# Experimental Results

## Forces, Power, Frequency, Mode shapes, Testing Conditions (ambient or partial vacuum) and Dimensions

The current best estimates for the parameters of various test articles run by public research institutions (NASA Eagleworks), universities (California State Univ., Physics Dept., Fullerton, USA; Northwestern Polytechnical University, College of Aeronautics, Xi'an, China), very small private companies (SPR Ltd., Cannae LLC.), and independent engineers/researchers, is here, along with the reported forces. Note that complete dimensions are not known in most cases, and some had to be determined via indirect methods (e.g., for Shawyer's Exp. and Demo, from the big diameter and the Design Factor, scaling from photographs, from Yang's frequency vs. dimension figures, etc.). See Building for details on drives built by do-it-yourselfers.

Credit to Dr. Rodal and others for the great effort in compiling these. Please note some caveats for this data, at that link.

Description Mode Shape[1] Pressure (Torr)[2] Cavity Length (m) big diameter (m) small diameter (m) sphrcl. r1 (m)[3] sphrcl. r2 (m) [3] cone 1/2 angle (deg) [3] Shawyer Design Factor[4] Dielectric Frequency (GHz) Input Power (W) Q [5] Force (mN) Force / PowerInput (mN/kW) Force/Power Multiple of Photon Rocket
Cannae LLC, G. Fetta, Superconducting[6] Ambient 0.03 0.220 0.200 0.316 0.348 18.43 n/a None 1.047 10.5 1.1*10^7 8-10 761.9 - 952.4 228400 - 285500
SPR Ltd, R. Shawyer, Experimental TM01p [7] Ambient 0.156 0.16 0.1025 0.2828 0.4414 10.44 0.497 [8] relative permittivity =38 2.45 850 5900 16 18.82 5640
SPR Ltd, R. Shawyer, Demonstration TE012 [7] Ambient 0.317 to 0.187 [9] 0.28 0.14921 0.2260 0.4241 19.28 0.844 None 2.45 421-1200 45000 102.30 80-243 23980 - 72830
SPR Ltd, R. Shawyer, Flight Thruster (Boeing project) TE013[10] Ambient 0.1386 [10] 0.2314[10] 0.1257[10] 0.1764 0.3247 20.87 0.635[10] None 3.85 426 (for Max. Force) 50,000 to 60,000[11] Max=174 235-408, Mean=326 Mean=97700
NASA Brady, White, March, Lawrence, and Davies, a [12] TM212 [13] Ambient 0.2286 0.2794 0.15875 0.3111 0.5475 14.78 extruded HDPE relative permitt. =2.26@1-3GHz 1.9326 16.9 7320 0.0912 5.40 1620
NASA Brady, White, March, Lawrence, and Davies, b [12] TM212 [13] Ambient 0.2286 0.2794 0.15875 0.3111 0.5475 14.78 extruded HDPE relative permitt. =2.26@1-3GHz 1.9367 16.7 18100 0.0501 3.00 899
NASA Brady, White, March, Lawrence, and Davies, c [12] TE012 Ambient 0.2286 0.2794 0.15875 0.3111 0.5475 14.78 extruded HDPE relative permitt. =2.26@1-3GHz 1.8804 2.6 22000 0.0554 21.3 6390
NASA Brady, White, March, Lawrence, and Davies, p.18, Section IV.F[12] [14] TE012 Ambient 0.2286 0.2794 0.15875 0.3111 0.5475 14.78 None 2.168 30 0 0 0
NASA March et.al. TM212 [15] 5*10^(-6) 0.2286 0.2794 0.15875 0.3111 0.5475 14.78 extruded HDPE relative permitt. =2.26@1-3GHz 1.9371 50 6726 0.055 1.10 330
NASA March et.al. reversed 180 degrees [15] TM212 5*10^(-4) 0.2286 0.2794 0.15875 0.3111 0.5475 14.78 extruded HDPE relative permitt. =2.26@1-3GHz 1.9372 35 0.0099 0.283 84
NWPU Prof. Juan Yang et.al.[16] TE012 Ambient 0.24 0.201 0.1492 0.6953 0.9367 6.159 0.664 None 2.45 150 1531[16] 160 1070 320000
NWPU Prof. Juan Yang et.al.[17] TE012 Ambient 0.24 0.201 0.1492 0.6953 0.9367 6.159 0.664 None 2.45 300 1531[16] 270 900 270000
Iulian Berca Tests 3 & 3.1 (averaged w/up/down directional effects subtracted) [17] TM212[18] Ambient 0.2286 0.2794 0.1588 0.3113 0.5477 14.78 0.515 None 2.45 800 2.3 2.8 850
Baby EM Drive, @movax (Paul Kocyla) and Jo Hinchliffe TE013 Ambient 0.02437 0.0296 0.01612 0.03024 0.05552 15.46 0.7311 None 24.1 0.04 ~ 0 ~ 0 ~ 0
California State Univ., Fullerton, Fearn, Zachar, Woodward & Wanser - piezoelectric MET thruster[19] n/a Partial Vacuum ? n/a n/a n/a n/a n/a n/a n/a 3.93*10^(-5) 170 22000 0.002 0.01176 3.526
Ad Astra VASIMR VX-200 with argon propellant [20] n/a Partial Vacuum ? n/a n/a n/a n/a n/a n/a n/a n/a n/a 200,000 n/a 5700 28.5 8500

