...I believe it unfair to insist on a ridged mathematical definition of words like "complex" when the discussion moves back and forth between mathematical models and practical engineering....
...For me it is clear the the mean difficulty of building an EMdrive (or even establishing that the effect is real) lays in the very fact it is a "complex system"
https://en.wikipedia.org/wiki/Complex_system
If you look at the characteristics of complex systems you'll see that many of those have been brought up on this forum.
...
. Hopefully we may reach a happy medium steering away from either end 
All:
This will be my last post of the day. The EW Integrated Copper Frustum Test Article (ICFTA) had metallic and plastic components with competing and non-linear thermal expansions and contractions when heated, see previous posted slides on this topic, that when driving the torque pendulum's center of gravity shifts, blurred the impulsive response of this test article in time, dependent on the magnitude of the impulsive force. For me, it is fully explained in the text of the JPP report, so please go back and read it this section again until it hopefully makes sense to you.
Best, Paul M.
JPP means the Journal of Propulsion and Power, right? I do not think the discussion is satisfactory. In particular, why does the measurement device respond so much faster to calibration impulses? And if there are significant non-linearities, how can you justify you measurement protocol, which (as far as I understand) _assumes_ linear superposition of thrust and thermal signal?Yeah, not looking good to me either. I don't see any model of how it "blurred the impulsive response of this test article in time", nor any empirical indication. What I see is that the response time for all of the calibration pulses is very consistently ~4 seconds at multiple positions of the pendulum, both before and after heating, including in the null test where the pendulum was still highly displaced by the thermal effects when they applied the second calibration pulse.
EW is not alone in observing there is a time for the force to build up.
Roger also observed it with both the Experimental and Demonstrator EmDrives as attached.
I believe it has to do with the operational best point of the EmDrive being slightly off and the EmDrive pulling the natural resonant freq to be a better match to that of the applied Rf.
Sort of how a slightly off freq magnetron will be pulled into a freq lock with a resonant load that has a higher Q than that of the magnetron even though the high Q load has a different resonant freq to the magnetron. Give them time and they will work it out and lock to each other.
May also be related to the force bandwidth being much narrower than the rtn loss bandwidth.
Point is that EmDrives do generate force but please do not think of that force as being like any force you have ever experienced before. It has very different characterists.
So YES EmDrives can SOMETIME be slow to generate their force as evident by both EW's data and by Roger's data. Here again EW confirm what Roger measured way back in 2002 and 2006.
However there IS still a real impulse force being generated in these in-vacuum runs that is riding on all the thermally induced TP cg shifts.
I wrote a popular article on the emerging EmDrive physical theory described in the EW paper. This is a short and hopefully readable outline of the developing theoretical model proposed by the NASA scientists. I think reversing the order of the considerations in the paper can make the outline easier to follow. Criticism welcome.
NASA Scientists Sketch Tentative Theory of EmDrive Propulsion
https://hacked.com/nasa-scientists-sketch-tentative-theory-emdrive-propulsion/
Nice job, but Prof's Woodward and Fern just published an article in JBIS that refutes NASA's Quantum Vacuum conjecture. I would be interested in seeing Dr. White's rebuttal of that article. In the way the model is presented, I think Woodward and Fern are correct. However, there are other ways to use the QV to accomplish this that they do not mention, and that differs from Dr. White's approach. (AKA my approach to QG.)
I have been working on a simulation of the recent NASA frustum with dialectric insert that includes modeling the antenna. What I found most interesting was comparing the e-fields and surface currents between the frustum with dialectric insert and the frustum without. While being the same mode, they appear quite different!Very nice.
I see from your results how the dielectric keeps the Electric Field E away from the small end, and it confines it to the Big End.
This agrees with NASA's experimental results that the heat dissipation (mainly due to the magnetic field producing eddy currents) was much larger at the big end than the small end, when using the dielectric.
It would be nice if you would also show the magnetic field with and without the dielectric for the same identical cases.
