# 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; TU Dresden, Aerospace Department, Germany, 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<ref name="mode shape definition">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.</ref> Pressure (Torr)<ref name="ambient pressure">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.</ref> Cavity Length (m) big diameter (m) small diameter (m) sphrcl. r1 (m)<ref name="Spherical geometry">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. </ref> || sphrcl. r2 (m) <ref name="Spherical geometry"></ref>||cone 1/2 angle (deg) <ref name="Spherical geometry"></ref> ||Shawyer Design Factor<ref name="design factor">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.</ref> || Dielectric || Frequency (GHz) || Input Power (W) || Q <ref name="Q">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]</ref> || Force (mN) || Force / PowerInput (mN/kW) ||Force/Power Multiple of Photon Rocket

Cannae LLC, G. Fetta, Superconducting<ref name="Cannae">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]</ref> TM010 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 <ref name="Shawyer Demonstrator Mode Shape">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</ref> Ambient 0.156 0.16 0.1025 0.2828 0.4414 10.44 0.497 <ref name="Shawyer Dielectric">UK Patent Application GB 2 334 761 A, date of publication 01.09.1999, application No 9809035.0, date of filing 29.04.1998</ref> relative permittivity =38 2.45 850 5900 16 18.82 5640
SPR Ltd, R. Shawyer, Demonstration TE012 <ref name="Shawyer Demonstrator">Nearest possible mode shape according to NASA's COMSOL analysis[4]. Also, @TheTraveller reported that Shawyer recommended a TE01p mode for the Flight Thruster. (Where p=3 for the Flight Thruster because it is excited at a higher frequency). Also Prof. Yang reports using TE01p modes, and @TheTraveller reports that Shawyer was an initial advisor. </ref> Ambient 0.317 to 0.187 <ref name="Shawyer Demonstrator Length">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

</ref> || 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<ref name="Shawyer Flight Thruster Dimensions">See these posts by TheTraveller on dimensions of the Flight Thruster[5] and [6] and [7]. </ref> Ambient 0.1386 <ref name="Shawyer Flight Thruster Dimensions 2"></ref> 0.2314<ref name="Shawyer Flight Thruster Dimensions 3"> </ref> 0.1257<ref name="Shawyer Flight Thruster Dimensions 4"> </ref> 0.1764 0.3247 20.87 0.635<ref name="Shawyer Flight Thruster Dimensions 2"> </ref> None 3.85 426 (for Max. Force) 50,000 to 60,000<ref name="Shawyer Flight Q">Second-hand information: TheTraveller reports that Roger Shawyer communicated this value of Q to him in personal exchanges[8]</ref> Max=174 235-408, Mean=326 Mean=97700
NASA Brady, White, March, Lawrence, and Davies, a <ref name="Brady et.al">"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,[[9]</ref> TM212 <ref name="brady">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</ref> 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 <ref name="Brady et.al"></ref> TM212 <ref name="brady"/> 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 <ref name="Brady et.al"></ref> 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<ref name="Brady et.al"></ref> <ref name="Brady et.al 2"> 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 [10] [11].</ref> 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 <ref name="Mode Shape verification">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</ref> 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 [12] 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.[13] TE012 Ambient 0.24 0.247 0.114425 0.21102 0.45552 15.44 None 2.45 150 1531<ref name="Q Yang">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 [14]. Notice that Prof. Yang reports different values in her tables because of her different convention.</ref> 160 1070 320000
NWPU Prof. Juan Yang et.al.[15] TE012 Ambient 0.24 0.247 0.114425 0.21102 0.45552 15.44 None 2.45 300 1531<ref name="Q Yang"></ref> 270 900 270000
NWPU Prof. Juan Yang et.al.2016[16] TE012 Ambient 0.24 0.247 0.114425 0.21102 0.45552 15.44 None 2.45 220 1531<ref name="Q Yang"></ref> 0 +/-0.7 0 +/-3.18 0 +/-954
TU Dresden, Tajmar & Fiedler (2015) (torsional balance)<ref name="Tajmar">"Direct Thrust Measurements of an EM Drive and Evaluation of Possible Side-Effects" M. Tajmar and G. Fiedler

51st AIAA/SAE/ASEE Joint Propulsion Conference. See this for explanation of corrected dimensions: [17]</ref>|| TM010||4*10^(-6)||0.072||0.1082||0.077||0.1777 ||0.2497 || 12.51 || ||None||2.44||700||20||0.02||0.0286 || 8.56

TU Dresden, Tajmar & Fiedler (2015) (beam balance)<ref name="Tajmar"></ref> TM010 Ambient 0.072 0.1082 0.077 0.1777 0.2497 12.51 None 2.44 700 48.8 0.1145 0.1636 49.01
Iulian Berca Tests 3 & 3.1 (averaged w/up/down directional effects subtracted) <ref>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 [18].</ref> TM212<ref name="Iulian Mode Shape">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 </ref> 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 ??? 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 <ref>[19]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.</ref> mechanical 1st longitudinal eigenmode 15*10^(-3) n/a n/a n/a n/a n/a n/a n/a n/a 3.93*10^(-5) 170 190 0.002 0.01176 3.526
California Polytechnic State Univ., San Luis Obispo, Zeller, Kraft, Echols <ref>[20]Investigation of Anomalous Thrust from a Partially Loaded Resonant Cavity</ref> TM 012? Ambient 0.180 0.1077 0.1077 n/a n/a n/a n/a HDPE 2.45 900 300 0 0 0
Eugene Samsonov<ref name=NullResultPaper>Samsonov, Eugene (2016), "Null Result for Prediction of Asymmetrical Anomalous Force from Frustum-shaped RF Resonant Cavity"</ref><ref>[21]Frustum dimensions violated Shawyer cut-off criteria at the small end.</ref> TE012 Ambient 0.204 0.264 0.158 n/a n/a n/a 0.77 None 2.3124 30 3100 0 0 0
Eugene Samsonov<ref name=NullResultPaper /><ref>[22]No known violations of Shawyer theory in this test.</ref> TE012 Ambient 0.196 0.264 0.162 n/a n/a n/a 0.69 None 2.331 28 2300 0 0 0
Ad Astra VASIMR VX-200 with argon propellant <ref>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:[23]</ref> 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 = [itex]\cfrac{1}{760} [/itex] of a standard atmosphere. [24]

Atmospheric pressure in low Earth orbit ("LEO") = 5x10^(-8) to 10^(-10) Torr [25]

Pressure in outer space between stars in the Milky Way = 10^(-17) Torr [26]

### Comparison to a Photon Rocket

For a perfectly-collimated beam photon rocket, for example a military searchlight acting as a photon rocket (see: [27], [28] [29]), the force per power input is as follows:

Photon Rocket Force / PowerInput = 1/c = 0.003336 mN/kW

where c is the speed of light.

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 [30]. 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: [31])

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