Investigation of Anomalous Thrust from a Partially Loaded

Resonant Cavity

By Kurt Zeller and Brian Kraft

California Polytechnic State University, San Luis Obispo, CA

Over a span of four months a number of tests were conducted in an attempt to prove the validity of the EM

Drive as a form of spacecraft propulsion. This experiment focused on the hypothesis that an asymmetric

resonance is required to produce thrust from an EM Drive. Utilizing a portion of the $4200 secured through

proposals to the Cal Poly Connect and Aerospace Student Fees Committees, a thrust measurement apparatus

was constructed with an accuracy of approximately ± 0.5 mN. Three dimensional finite element simulations

were performed to aid in the design of a partially loaded, cylindrical cavity. These designs were then verified

empirically using a Vector Network Analyzer and a mock magnetron antenna. Displacements were observed

corresponding to a calculated axial force of 2.4 mN. However, unexpected perpendicular displacements were

simultaneously observed which may be the result of spurious effects. Further funding is required to refine

and improve upon the experimental apparatus outlined in this document.

Nomenclature HDPE = High Density Polyethylene NSF = National Aeronautics and Space Administration Space Flight Forums PSD = Position Sensing Device Q = Quality Factor VNA = Vector Network Analyzer VSWR = Voltage Standing Wave Ratio

I. Introduction

A novel propulsion technology has been investigated at several institutions which utilizes an electromagnetic

resonant cavity to produce thrust without ejecting propellant. Several highly regarded institutions as well as a

variety of independent experimenters have observed thrust to varying degrees of success. The anomalous thrust has

not been fully explained within the current understanding of physical laws and should be further investigated.1-6

An experiment was developed to investigate the results observed using a symmetric cylindrical cavity partially

loaded with several different dielectrics. A microwave oven magnetron was used to provide the cavity with

approximately 950 W of RF power. A low thrust measurement apparatus was developed using a pendulum, laser,

and position sensing detector. This apparatus achieved a deflection resolution of 15-30 micrometers which

corresponded to a force resolution of 0.5 mN for a 3.315 kg pendulum.

Resonant positions were determined using a Vector Network Analyzer and results were compared with

computational simulations. The best resonance obtained using the cylindrical cavity had a reflection coefficient of

0.05% at the central frequency and a quality of 306. The wide bandwidth and sporadic nature of the output signal

made it difficult to resonate the cavity effectively. Reflected power from frequencies beyond the bandwidth of the

cavity may have caused severe arcing inside the magnetron resulting in an unstable output.

II. Project Description

A. Background

The main requirement for an EM Drive, as proposed by previous experimenters, is that it contains an

asymmetric, electromagnetic resonance. The asymmetry is thought to be required in order to create a momentum

differential which will result in a net 'thrust'. Maintaining resonance is required to amplify the energy that is put into

the system. This concept is analogous to a vibrating string whose amplitude can be built up over successive inputs at

a particular frequency. The amount of amplification a resonant cavity can provide is a function of its quality which

depends primarily on the inside surface finish. An asymmetric resonance can take on a variety of mode shapes

which can be described using the conventional cylindrical notation (TE or TM nml). Many have argued that thrust

without mass ejection cannot satisfy conservation of momentum, but experimental results refute this claim.

Furthermore, Dr. White's hypothesis that the EM Drive may be pushing off of quantum vacuum fluctuations has yet

to be disproven.

B. Cylindrical Design

For this experiment, a partially filled, symmetric, resonant cavity was utilized to create an asymmetric

resonance in the axial direction. The advantages of this design over the typical EM Drive frustum shape are

simplicity, adjustability, and power delivery. The first patent published by Roger Shawyer in 1988 consists of a

cylindrical cavity partially filled by a cone-shaped dielectric as seen in Fig. 1.

Figure 1. Roger Shawyer 1988 Patent Design

7. The triangular region on the left side of the cavity is a 2-

dimensional representation of the conical dielectric insert.

Several design iterations were made and the resulting product can be seen in Fig. 2, 3 and 4. This design

features a conducting rod which controls and internal movable plate with a removable dielectric attachment. The

cylindrical cavity has two end adapters welded around the circumference to allow plate attachments for the rod

guide, suspension connection, and magnetron mount. Subsequent VNA testing resulted in a change to the magnetron

mount (not pictured) which will be further discussed. One advantage of this design is that it allows the dielectric to

be spun inside the cavity, thus changing the screw location and the shape and quality of resonance. It was later

discovered that asymmetry could have resulted in a transverse thrust.