I have been working on a simulation of the recent NASA frustum with dialectric insert that includes modeling the antenna. What I found most interesting was comparing the e-fields and surface currents between the frustum with dialectric insert and the frustum without. While being the same mode, they appear quite different!Very nice.
I see from your results how the dielectric keeps the Electric Field E away from the small end, and it confines it to the Big End.
This agrees with NASA's experimental results that the heat dissipation (mainly due to the magnetic field producing eddy currents) was much larger at the big end than the small end, when using the dielectric.
It would be nice if you would also show the magnetic field with and without the dielectric for the same identical cases.
Here you go...
Just out of curiosity, I started building the Cannae geometry based on their patent dimensions as attached and ran an Eigenmode sweep. Came up with the TM010 at 1.09 GHz which is pretty close to their resonant frequency of 1.047 GHz. I probably didn't make the grooves perfectly as I wasn't sure what the 1.513 dimension was referring to (bottom right corner of the attached picture).
The next mode is the TM110 around 1.7 GHz.
I wonder what balance between E field intensity and power gradient would yield optimal thrust...
What do the surface currents look like, slots vs no slots?
Zellerium:
And what was the assumed ac resistivity of the niobium cavity and the RF input power that generated the calculated E-field values shown in your plots?
The bottom plate of the cavity has 72 identical slots. Each slot on the bottom plate has a mill-cut into both slot walls at approximately 1 mm below the primary plane of the bottom plate.
I have been working on a simulation of the recent NASA frustum with dialectric insert that includes modeling the antenna. What I found most interesting was comparing the e-fields and surface currents between the frustum with dialectric insert and the frustum without. While being the same mode, they appear quite different!Very nice.
I see from your results how the dielectric keeps the Electric Field E away from the small end, and it confines it to the Big End.
This agrees with NASA's experimental results that the heat dissipation (mainly due to the magnetic field producing eddy currents) was much larger at the big end than the small end, when using the dielectric.
It would be nice if you would also show the magnetic field with and without the dielectric for the same identical cases.
Here you go...
You need to increase the number of nodes, need a finer mesh. The results are quite a bit away from convergence, as seen in the contour plot for the small end (upper picture here http://forum.nasaspaceflight.com/index.php?topic=40959.msg1612536#msg1612536 ).
Also as seen by the fact that the contour plot for the electric field do not match well the COMSOL results from NASA with a dielectric
or the results from my exact solution without a dielectric.
...
The mesh of the vacuum on the slot side was specified to be inside>length based>7 mm (arbitrarily chosen) and the slot side cavity was surface>length based > 7 mm (also arbitrary) which resulted in ~225,000 tetrahedra.
...

...
They match, I just wasn't showing the correct "surface charge."
...
The mesh of the vacuum on the slot side was specified to be inside>length based>7 mm (arbitrarily chosen) and the slot side cavity was surface>length based > 7 mm (also arbitrary) which resulted in ~225,000 tetrahedra.
...Now, that's a fine mesh
How long does it take for this model to run ?
Took my 32 cores ~10 min
...
They match, I just wasn't showing the correct "surface charge."Your rainbow intensity also goes to red, but the charge contour does not go to red. How do you set the rainbow intensity limits?
and look at the currents on the big end for your model:
...
They match, I just wasn't showing the correct "surface charge."Your rainbow intensity also goes to red, but the charge contour does not go to red. How do you set the rainbow intensity limits?
and look at the currents on the big end for your model:
Also notice the electric charges are pixelated while the surface currents are not. The electric charges must be calculated differently using a less dense mesh. I also ran these using 40W, not 100W, so there will be a difference there.
