Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 3131824 times)

Offline aero

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An observation and a question.

As you may know, I have made a large number of Meep runs to detect forces from evanescent waves. One thing that I have noticed is that the quality factor, Q, is strongly related to the magnitude of the imaginary component of the resonant frequency and that the force/power of the evanescent waves seems to be related to this component also. Difference being that force/power is related to the signed value of the imaginary component of the complex resonant frequency. That is, the imaginary component is typically a small negative value but when it goes near zero, the Q goes way up, almost like 1/fi where fi is the imaginary coefficient of the complex frequency. Then, when fi goes positive, force/power detected from the external evanescent waves goes up.

Question. Does the described behavior relate to any theory we have thought about?
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Offline Rodal

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John Costella (PhD, Relativistic Electrodynamics  ??) is on record about his views about Shawyer's analysis of the EM Drive but I didn't know that he had also written about Prof. Yang's papers.

This pertains to our discussions (with Todd and others) of what exactly is Prof. Yang alluding to in her paper.

See:  https://johncostella.wordpress.com/2013/06/16/the-emdrive-the-cold-fusion-of-the-21st-century/

Quote from: Dr.Costella
The Yang Juan et al. paper, however, is more akin to that haystack. They quote many valid equations of electrodynamics, but then stitch them together with numerous assumptions, and then use numerical simulation to compute a result. Without having a spare year to dig through their calculations and simulations, it’s impossible to know where they made their mistake. (Now you know why the Patent Office refuses to accept any more applications for perpetual motion machines.) I recommend that they submit their paper, and simulation code, to a reputable physics journal like the Physical Review, who might be able to find a graduate student with nothing better to do than debunk their submission.

A possible source of their error is their Fig. 1. In diagram (a) they show an open system, where microwaves are thrust into outer space. Such a system would indeed show a tiny amount of thrust: the microwave photons are the propellant. But they reject diagram (a) because the microwaves leak out (obviously), which prevents a standing wave (Shawyer’s claimed mechanism for getting amplification of the tiny thrust) from being maintained. They then replace this with diagram (b), which has placed on the exhaust a “matched load used to absorb the heat transferred from reflected microwaves”. This statement makes no sense at all: reflected microwaves would not transfer heat—only momentum, namely, the force that would prevent the system from getting any net thrust. If something more sophisticated is meant, then it is not explained, and certainly not modeled in their equations. It is possible that neglect of the momentum transfer to this “matched load” is the missing force in their calculations.

I don't know what paper by Juan Yang contains this Fig 1 showing microwaves thrusting into space, and where is diagram b  which has placed on the exhaust a “matched load used to absorb the heat transferred from reflected microwaves”.   Does anybody know ?

That there is heat produced by induction heating from the magnetic field inside the cavity has been proven by NASA's experiments (for mode TM212):

« Last Edit: 06/17/2015 07:34 pm by Rodal »

Offline aero

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I just finished some Meep runs calculating resonance and Q for the Yang and Shawyer Demo devices using measurements posted.

             frequency    imag. freq.             Q
Yang    2.5387557535   -3.84E-005                33,024.11
Shawyer   2.5058375192   -9.72E-008          12,889,869.03

(To convert frequencies to SI units, multiply by c/0.3)

The frequencies are a little high it seems, and so are the Q values. I really could use that Drude model for copper, but all I really need is an accurate number for complex permittivity of copper at 2 GHz, er = e' + ie".
Experience with Meep with and without the imaginary component of the dielectric constant in the Brady cavity model shows that e" strongly affects both resonance and Q.
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Offline WarpTech

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... now I understand that the stored current may be DC and the associated magnetic field, stored in the small end of the frustum and caused by the time-asymmetry of the evanescent wave's near-field induction effects. Along the walls of the frustum, the gauge potential has a divergence, offset by a change in the refractive index. This divergent field can escape and away we go!

What is the best way to measure (or model) this field that's escaping the frustum and correlate it to measured thrust?

And how would the "DC" EMDrive be setup so as not to use microwaves?

I did the following calculation by hand.

Consider a Coaxial section, where the outer conductor is tapered wrt the inner conductor. At one end, they are connected at a point. At the other end, they are separated by a radial gap. Apply current, "in" through the inner connector and "out" though the outer conductor. This forms a 1-turn Inductor, with an azimuthal B-field.