Figure 2. Final Cylindrical Design.

Figure 3. Expanded View of the Movable Plate for the Final Cylindrical Design. This picture shows the

interconnections between different components in the movable plate system.

Figure 4. Expanded View of the Magnetron Input for the Final Cylindrical Design. This picture gives a better

representation of the coupling between the magnetron and the cavity.

The frame seen in Fig. 5 was designed so that it could fit in the Student Vacuum Chamber in the Spacecraft

Environments Laboratory at Cal Poly. Later considerations revealed complications with the magnetron inside the

chamber as well as with deflection measurements, therefore this setup was never attempted. L brackets (not

pictured) were also used to secure each leg to the vibrationally isolated optics table.

Figure 5. Student Vacuum Chamber Pendulum Design. This view shows how the cavity is suspended

from the frame in order to form a single pendulum system.

C. Apparatus Calibration

The final apparatus can be seen in Fig. 6. A calibration pulley was used to induce a known force in the axial

direction to measure displacement. A PSM2-10 position sensing device was used in conjunction with an OT-301

amplifier to determine the deflection of a laser. There is an origin for the PSM2-10 and all deflections are measured

relative to this point. A voltage is output by the PSM2-10 and this signal is then amplified by the OT-301 and sent to

a DSO-X 2002A oscilloscope for data acquisition. The higher the voltage seen on the oscilloscope the farther the

laser is from the center of the PSM2-10. Amplifiers can degrade over time therefore prior pendulum testing, the

linearity of the OT-301 amplifier was verified.

Figure 6. Picture of Experimental Setup. The different components of the entire experimental setup are depicted

here, notice the red and black wires used to deliver power to the cavity as well as the blue wire that was used for

grounding purposes.

For this procedure the PSM2-10 was placed on one end of the optics table and a 9 V DC 650 nm laser was

fixed to a micrometer at the opposite end. After recording an initial reading, the position of the laser was

incremented through ± 2 V in both the x and y dimensions. Readings were taken at 50 mV measurement divisions as

well as some at 100 mV divisions. After each increment a data run containing the average and peak to peak voltage

was recorded on the oscilloscope for further analysis in Matlab. After a large number of test runs the data was

plotted and the linearity of the amplifier was examined. Overall the device showed very high linearity and it was

determined that 1V corresponds to almost exactly 1 mm of deflection. After verification of the linearity of the OT-

301, the EM Drive was placed on the pendulum and the effective resolution of the test rig was verified. Fig. 9 shows

the mirror fixture on the back of the pendulum which was used to reflect the laser beam.

Figure 9. Detailed Shot of Laser Measurement System. PSM2-10 is labelled as the PSD in this picture

and the white, 9 V DC, 650 nm Laser can be seen at the bottom of the picture.

The typical noise in both the x and y axes was measured and it was determined that ± 2.5 mV for the x axis

and anywhere from ± 7.5-20 mV for the y axis was common for this setup. Afterwards, the pulley system was setup

to determine the accuracy of the equations derived in Appendix B. After connecting the pulley the average noise

increased significantly. This is likely due to the fact that the pendulum on the other side of the pulley couples with

the test rig pendulum to form a double pendulum system. The noise due to spurious effects such as air currents are

therefore amplified and the average noise on x and y axis was ± 20 mV and ± 40 mV respectively.

Initial runs were done using string and a 500 mg (4.9 mN) weight. The calculated force was of the same

order of magnitude as the expected force from the weight, however the percent error between the two values was

substantial for multiple test runs. The calculated thrust relies heavily on the accuracy of the dimensions that are

utilized in the displacement equation, therefore it is likely that small errors in each measurement could have resulted

in a large compounded error value. If the dimensions in the equation are varied by the associated tolerances a

solution can be obtained that corresponds to the appropriate expected thrust value. A graph of the y displacement

can be seen below in Fig. 10.

Figure 10. Y Displacement for a 500 mg Weight. This graph depicts the y displacement before and after the

weight is placed on the pulley. The pink line is the average voltage before the weight was added. The blue line

represents the average voltage after the weight is added.

Further test runs were conducted with a 200 mg and 100 mg weight. The results for these test runs are shown in Fig.

