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 copper frustum we built and now are using has the following internal copper surface dimensions.Large OD : 11.00 " (0.2794m)Small OD: 6.25" (0.1588 m) & Length : 9.00 " (0.2286m)

Bottom diam.: 11.01 inch (279.7 mm)Top diam.: 6.25 inch (0.1588 mm)Height: 9.00 inch (228.6 mm)Material: 101 Copper Alloy

....Rodal posted this back a few pages. It may or may not relate to other frustums and would probably depend on material thickness ect. It is the researchgate link. http://forum.nasaspaceflight.com/index.php?topic=39004.msg1468340#msg1468340 I think it mentioned time to buckle if I remember correctly. Edit: I don't think much long term thrust could be had from this after thermal equilibrium is reached. The force should decrease with time as the thermal expansion decelerates. It might be helpful to know the time to thermal equilibrium.Edit2: Also, any positive thrust signal observed due to thermal expansion should be an equal and opposite signal upon powering down. Thermal contraction would give a negative thrust.

Is it possible to evaluate these experimental device's sensitivities to deviations from the calculated optimum resonance frequency at this time?

...

Quote from: Rodal on 01/05/2016 12:37 PM...Thanks for clarifying that you addressed separately the buckling and expansion. I apologize as I may have not made that clear in my statement. I was away a day so wasn't able to respond immediately. I take it that buckling is a one time thing right? So if it occurs once it shouldn't occur again once the deformation is permanent? If so than yeah, I guess that would give a single impulse without a retraction event. You mentioned the artifact thrust from NASA is partly due to thermal expansion or displacement of mass center? Did they also observe the retraction of that center of mass when they shut down the power? I have to think back to those plots and I vaguely think that maybe there was a retraction event, but I will have to go back and look. I was thinking that if we knew the time to thermal equilibrium, would it be advisable to at least keep the frustum powered on for a time longer than that so that we are observing more than just those events?Edit: well to compound the problem in most cases the frustum is in air so there is the convection problem included with long term tests.Edit2: one thing that worries me is putting the frustum in an insulated box (closed system) might eliminate thermal equilibrium (continuous heating) unless maybe an internal heat sink could reduce that to some extent.

for NASA's experiment without a dielectric we can say that the exact solution says that there was indeed a natural frequency for mode TE012 within 0.1% of the measured frequency, but as to whether the measured frequency was at the resonant peak, one has to rely on NASA's team having actually found peak resonance with S21 and S11 measurements (because we don't know the dimensions of NASA's resonant cavity to the precision required to calculate the resonant peak with all the required digits of numerical precision).

EXPERIMENTAL PROOF THAT NASA'S TEST WITHOUT A DIELECTRIC INSERT WAS IN RESONANCE AT THE FREQUENCY REPORTED IN NASA'S REPORTSince we had concluded in http://forum.nasaspaceflight.com/index.php?topic=39214.msg1470613#msg1470613that:Quote for NASA's experiment without a dielectric we can say that the exact solution says that there was indeed a natural frequency for mode TE012 within 0.1% of the measured frequency, but as to whether the measured frequency was at the resonant peak, one has to rely on NASA's team having actually found peak resonance with S21 and S11 measurements (because we don't know the dimensions of NASA's resonant cavity to the precision required to calculate the resonant peak with all the required digits of numerical precision). Finally, we reproduce again the experimental data from NASA Johnson Eagleworks Laboratory that proves that their experiment without dielectric inserts in their frustum of a cone cavity was indeed in resonance.The resonance for mode shape TE012 without dielectric inserts was measured with an Agilent Model 9923A, 4.0 GHz Field Fox Vector Network Analyzer (VNA) both in the S11 and S21 modes (as shown in the pictures below) using the frustum RF loop antenna as input and the frustum sense antenna located 180 degrees around from the loop antenna with both antennas being at the same 15% of the height from the large end of the frustum, i.e., 0.15 * 9.00” = 1.35” or 34.29mm away from the large end. The TE012 resonant frequency without the dielectric PE disc inserts was measured at 2.167137 GHz using either the S11 or S21 methods as shown by the two attached VNA slides. Thus, any claims made about this test without dielectric inserts in NASA's frustum of a cone cavity with mode shape TE012 at 2.167 GHz not being in resonance are shown to be completely baseless, false and misleading.This, factual information shows without a doubt that indeed NASA's frustum of a cone without dielectric inserts was in resonance with mode shape TE012 at 2.167 GHz in agreement with NASA's report and in agreement with the COMSOL Finite Element Analysis calculation and in agreement with the exact solution I calculated using Wolfram Mathematica.

Quote from: Rodal on 01/11/2016 07:28 PMEXPERIMENTAL PROOF THAT NASA'S TEST WITHOUT A DIELECTRIC INSERT WAS IN RESONANCE AT THE FREQUENCY REPORTED IN NASA'S REPORTSince we had concluded in http://forum.nasaspaceflight.com/index.php?topic=39214.msg1470613#msg1470613that:Quote for NASA's experiment without a dielectric we can say that the exact solution says that there was indeed a natural frequency for mode TE012 within 0.1% of the measured frequency, but as to whether the measured frequency was at the resonant peak, one has to rely on NASA's team having actually found peak resonance with S21 and S11 measurements (because we don't know the dimensions of NASA's resonant cavity to the precision required to calculate the resonant peak with all the required digits of numerical precision). Finally, we reproduce again the experimental data from NASA Johnson Eagleworks Laboratory that proves that their experiment without dielectric inserts in their frustum of a cone cavity was indeed in resonance.The resonance for mode shape TE012 without dielectric inserts was measured with an Agilent Model 9923A, 4.0 GHz Field Fox Vector Network Analyzer (VNA) both in the S11 and S21 modes (as shown in the pictures below) using the frustum RF loop antenna as input and the frustum sense antenna located 180 degrees around from the loop antenna with both antennas being at the same 15% of the height from the large end of the frustum, i.e., 0.15 * 9.00” = 1.35” or 34.29mm away from the large end. The TE012 resonant frequency without the dielectric PE disc inserts was measured at 2.167137 GHz using either the S11 or S21 methods as shown by the two attached VNA slides. Thus, any claims made about this test without dielectric inserts in NASA's frustum of a cone cavity with mode shape TE012 at 2.167 GHz not being in resonance are shown to be completely baseless, false and misleading.This, factual information shows without a doubt that indeed NASA's frustum of a cone without dielectric inserts was in resonance with mode shape TE012 at 2.167 GHz in agreement with NASA's report and in agreement with the COMSOL Finite Element Analysis calculation and in agreement with the exact solution I calculated using Wolfram Mathematica.Based on this measurement data I've got a look to my calculated frequency for this case and find:Mode calculated(GHz) Comsol(GHz) diff Comsol(%) diff Comsol(GHz) measured NASA(GHz) diff measured(%)TE012 2,1653438127 2,1794 -0,64 -0,014 2,167138 -0,08279Maybe its based on tiny differences between the final real measured cavity and the Comsol simulation.Of course there are much larger differences for many of the other modes in my spreadsheet*. As I wrote elsewhere I believe more in field simulations because it works.* I use it only for general overview.

QUALITY OF RESONANCE "Q" FOR NASA'S TEST WITHOUT A DIELECTRIC INSERTFinally, what was the predicted Quality of Resonance ("Q") for NASA's test without a dielectric insert?Using the following resistivity for the copper alloy used for this test:Material: Copper alloy 101resistivity = 1.71*10^(-8) ohm meterSources for this material value: http://www.azom.com/article.aspx?ArticleID=2850#_Physical_Properties_of http://www.husseycopper.com/production/alloys/electrical/c-101-00/Using the following geometrical dimensions for the frustum of a cone, as used by Frank Davis:bigDiameter = (11.01 inch)*(2.54 cm/inch)*(1 m/(100 cm)); smallDiameter = (6.25 inch)*(2.54 cm/inch)*(1 m/(100 cm)); axialLength = (9 inch)*(2.54 cm/inch)*(1 m/(100 cm)); the exact solution, using Wolfram Mathematica to solve Maxwell's equations, gives:Q = 78642So, a very good Q value is predicted for mode shape TE012 at the frequency:measured frequency at which NASA test was performed: 2.168 GHzcalculated natural frequency (exact solution, Dr. Rodal using Wolfram Mathematica): 2.165 GHzfor NASA's test without a dielectric insert that resulted in no thrust.The fact that this NASA test resulted in zero "anomalous force", and that Paul March at NASA had the great insight to introduce dielectric inserts at the small end to produce the anomalous force, is one of the most important data point in the history of EM Drive experiments

...These are great news. I came to nearly the same conclusion some time last year(Q=79011). I never post it, at least I am not sure about the formula (found an approximation in an cern paper about cavities if my memory is correct) and my implementation. No -3dB bandwidth needed for the calculation, its mode,volume, conductivity dependent.Based on this the Q at larger volumes is in general (mode dependent) bigger than for smaller volume. I think more energy can be stored in larger volumes.If I try to use to divide all dimensions by a factor of 10, I get a 10 times higher resonant frequency (good so far) but a Q of only 24985. Could you so kind to check this please, I can feel something may still wrong with this calculation although the number for the original dimensions fits yours very well.

Quote from: X_RaY on 01/12/2016 09:19 PM...These are great news. I came to nearly the same conclusion some time last year(Q=79011). I never post it, at least I am not sure about the formula (found an approximation in an cern paper about cavities if my memory is correct) and my implementation. No -3dB bandwidth needed for the calculation, its mode,volume, conductivity dependent.Based on this the Q at larger volumes is in general (mode dependent) bigger than for smaller volume. I think more energy can be stored in larger volumes.If I try to use to divide all dimensions by a factor of 10, I get a 10 times higher resonant frequency (good so far) but a Q of only 24985. Could you so kind to check this please, I can feel something may still wrong with this calculation although the number for the original dimensions fits yours very well.You are correct on all counts I will be posting further...

The 1% error is due to this approximation:(∫ElectromagneticEnergy dV/ ∫ ElectromagneticEnergy dA) ~ ~ (ElectromagneticEnergy/ElectromagneticEnergy) (∫dV/ ∫ dA ) ~ InteriorVolume/InteriorSurfaceArea ~ π R^{2}L/(2 π R (R+L) ) ~ R/(2(1+R/L))approximating the behavior of the electromagnetic mode shape as being almost constant throughout the cavity (this approximation is pretty good for a low mode like TE012 but is expected to degrade if one considers higher modes)

Quote from: X_RaY on 01/12/2016 09:19 PM...These are great news. I came to nearly the same conclusion some time last year(Q=79011). I never post it, at least I am not sure about the formula (found an approximation in an cern paper about cavities if my memory is correct) and my implementation. No -3dB bandwidth needed for the calculation, its mode,volume, conductivity dependent.Based on this the Q at larger volumes is in general (mode dependent) bigger than for smaller volume. I think more energy can be stored in larger volumes.If I try to use to divide all dimensions by a factor of 10, I get a 10 times higher resonant frequency (good so far) but a Q of only 24985. Could you so kind to check this please, I can feel something may still wrong with this calculation although the number for the original dimensions fits yours very well.Please notice that when reducing the size to 1/10 of the original size, you calculate a Q=24,985 down from the original Q=79,011So that the scaling you calculate is:X-Ray calculated Q scaling: (79,011/24,985)/Sqrt[10] = 1.0000which goes exactly like the square root of the dimension, instead of my calculation (here: https://forum.nasaspaceflight.com/index.php?topic=39214.msg1474351#msg1474351 ) using the exact solution:Rodal calculated Q scaling: (78642.44767279371`/25104.934868706456`)/Sqrt[10] = 0.990599showing that the exact solution differs by 1% from the approximate rule of Q scaling like the square root.I justify the 1% difference between the exact solution for Q and the approximation involved in the scaling calculations for Q, as due to the approximation of the energy integral in my discussion of Q scaling:QuoteThe 1% error is due to this approximation:(∫ElectromagneticEnergy dV/ ∫ ElectromagneticEnergy dA) ~ ~ (ElectromagneticEnergy/ElectromagneticEnergy) (∫dV/ ∫ dA ) ~ InteriorVolume/InteriorSurfaceArea ~ π R^{2}L/(2 π R (R+L) ) ~ R/(2(1+R/L))approximating the behavior of the electromagnetic mode shape as being almost constant throughout the cavity (this approximation is pretty good for a low mode like TE012 but is expected to degrade if one considers higher modes)QUESTION to X-Ray; are you approximating the energy integral calculation in your Q calculation as above, and is that why your calculation results in perfect scaling of Q going like the square root of the dimension ?