The B-field between the two conductors is solely due to the inner conductor. The outer conductor does not contribute to the field inside. Outside, the 2 fields cancel, but penetrate the copper right up to the outer boundary.

I used Maxwell's equations and calculated the integral of the pressure x surface area for the conical outer conductor, the cylindrical inner conductor and a flat disk at the input end. The forces are as follows;

Inner conductor:  F = 0  The only contribution is radial from it's own B-field, and by symmetry it is cancelled completely.
Outer conductor: F = (u0/2*sin(θ))*I2 x ln(rb/ra)
In the "z" direction, multiply by sin(θ) to get;
Fz = (u0/2)*I2 x ln(rb/ra)
At the bottom disk, at the input end: F = -Fz

Now, remove the bottom disk, or remove it from the path of current flow such that J = 0 in the disk. The cone will be propelled by leakage inductance out the bottom. As it charges, there will be a force pushing toward the small end. It will be a photon rocket, proportional to u0*I*dI/dt.

I'm working on this as part of a paper, but it's not going quickly.
Todd
 


Offline DIYFAN

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Quote
(From Dr. Costella)
(Now you know why the Patent Office refuses to accept any more applications for perpetual motion machines.)

Actually, this is not entirely accurate.  While highly skeptical as they should be, there is no prohibition against filing an application for a perpetual motion machine--at least in the U.S.  There is a requirement that such a machine be physically presented at the Patent Office for verification before any patent would be granted.
« Last Edit: 06/17/2015 06:37 pm by Chris Bergin »

Offline flux_capacitor

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I don't know what paper by Juan Yang contains this Fig 1 showing microwaves thrusting into space, and where is diagram b  which has placed on the exhaust a “matched load used to absorb the heat transferred from reflected microwaves”.   Does anybody know ?
Yes, I found the paper:
Yang, Juan; Wang, Yu-Quan; Ma, Yan-Jie; Li, Peng-Fei; Yang, Le; Wang, Yang; He, Guo-Qiang (May 2013). "Prediction and experimental measurement of the electromagnetic thrust generated by a microwave thruster system" (PDF). Chinese Physics B (IOP Publishing) 22 (5): 050301. doi:10.1088/1674-1056/22/5/050301

Figure 1 a) and b) from that paper attached below.

Offline Rodal

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I don't know what paper by Juan Yang contains this Fig 1 showing microwaves thrusting into space, and where is diagram b  which has placed on the exhaust a “matched load used to absorb the heat transferred from reflected microwaves”.   Does anybody know ?
Yes, I found the paper:
Yang, Juan; Wang, Yu-Quan; Ma, Yan-Jie; Li, Peng-Fei; Yang, Le; Wang, Yang; He, Guo-Qiang (May 2013). "Prediction and experimental measurement of the electromagnetic thrust generated by a microwave thruster system" (PDF). Chinese Physics B (IOP Publishing) 22 (5): 050301. doi:10.1088/1674-1056/22/5/050301

Figure 1 a) and b) from that paper attached below.

Excellent thank you so much.

Offline Rodal

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Quote
(From Dr. Costella)
(Now you know why the Patent Office refuses to accept any more applications for perpetual motion machines.)

Actually, this is not entirely accurate.  While highly skeptical as they should be, there is no prohibition against filing an application for a perpetual motion machine--at least in the U.S.  There is a requirement that such a machine be physically presented at the Patent Office for verification before any patent would be granted.
1) The quote comes from Dr. Costella.  In his paper:  http://johncostella.webs.com/shawyerfraud.pdf

he lists his residence as being in Australia, so perhaps what he means is that the Australian Patent Office refuses to accept any more applications for perpetual motion machines.

This article http://blog.patentology.com.au/2015/04/patenting-perpetual-motion.html concludes: <<So, alleged perpetual motion machines certainly used to be patentable in Australia, and now they probably are not.>>

2) For people interested in sending their perpetual motion machines to the US Patent Office, their rules on models is here:  http://www.uspto.gov/web/offices/pac/mpep/s608.html#d0e50532.  I'm told by a friend Patent Attorney that used to work for them that they run out of room to store perpetual motion machine models a long time ago :)

3) I leave further discussion on perpetual motion machines on the capable hands of Messrs. @frobnicat and @deltaMass :)
« Last Edit: 06/17/2015 07:37 pm by Rodal »

Offline rfmwguy

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....If you can only excite at 2.45 GHz then make it around 9.91 inches....
...

