averaging with many measurements,
sub-nN resolution could be obtained as required.
This is the lowest noise level by many orders of
magnitude of thrust balances with a weight
capacity of up to 10 kg that we have found in the
literature.
Each measurement was subdivided into different
sectors of fixed durations with an initial off-period,
then ramping up to the desired power followed
again by ramping down to zero and maintaining a
second off-period. This allows to systematically
analyze drifts from the laser interferometer during
the off-periods as well as typical linear thermal
drifts during the on-periods. A LabView program
was developed to automatically detect and
compensate such drifts as illustrated in Fig. 4. A
script-based program controlled both balance and
thruster and performed a complete set of
calibration before and after each measurement
campaign as well as executing any measurements
with a pre-defined number of profiles to gain
statistical significance and to improve noise.
Finally, the balance with approximate dimensions
of 550x740x700 mm³ was put on passive dampers
into a large stainless-steel vacuum chamber with
dimensions 1.2x1.5x2.5 m³, which provided
sufficient distance to the walls as well as pumps
and gauges to eliminate electromagnetic
interactions. An Edwards oil-free scroll pump was
used to reach 10-2 mbar, which was sufficient to
avoid buoyancy and allowed quick turn-around
times to iterate or change setups on a daily basis.
The balance featured up to 20 liquid-metal pin
contacts that were optimized for vacuum as well as
minimum forces due to currents passing through
them. All cables were twisted in pairs to reduce
magnetic fields as much as possible. A FLIR
thermal camera was mounted inside the chamber
to observe the whole assembly and to identify hot
spots, which would cause thermal drifts.
Most important was mounting of the EMDrive to the
balance platform. In order to eliminate the
sensitivity to thermal drifts and center of gravity
shifts, the assembly was mounted hanging down
from a bearing, which consisted of a simple bolt in
the middle of the upper platform with its rotation
axis perpendicular to the thrust direction. This is
similar to the hook configuration on weight
balances and proofed to be very effective. In order
to illustrate the influence of mounting, we
performed the same measurement in three
different configurations as shown in Fig. 5: In
position A, the EMDrive was mounted on a cage
that made its center line align with the top platform,
in position B, the cage was removed and the
EMDrive was put standing on dampers on the top
platform, and finally in position C, where the
thruster package was mounted on the bolt bearing
hanging down from the middle point of the thruster
platform.
7
The corresponding measurements for identical
operating conditions in frequency and power are
shown in Fig. 6a, where the amplifier current
indicates when the thruster was on. Position A
produced a large force consisting of a plateau and
a drift similar to the ones reported in White et al [3]
with 1.5 µN for an input power of 10 W. This could
be amplified by mechanically fixing the cavity to the
cage rods with screws raising the thrust level to 20
µN as shown in Fig. 6b. That value is similar to what
we expected from White et al [3] with a claimed
thrust-to-power ratio of about one µN/W. However,
this was not a real thrust but originated from
mechanical stress due to the thermally expanding
cavity, which acted on the balance’s pivots. In
position B, mechanical stress was reduced by
eliminating the cage, however, small center of
gravity shifts due to thermal expansion were still
present and a thrust of around 200 nN was present.
Only after choosing position C, the thrust artefacts
disappeared and only noise was left.
5.2 EMDrive and Electrical Setup
Our cavity is based on the same geometry as the
one used by White et al [3] to compare with peer-
reviewed results. It consists of a tapered cone,
which was mechanically pressed, with a cylindrical
flange and a collar made out of 2 mm thick copper
as shown in Fig. 7. The large flat end surface can
be screwed onto the collar and the smaller end
surface can slide into the cylindrical flange with a
tight fit, which allows fine tuning. Two 20 mm thick
HDPE discs with a diameter of 155 mm are glued
together and fixed to the end surface using Scotch-
Weld 2216 adhesive. A loop antenna made of
1 mm thick copper wire with a diameter of
approximately 13 mm is used for the power feed.
The antenna is screwed into the cavity using an N-
type connector. For this purpose, a position was
chosen, which, according to COMSOL simulations,
lies within the range of high magnetic field
strengths of various modes. The antenna can be
aligned horizontally or vertically to improve
magnetic field excitation in the cavity.
In order to eliminate feedthrough problems due to
high currents or RF signals, we decided to operate
the EMDrive with a battery pack that provided
enough power for all components during a whole
night, which we preferred for measurements due to
low seismic noise. Only monitor and command
signals were still routed through the liquid metal pin
contacts during operation. The following electronic
components completed our circuit as shown in Fig.
