EmDrive (also Relativity Drive) is the name of a spacecraft propulsion system proposed by British aerospace engineer Roger J. Shawyer, who develops prototypes at Satellite Propulsion Research Ltd (SPR), the company he created for that purpose in 2000. New Scientist ran a cover story on EmDrive in its 8 September 2006 issue. The device uses a magnetron producing microwaves directed inside a specially shaped, fully enclosed tapering high Q resonant cavity whose area is greater at one end, upon which radiation pressure would act differently due to a relativistic effect caused by the action of group velocity in different frames of reference. The inventor claims that the device generates a thrust even though no detectable energy leaves the device. If proven to work as claimed, the EmDrive could allow the design of spacecraft engines that would be electrically powered and would require no reaction mass. Such an engine would be a breakthrough in airflight and spaceflight.
The device and its mode of operation are highly controversial. As of 2014[update], it is still not proven if the EmDrive is a genuinely new propulsion method; a misinterpretation of spurious effects mixed with mathematical errors; or a scam. The proposed theory immediately received virulent criticism because it seems to violate basic Newtonian laws of physics, notably conservation of momentum, though the inventor insists on the contrary. Whatever it be, peer reviewed independent replication has been provided by Chinese researchers from the Northwestern Polytechnic University on both mathematical and experimental grounds. in 2008, 2010, 2012, and 2013.
Should the EmDrive produce a real thrust, various conjectures have been made to explain the underlying physics. Shawyer claims the thrust would be caused by radiation pressure imbalance due to group velocities of electromagnetic waves within the framework of special relativity. Dr. Yang predicts a resulting net force using classical electromagnetism. A more complete theory has been proposed in 2013 by Argentine physicist Fernando Minotti from CONICET, who explains the alleged forces on asymmetric electromagnetic resonant cavities by a particular class of scalar-tensor theory of the Brans–Dicke type. Dr. Harold G. "Sonny" White, a NASA mechanical engineer and physicist investigating field propulsion at Johnson Space Center, notes that such resonant cavities may operate by creating a virtual plasma toroid that would realize net thrust using magnetohydrodynamics upon quantum vacuum fluctuations.
- 1 SPR Ltd claims
- 2 SPR Ltd devices
- 3 Chinese replication
- 4 Criticism
- 5 See also
- 6 References
SPR Ltd claims
Group velocities in tapered waveguides
The EmDrive exploits an idea first suggested by Allen Cullen in the 1950s, an electrical engineer then at University College London, that involves measuring forces created by radiation pressure of microwaves against the internal walls of a resonant cavity. Cullen published a number of articles on this topic during the 1950s, notably in Nature.
Cullen showed the propagation rate of electromagnetic waves in space (group velocity) and the resulting force it exerts can be varied depending on the geometry of a waveguide within which it travels. The increasing confinement of a narrowing waveguide (convergent) leads to a widening wavelength and a decrease of the group velocity (lower momentum transfer). Conversely, a widening waveguide (divergent) leads to a narrowing wavelength and an increase of the group velocity (higher momentum transfer).
Shawyer states that if the electromagnetic wave travelling in a tapered waveguide is bounced between two reflectors, with a large group velocity difference at the end surfaces, the force difference resulting from the radiation pressure difference will give a resultant thrust to the waveguide linking the two reflectors, in the direction of the larger surface.
This imbalance between the radiation pressures can be also strengthened by the addition, near the smaller end plate, of a dielectric resonator or a ferrite material, whose relative permeability or relative permittivity, or both, are higher than unity. Such electric materials weaken the group velocity of waves travelling through them, lowering further the radiation pressure at the small end reflector.
If the reflectors are separated by a multiple of half the effective wavelength of the electromagnetic wave, this thrust will be multiplied by the Q factor of the resulting resonant cavity. Thus looking for high Q cavities is necessary to significantly increase thrust magnitude.