My understanding is you need to insert the antenna at the internal diameter point where the effective guide wavelength is equal to the actual guide wavelength and the antenna should be a 1/4 wave stub at the effective guide wavelength.

In my EMDrive Calc, the lower left chart shows a red vertical line where that condition is satisfied.

Had a question on the chart below (my apologies in advance):

Not sure I understand the X and Y axis definitions. Know I'm looking for vertical transition, how does this define locale of rf injection? Thanks in advance...
« Last Edit: 06/17/2015 07:27 pm by rfmwguy »

Offline flux_capacitor

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The quote comes from Dr. Costella.  In his paper:  http://johncostella.webs.com/shawyerfraud.pdf
[…]

BTW you should know when citing Costella, that after the man criticized publicly Shawyer's EmDrive as being "a fraud" (not an "experimental error" but a "fraud" which can be considered as defamation according to the English law) that a question about the validly of SPR ltd research was raised in the UK House of Commons (logged on UK Parliament Publications and Records, Hansard Commons Debates, 5 Dec 2006, Column 340W, Electromagnetic Relativity Drive) caused in part by this claim of fraud.

Questioned on that investigation, Shawyer answered a background check was carried out by the UK authorities about Costella. This inquiry showed that he was not an electrodynamics expert working for the Australian Department of Defence, but had been briefly employed as a junior reliability engineer. He was however known to the Australian authorities as a persistent conspiracy theorist, as demonstrated by various comments he wrote on many blogs.

Not to play devil's advocate here, but sometimes things are not exactly what they seem to be. So everything on that matter that is not true facts (like falsifiable replicable experimental setups) should be taken with a grain of salt.
« Last Edit: 06/17/2015 07:30 pm by flux_capacitor »

Offline Rodal

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....

BTW you should know when citing Costella, that after the man criticized publicly Shawyer's EmDrive as being "a fraud" (not an "experimental error" but a "fraud" which can be considered as defamation according to the English law) that a question about the validly of SPR ltd research was raised in the UK House of Commons (logged on UK Parliament Publications and Records, Hansard Commons Debates, 5 Dec 2006, Column 340W, Electromagnetic Relativity Drive) caused in part by this claim of fraud.

Questioned on that investigation, Shawyer answered a background check was carried out by the UK authorities about Costella. This inquiry showed that he was not an electrodynamics expert working for the Australian Department of Defence, but had been briefly employed as a junior reliability engineer. He was however known to the Australian authorities as a persistent conspiracy theorist, as demonstrated by various comments he wrote on many blogs.

Not to play devil's advocate here, but sometimes things are not exactly what they seem to be. So everything on that matter that is not true facts (like falsifiable replicable experimental setups) should be taken with a grain of salt.
Thank you for the clarification.  The link you provide (http://www.publications.parliament.uk/pa/cm200607/cmhansrd/cm061205/text/61205w0031.htm) reads:

Quote from: UK Parliament
Electromagnetic Relativity Drive

Alan Duncan: To ask the Secretary of State for Trade and Industry how much his Department has provided to the electromagnetic relativity drive design proposed by Roger Shawyer; and from what budget funding has been drawn. [103254]

Margaret Hodge [holding answer 27 November 2006]: Awards have been made to Satellite Propulsion Research Ltd from the DTI’s Small Firms and Enterprise budget.

July 2001—£43,809 paid.

A feasibility study into the application of innovative microwave thruster technology for satellite propulsion. The study involved development of an experimental thruster followed by independent tests and evaluation.

August 2003—£81,291 total grant awarded, £68,399 paid to date.

A follow-on from the above project, to design and develop a demonstration model engine. To be tested on a dynamic test rig, to demonstrate continuous thrust and the conversion of thrust into kinetic energy.

Both grants were awarded against the criteria of the DTI’s Smart scheme that was designed to help fund pioneering and risky R and D projects in small and medium enterprises. Highly qualified technical experts and academics carried out an assessment on behalf of the Department. 
« Last Edit: 06/17/2015 07:44 pm by Rodal »

Offline rfmwguy

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Quote
(From Dr. Costella)
(Now you know why the Patent Office refuses to accept any more applications for perpetual motion machines.)