Quote from: Rodal on 01/15/2016 06:55 PMQuote from: X_RaY on 01/12/2016 09:19 PM...These are great news. I came to nearly the same conclusion some time last year(Q=79011). I never post it, at least I am not sure about the formula (found an approximation in an cern paper about cavities if my memory is correct) and my implementation. No -3dB bandwidth needed for the calculation, its mode,volume, conductivity dependent.Based on this the Q at larger volumes is in general (mode dependent) bigger than for smaller volume. I think more energy can be stored in larger volumes.If I try to use to divide all dimensions by a factor of 10, I get a 10 times higher resonant frequency (good so far) but a Q of only 24985. Could you so kind to check this please, I can feel something may still wrong with this calculation although the number for the original dimensions fits yours very well.Please notice that when reducing the size to 1/10 of the original size, you calculate a Q=24,985 down from the original Q=79,011So that the scaling you calculate is:X-Ray calculated Q scaling: (79,011/24,985)/Sqrt[10] = 1.0000which goes exactly like the square root of the dimension, instead of my calculation (here: https://forum.nasaspaceflight.com/index.php?topic=39214.msg1474351#msg1474351 ) using the exact solution:Rodal calculated Q scaling: (78642.44767279371`/25104.934868706456`)/Sqrt[10] = 0.990599showing that the exact solution differs by 1% from the approximate rule of Q scaling like the square root.I justify the 1% difference between the exact solution for Q and the approximation involved in the scaling calculations for Q, as due to the approximation of the energy integral in my discussion of Q scaling:QuoteThe 1% error is due to this approximation:(∫ElectromagneticEnergy dV/ ∫ ElectromagneticEnergy dA) ~ ~ (ElectromagneticEnergy/ElectromagneticEnergy) (∫dV/ ∫ dA ) ~ InteriorVolume/InteriorSurfaceArea ~ π R^{2}L/(2 π R (R+L) ) ~ R/(2(1+R/L))approximating the behavior of the electromagnetic mode shape as being almost constant throughout the cavity (this approximation is pretty good for a low mode like TE012 but is expected to degrade if one considers higher modes)QUESTION to X-Ray; are you approximating the energy integral calculation in your Q calculation as above, and is that why your calculation results in perfect scaling of Q going like the square root of the dimension ?

.../...and using this equation, one can plot the results in completely frame-indifferent terms:deltaMass/InitialMass = function (deltaV/c , InitialVelocity/c).../...

On a similar vein to frobnicat's post above: in the EM Drive thread you noted that deceleration requires significantly different negative mass creation than acceleration from rest.But consider this: a) use your device to accelerate something to some velocity b) turn it off, so that the device now moves at constant velocity c) move your frame of reference to that inertial frame, so that the device is once again at rest d) rotate the device 180 degrees then switch it back on, accelerating in that new inertial frame (and decelerating in the original frame).It is extremely hard to see how acceleration from rest in the opposite direction can require any different consumption of anything than in the original direction.R.[modified to make more sense after posting]

Quote from: Rodal on 02/03/2016 09:49 PM.../...and using this equation, one can plot the results in completely frame-indifferent terms:deltaMass/InitialMass = function (deltaV/c , InitialVelocity/c).../...It is not clear to me in your argument why InitialVelocity/c would qualify as "frame-indifferent". Different inertial observers could agree on deltaV/c but see different values for InitialVelocity/c, and hence predict different outcome deltaMass/InitialMass. The other way around, measuring a certain deltaMass/InitialMass and a certain deltaV/c would imply one peculiar InitialVelocity/c that would hold for one privileged inertial observer and not for the others. Am I misunderstanding something ?

Quote from: RERT on 02/05/2016 08:39 AM.../...It is extremely hard to see how acceleration from rest in the opposite direction can require any different consumption of anything than in the original direction..../....../...2) Take a look at the mathematical solution. The solution function is continuous, for negative values of deltaV/c it is double-valued. The asymmetry you are addressing in your response arises because you are arbitrarily taking into account only one of the possible values for negative deltaV/c. Mathematically and for consistency you should instead take into account all possible values of a multi-valued function, when addressing symmetry of a multi-valued function.Since the solution is multi-valued I need the time to further examine it in both directions, and assess its physical significance (if any, because the notion of negative mass and energy is anything but intuitive! )..../...

.../...It is extremely hard to see how acceleration from rest in the opposite direction can require any different consumption of anything than in the original direction..../...

Quote from: Rodal on 02/05/2016 07:59 PMQuote from: RERT on 02/05/2016 08:39 AM.../...It is extremely hard to see how acceleration from rest in the opposite direction can require any different consumption of anything than in the original direction..../....../...2) Take a look at the mathematical solution. The solution function is continuous, for negative values of deltaV/c it is double-valued. The asymmetry you are addressing in your response arises because you are arbitrarily taking into account only one of the possible values for negative deltaV/c. Mathematically and for consistency you should instead take into account all possible values of a multi-valued function, when addressing symmetry of a multi-valued function.Since the solution is multi-valued I need the time to further examine it in both directions, and assess its physical significance (if any, because the notion of negative mass and energy is anything but intuitive! )..../...Following from the relativistic momentum conservation (on a single axis) I get the same expression as what you wrote for deltaMassBar as a function of deltavc and vbarc. From the initial equality (momentum conservation) to this last equality there is no need to take a square root of the equation, nor solve for solutions of second degree polynomial : so why do you say the function is double-valued, and specifically for negative deltavc ?For instance with vbarc=1/2 and deltavc=-1/4 the expression unequivocally gives deltaMassBar=sqrt(5)-1 > 0What would be an other solution ?I understand this is under construction

It is extremely hard to see how acceleration from rest in the opposite direction can require any different consumption of anything than in the original direction.

...The solution makes sense for InitialVelocity/c = 0 (γ=1) (it agrees with Bondi's momentum equation for negative mass in that case). (H. Bondi, Negative Mass in General Relativity, Rev. Mod. Phys. 29, 423;1 July 1957)...

2) Forward (Robert Forward, "Negative matter propulsion", Journal of Propulsion and Power, Vol. 6, No. 1 (1990), http://arc.aiaa.org/doi/abs/10.2514/3.23219?journalCode=jpp), and Bondi, have used similar expressions when discussing momentum conservation (https://en.wikipedia.org/wiki/Negative_mass#Runaway_motion), but they only consider the case of two bodies, one with identical absolute value of mass: one body with mass +m and another one with mass -m instead of the case being discussed here of continuous variability in mass.

It is interesting to note that, in the spaceship consisting ofpositive and negative mass elements discussed by Forward, asthe total mass of the spaceship approaches zero (M _ - M+ =~ 0)the Brownian motion of the ship due to impact of various particles will buffet it around at increasingly large velocities. Evenin a perfect vacuum, photons of cosmic background radiationwill become important if the mass is low enough. AtM _ ~ M+. the mass of the ship equals zero and any impact willapparently send it moving off at the speed or light. (ActuallyM will never precisely equal zero, as the ship will be constantlyabsorbing and emitting thermal photons.)A particle hitting a zero mass spaceship would, of course,actually hit either the positive or negative mass portion. In aship consisting of nearly equal amounts of positive andnegative mass, the center of mass can move faster than eitherof the constituent masses and will do so whenever the distancebetween the two masses changes. Unless the ship is allowed tocome apart the true motion of the ship must eventually recon·cile with the motion of the center or mass. This occurs due tothe force on the link connecting the masses. The force on thelink will cause the masses to move as described by Forward, sothat even a small initial impulse will cause very large change invelocity if the positive and negative masses are nearly equal.This fact is of use in propulsion: a very nearly zero mass spaceshipcould be propelled by a flashlight.

Dr.Rodal -Frobnicat seems far more nimble than me at this stuff, but since you ask for some mathematical critique, I think I owe you a stab.There are three frames involved: frame 0, where the object is initially at rest. Frame 1, where it has acquired its initial velocity, and frame 2, where it has acquired its final velocity.The total mass-energy is thus m0c^2, and does not vary between frames: in fact I think your equationm1V1/gamma1 = m2V2/gamma2 should be replaced by the conservation of the norm of the energy momentum vector, vis:m0^2c^4 =gamma1^2*m1^2*c^4-gamma1^2*m1^2*v1^2 =gamma2^2*m2^2*c^4-gamma2^2*m2^2*v2^2[I may or may not have this right, but there will definitely be mass-energy terms mixed with the momentum terms.] I'd take a stab that this is the kind of covariant formulation Frobnicat eluded to above. I won't comment on later parts of the analysis, since if my comment is correct the rest would not follow.R.

.../...where, in the above equation and in the ones to follow, m is the rest mass m=m_{o}, the mass of an object in its rest frame. Also, as already discussed here: http://forum.nasaspaceflight.com/index.php?topic=39214.msg1488362#msg1488362 the InitialVelocity must be measured with respect to the same frame where the InitialMass of the object was measured. This is an acceleration problem, hence the frame where the rest mass is measured is a privileged, non-inertial frame. If other frames of reference are used, not only the Initial Velocity will be different, but the Initial Mass will be different too, if measured in any frame other than the object's initial frame of reference to measure its mass. .../...

...I don't see how you can start with a singleton lump closed system that's supposed to respect conservation of energy and conservation of mass in the framework of SR...

Dr Rodal, you insist that you are here doing a study of a closed system composed of a single lump of mass, i.e. that there is no separation (separation in 2 parts from a single part, as would be the case for action/reaction) nor joining ("melting" of 2 parts in a single part, as would be the case for an inelastic collision/aggregation) nor bounce (2 parts exchanging momentum but still being separate before and after such interaction). Do I understand correctly your premise ?...All right so we are not using so called relativistic mass m_{rel}, and by avoiding the traps of m_{rel} we are conforming to prescriptions of modern physics teaching. Fine with me. ...

...m^{2} c^{4} = E^{2} - p^{2} c^{2} ....

Hi,I did not follow the whole conversation during last few days. Why is a variable mass related to any force toward the small end of the cavity? If there IS a lower or higher mass related to the EM field inside the resonator what is that meaning? The smaller diameter side of the cavity itself have had a lower mass because it consists of less volume of copper as the larger side. Also the earth gravity is almost homogeneous over the size of the cavity. How it can generate a thrust in shifting the center of the mass of itself? A slightly other force composition in relation to the gravity field around ok but thrust generation? IMHO Only a negative mass value would explain thrust generation against the background gravity field at all (repulsive energy). The direction of this force would be against the attractive gravity of the biggest mass nearby: the earth it self.I think I have to study your the last posts.

..Quote...In order to have a non-dimensional scalar field φ of values around unity, in expression(1) the constant G0 representing Newton gravitational constant is included...Based on this statement in section 2. of the paper there is a (weak)coupling to the gravity and if so there is also coupling on the earth gravity field for this scalar. And yes gravity is a very weak force in comparison to the other forces inclusive electromagnetism. I read the paper one or two years ago and it's an impressive idea. I have to read it again to follow your statements but its hard stuff and it will take a while.

...In order to have a non-dimensional scalar field φ of values around unity, in expression(1) the constant G0 representing Newton gravitational constant is included...

4) Minotti's paper predicts, that for copper wall thickness ~1 mm, the thicker the copper (as long as significantly greater than the skin depth), the greater the force.

Ok, trying to wrap what's left of my mind around this:Quote4) Minotti's paper predicts, that for copper wall thickness ~1 mm, the thicker the copper (as long as significantly greater than the skin depth), the greater the force.So, say you have two EM Drive units that are identical, except one has 'skin depth' of 1 mm and the other has 'skin depth' of say 3 mm. According to this theory, the second device should perform significantly better. Is that correct? If so, this appears to be something within the capabilities of our DIY crowd.But...1 - would the increased weight of the device with the thicker skin offset the thrust measurements? (I suspect I am missing something glaringly obvious here.)2 - Does the entire skin need to be thicker, or just the end plates?