Conservation of momentum in open systems
Standard Newtonian mechanics and thus the law of conservation of momentum indicate that, no matter what shape the cavity is, the forces exerted upon it from within must balance to zero. Shawyer claims this statement ignores special relativity in which separate frames of reference have to be applied when velocities approach the speed of light. In the EmDrive, the system of electromagnetic waves and the waveguide can be regarded as an open system, both having separate frames of reference. This effect similarly explains the principle of the laser gyroscope, which is also an apparently closed system device, but where the beams act as if having an external frame of reference (which they have, since the speed of light is constant).
The following derivation is based on Cullen. The forces acting on each end reflector are:
- is the force acting on the large reflector
- is the force acting on the small reflector
- is the group velocity of microwaves at the end of the largest cross-section
- is the group velocity of microwaves at the end of the smallest cross-section
- is the wavelength of the microwaves in free-space propagation
- is the wavelength of the microwaves at the end of the largest cross-section
- is the wavelength of the microwaves at the end of the smallest cross-section
- is the input power
- is the speed of light
The concept of the microwaves and waveguide as an open system can be illustrated in a thought experiment where the waveguide is subject to a proper acceleration in the direction of the thrust until a significant fraction of the speed of light is reached. Newtonian mechanics can't apply and is replaced with special relativity, which involves two relativistic effects on the EmDrive:
First, as the two forces and are dependent upon the local group velocities of microwaves and , the thrust should be calculated according to Einstein's velocity-addition formula given by:
Secondly, as the wave velocities are not directly dependent on any velocity of the waveguide, the waves and waveguide form an open system. Thus the reactions at the end reflectors are not constrained within a closed system of waveguide and beam, but are reactions between waveguide and waves, each operating within its own frame of reference, in an open system.
If the waveguide moves at a velocity then as the end reflectors are also moving with velocity the forces acting on each end reflector, given by the previous equations, are modified as follows:
Subtracting - the net thrust is then:
This equation shows that as the waveguide is accelerated in the direction of thrust, the thrust will decrease to zero. The null thrust is reached when = .
If Einstein's velocity-addition formula is not used in the solution to the thrust equation, relative velocities and thrust would exceed the c limit, which is impossible and demonstrates that the EmDrive is an open system, where group velocities are independent of waveguide velocity, and that it is the relative velocities that give rise to the forces.
The momentum exchange is between the electromagnetic waves and the waveguide. As the vehicle accelerates, momentum is lost by the electromagnetic waves and gained by the waveguide.
Static thrust equation
The derivation of the basic thrust equation detailed by Shawyer is based on Cullen.
Assuming the vacuum permeability and the relative permittivity both equal to unity, and supposing that the waveguide is resonant at the microwave frequency, with conductive and dielectric losses such that there are Q return paths (each at power ), the total static thrust equation is:
- is the thrust
- is the power
- is the unloaded Q factor of the cavity
- is the wavelength of the microwaves in free-space propagation
- is the wavelength at the end of the largest cross-section
- is the wavelength at the end of the smallest cross-section
which can be simplified to:
where is the Design factor of the cavity.
Dynamic equation and conservation of energy
Any force produced by the engine and converted into kinetic energy is withdrawn from the energy stored in the cavity, through a decrease in the Q factor due to Doppler shift. In other words, during proper acceleration, the apparent force on the wider diameter of the cone lessens. Taking into account the input power, the circulating power, the output power transferred to the engine and the power losses in dynamic operation, Shawyer demonstrates the system fulfills the law of conservation of energy.
The maximum Q of the engine, under static thrust conditions, is defined as the unloaded Q. Under proper acceleration, the Q of the engine at an average velocity over time is defined as the loaded Q. The relationship between the unloaded Q and the loaded Q is given by the dynamic equation:
- is the Unloaded Q
- is the Loaded Q
- is the average velocity of the device over time
Conventional microwave and resonant cavity technologies limit the maximum Q of resonators to around 50,000. According to the thrust equation, this restricts the specific thrust to a maximum threshold for every velocity. For example, at a velocity of 3 km/s, the specific thrust of a resonator at such a Q would reach a limit of 200 millinewtons per kilowatt. Shawyer states this could allow "first generation engines" where typical applications would be transfers to low Earth orbit, maintenance of communications satellites and the primary propulsion for unmanned space missions.