Actually, this is not entirely accurate.  While highly skeptical as they should be, there is no prohibition against filing an application for a perpetual motion machine--at least in the U.S.  There is a requirement that such a machine be physically presented at the Patent Office for verification before any patent would be granted.
1) The quote comes from Dr. Costella.  In his paper:  http://johncostella.webs.com/shawyerfraud.pdf

he lists his residence as being in Australia, so perhaps what he means is that the Australian Patent Office refuses to accept any more applications for perpetual motion machines.

This article http://blog.patentology.com.au/2015/04/patenting-perpetual-motion.html concludes: <<So, alleged perpetual motion machines certainly used to be patentable in Australia, and now they probably are not.>>

2) For people interested in sending their perpetual motion machines to the US Patent Office, their rules on models is here:  http://www.uspto.gov/web/offices/pac/mpep/s608.html#d0e50532.  I'm told by a friend Patent Attorney that used to work for them that they run out of room to store perpetual motion machine models a long time ago :)

3) Further discussion on perpetual motion machines will be handled by Messrs. @frobnicat and @deltaMass :)

Interesting that an agency would block an application based on "common beliefs"...While reading this forum, I know there are opposing viewpoints, but think others should not try and discourage DIY attempts.

I am fully aware that this could be a "hoax of the century", something remarkable or somewhere in-between. To me it does not matter. Its the art of the build and the positive or negative results that may occur. It will be contributed to the knowledge-base, regardless.

What confounds me is criticism outside this forum based on theories and equations someone else came up with, not the posters or pdf writers...as if the posters had the skill or knowledge to prove it or disprove it themselves. Newton, Einstein and other can speak for themselves...negative handwavers need not parrot ;)

Speaking of parrot...be careful with Magnetron Voltages!


Offline dustinthewind

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...
However, I do not see a direct connection yet between the article in Nature and the work of Igor Pikovski, about quantum decoherence to what Todd has been proposing. 

The microwave electromagnetic fields inside the EM Drive are carried by photons, which are quantum particles.  Photons are capable of displaying quantum coherence and decoherence.   The laser, superconductivity and superfluidity are examples of highly coherent quantum systems whose effects are evident at the macroscopic scale.

I know of nothing in the EM Drive experiments that has shown a state of quantum coherence, and therefore nothing that has shown that decoherence takes place in the EM Drive.  So where is the connection to the EM Drive?

Regarding Todd's papers, if he posited quantum coherence, I missed that in his papers.  My understanding is the contrary, that his emphasis is on geometric attenuation producing evanescent waves that can carry momentum.  Todd is not even looking for a super-high Q, but portrays the tug-of-war between Q storage and attenuation and evanescent waves as what could enable the EM Drive to work.

Jose,

If I were talking about gravity in atoms, their paper would be a a spot-on way to look at it. Equation's (5) & (6) are similar in form to the Zitterbewegung motion of the electron in the Dirac equation that I typically refer to. When 2 particles are coupled, they have coherent states. In a gravitational field, we have asymmetry in time.

In the case of the frustum, it is not "quantum" but the standing waves are still a coherent state, just as they are in a laser or a maser. We have 2 waves, "forward" and "backward" that are phase shifted due to the asymmetrical attenuation, i.e., asymmetrical wave velocity, guide wavelength, geometry, whatever. The two waves are out of phase and you can see in their Fig. 1c, that the phase shifted superposition has a component along the "real" Power axis, i.e, the Power Factor is not 0.

This action causes the center of mass between the two to shift. The "decoherence" they are referring to, is what I've been referring to as "constructive and destructive interference". This is the information contained in the Matrix terms they are referring to. I'm just saying it in my own Engineering-speak. If the frustum were replaced by a cylinder, this phase interference would not happen. The frustum is a nice conical-section representation of a spherically symmetric gravitational field, that only exists over a very narrow bandwidth. :)
Todd

What about two cylindrical resonators that are at a set distance and close together but out of phase?  Doesn't this re-introduce the  phase shifted asymmetrical attenuation?
Follow the science? What is science with out the truth.  If there is no truth in it it is not science.  Truth is found by open discussion and rehashing facts not those that moderate it to fit their agenda.  In the end the truth speaks for itself.  Beware the strong delusion and lies mentioned in 2ndThesalonians2:11.  The last stage of Babylon is transhumanism.  Clay mingled with iron (flesh mingled with machine).  MK ultra out of control.  Consider bill gates patent 202060606 (666), that hacks the humans to make their brains crunch C R Y P T O. Are humans hackable animals or are they protected like when Jesus cast out the legion?