11 and12. It is worth noting that more than ten calibration test runs were performed to ensure consistent results.

Figure 11. Y Displacement for a 200 mg Weight. This graph depicts the y displacement before and after the

weight is placed on the pulley. The pink line is the average voltage before the weight was added. The blue line

represents the average voltage after the weight is added.

Figure 12. Y Displacement for a 100 mg Weight. This graph depicts the y displacement before and after the

weight is placed on the pulley. The magenta line is the average voltage before the weight was added. The blue line

represents the average voltage after the weight is added, and the green lines depict the peak-to-peak.

In Fig. 13 and 14 it is clear that the equations developed to calculate force from deflection are much more

accurate at small forces. Various different assumptions and small errors in measurement techniques are likely the

cause of the inconsistencies of the thrust prediction equations. This is a large area of concern and will need to be

further examined before more testing can occur.

Figure 13. Comparison of Different Thrust Measurement Equations for Large Forces. Three different equations

were derived for thrust measurement. The BK Force Eq. is the exact solution for thrust as a function of deflection

while the KZ Force Eq. and BE Force Eq. both utilize some form of small angle approximations.

Figure 14. Comparison of Different Thrust Measurement for Small Forces.

D. Magnetron Antenna

In order to find positions of resonance, an antenna was used to mimic the output power distribution of the

magnetron. First, a sacrificial magnetron was torn open to discover the optimal method of connection to the center

tap wire as seen in Fig. 15. This wire connects the inner resonant cavity of the magnetron to the tip of the antenna

for power output. Next an identical Galanz M24FB-610A was carefully cut open and the tap wire was detached from

the internal spokes of the magnetron so that the length of wire remained the same. The resulting magnetron antenna

can be seen in Fig. 16. Although professionally made antennas exist, this proved to be a cost effective method for

emulating the output power distribution.

Figure 15. Deconstructed Magnetron Cavity with Labels. Here the inner cavity of the magnetron can be seen,

this section is surrounded by the heat sinks and magnets in the intact magnetron at the top of the picture.

Figure 16. Magnetron Antenna for Resonance Testing. This antenna consists of the top ceiling of the magnetron

cavity shown in Fig. 15 as well as the actual magnetron antenna. An SMA connection was soldered to the central

wire of the magnetron for VNA testing.

E. VNA Testing

One of the biggest challenges associated with creating an EM Drive is obtaining resonance. A Vector

Network Analyzer (VNA) was utilized to measure frequencies of resonance inside the cylindrical cavity. The

internal plate was moved axially and spun azimuthally until the VNA displayed a resonance within our magnetron's

bandwidth (2450 MHz ± 30 MHz).

Initial resonance testing seen in Fig. 17 revealed that a waveguide delivery mechanism would be necessary

to improve the reflection from -10 dB to at least -30 dB. This was achieved by cutting out the delivery waveguide

used on the Hamilton Beach Microwave Oven where the Galanz was taken from. This resulted in a solid connection

between the magnetron and waveguide as well as the desired reduction in reflected power.

Figure 17. Picture of Experimental Setup for VNA Testing. The VNA can be seen on the left side of the picture,

which was attached to the desktop computer for data acquisition

An attempt was made to balance the energy reflected with the energy amplified in order to create a system

that didn't destroy the source but still amplified the energy enough to see thrust. Several design iterations were

introduced including a rough and polished inner surface as well as many types and thicknesses of dielectric. The

highest quality resonance observed seen in Fig. 18 was achieved using three dielectrics in series from least to

greatest dielectric constant: HDPE, Plexiglas, and Nylon. Unfortunately the polarity of Nylon causes it to heat

dramatically under RF power therefore it was unsuitable for future experiments.

Figure 18. S11 Plot for a Partially Loaded Resonator with HDPE, Plexiglas and Nylon Inserts. Point 4 denotes

the central frequency of the magnetron while point 2 and point 1 are the lower and upper limits of the bandwidth of

the signal. There is a -3 dB offset of the plot in order to better asses the quality of the resonance.

This resonance is perfectly situated at the central output frequency of the Galanz magnetron. A reflection of

-33 dB equates to 0.05% of the power at this frequency will be reflected back to the source. The half power

bandwidth of this resonance is approximately 8 MHz resulting in a quality of 306.25. (quality = central frequency

over-3 dB bandwidth) Although in practice resonant cavities can reach qualities in the tens of thousands, a quality of

that magnitude would reflect nearly all energy back into the magnetron. The Smith Chart in Fig. 19 depicts how well

the impedance is matched over the frequency range. Point 4 is within milliohms of the desired 50 Ohm perfect

match. Subsequently, points 2 and 3 are very far from matched which leads to an acceptable quality.