But superconducting microwave resonant cavities would tremendously boost the Q factor. In 1995, German superconducting resonant cavities for use in particle accelerators readily achieved Q of several billion.
Superconducting resonators would be used in "second generation engines" that would change everything: the German resonator having a Q of 5×109 would allow static specific thrust of about 3 kN/kW, that is 3 tonnes of thrust per kilowatt of input power, "enough to lift a large car" according to Shawyer.
However, with such high specific thrusts, those engines would be subject to the dynamic equation where the effect at these high values of unloaded Q is quite important. Thus in the example where the resonator has an unloaded Q of 5×109 and an average velocity of only 0.1 m/s, the dynamic equation quickly reduces the specific thrust from 3.15 tonne per kilowatt (static thrust at rest) to 0.93 tonne per kilowatt when Q is loaded. The dynamic equation therefore would constrain the applications of second generation engines to those where the acceleration and kinetic energy output is limited.
Thrust limitation by Doppler shift
The Q losses and the overall thrust reduction when the cavity is accelerated, while the electromagnetic waves inside are reflected back and forth between the two end plates of the resonator, has been found to be caused by the Doppler effect.
- With a positive acceleration, the overall Doppler shift inside the cavity is negative. This leads to a reduction in stored energy in the cavity, and thus a reduction in Q, and a reduction in thrust. The kinetic energy gained by the cavity is then balanced by the stored energy lost by the cavity. This is EmDrive in "motor" mode.
- With a negative acceleration, the overall Doppler shift is positive. This leads to an increase in stored energy, which is balanced by the loss of kinetic energy from the cavity. This is EmDrive in "generator" mode.
This dual mode illustrates that EmDrive works as a classic electrical machine. The "generator" mode offers a method of decelerating a vehicle.
More importantly, the Doppler shifts occuring in each transition will, under very high Q and high acceleration, cause the frequency of the electromagnetic wavefront to move outside the operating narrow resonant bandwidth of the cavity, dramatically limiting the thrust, thus the acceleration provided by the thruster.
A thruster has been designed with a compensating system where frequency offset is used as well as a dynamic modification of the axial length of the cavity over a few microns, according to the acceleration experienced by the engine. The extension results from a pulsed voltage being applied to piezoelectric elements in the sidewall of the cavity. This dynamic compensation enables the effect to be partially reduced, and allows acceleration of up to 0.5 m/s2 for a theoretical specific thrust of 1 tonne per kilowatt.
This acceleration limitation, in the vertical plane only, could allow second generation superconducting EmDrives to be deployed as lift engines in a number of aerospace vehicles.
The weight of such aircrafts being almost cancelled (but not their mass, hence inertia), they would have no need for wings anymore and could be designed with various shapes. The acceleration of the vehicle itself would be produced by conventional propulsion of limited power, like small propellers, gas turbines, rocket engines or even ion thrusters or plasma propulsion engines, although Shawyer suggests liquid hydrogen turbines would be the best choice as this fuel under cryogenic state could also cool down the superconducting resonators before being burnt in the small propelling turbines.
No peer reviewed publications has been proposed by Shawyer to date, as opposed to independent work by Chinese researchers at the Northwestern Polytechnical University in Xi'an and Argentine physicist Fernando Minotti.
He then regularly presented his work at various international conferences, in Brighton in 2005, at the 59th International Astronautical Congress (IAC) in Glasgow in 2008, the CEAS 2009 European Air and Space Conference held in Manchester, the 2nd Conference on Disruptive Technology in Space Activities (TECHNO DIS) at CNES' Toulouse Space Show, France in 2010, and at the 64th International Astronautical Congress, Beijing, China in 2013.
SPR Ltd devices
Feasibility Study and first prototype
In July 2001, A £45,000 Research and development grant was first awarded to SPR Ltd by the U.K. government's Department of Trade and Industry under their SMART award scheme, as part of a three-year, £250,000 programme, and the work started with a mission analysis phase. The two technical objectives of the initial study, completed in 2002, were the derivation of a thrust equation and the verification of that equation by experiment.