Assuming a cavity with thin walls (but much thicker than the penetration depth ,in order to the boundary conditions used to be correct) of mass surface density ...There are no details in the literature as to the precise dimensions of the cavitiesused in the experiments, so that an example roughly similar to the overall dimensionreported and with the proportions observed in the published photographs will be used.Assuming a wall of thickness 1 mm, and a copper mass density of 8.9 × 103 kg/m3, wehave = 8.9 kg/m2.

.../...Variable mass, implying the need for negative mass to self-accelerate, addresses both conservation of momentum and it also addresses conservation of energy.Energy is conserved, and such a propulsion device is not a free-energy machine, because the greater the speed, the lower the mass. More on that later...(The practical problem of course is that up to now, nobody has found experimental evidence of negative mass )

.../...4) The EM Drive is a closed system, in which case the only way I see to conserve momentum-energy for acceleration of the EM Drive is to have creation of negative mass-energy in the EM Drive.../...

Dr Rodal, thanks for answering my comments about your work around "negative mass" creation and conservation of momentum. It was clear from the equations that you considered only conservation of momentum and didn't consider conservation of total energy, but from early posts (on the main EM drive thread) I had the impression that you were assuming some compatibility with conservation of energy, for instance (bold added by me for emphasis) :Quote from: Rodal on 02/03/2016 01:27 PM.../...Variable mass, implying the need for negative mass to self-accelerate, addresses both conservation of momentum and it also addresses conservation of energy.Energy is conserved, and such a propulsion device is not a free-energy machine, because the greater the speed, the lower the mass. More on that later...(The practical problem of course is that up to now, nobody has found experimental evidence of negative mass )

...I see two different problems. Possibility of negative mass, that is Weak Energy Condition breaking, is one thing. But modification of rest (invariant) mass in a closed system without a balanced counterpart in changes in kinetic energy is another one, it looks more like conservation of (total) energy breaking, whether the change appears as + or - mass. As an example of the difference between those 2 hypothesis : we can apply usual SR for conservation of energy and momentum when considering a single particle of mass m1>0 splitting into two particles of mass m2>m1 and m3<0. The hypothesis of the existence of particle of mass<0 doesn't change the equations. But your approach seems to ignore one equation (conservation of energy) and hence gives the system a degree of freedom absent of this initial example. Negative mass deltas is then not specifically implicated, and indeed your solution space also shows positive (unbalanced) delta mass, i.e. actually either positive or negative total energy evolutions.Your latest answer clarifies this as citing a scalar field or supplementary spatial dimension as required to make sense of such mass variation... I would have a hard time following in detail Minotti (or you following Minotti) on such topic outside of usual SR application, but maybe could understand a few words of how, one way or another, energy is conserved in the end to say that the approach "conserves momentum-energy" ?...

Is the concept of a time-dependent, variable "rest-mass" (mass that would be measured at rest), allowed by the following theories?1) Special Relativity: NO. The rest mass cannot be a function of the time coordinate, as Lorentz covariance would not be preserved. Variation of rest mass cannot be due to kinematic (velocity or position) evolution....

Is the concept of a time-dependent, variable "rest-mass" (mass that would be measured at rest), allowed by the following theories?...2) Einstein's General Relativity (GR): It appears as NO. It appears that a time-dependent variable mass would give rise to a time-dependent Energy Stress tensor, solely due to the mass variability with time, which is not consistent with Einstein's GR theory of gravitation. Also it appears that Relativity's Energy-Momentum equation:m^{2} c^{4} = E^{2} - p^{2} c^{2} may prevent general time-dependent variable mass.Note: I need to review how does Woodward accommodate variable negative mass-energy in his theory (which I understand he states is consistent with Einstein's General Relativity), as it appears to me that there should be an issue with the time-dependent Energy-Stress tensor and with the Energy-Momentum equation in such a theory....

Quote from: frobnicat on 02/10/2016 03:31 PMDr Rodal, thanks for answering my comments about your work around "negative mass" creation and conservation of momentum. It was clear from the equations that you considered only conservation of momentum and didn't consider conservation of total energy, but from early posts (on the main EM drive thread) I had the impression that you were assuming some compatibility with conservation of energy, for instance (bold added by me for emphasis) :Quote from: Rodal on 02/03/2016 01:27 PM.../...Variable mass, implying the need for negative mass to self-accelerate, addresses both conservation of momentum and it also addresses conservation of energy.Energy is conserved, and such a propulsion device is not a free-energy machine, because the greater the speed, the lower the mass. More on that later...(The practical problem of course is that up to now, nobody has found experimental evidence of negative mass )1) The above statement that negative mass addresses the conservation of energy problem is correct in the specific instance of constant zero initial lumped mass.

Specifically, the initial condition of lumped rest mass=0, staying constant (for example as a result of equal magnitude negative mass as positive mass) answers all your previous posts regarding conservation of energy, and it does so trivially, as the kinetic energy is zero for zero mass, and you cannot use the EM Drive as a generator if it has effective zero inertial mass. (Effectively I know that even photons, with zero rest mass have energy, so if you want you can throw an expression with the Plank constant there, and replace zero kinetic energy with very very small kinetic energy).

If my memory is correct, in your consideration of energy conservation you never considered that the rest mass could be zero.

You assumed (unstated) that the rest mass was greater than zero.

The concept which you addressed in your energy conservation statements, the EM Drive, has been discussed by Dr. White and by Dr. Minotti as involving negative energy-mass, so one should discuss the consequences of such negative energy-mass in considerations of energy conservation, instead of ignoring it, and assuming as in your considerations, that the energy-mass was positive, and constant. In other words, your energy considerations for the EM Drive, ignore the premise of these authors.

2) The argument that <<nobody has found experimental evidence of negative mass >> is a non-starter in this discussion ...

... because: eminent physicists like Kip Thorne, Hawking and others have discussed negative mass (to stabilize wormholes for example), so there is no "shame" in theoretically considering negative mass. As to experimental evidence, whether Casimir effect and other types of negative energy can indeed be considered experimental evidence of negative energy is up for discussion, but again eminent physicists (for example in discussion of stabilization of wormholes posit the Casimir energy as the means for the negative energy).

And again, in your considerations of conservation of energy you are dealing with a concept where some authors (Dr. White and Dr. Minotti) explicitly state that they are considering negative energy !

Therefore, since your conservation of energy considerations ignore negative energy-mass, your considerations of energy conservation seem to be inapplicable to the concepts advanced by Dr. White and Dr. Minotti.

Quote from: frobnicat on 02/10/2016 03:31 PM...I see two different problems. Possibility of negative mass, that is Weak Energy Condition breaking, is one thing. But modification of rest (invariant) mass in a closed system without a balanced counterpart in changes in kinetic energy is another one, it looks more like conservation of (total) energy breaking, whether the change appears as + or - mass. As an example of the difference between those 2 hypothesis : we can apply usual SR for conservation of energy and momentum when considering a single particle of mass m1>0 splitting into two particles of mass m2>m1 and m3<0. The hypothesis of the existence of particle of mass<0 doesn't change the equations. But your approach seems to ignore one equation (conservation of energy) and hence gives the system a degree of freedom absent of this initial example. Negative mass deltas is then not specifically implicated, and indeed your solution space also shows positive (unbalanced) delta mass, i.e. actually either positive or negative total energy evolutions.Your latest answer clarifies this as citing a scalar field or supplementary spatial dimension as required to make sense of such mass variation... I would have a hard time following in detail Minotti (or you following Minotti) on such topic outside of usual SR application, but maybe could understand a few words of how, one way or another, energy is conserved in the end to say that the approach "conserves momentum-energy" ?...In the above post: http://forum.nasaspaceflight.com/index.php?topic=39214.msg1489632#msg1489632, I already addressed the fact that I think that variable rest mass is incompatible with Special Relativity, and so it is perplexing why you are bringing Special Relativity (assuming this is what you mean by "SR") into the picture again, as if demanding that Special Relativity should be obeyed.I thought this was clear:Quote from: Rodal on 02/09/2016 05:30 PMIs the concept of a time-dependent, variable "rest-mass" (mass that would be measured at rest), allowed by the following theories?1) Special Relativity: NO. The rest mass cannot be a function of the time coordinate, as Lorentz covariance would not be preserved. Variation of rest mass cannot be due to kinematic (velocity or position) evolution....

As to conservation of energy, I thought that this was also clear:Quote from: Rodal on 02/09/2016 05:30 PMIs the concept of a time-dependent, variable "rest-mass" (mass that would be measured at rest), allowed by the following theories?...2) Einstein's General Relativity (GR): It appears as NO. It appears that a time-dependent variable mass would give rise to a time-dependent Energy Stress tensor, solely due to the mass variability with time, which is not consistent with Einstein's GR theory of gravitation. Also it appears that Relativity's Energy-Momentum equation:m^{2} c^{4} = E^{2} - p^{2} c^{2} may prevent general time-dependent variable mass.Note: I need to review how does Woodward accommodate variable negative mass-energy in his theory (which I understand he states is consistent with Einstein's General Relativity), as it appears to me that there should be an issue with the time-dependent Energy-Stress tensor and with the Energy-Momentum equation in such a theory....Also it is perplexing why you keep bringing up conservation of energy for a variable mass problem in a closed system, when it was stated repeatedly that any such variable mass in a closed system to make sense it would involve creation (or destruction) of negative energy-mass.

As to how variable mass can be addressed in scalar-tensor theories of gravitation, this has already been done prior to my posting. I'll try to find the references... In your discussion of conservation of energy in the EM Drive: you disregard the fact that authors like Dr. White and Dr. Minotti posit a solution that involves negative energy-mass, and instead you insist in considerations of energy conservation that involve the assumption of constant positive energy-mass, an assumption in contradiction with the assumptions of the authors of the concept (EM Drive) you are addressing in your consideration.Rather than insisting on obeying Special Relativity and constant energy-mass, when discussing the EM Drive concept, it seems to me that it is better for me (and you too) to address the fact that the authors (Dr. White and Dr. Minotti) posit negative energy-mass, rather than disregarding the author's assumptions.

...This is a lot of trouble just for asserting that it could conceivably be a closed system when, given the phenomenology of the considered equations, all indicates that it is open....

....My considerations of energy conservation, since I made them under the specific situation of stationary thrust and stationary velocity, quite don't care about the sign of energy or mass terms. They care about some lack of equality, the fact that so far we are not aware of a frame agnostic definition of total Energy for the whole system, in a deep space context (not reacting on lab's walls), such that we don't see E_{tot}(t+Δt)≠E_{tot}(t). While it's true I spoke mainly about apparent excess of energy, the same idea (stationary thrust at stationary velocity) can be applied to make apparent complete wipeout of some energy content, that is as problematic.

so far we are not aware of a frame agnostic definition of total Energy for the whole system, in a deep space context (not reacting on lab's walls), such that we don't see E_{tot}(t+Δt)≠E_{tot}(t)

Quote from: frobnicat on 02/11/2016 12:11 AM...This is a lot of trouble just for asserting that it could conceivably be a closed system when, given the phenomenology of the considered equations, all indicates that it is open....My God, I posted with bold red signs and a moving banner, something titled "Under construction" and now you are stating that I am asserting that the EM Drive is a closed system that works on spontaneous and continuous creation of negative mass-energy Considering what are the implications if the EM Drive would be a closed-system does not at all mean that one is "asserting" that it is Such considerations are par for the course for anybody involved in R&D !