, Since I have no full version the model size is limited to ~1GB only, therefore I have no chance to calculate a mesh like shown below. Nevertheless a 1GB model with standard mesh and limited frequuency range, lets say 0.5GHz needs up to a full day using my old PC where the program is installed on. )3.10.3 Automatic meshing
Automatic meshing takes several model properties into account and generates a mesh appropriate for the configuration. Local refinement may still be necessary, but in most cases the automatic meshes will give a reasonable mesh. A mesh is built relative to the wavelength of an electromagnetic wave in the medium of propagation. Each solution method has different requirements and often the model itself will influence the accuracy of results. The following model properties are considered:
Frequency
The shortest wavelength corresponds to the highest simulation frequency. Note then that the frequency range for the simulation must be set before automatic meshes can be generated.
Solution method
Depending on the solution method being used to solve the problem, different mesh requirements may be needed. For example, a FEM model requires settings for tetrahedra, a MoM solution requires settings for triangles and wires, while a hybrid solution needs to take both into account.
Dielectric properties
The dielectric properties of the media in the model will affect the propagation speed of an electromagnetic wave in a medium, which will in turn affect the wavelength. Dielectric media are taken into account in all cases except in the case where infinite layers are being used. In these cases, local refinement must be applied.
Geometry curvature
Even in cases where a finer mesh isn't required for accurate solution results, it may still be required to accurately model aspects of the geometry. Automatic meshes will attempt to reasonably conform to the original geometry, the settings of which can be modified on the Advanced tab.
Local mesh refinement settings may still be applied to individual components in a model. Any local mesh refinement settings will be respected, meaning that a user's local mesh refinement setting will never be overwritten.
Wires
For wires, the wavelength (λ) is determined based on the maximum simulation frequency and the surrounding medium, see Table 3-8.
Table 3-8: Automatic meshing for wires.
Type Fine Standard Coarse
Method of moments (MoM) 1/25λ 1/12λ 1/8λ
Faces and edges
If any of the bounding regions of a face have user-defined local mesh sizes, then the face will inherit the smallest of these local mesh sizes. An edge will inherit the smallest mesh size from its bounding faces. If a face is the bounding face of a FEM region, then the first order automatic mesh size of that region will be used. If a face is the bounding face of a VEP region, then the mesh size of that region will be used. For a metal face bounding a SEP region, the smallest wavelength in the media bounding the face will be used to determine the mesh size. In all other cases the largest wavelength for the bounding media is used to determine the mesh size. When higher order basis functions are used for the MoM, junction edges (where multiple faces share an edge) and open edges (where an edge only has one face bordering it) are meshed as for RWG or order 0.5. See Table 3-9 for the automatic meshing for faces and edges.
Table 3-9: Automatic meshing for faces and edges.
Type Fine Standard Coarse
MoM (RWG or 0.5 order basis function) 1/16λ 1/12λ 1/8λ
MoM (1.5 order basis function) 3/16λ 1/4λ 3/8λ
MoM (2.5 order basis function) 1/3.2λ 1/2.4λ 1/1.6λ
MoM (3.5 order basis function) 1/1.6λ 1/1.2λ 1/0.8λ
Physical optics (PO) 1/10λ 1/8λ 1/6λ
Large element PO (LE-PO) 9/5λ 9/5λ 9/5λ
Geometrical optics (RL-GO) ∞ ∞ ∞
Regions
For regions, the wavelength (λ) is determined based on the maximum simulation frequency and the medium properties of the region, see Table 3-10. The specified lengths will be applied to the tetrahedron edge lengths.
Table 3-10: Automatic meshing for regions.
Type Fine Standard Coarse
Finite element method (1 st order FEM) 1/15λ 1/10λ 1/6λ
Finite element method (2 nd order FEM) 1/12λ 1/8λ 1/6λ
Volume equivalence principle (VEP) 1/16λ 1/12λ 1/8λ
Voxels
For voxels, the wavelength (λ) is determined based on the maximum simulation frequency and the medium properties of the region, see Table 3-1120 The specified size will be applied to the voxel edge length.
Table 3-11: Automatic meshing for voxels.