The first objective has been achieved with the completion of the theory paper. For the second goal, an experimental prototype was designed and built with the following measured characteristics:
|Big end||160 mm|
|Small end||100 mm|
|Operating frequency||2.45 GHz|
|Max. input power||850 W|
|Max. measured thrust||16×10−3 N|
The couple thruster + magnetron weighted 9.4 kg (15 kg with the electromagnetic shielding enclosure on). The maximum thrust measured was very close to the 16.6 mN thrust predicted from the static thrust equation of the theory paper. The thrust could be varied from zero to maximum by varying the input power, or by varying the resonant frequency of the thruster. Efforts were made to test for possible thermal and electromagnetic spurious effects: the primary method was to carry out all tests in both nominal and inverted orientations, and to take the mean of the results. The thruster was also sealed into a hermetic enclosure to eliminate coupling with electromagnetic radiation and any buoyancy effects of the cooling air. Three different types of test rig were used, two using 1 mg resolution balances in a counterbalance test rig, and another using a 100 mg resolution balance in a direct measurement of thruster weight. Comparison of the rates of increase of thrust for the different spring constants, using pulsed input power, indicated that the thrust would be produced by momentum transfer and would not be caused by any unknown spurious effect. The total test programme encompassed 450 test runs of periods up to 50 seconds, using 5 different magnetrons.
In 2003, after the positive results of the experimental prototype, a review of the study programme was examined by John Spiller, an independent space engineer hired by the U.K. government for that purpose. Spiller concluded in his report:
|“||The thruster's design is practical and could be adapted fairly easily to work in space […] The drive needs to be developed further and tested by an independent group with its own equipment. […] It certainly needs to be flown experimentally.||”|
—John Spiller, in his review of SPR Ltd work.
Shawyer claimed at that time that he had been visited by representatives from China and the U.S. Air Force, but ESA didn't show much interest. He estimates that his design could save the aerospace community $15 billion over ten years.
In August 2003, following Spiller's positive conclusions, a £81,000 Research and Development grant was again awarded by the DTI for a Demonstrator program. The agreement covered the design, production and test of an S band Demonstrator Engine. Unlike the first experimental thruster which could only be run for short periods before burning out its magnetron, the Demonstrator Engine was water cooled and thus rated for continuous operation. Extensive design work was required to increase the specific thrust by raising the design factor and the unloaded Q.
Static thrust tests
To get close to the predicted thrust, the engine was required to maintain stable resonance at this high Q value. Major design challenges included thermal compensation, tuning control and source matching. The engine was tested in a large static test rig employing a calibrated composite balance to measure thrust in both vertical and horizontal directions, in three possible engine orientations. A total of 134 test runs were carried out. A problem identified during the tests is the detuning of the resonant cavity caused by mechanical deformation due to internal radiation pressure.
In 2006, New Scientist reported a performance comparison diagram entitle "How electromagnetic drives compare" between the SMART-1 ion thruster and a hypothetical space probe equipped with an EmDrive consuming the same amount of power, based on Shawyer's calculation:
|Engine||European Space Agency's
SMART-1 ion engine
|Power required||700 W||700 W|
|Thrust generated||70 millinewtons||88 millinewtons|
|Operational life||1.6 year||15 years|
|Weight||94 kilograms||9 kilograms|
The original New Scientist diagram is still accessible online in a 2013 article of DVICE.
Dynamic thrust tests
In 2007, Eureka magazine reported dynamic tests on a rotating rig, the whole device weighing 100 kg, comprising the thruster and its cooling system mounted on a beam supported on a low-friction air bearing. The device reportedly consumed 300 W of power and produced a force of 96.1 mN, a maximum speed of 2 cm/s over 185 cm during testing in October 2006.