Quote from: Rodal on 02/11/2016 12:30 AMQuote from: frobnicat on 02/11/2016 12:11 AM...This is a lot of trouble just for asserting that it could conceivably be a closed system when, given the phenomenology of the considered equations, all indicates that it is open....My God, I posted with bold red signs and a moving banner, something titled "Under construction" and now you are stating that I am asserting that the EM Drive is a closed system that works on spontaneous and continuous creation of negative mass-energy Considering what are the implications if the EM Drive would be a closed-system does not at all mean that one is "asserting" that it is Such considerations are par for the course for anybody involved in R&D ! I'm not stating that you are asserting that the EM Drive is a closed system, I say that this assertion (that your thought experiment and derivation imply, as an hypothesis) would be a lot of trouble... You were clear enough about the speculative nature of all that. Sorry if I'm cluttering this thread, hope this can be of use as possibly representative of the kind of indignation you'll have to face if you were to present that to a wider audience, and help toward a more explicit exposition of the premises. I'll be back after construction, to haunt the basement

I think about the "better as large as possible" condition to get very high Q value. Using the linear Q approximation it follows that the Q factor will be larger also the higher the mode indices be. Using well known dimensions, of course at higher frequencies, for the Brady frustum I get a Q value at ~24.5GHz of ~730000 for TE45(34) [the mode number is only used as an example]. The total number may be wrong** but the context still holds. Now based on this I understand the usage of whispering modes gallery in the Cannae thruster much better, it simply leads to higher Q values. It's not only the volume of the cavity, in general frequency volume and mode number are of interest*.It's simply another solution/expression of the linearity of the maxwell equations while scaling some factors.* Beside other effects like ε_{r} & tanδ of the volume material and the cavity wall conductivity (σ) and so on.** As discussed in this thread the total Q number for higher than the fundamental modes don't holds using a simple approximation formula. https://forum.nasaspaceflight.com/index.php?topic=39214.msg1476709#msg1476709

Quote from: X_RaY on 03/25/2016 08:07 PMI think about the "better as large as possible" condition to get very high Q value. Using the linear Q approximation it follows that the Q factor will be larger also the higher the mode indices be. Using well known dimensions, of course at higher frequencies, for the Brady frustum I get a Q value at ~24.5GHz of ~730000 for TE45(34) [the mode number is only used as an example]. The total number may be wrong** but the context still holds. Now based on this I understand the usage of whispering modes gallery in the Cannae thruster much better, it simply leads to higher Q values. It's not only the volume of the cavity, in general frequency volume and mode number are of interest*.It's simply another solution/expression of the linearity of the maxwell equations while scaling some factors.* Beside other effects like ε_{r} & tanδ of the volume material and the cavity wall conductivity (σ) and so on.** As discussed in this thread the total Q number for higher than the fundamental modes don't holds using a simple approximation formula. https://forum.nasaspaceflight.com/index.php?topic=39214.msg1476709#msg1476709Very interesting. How did you calculate the Q for TE45? Is m=4, n=5 ? What is p?Did you use FEKO?I would like to have an analytical result showing this to check it and understand it. Essentially one needs a mode shape that maximizes the following quantity:∫ElectromagneticEnergy dV/ ∫ ElectromagneticEnergy dA

If I have the time I could check this using EMPro within the next week's. Using the eigen resonance solver the resonant frequency and the Q will be displayed directly for each mode.For now I only have the results of the spreadsheet with the approximation formulas.

Dr. Rodal is it possible that the displacement of a large number of electrons inside the copper walls could cause a temporal displacement of the cavity/ force on the cavity? Since electrons will driven by thermal currents, they travel away from the heat source into the direction of the heatsink (cooler end of the cavity) due to their statistical velocity**. The center of mass may also change due to this effect. In the case of the (comsol)pic below the electrons will driven in the direction of the small end while the displacement of the cavity itself would be forwards into the direction of the big end diameter. Of course this effect is reversible and holds only as long as a thermal equilibrium is re-established.https://en.wikipedia.org/wiki/Thermophoresishttp://aerosols.wustl.edu/Education/Thermophoresis/section02.html**Some years ago I measured this kind of termal driven electron current using a brass rod and a very high sensitive fluxgate sensor system. One end of the rod was heated by a flame for a few seconds the other not. It was easy to measure the magnetic field of this current and its direction/sign dependent on which end of the rod was heated (while the position of the sensor and the rod was static all time) . When no temperatur gradient was present, no field could be detected.

Quote from: X_RaY on 03/31/2016 06:35 PMDr. Rodal is it possible that the displacement of a large number of electrons inside the copper walls could cause a temporal displacement of the cavity/ force on the cavity? Since electrons will driven by thermal currents, they travel away from the heat source into the direction of the heatsink (cooler end of the cavity) due to their statistical velocity**. The center of mass may also change due to this effect. In the case of the (comsol)pic below the electrons will driven in the direction of the small end while the displacement of the cavity itself would be forwards into the direction of the big end diameter. Of course this effect is reversible and holds only as long as a thermal equilibrium is re-established.https://en.wikipedia.org/wiki/Thermophoresishttp://aerosols.wustl.edu/Education/Thermophoresis/section02.html**Some years ago I measured this kind of termal driven electron current using a brass rod and a very high sensitive fluxgate sensor system. One end of the rod was heated by a flame for a few seconds the other not. It was easy to measure the magnetic field of this current and its direction/sign dependent on which end of the rod was heated (while the position of the sensor and the rod was static all time) . When no temperatur gradient was present, no field could be detected.Interesting. For resonant cavities used in particle accelerators, there is also the phenomenon of multipaction that has long been known to be a problem for operation of resonant cavities. Multipaction is described as an electron resonance effect that occurs when radio frequency fields accelerate electrons in a vacuum and cause them to impact with a surface, which depending on its energy, release one or more electrons, and hence the effect cascades:https://en.wikipedia.org/wiki/Multipactor_effectIt is not clear to me how these effects would result in self-acceleration of the cavity, since they are all internal effects and no mass or energy is expelled out of the cavity. So, the mass and energy of the cavity doesn't change, does it? Is there a way to explain self-acceleration ?

Q measurement of a resonator with matched antenna impedanceIn the orginal EMDrive forum at NSF there where discussions how to measure the Q in general.This sample measurement shows the difference of the correct Q measurement in contrast to a bad one. The DUT is a conical cavity resonator made of steel with a conductivity of ~1.4e6 S/m, the mode is TE011 @ 24.192318GHz, the antenna is optimized to excite this mode shape and the antenna feed contains adjusting elements for impedance match. The following example shows a S11 measurement.Rather than measure the 3dB above from the peak of the resonance curve which leads to absurd high Q value (see last pic) one has to measure the -3dB loss from the maximal reflected energie level down*. Pic 1 shows this, pic 2 confirms the measurement conditions in the complex plane. This kind of go ahead as consistent as be shown in many textbooks.(Nasa report also shows how to measure the correct value!)Marker 1 shows the center of the peakMarker 5 & 6 marks the -3dB border measured from the reference Marker 4 at -0.9dB.Q=f/dfQ=f_{center}/f_{high} - f_{low}The result is a loaded Q of ~1055 which is a natural value for a steel cavity resonator in this frequency regime.(The result is backed by EMPro calculations also)In contrast to the upper result while using measurements like in the last pic, 3dB above the peak the calculation leads to a Q of ~22000 what ist quite unrealistic for this frequency, mode and cavity material.*Please note that this simple metode is usable under impedance matched conditions, for great over- or under-coupling the situation is more complicated and the calculation is more complex. Here the simple -3dB approximation condition is not longer useful.For more details see here:http://www-elsa.physik.uni-bonn.de/Lehrveranstaltungen/FP-E106/E106-Erlaeuterungen.pdf

Quote from: X_RaY on 04/01/2016 09:37 PMQ measurement of a resonator with matched antenna impedanceIn the orginal EMDrive forum at NSF there where discussions how to measure the Q in general.This sample measurement shows the difference of the correct Q measurement in contrast to a bad one. The DUT is a conical cavity resonator made of steel with a conductivity of ~1.4e6 S/m, the mode is TE011 @ 24.192318GHz, the antenna is optimized to excite this mode shape and the antenna feed contains adjusting elements for impedance match. The following example shows a S11 measurement.Rather than measure the 3dB above from the peak of the resonance curve which leads to absurd high Q value (see last pic) one has to measure the -3dB loss from the maximal reflected energie level down*. Pic 1 shows this, pic 2 confirms the measurement conditions in the complex plane. This kind of go ahead as consistent as be shown in many textbooks.(Nasa report also shows how to measure the correct value!)Marker 1 shows the center of the peakMarker 5 & 6 marks the -3dB border measured from the reference Marker 4 at -0.9dB.Q=f/dfQ=f_{center}/f_{high} - f_{low}The result is a loaded Q of ~1055 which is a natural value for a steel cavity resonator in this frequency regime.(The result is backed by EMPro calculations also)In contrast to the upper result while using measurements like in the last pic, 3dB above the peak the calculation leads to a Q of ~22000 what ist quite unrealistic for this frequency, mode and cavity material.*Please note that this simple metode is usable under impedance matched conditions, for great over- or under-coupling the situation is more complicated and the calculation is more complex. Here the simple -3dB approximation condition is not longer useful.For more details see here:http://www-elsa.physik.uni-bonn.de/Lehrveranstaltungen/FP-E106/E106-Erlaeuterungen.pdfIs simple to directly measure the unloaded Q of a resonant cavity by using TC = Qu / (2 Pi Fres)With an empty cavity, apply a resonant Rf signal and measure the time it takes forward power to increase from the initial value of 0 to 63.2% of the final value. That is 1 TC time. Then Qu = 1 TC time X 2 Pi Fres.

Quote from: X_RaY on 03/26/2016 02:50 PMIf I have the time I could check this using EMPro within the next week's. Using the eigen resonance solver the resonant frequency and the Q will be displayed directly for each mode.For now I only have the results of the spreadsheet with the approximation formulas.It would be great if you check this with EMPro. It seems to me that to maximize Q one wants to maximize∫ElectromagneticEnergy dV/ ∫ ElectromagneticEnergy dAthis means minimizing ∫ ElectromagneticEnergy dAwhile maximizing∫ElectromagneticEnergy dVthis means a mode shape that would have most of the high electromagnetic energy in the interior volume of the cavity instead of the exterior of the cavity near the metal

Quote from: Rodal on 03/26/2016 03:01 PMQuote from: X_RaY on 03/26/2016 02:50 PMIf I have the time I could check this using EMPro within the next week's. Using the eigen resonance solver the resonant frequency and the Q will be displayed directly for each mode.For now I only have the results of the spreadsheet with the approximation formulas.It would be great if you check this with EMPro. It seems to me that to maximize Q one wants to maximize∫ElectromagneticEnergy dV/ ∫ ElectromagneticEnergy dAthis means minimizing ∫ ElectromagneticEnergy dAwhile maximizing∫ElectromagneticEnergy dVthis means a mode shape that would have most of the high electromagnetic energy in the interior volume of the cavity instead of the exterior of the cavity near the metalI have not forgotten this calculation, but have to much other things to do at the moment.I will check it if I have time while future calculations at our local university.

I found the Q increase linear with the index "p" for this mode (of course the higher the modenumber the higher the resonant frequency).

Quote from: X_RaY on 05/18/2016 07:06 PMI found the Q increase linear with the index "p" for this mode (of course the higher the modenumber the higher the resonant frequency). Looks like about a 10.4% increase in Q for each higher mode number. Nice!Increasing the size of the frustum lowers the resonant frequency. Just build a bigger frustum...