Figure 19. Smith Chart for a Partially Loaded Resonator with HDPE, Plexiglas and Nylon Inserts. Point 4

corresponds to the position of resonance shown in Fig. 18. The distance between Point 4 and the number one

located on the dotted central axis denote a well impedance matched resonance.

In this experiment, the quality was severely limited by the magnetron's output. Because the output has a

relatively wide bandwidth and can be unstable, it is difficult to pair this source with a high quality cavity on the

order of 20,000. A significant portion of the energy delivered to this cavity would be rejected back into the

magnetron which could potentially be damaging. On the other hand, a low quality on the order of 50 would accept

the entire bandwidth of the magnetron (as done by Tajmar et al5) but would do little to amplify the energy. Fig. 18

depicts the bandwidth of the resonator and one can clearly see that this sharp position of resonance can not accept all

of the power that is produced across the magnetron's bandwidth. Points 2 and 3, corresponding to the upper and

lower limits of the signal, are well beyond the bandwidth of the resonator.

F. EM Pro Verification

A different resonance using only HDPE was further analyzed in EM Pro to compare the validity of

computer simulations to actual experimental results. Fig. 20 shows the S11 output from EM Pro which matches

exceedingly well to the S11 plot obtained using the VNA seen in Fig. 19. The slight difference in central frequency

can be attributed to the differences in excitation. In order to model the system in EM Pro, a 1 W modal power feed

plane wave excitation was created at an input port identical to the opening of the microwave oven waveguide as seen

in Fig. 21.

Figure 19. S11 Plot for a Partially Loaded Resonator with HDPE. Point 1 denotes the central frequency of the

magnetron while point 2 and point 3 are the lower and upper limits of the bandwidth of the signal. There is a -3 dB

offset of the plot in order to better asses the quality of the resonance.

Figure 20. Simulated S11 Chart for a Partially Loaded Resonator with HDPE. This plot can be compared to the

experimental results in Fig. 19.

Figure 21. Depiction of the Plane Wave Excitation used to Simulate the Magnetron Source. The color bar in

this picture is used to depict the strength of the electric field at the input to the cavity. Red corresponds to a strong

electric field while the yellow areas indicate a weaker electric field.

The Smith Chart in Fig. 22 exemplifies this source difference and shows that in input impedance around the

central frequency varies dramatically between the plane wave excitation and the magnetron antenna. This is most

likely due to the difference in location that the impedance is being measured.

Figure 22. Simulated Smith Chart for a Partially Loaded Resonator with HDPE Inserts. This plot can be

compared to the experimental results seen in Fig. 19.

In Fig. 23 and 24 we can see each figures' respective electric and magnetic field lines with their

corresponding magnitudes and directions. Notice that the strength of the electric field is about three orders larger

than the strength of the magnetic field. This is partially due to an excitation of a transverse magnetic mode which

orients the electric field in the axial direction.

Upon further inspection it can be seen that both fields are compressed within the dielectric due to the high

dielectric constant. This is a key feature of the asymmetric resonance that seems key to producing thrust. The

surface currents can be seen in Fig. 24, which correspond to the associated electric fields. The concentration of

surface currents highlights a key problem with the movable plate design. Due to a lack of connection between the

movable plate and cylindrical cavity, arcing often occurred between the closest edges. Once an electrical connection

was established between the internal plate and the cylinder arcing was mitigated.

Figure 23. Simulated Electric Fields for a Partially Loaded Resonator with HDPE Inserts. The transparent red

sections display the outer walls of the cavity while the orange cylinders depict the screws used to fasten the

dielectric. Colored arrows are used to display the magnitude and direction of the electric fields, higher values appear

red or yellow while weaker values appear green or blue.

Figure 24. Simulated Magnetic Fields for a Partially Loaded Resonator with HDPE Inserts. The transparent

red sections display the outer walls of the cavity while the orange cylinders depict the screws used to fasten the

dielectric. Colored arrows are used to display the magnitude and direction of the Magnetic fields, higher values

appear red or yellow while weaker values appear green or blue.