Offline rfmwguy

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The quote comes from Dr. Costella.  In his paper:  http://johncostella.webs.com/shawyerfraud.pdf
[…]

BTW you should know when citing Costella, that after the man criticized publicly Shawyer's EmDrive as being "a fraud" (not an "experimental error" but a "fraud" which can be considered as defamation according to the English law) that a question about the validly of SPR ltd research was raised in the UK House of Commons (logged on UK Parliament Publications and Records, Hansard Commons Debates, 5 Dec 2006, Column 340W, Electromagnetic Relativity Drive) caused in part by this claim of fraud.

Questioned on that investigation, Shawyer answered a background check was carried out by the UK authorities about Costella. This inquiry showed that he was not an electrodynamics expert working for the Australian Department of Defence, but had been briefly employed as a junior reliability engineer. He was however known to the Australian authorities as a persistent conspiracy theorist, as demonstrated by various comments he wrote on many blogs.

Not to play devil's advocate here, but sometimes things are not exactly what they seem to be. So everything on that matter that is not true facts (like falsifiable replicable experimental setups) should be taken with a grain of salt.

Hmmmm...meet Mr Costella, now a Facebook software engineer: https://www.linkedin.com/in/johncostella

Offline deltaMass

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The quote comes from Dr. Costella.  In his paper:  http://johncostella.webs.com/shawyerfraud.pdf
[…]

BTW you should know when citing Costella, that after the man criticized publicly Shawyer's EmDrive as being "a fraud" (not an "experimental error" but a "fraud" which can be considered as defamation according to the English law) that a question about the validly of SPR ltd research was raised in the UK House of Commons (logged on UK Parliament Publications and Records, Hansard Commons Debates, 5 Dec 2006, Column 340W, Electromagnetic Relativity Drive) caused in part by this claim of fraud.

Questioned on that investigation, Shawyer answered a background check was carried out by the UK authorities about Costella. This inquiry showed that he was not an electrodynamics expert working for the Australian Department of Defence, but had been briefly employed as a junior reliability engineer. He was however known to the Australian authorities as a persistent conspiracy theorist, as demonstrated by various comments he wrote on many blogs.

Not to play devil's advocate here, but sometimes things are not exactly what they seem to be. So everything on that matter that is not true facts (like falsifiable replicable experimental setups) should be taken with a grain of salt.

Hmmmm...meet Mr Costella, now a Facebook software engineer: https://www.linkedin.com/in/johncostella
Wrong guy. Try this
http://spartacus-educational.com/JFKcostella.htm

Two degrees plus 3 years postdoc physics is a little different to the picture painted by Shawyer of a "junior engineer".

I first encountered Shawyer via Costella's paper. I am grateful to Costella for pointing out that not only does Shawyer not understand Newton's laws (or if he does, is unable to communicate them clearly), but also seems incapable of correctly drawing force vectors at the sidewall. This in Shawyer's mind gave a finite net thrust, based purely on the summation of his incorrect reflected force vectors over the complete surface of the frustum. A childish error unworthy of even a junior reliability engineer, one might say?
« Last Edit: 06/17/2015 08:17 pm by deltaMass »

Offline rfmwguy

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The quote comes from Dr. Costella.  In his paper:  http://johncostella.webs.com/shawyerfraud.pdf
[…]

BTW you should know when citing Costella, that after the man criticized publicly Shawyer's EmDrive as being "a fraud" (not an "experimental error" but a "fraud" which can be considered as defamation according to the English law) that a question about the validly of SPR ltd research was raised in the UK House of Commons (logged on UK Parliament Publications and Records, Hansard Commons Debates, 5 Dec 2006, Column 340W, Electromagnetic Relativity Drive) caused in part by this claim of fraud.

Questioned on that investigation, Shawyer answered a background check was carried out by the UK authorities about Costella. This inquiry showed that he was not an electrodynamics expert working for the Australian Department of Defence, but had been briefly employed as a junior reliability engineer. He was however known to the Australian authorities as a persistent conspiracy theorist, as demonstrated by various comments he wrote on many blogs.

Not to play devil's advocate here, but sometimes things are not exactly what they seem to be. So everything on that matter that is not true facts (like falsifiable replicable experimental setups) should be taken with a grain of salt.