Type Fine Standard Coarse
Finite difference time domain (FDTD) 1/28λ 1/20λ 1/14λ
I wrote a popular article on the emerging EmDrive physical theory described in the EW paper. This is a short and hopefully readable outline of the developing theoretical model proposed by the NASA scientists. I think reversing the order of the considerations in the paper can make the outline easier to follow. Criticism welcome.
NASA Scientists Sketch Tentative Theory of EmDrive Propulsion
https://hacked.com/nasa-scientists-sketch-tentative-theory-emdrive-propulsion/
One issue is NASA measured static force generation big to small with a dielectric at the small end and small to big when the dielectric was not used.
Roger Shawyer, in 2002 and in 2006 also measured static force being generated in non dielectric frustums small to big as attached.
Would like to see any of these theories explain the small to big non dielectric static force generation that has been measured by NASA and Roger.
For sure, any theory needs to be able to explain ALL the measured data.
Or the systemic and/or experimental error that lead to the data in question....
I harp on this because even though you continue to point to Shawyer's past claimed results, there is very little in the way of published design detail of either the frustums or experimental equipment and environment, he used.
It makes the claims sound a great deal more like hearsay, than the result of real experimental data... And I am not saying that there was not data, just that it does not seem to be available for critical examination.
Simple feedback or energy dissipation, by themselves, do not make a copper cavity a complex system...
For me, as an engineer that builds EmDrives by applying Roger's theory equations, it is not complex at all. I understand the physics, as explained by Roger, and when applied to the real world, see it generate the predicted results.
As for Q * power scaling linear with force generation, that is just accelerator physics as is the relationship between Q and Rs and temp and freq. Of course in the real world not everything scales linear but as I see it, the vast majority of the effects do scale linear because if not there would not be accelerator cavities with Q 5x10^11.
So for sure it will not be a simple build to get a high performance room temp cavity to work well when immersed in LN2, but doing so it not something that has never been done before and thankfully Google is really good at digging out build data.
With a Cu 300K (room temp) Rs of around 8,000uOhm and a 77K Rs of around 15uOhm, there is more than ample margin to experimentally measure both the resultant Qu from doing forward power 1x Tc rise time calcs and doing force generation.
It then gets very exciting and interesting to do real time Q measurements with a non accelerating and accelerating thruster to see if the Q drops during acceleration and then to measure the energy representative of the Q drop which has exited the cavity and is doing work to accelerate the EmDrive.
That should be VERY interesting data as only a small increase in angular velocity on a rotary test rig should be sufficient to measure gained KE vs cavity energy drop from dropped Q.
More data will be added by reducing Rf amp power to become low enough to maintain constant velocity as against rotary test rig static and dynamic air resistance load and again record what happens to cavity Q as power is varied up and down around that constant velocity point.
Interesting times ahead.
And then again...,
There is a difference between Shawyer's theory and the formulas he and it seems you use to describe and predict, the design and performance of an EmDrive. It has always seemed to me that Shawyer's evolution of the EmDrive has been based on an engineering based trial and error. Thus his math based formulas also seem closer to having been derived from the engineering experience.., trial and error...
Beyond that I remind you again that any attempt to use how the efficiency of particle accelerators scales is fatally flawed in that the EmDrives being publicly discussed operate at very different frequencies and incorporate very different technologies. That being the case a there is a far greater burden on you to explain just why what is seen in the case of an accelerator, might apply in the case of a copper box filled with microwaves....
...
They match, I just wasn't showing the correct "surface charge."Your rainbow intensity also goes to red, but the charge contour does not go to red. How do you set the rainbow intensity limits?
and look at the currents on the big end for your model:Could you show the magnetic fields please? TM010 especially.
Thanks!!!!
Shell
...
Due to the meshing rules of FEKO the grid is sweatable as compared to the highest calculated/involved frequency. Sure there are a number of ways to override the standard settings to increase the number of nodes if needed. (Oh man it costs much more cpu time so far for each finer grid definition)...
...