In 2008, Shawyer has released a video of this dynamic thrust test to the public, purportedly demonstrating his device working. He states the engine starts to accelerate only when the magnetron frequency locks to the resonant frequency of the thruster, following an initial warm up period; this eliminating possible spurious forces.
|Static tests||Dynamic tests|
|Overall diameter||280 mm|
|Operating frequency||2.45 GHz|
|Input power||1100 W||421 W|
|Max. thrust||–||102×10−3 N|
|Max specific thrust||214 mN/kW||315 mN/kW|
Flight thruster programme
In 2008, the thirst development stage at SPR Ltd was started as the Flight thruster programme, which covers the design and development of a 300 Watt C Band resonator intended to be tested aboard a satellite.
In 2010, an operational thruster has been built, designed to be powered from existing flight qualified TWTAs. The thruster was tested on a calibrated balance test rig, mounted to provide thrust in up and down directions. Tests were carried out over an input power range of 150 W to 450 W, and up to 600 W in later tests, although thrust levels at this higher power are not known. Results presented below account for 19 low power test runs of up to 90 seconds duration.
|Overall diameter||265 mm|
|Overall height||164 mm|
|Operating frequency||3.85 GHz|
|Input power||150–450 W|
|Max. measured thrust||174×10−3 N|
|Average specific thrust||326×10−3 N/kW|
Shawyer expressed interest to test his thruster in space. He claims to have undergone seven independent positive reviews from experts at BAE Systems, EADS Astrium, Siemens and the IEE. But as of 2014, no EmDrive has been tested in microgravity yet.
The second limiting factor of those thrusters, besides the cavity detuning stress under radiation pressure, is the lowering Q factor of the cavity as microwave energy lost to impart momentum and heating the cavity reduces the field strength within. So Shawyer investigated cavities lined in a superconducting material that may produce very high Q sufficient to achieve high trust.
2G superconducting thruster programme
In 2010, a preliminary "second generation", low power high-temperature superconducting cavity has been manufactured, operating at 3.8 GHz and designed for very high unloaded Q of 6.8×106 with liquid nitrogen at a temperature of 77 kelvin, and consequently lined up for high specific thrust. Superconducting coating of the surfaces were formed from YBCO thin films on sapphire substrates.
Since 2013, a high power experimental version is under development, including compensation techniques of cavity length extension and frequency offset, and cooling with liquid hydrogen to reach a very high unloaded Q of 109. Latest Shawyer's patent reflects the design enhancements for second generation thrusters, the most obvious being the shape of the cavity, changed from a truncated cone to a cylindrical sector. Amongst other things, this would enable several cavities to stack next to each others as an array.
Specific thrust of almost one tonne per kilowatt is theoretically predicted with an acceleration limit of 0.5 m/s2 for this kind of thruster. With this goal in mind, Shawyer claims that commercial terrestrial aircrafts incorporating 2G EmDrive as lift engines could be ready by 2020.
In 2008, Wired magazine reported that a team of Chinese researchers led by Dr. Juan Yang (杨涓), professor of propulsion theory and engineering of aeronautics and astronautics at Northwestern Polytechnical University (NPU) in Xi'an, claimed to have confirmed the theory behind the drive and are proceeding to build a demonstration version. Yang's group had just published the first peer reviewed paper about the EmDrive in the Chinese Journal of Astronautics.
In 2010, the Chinese group published a second paper in another scientific journal where they quantify the theoretical maximum specific thrust of the prototype they have built (456 mN/kW) and announce their first positive experimental results: 315 mN/kW for a 1000W power input. The practical results were consistent with their theoretical predictions, both in term of thrust magnitude than in respect to the various shapes of resonant cavities tested. It is interesting to note that Yang's group calculated the theoretical thrusts of their experimental device applying a method involving a set of steady-state single-fluid MHD equations that was reformed by other Chinese researchers to quantify forces in a plasma generated in front of a vehicle embedded in a hypersonic flow, whereas Shawyer calculated similar predictions from the derivation of Cullen's equations. The original paper (in Chinese) is available on the SPR Ltd web site, as well as a professional English translation.