Figure 25. Surface Currents for a Partially Loaded Resonator with HDPE Inserts. Colors are used to display

the magnitude of surface currents, higher values appear red or yellow while weaker values appear green or blue.

G. Results

Although the majority of tests resulted in zero deflection, several tests yielded deflections in both

X and Y directions. All of the Y deflections observed were in the direction of the dielectric, and

corresponded to a maximum calculated force of 2.4 mN. The deflection plots for this force can be seen in

Fig. 26. The source of the X deflection was not definitively proven but there may be several effects taking

place. Because the pendulum mirror was not perfectly aligned in the Y direction, as can be seen in Fig. 9,

some of the Y deflection contributed to X deflection, although the magnitude would be a component of

the Y deflection. However the majority of the X displacement most likely came from an asymmetric flow

of current. The cavity was not electrically sealed therefore the current traveled through the suspension

wires to the table, finding the path of least resistance. On the other hand, there could have been an "EM

Drive effect" in a direction that was misaligned with the cylinder axis due to an asymmetric placement of

the screws.

Figure 26. Maximum X and Y Displacements Observed with 1.675 Inches of HDPE The vertical black lines

indicate where the microwave was turned on and off. This test lasted a duration of 12 second.

Many early tests resulted in dramatic RF interference with the PSD which can be seen in Fig. 27. This interference

was eliminated using microwave absorbing sheets around the PSD.

Figure 27. Example of X and Y Displacements Observed with 0.99 Inches of HDPE This example was chosen to

illustrate the effect of RF interference on the PSD..

III. Conclusion

Further experimentation must be performed to verify or disprove the functionality of the EM Drive.

Although displacements were observed it is difficult to assert that the displacements were caused by the reported

'thrust' or another spurious effect. Asymmetric current flow could be a major factor in the observed data. An

electromagnetic choke could be used in future experimentation to simplify the grounding requirements associated

with movable components. Furthermore, air currents from thermal effects and the air conditioning system had an

impact on the noise of the signal. Future testing will utilize a vacuum chamber to reduce the impacts of air flow. A

new proposal has been prepared which will address some of the issues outlined above as well as improve upon

various parameters including engineering tolerances, VSWR, quality, and most importantly, power delivery.

Implementing these changes will produce an environment where the validity of the EM Drive can be assessed with

high confidence and accuracy.

Acknowledgements

K. Zeller and B. Kraft would like to thank their advisor, Dr. Echols, for his unyielding support. His encouragement

greatly enhanced their dedication to this endeavor. They would also like to thank the participants on the NASA

Space Forum as well as the various manufacturers who have provided great insight into all facets of the previous

experiments as well as this particular campaign.

References

1Brady, D. A, White H. G, March P., Lawrence J.T., and Davies F. J., "Anomalous Thrust Production from an

RF Test Device Measured on a Low-Thrust Torsion Pendulum", NASA Lyndon B. Johnson Space Center, Houston,

Texas 77058, July 2014. 2Juan Y., Yu-Quan W., Yan-Jie M., Peng-Fei L., Le Y., Yang W., and Guo-Qiang H., "Prediction and

Experimental Measurement of the Electromagnetic Thrust Generated by a Microwave Thruster System", College of

Astronautics, Northwestern Polytechnic University, Xi’an 710072, China, Dec 2012. 3Juan Y., Yu-Quan W., Yan-Jie M., Peng-Fei L., Le Y., Yang W., and Guo-Qiang H., "", College of

Astronautics, Northwestern Polytechnic University, Xi’an 710072, China, Dec 2014.

4Shawyer R., "The EM Drive-A New Satellite Propulsion Technology", SPR. Ltd., UK.

5Fetta G., "Numerical and Experimental Results for a Novel Propulsion Technology Requiring no On-Board

Propellant", Cannae LLC., Doylestown PA, 18901, July 2014. 6Tajmar, M., Fiedler, G., "Direct Thrust Measurements of an EM Drive and an Evaluation of Possible Side-

Effects", Institute of Aerospace Engineering, Technische Universität Dresden, 01062 Dresden, Germany. 7Shawyer, Roger. 'Electrical Propulsion Unit For Spacecraft'. 1988

Appendices

A: Investigation and Analysis of Anomalous Electromagnetic Propulsion Devices B: Derivation of Thrust as a Function of Displacement