n/a = Not applicable

Environmental pressure unit: 1 Torr = $\cfrac{1}{760}$ of a standard atmosphere. [18]

Atmospheric pressure in low Earth orbit ("LEO") = 5x10^(-8) to 10^(-10) Torr [19]

Pressure in outer space between stars in the Milky Way = 10^(-17) Torr [20]

### Comparison to a Photon Rocket

For a perfectly-collimated beam photon rocket, without the benefits of a resonant optical cavity [21], for example a military searchlight acting as a photon rocket (see: [22], [23] [24]), the force per power input is as follows:

Photon Rocket Force / PowerInput (mN/kW) = 0.003337

This represents the force/PowerInput exerted by the radiation pressure of light in free space, which is not the same as the forces and momentum imparted to a massive object [25]. If the results above are validated, the EM Drive would greatly exceed that ratio. However, this does not imply that an EM Drive could achieve steady constant acceleration for constant power input, as this is prevented by energy conservation (see: [26])

## Notes and references

1. Mode shapes for the EM Drive truncated cone geometry are given according to the closest mode shape for a cylindrical geometry, instead of given by the eigenparameters of the truncated cone eigensolution (for example, using the wavenumber). The reason for this is two fold: 1) There is no standard convention on how to number mode shapes for a truncated cone, and 2) the truncated cone geometry used by the EM Drive researchers has been close to a cylinder: the cone angles have been relatively small. Therefore the mode shapes resemble those of a cylinder. TM means "transverse magnetic": a mode shape where the magnetic field is in the azimuthal, solenoidal direction and the electric field is in the transverse and longitudinal direction. TE stands for "transverse electric": a mode shape where the electric field is in the azimuthal, solenoidal direction and the magnetic field is in the transverse and longitudinal direction. The subscripts m,n,p in TMmnp and TEmnp, stand for the mode shape quantum numbers in the azimuthal (m), transverse (n) and longitudinal (p) directions respectively.
2. This field denotes whether the test was performed in ambient conditions (hence the field labeled as "Ambient") or in a partial vacuum. When the researcher has provided the pressure in the partial vacuum condition, this is given in the units of Torrs.
3. The cavity dimensions in a spherical coordinate system as shown here:

The bases of the truncated cone used in the experiments are flat, so in the spherical geometry the flat base is described by the secant to the circular arcs joining the intersections between the circular arcs and the lateral walls of the cone.
4. Shawyer's Design Factor, when not provided independently (for example by Shawyer in his pubblications) was calculated for cavities without dielectric inserts with TM010 as the cutoff frequency for TM01p modes, with TE010 for TE01p modes and TM210 for TM21p modes. For cavities with a dielectric insert it is not calculated.
5. Quality factor of resonance: a dimensionless measure inverse to damping: the higher the Q, the lower the damping. Infinite Q corresponds to zero damping. Critical damping occurs for a value of Q = 1/2.[1]
6. Test conducted in January 2011 by G. Fetta, with a completely different shape from the other EM Drives: this is not a truncated cone, but instead it is shaped like a pillbox with a circular cross-section. Results were posted in the Cannae webpages. Page is no longer available, but an archived version as of 2 November 2012 is available at archive.org:[2]. A better description is available in this US Patent Application [3]
7. Based on Shawyer's patent applications and papers at the time or prior to the time of this Experimental test, and the fact that it used a dielectric that could benefit from an axial electric field, it looks like the mode shape for this test may have been TM01p where the value of p is unknown. This is also supported by the Design Factor reported by Shawyer as only 0.497 which appears to be based on TM010 cut-off, as a TE010 cutoff would result in a higher Design Factor based on the published photographs and therefore the relative dimensions of the Experimental EM Drive. Depending on the size and location of the dielectric, but most likely p was either 2 or 3 based on the dimensions of the Experimental EM Drive Cite error: Invalid <ref> tag; name "Shawyer_Demonstrator" defined multiple times with different content
8. UK Patent Application GB 2 334 761 A, date of publication 01.09.1999, application No 9809035.0, date of filing 29.04.1998
9. The cavity length is estimated as 0.317 to 0.187. The larger number takes into account the full length of the cylindrical part of the EM Drive Demo and the smaller number corresponds only to the length of the truncated cone section. Please notice that the Demo has a variable length actuated by a gear mechanism, in order to tune the cavity to achieve resonance
10. See these posts by TheTraveller on dimensions of the Flight Thruster[4] and [5] and [6]. Cite error: Invalid <ref> tag; name "Shawyer_Flight_Thruster_Dimensions" defined multiple times with different content Cite error: Invalid <ref> tag; name "Shawyer_Flight_Thruster_Dimensions" defined multiple times with different content Cite error: Invalid <ref> tag; name "Shawyer_Flight_Thruster_Dimensions" defined multiple times with different content
11. Second-hand information: TheTraveller reports that Roger Shawyer communicated this value of Q to him in personal exchanges[7]
12. "Anomalous Thrust Production from an RF Test Device Measured on a Low-Thrust Torsion Pendulum" AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 28-30, 2014,[[8]
13. Mode shape is noted as TM211 in Brady et.al.'s report. However, calculations show that TM211 should take place at a significant lower frequency and that this mode must have been TM212. Notice that Brady et.al. b took place practically at the same frequency as March TM212 test in vacuum
14. The Brady et.al. report reads: <<We performed some very early evaluations without the dielectric resonator (TE012 mode at 2168 MHz, with power levels up to ~30 watts) and measured no significant net thrust.>>. The test was performed at the very earliest in Brady et.al.'s testing program. The test was performed without a magnetron, only using the 25W Mini-Circuit Amp, since at the time of this particular test, NASA Eagleworks did not have the PLL circuit running for this data run. Brady et.al. do not provide the Q quality factor of resonance for this test. @TheTraveller made an argument that the test may have been conducted at the wrong (too low) frequency for resonance [9] [10].
15. This test is the only reported test that has verified the mode shape with experimental measurements. A thermal camera was used that showed the same temperature profile as predicted from induction heating resulting from mode shape TM212
16. Q calculated from Fig.5 "frustum microwave cavity actual resonance curve"of "Net thrust measurement of propellantless microwave thrusters", 2011, where Frequency Bandwidth=0.0016GHz, Frequency=2.45 GHz, hence Q=2.45/0.0016=1531. This is the value of Q calculated according to the convention in the West. See definition of quality factor Q [11]. Notice that Prof. Yang reports different values in her tables because of her different convention.
17. See http://www.masinaelectrica.com/emdrive-independent-test/. Because of the high profile nature of the tests, they are included here merely to give a rough comparison to the more scientifically rigorous tests. The measured thrust in this table is an average of multiple runs in tests 3 and 3.1, subtracting out the likely effects of hot air. @deltaMass calculated the net thrust for the EmDrive across both test. See [12].
18. Iulian Berca used the same dimensions as NASA's truncated cone, but without a dielectric. Mode shape is predicted to be TM 212 according to NASA's COMSOL FEA analysis 2/6/2014 by Frank Davies NASA/JSC/EP5 (2.458 GHz) and to Rodal's exact solution calculation (2.423 GHz). Actual mode participation depends on the spectrum of frequencies excited by the magnetron, the geometrical placement of the RF source in the EM Drive, and the number of eigenfrequencies in and near the magnetron's spectrum
19. [13]Forum post by @Rodal - Included here because Prof. Woodward's device is also a propellant-less concept, and because Paul March (NASA) maintains that Prof. Woodward's Mach Effect theory might also be, in his opinion, an explanation for thrust for the EM Drive.
20. Ad Astra VASIMR is not a propellant less rocket, it is a magnetoplasma engine that uses argon propellant, but it is included here for comparison purposes, See:[14]