The relationship between radiation PRESSURE and the POYNTING VECTORA common misconception is that the radiation pressure can always be obtained from the Poynting vector simply by the cyclic average of the Poynting vector divided by the speed of light:In a "monochromatic"(=single frequency) plane electromagnetic travelling wave, the Poynting vector points in the direction of propagation while oscillating in magnitude at twice the frequency of the travelling wave. The time-averaged magnitude of the Poynting vector is:<S> = ½(1/μ_{o})Re([E_{m}] x [B_{m}*])where E_{m} is the peak-amplitude of the (complex) electric field E_{m} e^{iωt}, and B_{m}* is the complex-conjugate peak-amplitude of the magnetic field B_{m} e^{iωt}, which, in a plane wave are exactly in phase with each other. If the electromagnetic fields are described in terms of their root mean square (rms) values then the factor of ½ should be replaced by a factor of 1.The problem with using the cyclic average of the Poynting vector divided by the speed of light to obtain the radiation pressure is that the electric field parallel to a conductive surface must be zero, and that the electric field in a plane electromagnetic wave propagating normal to a conductive surface is parallel to the surface, and hence it should be zero. Hence at the surface of the conductor, E=0, therefore E_{m} = 0 and therefore the Poynting vector must be zero to satisfy the boundary conditions at the conductive surface: S=0 and <S>=0. There cannot be real power transmitted by a planar electromagnetic wave into a conductive surface. One arrives at the conclusion that either 1) the electric field component parallel to the wall must be zero, hence the electromagnetic plane wave has zero amplitude electric field everywhere. Therefore its Poynting vector is zero and the radiation pressure is zero at the wall or2) the electromagnetic wave satisfying the boundary condition cannot be an electromagnetic plane wave, as somehow the electromagnetic wave's electric field has to decay to zero to match the boundary conditions at the conductive wall.Now, you may say: this is similar to the mechanical momentum of a ball hitting a perfectly reflecting surface, it makes sense that the momentum at the wall should be zero, because the velocity of the ball at the surface is zero. What happens at the wall is the interference of two momenta: the momentum of the ball hitting the wall interfering with the opposite momentum of the ball bouncing from the wall. Similarly, in the electromagnetic case of a wave hitting a conductive surface one gets a standing wave, that results from the interference of a travelling wave propagating against the wall and bouncing back, (counter-propagating) from the wall. You may say OK, I agree with that, but why can't I take the momentum of the planar electromagnetic field far away from the wall, in the far-field, its Poynting vector far away, where the electric field has a well-defined sinusoidal value and let's don't worry too much about the details of what really happens to my travelling plane wave as it hits the conductive surface and has to satisfy the boundary condition. I think that this is what many introductory texts may be assuming (actually if one looks at many introductory texts that discuss using the time-average of the Poynting vector as a measure of radiation pressure they seldom discuss a conductor: instead they usually just say: an absorbing surface or a perfectly-reflecting surface).A single travelling plane electromagnetic wave cannot exist inside a resonant cavity: it cannot meet the boundary conditions at the metal surfaces. The solution for a conical waveguide comprises spherical propagating waves. The solution for a truncated conical cavity comprises spherical standing waves.Even considering a cavity with constant cross-section, the standing wave solution responsible for transverse electric (TE) or transverse magnetic (TM) modes varies sinusoidally in the lengthwise direction. In a truncated cone the standing wave solution varies like a spherical Bessel function in the lengthwise direction of the cavity, such that the wavelength becomes longer as one approaches the small end of the cone:The relationship between radiation PRESSURE and the ENERGY DENSITYThere is a more general approach to calculate the radiation pressure, which instead of considering the Poynting vector, considers the pressure as being due to the energy density, as for example in the following discussion by Richard Fitzpatrick, Professor of Physics at The University of Texas at Austin: http://farside.ph.utexas.edu/teaching/em/lectures/node90.htmlIn this better approach, the radiation pressure is obtained from the cyclic time-average of the energy density:P_{radiation} = <u>Such an analysis is consistent with the derivation in https://forum.nasaspaceflight.com/index.php?topic=39214.msg1526577#msg1526577 that the radiation pressure, for the case in which the Coulomb pressure is zero, is really due to the energy density.As we have shown, one cannot simply calculate the radiation pressure in a resonant cavity using the cyclic average of the Poynting vector divided by the speed of light: since 1) the Poynting vector is zero at the metal walls for TE modes and 2) the Poynting vector does not have a constant magnitude in the longitudinal direction for standing waves in a cavity, for any mode shape. On the other hand, as we have shown, one can certainly calculate the radiation pressure at the walls of resonant cavity based on the energy density value at the wall for TE modes, or in general, based on the energy density and the Coulomb pressure at the wall for any mode shape, hence obtaining the radiation pressure from the energy density is a more general approach than obtaining it from the Poynting vector field.

...Is it possible that thrust generation is based on the magnetic field vectors (rotation vector of the standing wave{curl_H}) acting at the sidewall(s) instead of radiation pressure at the end pates?

Quote from: X_RaY on 05/26/2016 08:46 PM...Is it possible that thrust generation is based on the magnetic field vectors (rotation vector of the standing wave{curl_H}) acting at the sidewall(s) instead of radiation pressure at the end pates?In here https://forum.nasaspaceflight.com/index.php?topic=39214.msg1526577#msg1526577:I show that for TE modes the stress at the conical walls is compressive and entirely due to the energy density, due to the magnetic component in the longitudinal direction, parallel to the conical side walls. Therefore if thrust is real for mode shapes TE012 and TE013 used by Shawyer, it must be due to the magnetic field vector parallel to either the conical walls, and/or the magnetic field vector parallel to the end plates.

Quote from: Rodal on 05/26/2016 08:56 PMQuote from: X_RaY on 05/26/2016 08:46 PM...Is it possible that thrust generation is based on the magnetic field vectors (rotation vector of the standing wave{curl_H}) acting at the sidewall(s) instead of radiation pressure at the end pates?In here https://forum.nasaspaceflight.com/index.php?topic=39214.msg1526577#msg1526577:I show that for TE modes the stress at the conical walls is compressive and entirely due to the energy density, due to the magnetic component in the longitudinal direction, parallel to the conical side walls. Therefore if thrust is real for mode shapes TE012 and TE013 used by Shawyer, it must be due to the magnetic field vector parallel to either the conical walls, and/or the magnetic field vector parallel to the end plates.In the meep simulation which I have subsequently animated (December 2015), the magnetic fields are most definitely NOT parallel to the small end or the side sloped walls. They ARE parallel to the big end plate.Original Post: http://forum.nasaspaceflight.com/index.php?topic=39004.msg1467619#msg1467619

My biggest problem with the meep pics was that the single pics only represent single vector components (most of what we saw was autoscaled), so this has generated a lot of confusion.

Quote from: X_RaY on 05/29/2016 03:42 PMMy biggest problem with the meep pics was that the single pics only represent single vector components (most of what we saw was autoscaled), so this has generated a lot of confusion.Just to clear up any possible confusion as to what the animation in that post shows: http://forum.nasaspaceflight.com/index.php?topic=39004.msg1467619#msg1467619The animation in the linked post is 3D vectors plotted with origin, direction, and amplitude, of the H field for two slices across the X plane (x=0, x=10). There is a min(always 0) and max (for scale) in numbers along with the frame number on the top left. All values are in 'meep units' which aero tells me should be multiplied by 3.33 to get to 'engineering units'.The meep simulation is 291x390x327 elements (~37M elements) (on the order of 1/100 of the wave size), and ~3.2 degrees of phase per frame (112 frames within one waveform). The E fields are indeed parallel to the surfaces. The H fields are not.

Quote from: VAXHeadroom on 05/29/2016 05:50 PMQuote from: X_RaY on 05/29/2016 03:42 PMMy biggest problem with the meep pics was that the single pics only represent single vector components (most of what we saw was autoscaled), so this has generated a lot of confusion.Just to clear up any possible confusion as to what the animation in that post shows: http://forum.nasaspaceflight.com/index.php?topic=39004.msg1467619#msg1467619The animation in the linked post is 3D vectors plotted with origin, direction, and amplitude, of the H field for two slices across the X plane (x=0, x=10). There is a min(always 0) and max (for scale) in numbers along with the frame number on the top left. All values are in 'meep units' which aero tells me should be multiplied by 3.33 to get to 'engineering units'.The meep simulation is 291x390x327 elements (~37M elements) (on the order of 1/100 of the wave size), and ~3.2 degrees of phase per frame (112 frames within one waveform). The E fields are indeed parallel to the surfaces. The H fields are not.I am sure you (and aero) put many work into these calculations as well as in the visualisation. I am sorry but Dr.Rodal is absolutely right about the related physical basics. The E-field vector close to a conductive wall can´t be parallel to that wall and so on.. Boundary conditions of electromagnetic fields are non-negotiable

Quote from: Rodal on 05/06/2016 05:31 PMQuote from: SeeShells on 05/06/2016 05:10 PM...The momentum of light in media remains one of the most controversial topics in physics [1–6]. The debate has continued for more than a century since Minkowski and Abraham formulated 4 × 4 energy-momentum tensors in the early 1900s [7–9].https://www.researchgate.net/publication/292342272_Kinetic-energy-momentum_tensor_in_electrodynamicsProfessor Melcher at MIT (and previously Prof. Chu and others at MIT's Radiation Laboratory) was already showing decades ago in MIT classes that the Einstein-Laub formulation of electrodynamics is invalid since it yields a stress-energy-momentum tensor that is not frame invariant. (It is an interesting historical vignette that Einstein did not realize this at the time he wrote the paper with Laub)They do credit Prof. Chu with the correct invariance relations. But that is one of the reasons why Prof. Chu at MIT developed his formulation.This was known by students that listened to the lectures of Prof. Chu and Melcher at MIT Reference: Prof. Melcher's masterpiece "Continuum Electromechanics" which he wrote in 1972-1973 while he was in sabatical at Cambridge University working with Sir Taylor and G. BatchelorCorrect, although The Einstein-Laub formulation of electrodynamics does work in a real world lab. 1973, Ashkin and Dziedzic performed a experiment in which they focused a green laser beam on the surface of water and saw what they called "the toothpaste tube effect" where a bulge appeared in the surface of the water. Using a Lorentz formula the existence of expansive and compressing forces effectively cancel out, negating a possible bump forming on the water surface. The real world lab test showed where pure theoretical extraction detailing out why there are thrusts from a asymmetrical cavity are lacking. . . This is why lab data is king right now. ShellBack to work... will be on later. Have company helping me move my new frame for the lab.

Quote from: SeeShells on 05/06/2016 05:10 PM...The momentum of light in media remains one of the most controversial topics in physics [1–6]. The debate has continued for more than a century since Minkowski and Abraham formulated 4 × 4 energy-momentum tensors in the early 1900s [7–9].https://www.researchgate.net/publication/292342272_Kinetic-energy-momentum_tensor_in_electrodynamicsProfessor Melcher at MIT (and previously Prof. Chu and others at MIT's Radiation Laboratory) was already showing decades ago in MIT classes that the Einstein-Laub formulation of electrodynamics is invalid since it yields a stress-energy-momentum tensor that is not frame invariant. (It is an interesting historical vignette that Einstein did not realize this at the time he wrote the paper with Laub)They do credit Prof. Chu with the correct invariance relations. But that is one of the reasons why Prof. Chu at MIT developed his formulation.This was known by students that listened to the lectures of Prof. Chu and Melcher at MIT Reference: Prof. Melcher's masterpiece "Continuum Electromechanics" which he wrote in 1972-1973 while he was in sabatical at Cambridge University working with Sir Taylor and G. Batchelor

...The momentum of light in media remains one of the most controversial topics in physics [1–6]. The debate has continued for more than a century since Minkowski and Abraham formulated 4 × 4 energy-momentum tensors in the early 1900s [7–9].https://www.researchgate.net/publication/292342272_Kinetic-energy-momentum_tensor_in_electrodynamics

The Ashkin and Dziedzic experiment observed an outward bulge on an illuminated water surface, apparently consistent with the sign of the Poynting surface force and the value of the Minkowski momentum. In agreement with Gordon, it is shown here that the effect is governed by a radial force and it provides no information on the longitudinal force associated with the linear momentum of light.

Obviously the right hand of Eq. (8) is the EM force exerted on the EM field boundary of the limited closed volume

@FattyLumpkinThis is the best Cannae like design I could get out of FEKO LITE till now. Would need a full version to come close to Monomorphic´s sims. https://forum.nasaspaceflight.com/index.php?topic=39772.msg1530441#msg1530441

Quote from: X_RaY on 06/13/2016 08:17 PM@FattyLumpkinThis is the best Cannae like design I could get out of FEKO LITE till now. Would need a full version to come close to Monomorphic´s sims. https://forum.nasaspaceflight.com/index.php?topic=39772.msg1530441#msg1530441Great work!1) Have you also tried to model the Cannae device with EM Pro, for which you do not have the limitations of FEKO Light?2) When you used EM Pro in the previous pages for other calculations, did you use the Finite Element module of EM Pro or the finite difference module of EM Pro?