In 2012, more detailed results are published from the 2010 device in Acta Physica Sinica, also available on the SPR Ltd web site. Yang's team achieved a maximum thrust of 720 mN for an input power of 2.5 kW (specific thrust of 288 mN/kW). The paper also specifies the net thrust measurements were conducted on a patented aerospace engine test stand called the Rocket Indifferent Equilibrium Thrust Measurement Device usually used to precisely test spacecraft engines like ion drives. A magnified version of the diagram showing the evolution of thrust generated as a function of input power is available on the SPR Ltd web site.
By comparison, the NASA HiPEP ion thruster, intended for use on the cancelled JIMO mission, produced up to 670 mN of thrust at a power level of 39.3 kW (specific thrust of 17 mn/kW) while using 7 mg/s of xenon gas as propellant. When the xenon gas is depleted, the thruster ceases to function. It is claimed that the EmDrive, because it does not rely on reaction mass, would work indefinitely without any fuel other than that which might be required to generate electricity. Because the reaction mass typically forms 90% or more of the total weight of a spacecraft, a thruster that did not require reaction mass would represent a fundamental breakthrough in spacecraft design and propulsion.
Following these results, Dr. Yang and her team published another paper in English in an international scientific journal in 2013.
Violation of conservation of momentum
Any apparent reactionless drive is treated with skepticism by the physics community, since such a drive would violate the well-established principle of the conservation of momentum, which has enormous experimental support. Shawyer claims that his drive does not violate the conservation of momentum.
Since there are no known phenomena that do not conserve energy, any calculation based on standard physical theory that predicts a violation of the conservation of energy is almost certainly in error. This is a non-controversial and fundamental fact regarding the mathematical structure of the theories, regardless of whether the theories themselves are or are not correct descriptions of the physical world. Shawyer asserts the energy is conserved in the EmDrive, through a decrease in the Q factor and the stored energy when the device experiences a proper acceleration, due to the Doppler shift.
Conservation of momentum is also required and maintained in Maxwell's equations, Newtonian mechanics, special relativity, electrodynamics and quantum mechanics (and their combination, quantum electrodynamics), so this claim cannot be valid unless these well-established physical theories are false or can be otherwise explained in terms within these existing theories. However, in electrodynamics and quantum electrodynamics, energy and momentum are each separately conserved. Thus in order to be consistent with established physical theories, a valid description of the device's operation would have to separately account for any transfers of energy or momentum between any physical systems involved.
As for the various experimental prototypes, the effective thrusts measured in laboratory could actually be spurious effects caused by air currents, friction, ionization, electromagnetic interferences or mechanical coupling of Dean drive effects that would not exist in a completely closed and isolated EmDrive in vacuum, all objections that Shawyer refutes. As for the Chinese experiment, the fact it has been carried off an industrial aerospace engine test stand greatly reduces such possibility.
Treatment of New Scientist
After receiving criticism that no peer reviewed publications on the subject had been made, Shawyer submitted a theory paper to New Scientist, a weekly science magazine which is not a peer reviewed scientific journal.
The EmDrive was consequently featured on the cover of the 8 September 2006 issue of the magazine. The article portrayed the device as plausible, and emphasized the arguments of those who held that point of view, although it did quote one engineer as saying "it's a load of bloody rubbish."
New Scientist has drawn great criticism from the scientific community due to this uncritical treatment of EmDrive in its article. The following month, the editor partially addressed it in its publisher's blog, allowing readers to comment as well as offering Roger Shawyer a right to reply.
Science fiction writer Greg Egan distributed a public letter stating that "a sensationalist bent and a lack of basic knowledge by its writers" was making the magazine's coverage sufficiently unreliable "to constitute a real threat to the public understanding of science". In particular, Egan found himself "gobsmacked by the level of scientific illiteracy" in the magazine's coverage of the EmDrive, where New Scientist allowed the publication of "meaningless double-talk" designed to bypass a fatal objection to Shawyer's proposed space drive, namely that it violates the conservation of momentum. Egan urged those reading his letter to write to New Scientist and pressure the magazine to raise its standards, instead of "squandering the opportunity that the magazine's circulation and prestige provides" for genuine science education. The letter was endorsed by mathematical physicist John C. Baez and posted on his blog. Egan has also recommended that New Scientist publish Dr. Costella's refutation of Shawyer's theory paper.