8:
- Battery pack with six 18650 Lithium-Ion cells
and balancing electronics as well as DC-DC
converters for all other components. This was
re-charged before any measurement
campaign.
- Mini-Circuits ZX95-2041-S+ voltage-controlled
frequency generator.
- Mini-Circuits ZX73-2500-S+ voltage-controlled
attenuator to control the output power.
- EMPower SKU 1164 RF solid-state amplifier
with a maximum output power of 50 W and an
amplification of 47 dB according to our
measurements.
- MECA CN-1.950 circulator that prohibits
damage to the amplifier by re-directing any
reflected power to a separate output, which
was measured by a Mini-Circuits BW-
N30W20+ fixed attenuator and a Mini-Circuit
XZ47-40LN-S+ power meter. This is similar to
the setup used by Shawyer [17].
- Maury Microwave 1878B three-stub tuner for
impedance matching directly next to the
antenna.
This enabled us to operate the EMDrive at a wide
frequency range and at power levels comparable
to White et al [3]. However, we chose a cavity input
power of around 10 W compared to 40-80 W by
White et al due to our battery and in order to reduce
thermal load. Nevertheless, the power values in our
setup are also more reliable as we only used a
circulator and one power meter instead of a
directional coupler like White et al, which we found
to produce values that can be significantly off-value
due to reflections from the cavity. The amplifier had
a more or less constant power consumption when
turned on consuming 2.5 A at a battery voltage of
24.6 V. This is more than 60 W and comparable to
White’s input power. The overall power
consumption was even 10% higher taking into
account all other electronics in our setup. All
components are frequency- and temperature-
dependent. Therefore, their characteristics were
evaluated before use and calibrated.
To provide maximum power transfer from the
power generating system into the cavity, it has to
be matched to the 50 Ω wave-impedance coaxial
components. Typically, this matching occurs at a
resonant frequency. Further fine tuning by applying
additional capacitive and inductive parts to the
wave impedance can be realized with a three-stub
tuner. For fast and precise tuning, a single port
Vector Network Analyzer (VNA) Anritsu MS46121A
was used. The EMDrive was matched to a
resonant frequency of 1,914 MHz, which was close
to the 1,937 MHz used by White et al [3]. This
frequency showed a reflection coefficient of about
8
-45 dB and an unloaded Qu factor of approximately
23,000, similar to other cavities as reviewed above.
We scanned from around 1850 MHz to above 2000
MHz and could identify also other resonance
frequencies, however with a lower Qu factor as
shown in Fig. 9.
Thermocouples were used to monitor the thermal
behavior of the amplifier, the fixed attenuator at the
circulator, the RF cables and the cavity near the
emitter antenna. In this way it was possible to
ensure that RF power was fed into the cavity in
resonant mode and to the fixed attenuator at anti-
resonance. The amplifier temperature was logged
to avoid overheating and degradation during
measurements in vacuum.
5. MEASUREMENT SUMMARY
In order not to miss any effect, we decided to
perform a complete sweep from 1850 up to
2000 MHz with a step size of 5 MHz, which
included our tuned resonance frequency, other
resonances and data in between. More
measurements with a smaller step size were taken
close to the resonances. Fig. 10 shows a summary
of this effort, where each data point consists of an
average of three single measurements at the
respective frequency. The plot also shows the RF
input power at the cavity for each frequency step.
To obtain it, we did a separate calibration run by
flipping the circulator such that the output power
from the amplifier was now not going into the cavity
but directly into our power meter. This value was
reduced by the circulator power measurement
during the regular measurements, which then gave
the real input power to the cavity. We can see that
up to 11 W were going into the cavity at the same
resonance frequencies as previously identified with
the network analyzer in Fig. 9 and around 4 W
outside the resonances. All thrust values were
below 3020 nN.
From Eq. 1 we would have expected around 1 mN
using a design factor of 0.56 calculated from our
used geometry, which is around 5 orders of
magnitude above our measurements. Following
the data from White et al [3], we would have
expected at least some 10 µN, which is still
three orders of magnitude above our data.