Further to this issue about Boundary Conditions, Jackson has an excellent discussion in his masterpiece Classical Electrodynamics, 3rd Edition, pages 352 to 356 (ISBN-10: 047130932X; ISBN-13: 978-0471309321). Pay special attention to the graph on page 355, Fig. 8.2 "Fields near the surface of a good, but not perfect conductor". For a good but not perfect conductor, for example copper as used in the EM Drive, and as modeled in Meep with the Drude equation model, a very tiny magnitude electric field parallel to the surface will be present, as well as a very tiny magnetic field perpendicular to the surface. The electric field parallel to the surface is inversely proportional to the square root of the conductivity:This solution exhibits the expected rapid exponential decay (skin depth), and Pi/4 phase difference. For a good conductor, the fields inside the metal conductor are parallel to the surface and propagate normal to it, with magnitudes that depend only on the tangential magnetic field parallel to the surface, that exists just outside the surface of the metal conductor.As shown in the graphs in Jackson's book, and as one can readily calculate these fields are practically zero, insignificant for copper, due to its very high conductivity. Therefore it is not a surprise that Meep does not show a significant difference in the fields calculated using the perfect conductor model vs. the Drude model. The main influence of the finite conductivity Drude model is to allow the calculation of a finite Q (instead of an infinite Q). But again, the boundary condition is such that the electric field parallel to the surface and the magnetic field perpendicular to the surface must be practically zero at the surface, due to the very high conductivity of copper. This is particularly so for the experiments of EM Drive where experimenters seek a high Q, which is tantamount to practically zero fields for these variables. It is completely inconsistent for EM Drive experimenters to advocate a high Q (Shawyer even claiming to research superconducting EM Drives) and not realize that these boundary conditions are such that these fields must be practically zero at the surface of the good conductor.NOTE: for those not having ready access to Jackson's monograph, the following discussion by a professor at Duke University is also good: https://www.phy.duke.edu/~rgb/Class/phy319/phy319/node59.html

Quote from: FattyLumpkin on 09/05/2016 11:47 PMI hope there is no confusion re the various projects going on at Cannae...as folks know I've been conducting a study of them1) for the cubesat, they say they are orbiting it at less than 150 miles...not kilometers. Mr. Feta told me there would be no super-cooling of this device. I'm left to conclude that the cooling of their thruster will be passive and that the thruster will be kept in shadow at all times...So they are using miles instead of kilometers to specify an orbit?150*1.60934=241So their orbit is really 241 km ?That makes a difference ! ThanksI calculated with 150 km. (I recall pointing this out weeks ago, when they first announced, that instead of using customary SI units, Cannae is using Miles, oh well )Just like the probe that crashed on Mars years ago (different units !) Will recalculate with 150 miles tomorrow (Is it US Miles )US Survey mile = International mile =1.60934 kmNautical mile = 1.852 kmRoman mile = 1.481 kmChinese mile = 0.5 km

I hope there is no confusion re the various projects going on at Cannae...as folks know I've been conducting a study of them1) for the cubesat, they say they are orbiting it at less than 150 miles...not kilometers. Mr. Feta told me there would be no super-cooling of this device. I'm left to conclude that the cooling of their thruster will be passive and that the thruster will be kept in shadow at all times...

British mathematician Desmond King-Hele of the Royal Aircraft Establishment predicted in 1973 that Skylab would de-orbit and crash to earth in 1979, sooner than NASA's forecast, because of increased solar activity. Greater-than-expected solar activity heated the outer layers of Earth's atmosphere and increased drag on Skylab.

Our thruster configuration for the cubesat mission with Theseus is anticipated to require less than 1.5 U volume and will use less than 10 watts of power to perform station keeping thrusting.

I know I sound like a broken record, but I would really like to know how they plan to separate out thrust effects from the high variability of atmospheric density at those altitudes.

Atmospheric drag on the sat is measurable, but it cannot be ameliorated by always keeping the sat solar array parallel to the orbital velocity vector

The satellite must rotate about its own axis about once every 90 minutes to keep the array pointed at the sun. This rotation will continue in Earth's shadow....

Quote from: Rodal on 11/08/2016 02:22 PMQuote from: X_RaY on 11/08/2016 02:20 PMIs there anyone who has study a half-sphere shaped resonator regarding the emdrive?In contrast to a parabolic one (where the focal depth for rays much shorter than the size of the structure itself was equal to the point where the baseplate was present).http://forum.nasaspaceflight.com/index.php?topic=39214.msg1607020#msg1607020 Now I did an FEA with the half-sphere shape. What I found is a massive fieldstrength, much higher than I ever have observed in the sims before. The Q should be very high.1) What is the numerical analysis package you are using ? (FEKO, etc.) 2) What numerical technique are you using to solve the equations? (Finite Element Method?, Boundary Element Method?, Finite Difference Method Space Domain?)?3) What is the type of solution method? A) Is it an eigensolution to the eigenvalue problem where there is no antenna in the model? B) Or a steady state solution using an antenna and a spectral method to obtain a solution? C) Or a transient solution using an antenna and a Finite Difference Time Domain to obtain a solution?D) If you used an antenna, with a spectral steady-state solution or a transient Finite-Difference-Time-Domain solution, what was the type of antenna and where was it located?4) What are the boundary conditions that you use in the model? Are you assuming a perfect conductor?If not, how are you modeling an imperfect conductor like copper?5) How is the quality factor (Q) calculated?6) How are eddy currents calculated in the model?Thanks1. FEKO 2. MOM & FEM3. ? A. No, no eigenvalue calculation, magnetic Dipole (30mm above the flat plate at the central axis)B. FEM C. No FDTD4.First time the boundary was defined to be PEC. Couldn't believe this numbers, therefore I used Copper, thickness 1mm for the second run (see diagrams).Field pics are from the PEC-run.5.No till now the Q is not calculated. My statement was due to the fieldstrength. 6. Good question, It's a internal calculation of FEKO, don't know their code

Quote from: X_RaY on 11/08/2016 02:20 PMIs there anyone who has study a half-sphere shaped resonator regarding the emdrive?In contrast to a parabolic one (where the focal depth for rays much shorter than the size of the structure itself was equal to the point where the baseplate was present).http://forum.nasaspaceflight.com/index.php?topic=39214.msg1607020#msg1607020 Now I did an FEA with the half-sphere shape. What I found is a massive fieldstrength, much higher than I ever have observed in the sims before. The Q should be very high.1) What is the numerical analysis package you are using ? (FEKO, etc.) 2) What numerical technique are you using to solve the equations? (Finite Element Method?, Boundary Element Method?, Finite Difference Method Space Domain?)?3) What is the type of solution method? A) Is it an eigensolution to the eigenvalue problem where there is no antenna in the model? B) Or a steady state solution using an antenna and a spectral method to obtain a solution? C) Or a transient solution using an antenna and a Finite Difference Time Domain to obtain a solution?D) If you used an antenna, with a spectral steady-state solution or a transient Finite-Difference-Time-Domain solution, what was the type of antenna and where was it located?4) What are the boundary conditions that you use in the model? Are you assuming a perfect conductor?If not, how are you modeling an imperfect conductor like copper?5) How is the quality factor (Q) calculated?6) How are eddy currents calculated in the model?Thanks

Is there anyone who has study a half-sphere shaped resonator regarding the emdrive?In contrast to a parabolic one (where the focal depth for rays much shorter than the size of the structure itself was equal to the point where the baseplate was present).http://forum.nasaspaceflight.com/index.php?topic=39214.msg1607020#msg1607020 Now I did an FEA with the half-sphere shape. What I found is a massive fieldstrength, much higher than I ever have observed in the sims before. The Q should be very high.

The White et al. 2016 paper (the leaked, non-peer reviewed version, which still can be downloaded from http://www.nextbigfuture.com/2016/11/new-nasa-emdrive-paper-shows-force-of.html):I haven't read a lot of discussion of the paper yet. Some remarks can be made, though, and questions asked. It looks like a solid piece of work, greatly admirable engineering work and clear discussion. We don't know from when this version is (the pdf I downloaded doesn't give a creation date, only 26 Aug 2016 as modification date). It doesn't look like two years of work to me (but probably they could not work full-time on it). I am a bit disappointed that they don't show results of other dielectric inserts (what they probably did).A few issues and questions:- I wonder whether switching direction in their way, with the whole RF stuff (amplifier etc) attached to the large endplate, is the best to do. As they write, they had retuning problems when using a 'split configuration mode'. But if you use a flexible cable, it should be possible to turn only the cavity by 180 degrees and leave the RF stuff at the same position and orientation.- Do I see a saturation effect around 60 W? See Figs. 13, 15 and 19. It does not seem to be so much work to perform, say, 100 measurements. Then they could have shown with statistics that there is a difference in force between the 60 W and the 80 W input, or not. Now that is not clear (their premise is probably that there SHOULD be a linear dependence on power: dangerous).- I am still a bit worried about the liquid metal contacts they use to supply the DC power to the torsion balance (many amps!). It is not likely that these will give rise to the signals they observe, but I haven't seen a test of their influence on the measurement.Maybe more later,Peter.

"According to Woodward, who saw a copy of the paper shortly after it had been accepted for peer review, the main difference between the accepted copy and the leaked early release is that the latter has way more theory trying to explain the results. Supposedly the AIAA would only accept the paper if White and his colleagues ditched the quantum vacuum theory and just published the results of their research without trying to explain it."http://motherboard.vice.com/read/the-fact-and-fiction-of-the-nasa-emdrive-paper-leak

Quote from: Peter Lauwer on 11/15/2016 10:07 AM"According to Woodward, who saw a copy of the paper shortly after it had been accepted for peer review, the main difference between the accepted copy and the leaked early release is that the latter has way more theory trying to explain the results. Supposedly the AIAA would only accept the paper if White and his colleagues ditched the quantum vacuum theory and just published the results of their research without trying to explain it."http://motherboard.vice.com/read/the-fact-and-fiction-of-the-nasa-emdrive-paper-leakSo this is not true. Their pilot wave theory is still in the Discussion.

Quote from: X_RaY Very impressive is the coordinate probability of detection of the droplet equals a similar quantum system as compared, see video at 1:40.Would that also find application in quantum cypher decoding?

Very impressive is the coordinate probability of detection of the droplet equals a similar quantum system as compared, see video at 1:40.

Results for Brady cone with HDPE-disc at the small end plate. Source power was defined to be 1Watt (30dBm). εR=2.27tanδ=0.00031DIA*=158.75mmHeight=54mm* to simplify the model I used a diameter equal to the end plate diameter instead of the 156.7mm reported by EW

Quote from: X_RaY on 11/13/2016 04:44 PMResults for Brady cone with HDPE-disc at the small end plate. Source power was defined to be 1Watt (30dBm). εR=2.27tanδ=0.00031DIA*=158.75mmHeight=54mm* to simplify the model I used a diameter equal to the end plate diameter instead of the 156.7mm reported by EW8X_Ray, we have to be careful with calling this mode shape "TM010". While that name is correct for a cylinder, which can have a constant field in the longitudinal direction. We know that the fields cannot be constant in the longitudinal direction for a cone, from the exact analytical solution, because a constant electromagnetic field in the longitudinal direction cannot satisfy the boundary conditions for a cone, (as verified by your FEKO boundary element analysis results). Since the electromagnetic fields are not constant in the longitudinal direction, p is not equal to zero. So this is a degenerate form of TM010, perhaps we should call it TM01?. This mode shape becomes TM010 as one varies the cone angle to zero, such that the cone becomes a cylinder. As the cone becomes a cylinder, the electromagnetic fields become constant in the longitudinal direction.In particular, it is interesting how the electromagnetic fields, in particular the E field has a gentle gradient at each end, in order to accommodate the boundary conditions at each end, and the fact that the field cannot be constant in the longitudinal direction....snip...

Results for Brady cone with HDPE-disc at the small end plate. Source power was defined to be 1Watt (30dBm). εR=2.27tanδ=0.00031DIA*=158.75mmHeight=54mm* to simplify the model I used a diameter equal to the end plate diameter instead of the 156.7mm reported by EW8

...snip...Yes I have to agree. Especially in the case where the dielectric is at the big end it causes to make the frustum virtually even more asymmetric due to the contracted wavelength inside the dielectric disc. Thefore the field at the small end tends to zero and the standardnotation for cylindrical cavities doesn't make sense any more.If my memory serves this problem remains over several threads now, but till now I have no idea for a notation that make more sense. In this regard conclusive ideas are very welcome to solve this issuse!EDITMaybe a notation based on spherical coordinates fits better?Rectangular cavity --> TX x,y,zCylindrical cavity--> TX φ,R,zsections of a sphere just like Conical cavities --> TX φ,θ,r or semi-spherical TX φ,R,rWhile TE/TM depends on the dominant component into "r" direction? Does this make sense? Which notation would make sense in a wedge shaped cavity?Regarding boundary conditions, what if the modal shape inside the small end don't equals at all the shape near the larger end?