They match, I just wasn't showing the correct "surface charge."Your rainbow intensity also goes to red, but the charge contour does not go to red. How do you set the rainbow intensity limits?
and look at the currents on the big end for your model:
snipCould you show the magnetic fields please? TM010 especially.
Thanks!!!!
Shell
All:
This will be my last post of the day. The EW Integrated Copper Frustum Test Article (ICFTA) had metallic and plastic components with competing and non-linear thermal expansions and contractions when heated, see previous posted slides on this topic, that when driving the torque pendulum's center of gravity shifts, blurred the impulsive response of this test article in time, dependent on the magnitude of the impulsive force. For me, it is fully explained in the text of the JPP report, so please go back and read it this section again until it hopefully makes sense to you.
Best, Paul M.
JPP means the Journal of Propulsion and Power, right? I do not think the discussion is satisfactory. In particular, why does the measurement device respond so much faster to calibration impulses? And if there are significant non-linearities, how can you justify you measurement protocol, which (as far as I understand) _assumes_ linear superposition of thrust and thermal signal?Yeah, not looking good to me either. I don't see any model of how it "blurred the impulsive response of this test article in time", nor any empirical indication. What I see is that the response time for all of the calibration pulses is very consistently ~4 seconds at multiple positions of the pendulum, both before and after heating, including in the null test where the pendulum was still highly displaced by the thermal effects when they applied the second calibration pulse.
EW is not alone in observing there is a time for the force to build up.
Roger also observed it with both the Experimental and Demonstrator EmDrives as attached.
I believe it has to do with the operational best point of the EmDrive being slightly off and the EmDrive pulling the natural resonant freq to be a better match to that of the applied Rf.
Sort of how a slightly off freq magnetron will be pulled into a freq lock with a resonant load that has a higher Q than that of the magnetron even though the high Q load has a different resonant freq to the magnetron. Give them time and they will work it out and lock to each other.
May also be related to the force bandwidth being much narrower than the rtn loss bandwidth.
Point is that EmDrives do generate force but please do not think of that force as being like any force you have ever experienced before. It has very different characterists.
So YES EmDrives can SOMETIME be slow to generate their force as evident by both EW's data and by Roger's data. Here again EW confirm what Roger measured way back in 2002 and 2006.
Phil:
Your above explanation does cover some of what is going on in the slower than expected build up in the force profile for these fall 2015 in-vacuum EW Lab data runs, but IMO not all. First off through 20/20 hindsight it became apparent we picked the worst possible way from a thermal interaction viewpoint to integrate the PLL box and RF amp & its ~5kg heat-sink with the copper frustum. We would have been much better off to have mounted the RF amp and heat-sink at right angles to the frustum's Z-axis thrust axis so their thermally driven expansions and contractions did not interact with the torque pendulum in the very detrimental way they did where we ran them for this fall 2015 test series. My bad! If I had followed the right angle mounting approach the force plots would be much more prompt as was shown in figure 12 in the EW Journal of Propulsion and Power report where the RF amp and heat-sink were used as the torque pendulum's counter mass at the other end of the TP and were their major thermal expansion axis was mounted at right angles to the frustum's thrust axis.
BTW, the EW torque pendulum (TP) was always balanced with one end slightly down relative to the other end, so that it would have a gravity gradient induced preference to home on a zero force point. Otherwise the TP's long-term zero-thrust baseline drift wandered all over the place in a chaotic manner that made repetitive testing near impossible. This TP baseline homing when combined with the center of gravity shifts induced in the TP by my bad integration design choice for the ICFTA is another reason why these in-vacuum force plots look so ugly. However there IS still a real impulse force being generated in these in-vacuum runs that is riding on all the thermally induced TP zero-thrust cg-baseline shifts. Next time around though with the use of spherical endcaps in the frustums, we shouldn't have to worry so much about these thermal issues if we can match or better your TE013 ~8-milli-Newton thruster performance.
Best, and get well soonest.
Paul M.