Debate over Shawyer's theory paper
Shawyer's paper published in New Scientist was indeed almost immediately challenged by Dr. John P. Costella, a theoretical physicist and electrical engineer who works for the Australian Department of Defence, whose Ph.D. is in relativistic electrodynamics, the field of physics that Shawyer relies on to support his theory. According to Costella, the angles of the force vectors are calculated incorrectly. You can use high school physics to find the correct angles and reach the conclusion that momentum is conserved and the drive can't work as postulated. He says that the rest of of the paper has theory that is correct, but which doesn't demonstrate anything about how the drive works.
Shawyer says that Dr. Costella didn't disprove his derivation of the static thrust equation (related to the law of conservation of momentum) nor the dynamic thrust equation (related to the law of conservation of energy), and didn't comment about thrusts measured in the experiments neither. According to Shawyer, what Dr. Costella criticized as being "a fraud" in Shawyer's founding theoretical paper was some vectors pointing the wrong direction in a diagram of Shawyer's theoretical paper by then (version 9.3, fig. 2.4) still available on New Scientist web site:
|“||Look at the arrows that Shawyer labels Fs1 and Fs2 on his Figure 2.4. These are supposed to be the forces that the particle imparts to the wall of the conical part of his contraption. But hang on a minute! When a particle bounces elastically off a wall, doesn't the wall feel a force that is perpendicular to the wall? Of course it does: if you remember your high school physics, you subtract the initial momentum vector from the final momentum vector, and the resultant force points into the wall. (OK, it's actually called the impulse, not the force, but it's effectively the same thing for what we're talking about here).
Now look back at Shawyer's Figure 2.4. He has Fs1 and Fs2 pointing perpendicular to the axial direction, not perpendicular to the cone's walls. His arrows are wrong. This is the fundamental blunder that renders Shawyer's paper meaningless. There is no 'drive'. [...] Shawyer's 'electromagnetic relativity drive' is a fraud.
—Dr. John Costella, Why Shawyer's 'electromagnetic relativity drive' is a fraud (in reference to version 9.3 of Shawyer's theory paper).
Shawyer has since published an updated theory paper (version 9.4) where the diagram criticized by Costella is simply omitted. Yet it should be noted in this debate that Shawyer does not compute theoretical thrusts subtracting vectors off a diagram, but uses thrust equations whose derivation is done from Cullen's work involving wavelengths, frequencies, group velocities, Q factors, relativistic law of addition of velocities, and so on. As a consequence, a valid refutation of Shawyer's theory whould show where the maths are wrong.
Debate over Chinese results
Contacted again in 2013 by Wired magazine about Shawyer's maths being validated and his experiments successfully reproduced by the Chinese team at Northwestern Polytechnical University, Dr. Costella avoided providing a scientific analysis of the equations and basically answered on his blog that he didn't have time to find a possible mathematical flaw in the papers and suggested a simple graduate student should do it, ignoring the fact the papers were already published in three scientific journals, i.e. after validation from referees.
As Dr. Costella implied, Shawyer may have incorrectly identified the forces on the sides of the waveguide. If an error is present, it is most likely that the thrust is eliminated and the drive then cannot accelerate. Following this hypothesis, the Chinese team would have done the same basic error, and their positive experimental results correlated with their theoretical predictions would be another coincidence.
The redactor of Wired magazine who regularly covered the experimental results in the news declared he received some comments from the Chinese stating "the publicity was very unwelcome, especially any suggestion that there might be a military application" and that Pr. Yang told him that "she is not able to discuss her work until more results are published".
Any dispute will be settled when more independent observations are able to conclude whether or not the machine works in the way it is claimed. Dr. Costella precisely suggested to test a completely closed EmDrive in space. Such experiments in microgravity are indeed proposed by NASA, as CubeSats released from the International Space Station. A small sized CubeSat costs far cheaper than most satellite launches, with an estimated $65,000-80,000 per launch.
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