Hmmmm...meet Mr Costella, now a Facebook software engineer: https://www.linkedin.com/in/johncostella
Wrong guy. Try this
http://spartacus-educational.com/JFKcostella.htm

Two physics degrees is a little different to the picture painted by Shawyer of a "junior engineer".

I first encountered Shawyer via Costella's paper. I am grateful to Costella for pointing out that not only does Shawyer not understand Newton's laws (or if he does, is unable to communicate them clearly), but also seems incapable of correctly drawing force vectors at the sidewall. This in Shawyer's mind gave a finite net thrust, based purely on the summation of his incorrect reflected force vectors over the complete surface of the frustum. A childish error unworthy of even a junior reliability engineer, one might say?

Same dude...

Your guy: "John Costella was born in Australia. After graduating with honors degrees in both electrical engineering and the sciences from the University of Melbourne, he completed a Ph.D. in theoretical physics. After three years of postdoctoral research and lecturing at the University of Melbourne he was appointed as a teacher of Mathematics, Physics and Information Technology at Mentone Grammar.

Costella has researched the assassination of John F. Kennedy and has undertaken a sophisticated analyses of the Zapruder Film. Two of his articles, A Scientist's Verdict: The Film is a Fabrication and Mary Moorman and Her Polaroids appeared in The Great Zapruder Film Hoax (edited by James H. Fetzer)."

My guy, Linkedin Experience summary:

"Experience

Software Engineer
Facebook

October 2012 – Present (2 years 9 months)|San Francisco Bay Area
Data science infrastructure; sentiment analysis; statistics; image processing

Senior Data Scientist
Intelematics Australia
September 2011 – October 2012 (1 year 2 months)|Richmond, Victoria, Australia
Live vehicular traffic measurement, prediction, and broadcast

Physics Research Developer
Peter MacCallum Cancer Centre
July 2010 – September 2011 (1 year 3 months)|East Melbourne, Australia
Cancer research: volumetric radiation dose and radiobiological model analysis

Product Consultant
Thomson Reuters
March 2011 – July 2011 (5 months)|Greater New York City Area
Financial markets database systems: Enterprise Platform for Velocity Analytics (Vhayu Velocity)

Data Analyst
Bourse Data Pty Ltd
June 2010 – July 2010 (2 months)|Melbourne Area, Australia
Financial markets data systems and analysis

Data Manager and Senior Research Scientist
Portland House Research Group
April 2007 – May 2010 (3 years 2 months)|Melbourne Area, Australia
Black-box quantitative financial market research and operations

Reliability Engineer
Department of Defence, Australia
February 2006 – April 2007 (1 year 3 months)|Melbourne, Australia
Reliability, Availability, Maintainability; statistical analysis

Teacher
The Peninsula School
January 2005 – February 2006 (1 year 2 months)|Melbourne Area, Australia
High school mathematics

Teacher
Mentone Grammar
July 1997 – December 2004 (7 years 6 months)|Melbourne Area, Australia
High school mathematics


Postdoctoral Research Physicist
The University of Melbourne
July 1994 – December 1996 (2 years 6 months)|Melbourne, Australia
Theoretical particle physics"


Offline deltaMass

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I stand corrected. Apparently he is all of the above and more.  I was also misled by the great apparent difference between the portrait photos.

Offline flux_capacitor

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Yes this is the same person. He has many interests and you can see some of them on his personal web page that will reconcile what you found about him: http://johncostella.webs.com
« Last Edit: 06/17/2015 08:42 pm by flux_capacitor »

Offline flux_capacitor

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I am grateful to Costella for pointing out that not only does Shawyer not understand Newton's laws (or if he does, is unable to communicate them clearly), but also seems incapable of correctly drawing force vectors at the sidewall. This in Shawyer's mind gave a finite net thrust, based purely on the summation of his incorrect reflected force vectors over the complete surface of the frustum. A childish error unworthy of even a junior reliability engineer, one might say?

Are you seriously considering Roger Shawyer predicted the forces produced by his EmDrive using… arrows on a drawing, instead of equations?
« Last Edit: 06/17/2015 09:00 pm by flux_capacitor »

Offline rfmwguy

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I stand corrected. Apparently he is all of the above and more.  I was also misled by the great apparent difference between the portrait photos.

I did a double-take on the pics as well...big difference for sure.

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