However, such a value is similar to the false-
positive thrust that we have seen due to thermally
induced mechanical stress on the balance in
Fig. 6b. Taking the 11 W for our photon force
benchmark, this translates into 36 nN as indicated
by the shaded region in Fig. 10. Therefore, our
measurements show, that any anomalous thrust
from an EMDrive must be on the order of or below
the photon thrust limit. Considering that the
amplifier alone required 60 W of power, the limit
raises up 200 nN, which is an order of magnitude
above our data.
Fig. 11 shows the detail of a single frequency
measurement close to our tuned resonance at
1,912 MHz together with the current that goes into
the amplifier to see when power was on. We also
see that the temperature on the amplifier raises by
around 5 degrees, which can cause thermal drifts,
shifts in the center of gravity and related issues as
evaluated above. Only the correct mounting of the
thruster package enabled us to get rid of these
issues to reach the photon thrust sensitivity.
Although some measurements were done with a
frequency tracker targeting always minimum
circulator power (=maximum cavity input power),
we found that fixed frequency measurements were
sufficient as the circular power monitor did not
change throughout the measurement.
At last, Fig. 12 shows a thrust-frequency sweep
from the 1,850-2,000 MHz range without taking
individual profiles but by quickly scanning through
all frequencies with very small steps. Again, only
noise and no thrust signal is visible. We repeated
the same measurement by using a 300 Hz square
wave to switch the amplifier on/off as suggested by
Shawyer [9] without seeing any change. We also
tested this pulse modulation with our false-positive
signals and saw that the thrust decreased by about
a factor of two consistent with the fact that in this
case the average power going to the cavity was
reduced by the same amount. Also the claimed
necessity of a pre-load was present in our setup as
we did use torsion springs similar to the linear
springs used in all setups by Shawyer [15]–[17].
6. CONCLUSION AND OUTLOOK
We did a thorough assessment of previous
measurements on the EMDrive and tested different
balances and mounting options to identify the most
critical measurement artefacts that can create
false-positive thrust signatures, which can even
pass consistency checks like being dependent on
the orientation of the thruster on the balance.
Finally, the development of an inverted
counterbalanced double pendulum with bearing
mounting and the assembly of a battery-powered
EMDrive inside a sufficiently large vacuum
chamber eliminated all mostly thermal-induced
drifts as well as magnetic interaction. This allowed
reaching a sensitivity equivalent to the force
produced by the power going into the EMDrive and
being radiated in a single direction like state-of-the-
art propellant propulsion.
9
Our measurements span over a wide frequency
range including at least three resonances and off-
resonance regions. Although geometry,
resonance frequency, Q-factors and power values
were similar compared to data published by White
et al [3], our measurements limit any anomalous
thrust three orders of magnitude below their
claimed values. All data stayed within the limit of
classical radiation pressure propulsion, which puts
strong limits on all theories that were proposed in
support of the EMDrive.
Future work will concentrate on a superconducting
cavity as suggested previously by Shawyer [9],
which should boost the Q factor by many orders of
magnitude in order to explore any anomalies also
in this regime.
7. ACKNOWLEDGMENT
We gratefully acknowledge the support for
SpaceDrive by the German National Space Agency
DLR (Deutsches Zentrum fuer Luft- und
Raumfahrttechnik) by funding from the Federal
Ministry of Economic Affairs and Energy (BMWi) by
approval from German Parliament (50RS1704).
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Table 1 Summary of Past Experiments and Comparison to this Work as well as the Photon Thrust Limit
Reference
Dielectric
Power
Source
Frequency
[MHz]
Qu Factor
Cavity
Power
[W]
Thrust [µN]
T/P Ratio
[µN/W]
Shaywer [15]
Yes
Magnetron
2,450
2,500-5,900
850
10,000
12
Shaywer [16]
No
Magnetron
2,450
19,521
744
82,000
110
Shaywer [17]
No
TWTA
3,850
55,172
300
100,000
326
Yang [20]
No
Magnetron
2,450
N/A
230
<700
<3
Brady [22]
Yes
Solid State
937
N/A
28
22.5
0.8
White [3]
Yes
Solid State
1,937
7,123 (loaded)
40-80
30-130
1.2
Sokoloff [24]
No
Solid State
2,450
3,550
200
<5,000
<25
Peyre [25]
No
Solid State
2,450
18,500
150
<100
<0.7
Tajmar [26]
No
Magnetron
2,450
50
700
<20
<0.03
Tajmar [6]
No
Solid State
1,865
20,000
2
<1
<0.5
This work
Yes
Solid State
1,914
23,000
11
<0.03±0.02
<0.003±0.002
Photon Thrust
0.0033
11
Fig. 1 Schematic Illustration of Inverted Counterweight Double Balance and Position in Vacuum Chamber
Fig. 2 Balance Calibration
Fig. 3 Thrust Noise Example
Fig. 4 Example of Thermal Drift Compensation
and Sector Classification (I,V..Off, II..Ramp Up,
III..On, IV..Ramp Down)
-3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Commanded Force [µN]
Measured Displacement [µm]
Consecutive Measurements
Linear Regression
Linear Fit y = a + b*x
Calibrati on-Factor 1.55265 ± 0.0011
Unit µN/µm
Correlation Coeff .