(**) Mode shape nomenclature is adopted as per the cylindrical cavity (with constant circular cross section) designation, because there is no standardized way to number truncated cone mode shapes. I am aware that there is no mode shape for a truncated cone with electromagnetic fields constant in the longitudinal direction, unlike cylindrical cavities which have TM mode shapes with "p=0". Still, because the truncated cone geometries used up to now have shapes that are not too far from a cylinder with constant cross section (because small cone angles are used and the cones are truncated far from the cone vertex) it is possible to use a cylindrical cavity mode shape designation and select m,n,p accordingly.

If you increase the diameter for the large end to cover it completely...

Looks better now Not exact 50 Ohm but very close.

Quote from: X_RaY on 11/28/2016 05:13 AMLooks better now Not exact 50 Ohm but very close.Can you post the antenna location and dims? Here is my second try. Why is is pointed? How did you get yours to be a nice circle?

...Do not use a very coarse self defined mesh if possible.My PC runs all night to solve a model need a new one.

Quote from: X_RaY on 11/28/2016 04:16 PM...Do not use a very coarse self defined mesh if possible.My PC runs all night to solve a model need a new one.Monomorphic, we had discussed previously my viewpoint that the mesh in your FEKO analyses are too coarse. This would be an interesting case study where you could perform a convergence analysis to analyze the effect of mesh size on these parameters. Then you could post it here for posterity so that we can all learn about the dependence of the solution on the mesh size.

Currently I'm solving monomorphics model with spherical end plates with a modified loop antenna, i.e. position and diameter. The current result is shown below. It shows that using the related dimensions leads to a coupling factor below 1.

Quote from: X_RaY on 11/30/2016 07:57 PMCurrently I'm solving monomorphics model with spherical end plates with a modified loop antenna, i.e. position and diameter. The current result is shown below. It shows that using the related dimensions leads to a coupling factor below 1.Are you also using FEKO?How come you get a perfect circle instead of the unphysical coarse-sided polygon in Monomorphic's FEKO results?

Satisfying Gauss's law and conservation of momentum.

Quote from: X_RaY on 11/30/2016 07:57 PMCurrently I'm solving monomorphics model with spherical end plates with a modified loop antenna, i.e. position and diameter. The current result is shown below. It shows that using the related dimensions leads to a coupling factor below 1.Can you please double check the dimensions for the antenna? A radius of 15mm seems large and i'm still showing over coupled. Did you mean a diameter of 15mm? That seems more in line with EW's 13.5mm diameter loop antenna.

I don't change anything else but the antenna position, the configuration is still the one, James has send to me.I tink thats good enough to go with. In a real world construction due to imperfections, in any case the exact antenna position has to be tuned/verified with a VNA. The basic system impedance will almost never be exact 50Ω and so on... Nevertheless there will be only a small impedance mismatch that has to tuned out with an external tuner, this minimize the losses that is produced within the tuner (compared to the situation where the impedance difference is much grater).From a construction viewpoint the position is almost ideal because there are no long wires necessary to feed the loop antenna. That configuration minimize the excitation of other modes inside the frequency range. TE01p is degenerate with TM11p (at least in a cylindrical cavity almost exact at the same frequency, while the conically shape seperates both modes, but not that much regarding to the eigen-frequency)

Quote from: Monomorphic on 12/03/2016 01:52 PMQuote from: X_RaY on 12/02/2016 06:01 PMI don't change anything else but the antenna position, the configuration is still the one, James has send to me.I tink thats good enough to go with. In a real world construction due to imperfections, in any case the exact antenna position has to be tuned/verified with a VNA. The basic system impedance will almost never be exact 50Ω and so on... Nevertheless there will be only a small impedance mismatch that has to tuned out with an external tuner, this minimize the losses that is produced within the tuner (compared to the situation where the impedance difference is much grater).From a construction viewpoint the position is almost ideal because there are no long wires necessary to feed the loop antenna. That configuration minimize the excitation of other modes inside the frequency range. TE01p is degenerate with TM11p (at least in a cylindrical cavity almost exact at the same frequency, while the conically shape seperates both modes, but not that much regarding to the eigen-frequency)With the antenna in that configuration I get a huge -39dB reflection coeficient with a Q factor of 111,454! Q sounds a little bit high, how is it calculated? f/df (-3dB down from the baseline for S11)?

Quote from: X_RaY on 12/02/2016 06:01 PMI don't change anything else but the antenna position, the configuration is still the one, James has send to me.I tink thats good enough to go with. In a real world construction due to imperfections, in any case the exact antenna position has to be tuned/verified with a VNA. The basic system impedance will almost never be exact 50Ω and so on... Nevertheless there will be only a small impedance mismatch that has to tuned out with an external tuner, this minimize the losses that is produced within the tuner (compared to the situation where the impedance difference is much grater).From a construction viewpoint the position is almost ideal because there are no long wires necessary to feed the loop antenna. That configuration minimize the excitation of other modes inside the frequency range. TE01p is degenerate with TM11p (at least in a cylindrical cavity almost exact at the same frequency, while the conically shape seperates both modes, but not that much regarding to the eigen-frequency)With the antenna in that configuration I get a huge -39dB reflection coeficient with a Q factor of 111,454!

X_Ray, have you had any luck with doing a Time Domain Analysis in the 2.4Ghz range? I need to solve for f_{min} and f_{max}. Basically we need to figure out how to make the simulated frequency range equal to the time signal bandwidth. In my case that is 2.4054Ghz and 2.4059Ghz.

In a PM with @zellerium, we were discussing the software he uses and I started to think about why I wanted it. It just dawned on me that this would be much faster as a team effort. So I would like to make this proposal to those who have modeling capability. We need organization. Dr. Rodal's recent paper shows us how detailed we need to be in every aspect of this analysis, in order to find the right answers. The following list is the "data" that needs to be modeled and recorded. Starting with a frustum. I propose we use TT's design with the spherical end caps, or model Shawyer's latest design, but I'm open to suggestions. The point is, we choose 1 model, and model it to death, to get all the relevant data into a report. I do not mind preparing that report if the modelers can do the real work.This list for data is based on much of what we've been doing here already, as much as on my own wish list. It is open for discussion and starts like this;1. Optimal location for the antenna to excite TE013 and have ~50 Ohm input Z.2. Optimal length, width, shape of the antenna for 50 Ohms.3. Optimal location for probes to identify frequency and decay time at big end, small end and center wall. i.e., determine Q from the w*t and do VNA at each port.4. Relative E, H and A, vector field strengths for different materials, PC, Ag, Cu, Al, etc. as a color plot, values & vectors. Everything consistent so they can be compared.5. Relative Energy Density for different materials, PC, Ag, Cu, Al, etc. as a color plot and values.6. Relative surface power dissipation for each material, color plot and values.7. Relative temperature for each material, color plot.I would put this together into a report or Smartsheet. http://www.smartsheet.com/for each Frustum shape/design/frequency mode. The key to me is to be consistent and thorough with each design, and repeat this for each mode shape and material. It's a lot of work to be thorough!Dr. Rodal has done real research reports on the truncated cavity last year and now on the Mach effects in the MEGA drive. This type of research takes a lot of time and effort and needs to be coordinated and documented. That's why I want the software so I can do what is needed to advance the cause, but if we work as a team, we can do it together, under budget and ahead of schedule. Todd

Has anyone considered that the thrust from the emdrive found in recent experiments might result from the Coriolis Effect. I have not researched this type of drive and only came across articles about this topic by accident so forgive me if this has been suggested already. In this type drive the microwaves would probably setup vibrations in the drive casing. This vibration might result in an effective force on the support structure as the Earth rotates. This might be interpreted as thrust. The Coriolis Effect is used in vibrating structure gyroscopes and mass flow meters. I haven't thought this out in detail but it seems a simple explanation given the small thrust. It could be tested by changing the drive orientation in relation to the Earth's rotation and by measuring and varying the casing vibration. I really hope this type of drive is real and physics are found to it explain it's operation bUT it seems a reach.

Nice! Similar to some results I had a while back. Notice the counting in ns. This is not TE013, but another mode.

Quote from: flux_capacitor on 12/26/2016 01:10 AMChen Yue's RF resonant cavity thruster may be not a frustum, but a semicylinder!Excerpts from "An electromagnetic propulsion system and method" CN 105947224 A• English translation• Original PDF in Chinese with picturesQuote from: Chen YueBRIEF DESCRIPTION[0029] FIG. 1 a typical electromagnetic propulsion resonator body diagram;[0030] FIG. 2 (a) is a typical view of the XY plane electromagnetic propulsion of resonance cavity, (b) is a typical view of the XZ plane electromagnetic propulsion of resonance cavity, (c) is a typical resonant cavity electromagnetic propulsion YZ plane view, (d) is a typical perspective view of the electromagnetic propulsion of resonance cavity;[0031] FIG. 3 electromagnetic waves in the resonant cavity of the uneven distribution diagram;[0032] FIG. 4 block diagram of an electromagnetic propulsion program.detailed description[0038] The electromagnetic propulsion power module input signal is less than equal to the maximum power capacity of electromagnetic propulsion module to obtain electromagnetic propulsion module to work required thrust power ratio; the electromagnetic propulsion module frequency of the input signal to the electromagnetic propulsion module the resonant frequency is preferably in the center of the 3dB bandwidth of the electromagnetic propulsion module to work properly.[0039] The electromagnetic propulsion module includes a resonant cavity inside an asymmetric structure, the use of electromagnetic propulsion module inside the resonator cavity asymmetric structure, produce uneven microwave radiation pressure, and then in the resonant cavity be unbalanced electromagnetic force to external output thrust. Asymmetric structure is preferable to adopt a resonant cavity electromagnetic propulsion resonant cavity, electromagnetic propulsion system around the resonant cavity electromagnetic propulsion structures, electromagnetic propulsion resonant cavity shown in FIG. 1, respectively. As can be seen, electromagnetic propulsion resonant cavity is divided into four faces: plane Sa, surface Sb, plane Sc, plane Sd, as shown in FIG. Sa mounted on a plane microwave power input device on a plane Sc plane fitted with microwave power extraction apparatus. Input to the feedback power control module from the microwave power extraction means to extract microwave power as a feedback power. Electromagnetic propulsion thrust output of the resonant cavity Preferred conditions: input microwave power frequency electromagnetic propulsion within 3dB bandwidth of the center frequency of the resonant cavity. Under the operating conditions of the effect of microwave power, electromagnetic propulsion resonant cavity can be unbalanced microwave radiation pressure, and thus in the resonant cavity be unbalanced electromagnetic force, thrust externally output, as shown in FIG. Select the lowest electromagnetic propulsion mode resonator center frequency f〇 electromagnetic propulsion system frequency. Semicylindrical cavity of the radius R (meters), length L (in meters) and preferably the relationship between the center frequency F0 (Unit GHz) between the semi-cylindrical cavity of:[0040] ⑴[0041] Preferably R = 86 mm, L = 117.7 mm, using the formula (1) f0 were solver to 2.45 GHz. ...Short calc results using the given dimensions, source was a electric dipole.