R² 0.99992
Identification of the Calibration-Factor
010 20 30 40 50 60 70 80 90 100 110 120 130 140 150
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6 Measured Displacement
Commanded Force
Time [s]
Force [µN]
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Identification of the Calibration-Factor (± 0.45µN ; 0.05µN Steps)
015 30 45 60 75 90 105 120 135 150
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
Thrust [nN]
Time [s]
EMDrive - Thrust Balance Noise (85 Profiles)
020 40 60 80 100 120 140
-10
-8
-6
-4
-2
0
2
4
6
8
10 I
Thrust-Balance Drift
Thermal Drift Removed
Time [s]
Thrust [nN]
Thermal Drift Removal
IVII III V
12
Fig. 5 Different Mounting Configuration of EMDrive on Thrust Balance (A..On Cage, B..On Top of Platform,
C..Hanging from Bolt Bearing)
a.) Comparison between Mounting Options A-C
b.) Option A with Mechanical Fixation of Cavity on
Cage
Fig. 6 False-Positive Thrust Signals
Fig. 7 EMDrive Cavity Dimensions with Two HDPE Dielectric Discs (Shaded Region)
050 100 150 200 250 300
0.0
0.5
1.0
1.5
2.0 Force - Cage Mount (A)
Force - Cavity On Top (B)
Force - Bearing (C)
Amplifier Current - Cage Mount (A)
Amplifier Current - Cavity On Top (B)
Amplifier Current - Bearing (C)
Time [s]
Thrust [µN]
EMDrive - Mounting Comparison
0
1
2
3
4
Current [A]
050 100 150 200 250 300
0
5
10
15
20
25 Force - Mechanical Fixation (A)
Amplifier Current - Mechanical Fixation (A)
Time [s]
Thrust [µN]
EMDrive - Mechanical Fixation between Cavity and Thrust Balance
0
1
2
3
4
Current [A]
13
Fig. 8 Electrical Setup
1850 1875 1900 1925 1950 1975 2000 2025 2050
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
1500
250
S11 [dB]
Frequency [MHz]
Q3dB=3400
Reflection Coefficient
23000
Fig. 9 Reflection Coefficient Measurement
14
Fig. 10 Measurement of Thrust Spectrum in Steps of 5 MHz, Each Measurement is an Average of Three
Single Runs (Photon-Thrust Limit Equals to 11 W Maximum Input Power)
Fig. 11 Thrust Measurement at Fixed Frequency 1912 MHz
Fig. 12 Thrust-Frequency Sweep
1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
-100
-80
-60
-40
-20
0
20
40
60
80
100
Thrust - EMDrive [nN]
RF Input Power* [W]
Photon-Thrust-Limit [nN]
Frequency [MHz]
Thrust [nN]
* Measured at Circulator Forward minus Reverse Position 0
1
2
3
4
5
6
7
8
9
10
11
12
Power [W]
EMDrive - Thrust Spectrum
050 100 150 200 250 300
-100
-80
-60
-40
-20
0
20
40
60
80
100
Thrust [nN]
Force - EMDrive
Amplifier Current [A]
Temperature [°C]
Time [s]
EMDrive - Fixed Frequency 1912 MHz
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Current [A]
44
46
48
50
52
54
56
58
Temperature [°C]
050 100 150 200 250 300
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0 EMDrive Force - Pulsed Frequency Sweep (300Hz)
EMDrive Force - Frequency Sweep (0Hz)
Frequency Sweep
Time [s]
Thrust [µN]
EMDrive - Frequency Sweeps Pulsed/Not-Pulsed
1840
1860
1880
1900
1920
1940
1960
1980
2000
Frequency [MHz]