Chen Yue's RF resonant cavity thruster may be not a frustum, but a semicylinder!Excerpts from "An electromagnetic propulsion system and method" CN 105947224 A• English translation• Original PDF in Chinese with picturesQuote from: Chen YueBRIEF DESCRIPTION[0029] FIG. 1 a typical electromagnetic propulsion resonator body diagram;[0030] FIG. 2 (a) is a typical view of the XY plane electromagnetic propulsion of resonance cavity, (b) is a typical view of the XZ plane electromagnetic propulsion of resonance cavity, (c) is a typical resonant cavity electromagnetic propulsion YZ plane view, (d) is a typical perspective view of the electromagnetic propulsion of resonance cavity;[0031] FIG. 3 electromagnetic waves in the resonant cavity of the uneven distribution diagram;[0032] FIG. 4 block diagram of an electromagnetic propulsion program.detailed description[0038] The electromagnetic propulsion power module input signal is less than equal to the maximum power capacity of electromagnetic propulsion module to obtain electromagnetic propulsion module to work required thrust power ratio; the electromagnetic propulsion module frequency of the input signal to the electromagnetic propulsion module the resonant frequency is preferably in the center of the 3dB bandwidth of the electromagnetic propulsion module to work properly.[0039] The electromagnetic propulsion module includes a resonant cavity inside an asymmetric structure, the use of electromagnetic propulsion module inside the resonator cavity asymmetric structure, produce uneven microwave radiation pressure, and then in the resonant cavity be unbalanced electromagnetic force to external output thrust. Asymmetric structure is preferable to adopt a resonant cavity electromagnetic propulsion resonant cavity, electromagnetic propulsion system around the resonant cavity electromagnetic propulsion structures, electromagnetic propulsion resonant cavity shown in FIG. 1, respectively. As can be seen, electromagnetic propulsion resonant cavity is divided into four faces: plane Sa, surface Sb, plane Sc, plane Sd, as shown in FIG. Sa mounted on a plane microwave power input device on a plane Sc plane fitted with microwave power extraction apparatus. Input to the feedback power control module from the microwave power extraction means to extract microwave power as a feedback power. Electromagnetic propulsion thrust output of the resonant cavity Preferred conditions: input microwave power frequency electromagnetic propulsion within 3dB bandwidth of the center frequency of the resonant cavity. Under the operating conditions of the effect of microwave power, electromagnetic propulsion resonant cavity can be unbalanced microwave radiation pressure, and thus in the resonant cavity be unbalanced electromagnetic force, thrust externally output, as shown in FIG. Select the lowest electromagnetic propulsion mode resonator center frequency f〇 electromagnetic propulsion system frequency. Semicylindrical cavity of the radius R (meters), length L (in meters) and preferably the relationship between the center frequency F0 (Unit GHz) between the semi-cylindrical cavity of:[0040] ⑴[0041] Preferably R = 86 mm, L = 117.7 mm, using the formula (1) f0 were solver to 2.45 GHz. ...

BRIEF DESCRIPTION[0029] FIG. 1 a typical electromagnetic propulsion resonator body diagram;[0030] FIG. 2 (a) is a typical view of the XY plane electromagnetic propulsion of resonance cavity, (b) is a typical view of the XZ plane electromagnetic propulsion of resonance cavity, (c) is a typical resonant cavity electromagnetic propulsion YZ plane view, (d) is a typical perspective view of the electromagnetic propulsion of resonance cavity;[0031] FIG. 3 electromagnetic waves in the resonant cavity of the uneven distribution diagram;[0032] FIG. 4 block diagram of an electromagnetic propulsion program.detailed description[0038] The electromagnetic propulsion power module input signal is less than equal to the maximum power capacity of electromagnetic propulsion module to obtain electromagnetic propulsion module to work required thrust power ratio; the electromagnetic propulsion module frequency of the input signal to the electromagnetic propulsion module the resonant frequency is preferably in the center of the 3dB bandwidth of the electromagnetic propulsion module to work properly.[0039] The electromagnetic propulsion module includes a resonant cavity inside an asymmetric structure, the use of electromagnetic propulsion module inside the resonator cavity asymmetric structure, produce uneven microwave radiation pressure, and then in the resonant cavity be unbalanced electromagnetic force to external output thrust. Asymmetric structure is preferable to adopt a resonant cavity electromagnetic propulsion resonant cavity, electromagnetic propulsion system around the resonant cavity electromagnetic propulsion structures, electromagnetic propulsion resonant cavity shown in FIG. 1, respectively. As can be seen, electromagnetic propulsion resonant cavity is divided into four faces: plane Sa, surface Sb, plane Sc, plane Sd, as shown in FIG. Sa mounted on a plane microwave power input device on a plane Sc plane fitted with microwave power extraction apparatus. Input to the feedback power control module from the microwave power extraction means to extract microwave power as a feedback power. Electromagnetic propulsion thrust output of the resonant cavity Preferred conditions: input microwave power frequency electromagnetic propulsion within 3dB bandwidth of the center frequency of the resonant cavity. Under the operating conditions of the effect of microwave power, electromagnetic propulsion resonant cavity can be unbalanced microwave radiation pressure, and thus in the resonant cavity be unbalanced electromagnetic force, thrust externally output, as shown in FIG. Select the lowest electromagnetic propulsion mode resonator center frequency f〇 electromagnetic propulsion system frequency. Semicylindrical cavity of the radius R (meters), length L (in meters) and preferably the relationship between the center frequency F0 (Unit GHz) between the semi-cylindrical cavity of:[0040] ⑴[0041] Preferably R = 86 mm, L = 117.7 mm, using the formula (1) f0 were solver to 2.45 GHz.

Quote from: Rodal on 01/05/2017 09:31 PMQuote from: X_RaY on 01/05/2017 08:34 PMQuote from: Monomorphic on 01/05/2017 08:31 PMQuote from: X_RaY on 01/05/2017 08:17 PMAs you can see in the first two results the situation differs from calculation to calculate. The reason is slightly different mesh size and coupling factors. Don't forget to include the spherical end-plate frustum with Q of 111,454. That is a pretty significant increase.Again, at the moment I don't believe in this Q values based on calculations with HOBF. I get freaky inconclusive results when using it.EDITThis is the same frustum as used for the Q compare but using HOBF and fine mesh. Instead of natural possible Q_{L}~36000, i get 207000 loaded Q! Can EmPro calculate Q?If yes can you check the results with EmPro?https://forum.nasaspaceflight.com/index.php?topic=41732.msg1626572#msg1626572FEKO SE calculation is above, EMPro (FEM Eigenresonance solver) below. Dimensions are the same, material is copper in both cases. EMPro results should show Q_{0}.

Quote from: X_RaY on 01/05/2017 08:34 PMQuote from: Monomorphic on 01/05/2017 08:31 PMQuote from: X_RaY on 01/05/2017 08:17 PMAs you can see in the first two results the situation differs from calculation to calculate. The reason is slightly different mesh size and coupling factors. Don't forget to include the spherical end-plate frustum with Q of 111,454. That is a pretty significant increase.Again, at the moment I don't believe in this Q values based on calculations with HOBF. I get freaky inconclusive results when using it.EDITThis is the same frustum as used for the Q compare but using HOBF and fine mesh. Instead of natural possible Q_{L}~36000, i get 207000 loaded Q! Can EmPro calculate Q?If yes can you check the results with EmPro?

Quote from: Monomorphic on 01/05/2017 08:31 PMQuote from: X_RaY on 01/05/2017 08:17 PMAs you can see in the first two results the situation differs from calculation to calculate. The reason is slightly different mesh size and coupling factors. Don't forget to include the spherical end-plate frustum with Q of 111,454. That is a pretty significant increase.Again, at the moment I don't believe in this Q values based on calculations with HOBF. I get freaky inconclusive results when using it.EDITThis is the same frustum as used for the Q compare but using HOBF and fine mesh. Instead of natural possible Q_{L}~36000, i get 207000 loaded Q!

Quote from: X_RaY on 01/05/2017 08:17 PMAs you can see in the first two results the situation differs from calculation to calculate. The reason is slightly different mesh size and coupling factors. Don't forget to include the spherical end-plate frustum with Q of 111,454. That is a pretty significant increase.

As you can see in the first two results the situation differs from calculation to calculate. The reason is slightly different mesh size and coupling factors.

The quote attached is a copy of my post in the EMDrive main thread #9.The simulations are related to the discussion of the {Q}uality -factor when the small end of a truncated conical cayity resonator is below, at or above the cutoff diameter of a cylindrically waveguide. To use the related value is frequently stated by TheTraveller(TT) (he says he quotes Shawyer in this regard) and have suggested to take it as a rule, i.e. to make the small diameter equal to the cutoff diameter.Several explanations where given by TT but nothing conclusive.For example, that there is no reflection at all if the small end plate diameter is below this cutoff rule. This was debunked as nonsense by Dr.Rodal and others. As one of lastest "explanations" TT stated that the Q for such a cavity is much smaller ( or even: "...below anything usefull..") than for a cavity that fits the so called cutoff rule. The results shown here debunk this to be nonsense also.Please note that this tells nothing about differences related to (possible) thrust generation.Quote from: X_RaY on 01/12/2017 04:43 PMQuote from: Rodal on 01/05/2017 09:31 PMQuote from: X_RaY on 01/05/2017 08:34 PMQuote from: Monomorphic on 01/05/2017 08:31 PMQuote from: X_RaY on 01/05/2017 08:17 PMAs you can see in the first two results the situation differs from calculation to calculate. The reason is slightly different mesh size and coupling factors. Don't forget to include the spherical end-plate frustum with Q of 111,454. That is a pretty significant increase.Again, at the moment I don't believe in this Q values based on calculations with HOBF. I get freaky inconclusive results when using it.EDITThis is the same frustum as used for the Q compare but using HOBF and fine mesh. Instead of natural possible Q_{L}~36000, i get 207000 loaded Q! Can EmPro calculate Q?If yes can you check the results with EmPro?https://forum.nasaspaceflight.com/index.php?topic=41732.msg1626572#msg1626572FEKO SE calculation is above, EMPro (FEM Eigenresonance solver) below. Dimensions are the same, material is copper in both cases. EMPro results should show Q_{0}.

Quote from: X_RaY on 01/12/2017 09:02 PMThe quote attached is a copy of my post in the EMDrive main thread #9.The simulations are related to the discussion of the {Q}uality -factor when the small end of a truncated conical cayity resonator is below, at or above the cutoff diameter of a cylindrically waveguide. To use the related value is frequently stated by TheTraveller(TT) (he says he quotes Shawyer in this regard) and have suggested to take it as a rule, i.e. to make the small diameter equal to the cutoff diameter.Several explanations where given by TT but nothing conclusive.For example, that there is no reflection at all if the small end plate diameter is below this cutoff rule. This was debunked as nonsense by Dr.Rodal and others. As one of lastest "explanations" TT stated that the Q for such a cavity is much smaller ( or even: "...below anything usefull..") than for a cavity that fits the so called cutoff rule. The results shown here debunk this to be nonsense also.Please note that this tells nothing about differences related to (possible) thrust generation.Quote from: X_RaY on 01/12/2017 04:43 PMQuote from: Rodal on 01/05/2017 09:31 PMQuote from: X_RaY on 01/05/2017 08:34 PMQuote from: Monomorphic on 01/05/2017 08:31 PMQuote from: X_RaY on 01/05/2017 08:17 PMAs you can see in the first two results the situation differs from calculation to calculate. The reason is slightly different mesh size and coupling factors. Don't forget to include the spherical end-plate frustum with Q of 111,454. That is a pretty significant increase.Again, at the moment I don't believe in this Q values based on calculations with HOBF. I get freaky inconclusive results when using it.EDITThis is the same frustum as used for the Q compare but using HOBF and fine mesh. Instead of natural possible Q_{L}~36000, i get 207000 loaded Q! Can EmPro calculate Q?If yes can you check the results with EmPro?https://forum.nasaspaceflight.com/index.php?topic=41732.msg1626572#msg1626572FEKO SE calculation is above, EMPro (FEM Eigenresonance solver) below. Dimensions are the same, material is copper in both cases. EMPro results should show Q_{0}.Can you lower the frequency of the one on the right to 2.45 GHz, by expanding the Big diameter? I need to know what those dimensions would be. 2.6 GHz is too far outside the amplifier's range.

Quote from: WarpTech on 01/13/2017 05:54 PMCan you lower the frequency of the one on the right to 2.45 GHz, by expanding the Big diameter? I need to know what those dimensions would be. 2.6 GHz is too far outside the amplifier's range.Todd I am not sure this is what you like to see. However, the field pattern looks very interesting.Q_{0}=74382

Can you lower the frequency of the one on the right to 2.45 GHz, by expanding the Big diameter? I need to know what those dimensions would be. 2.6 GHz is too far outside the amplifier's range.

Quote from: X_RaY on 01/15/2017 03:09 PMQuote from: WarpTech on 01/13/2017 05:54 PMCan you lower the frequency of the one on the right to 2.45 GHz, by expanding the Big diameter? I need to know what those dimensions would be. 2.6 GHz is too far outside the amplifier's range.Todd I am not sure this is what you like to see. However, the field pattern looks very interesting.Q_{0}=74382Very interesting indeed! I like it. Don't know what will happen, but the fact that the Q when up and the surface current went up is promising. My model and @notsosureofit's both predict that the larger angle should help. It definitely concentrated sidewall losses to one end. Thank you!Edit: is there a particular location for the antenna, that gives this nice 50 Ohm impedance?