Author Topic: EM Drive Developments - related to space flight applications - Thread 2  (Read 2102319 times)

Offline zen-in

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I have some new observations and theory.   I lifted the first picture from the Aug. '14 paper, which shows the linear displacement sensor.   This device tracks the position of a reflected laser dot on a CMOS image sensor.  This is usually done by calculating the center of luminance of the laser dot; a measurement that has an accuracy of a small fraction of the width of a pixel.   The second picture describes a typical LDS that has sub-micron accuracy.

The only control or "NULL" experiment described in the Aug. 14 paper related to the Eagleworks device was when the dummy load was used instead of sending RF into the cavity.   This of course shields the RF very well.   The dummy load is 50 Ohms and so the SWR is 1:1.   However when the cavity is loaded and the dielectric material is inside the cavity it's possible the SWR is much higher.    This would result in RF being reflected back to the amplifier and being radiated from the shield of the RF cable.   This is what happens when the SWR is not 1:1.   It's possible this RF noise is interfering with the LDS.  When the dielectric is not inside the cavity the SWR is lower so no interference takes place.    This theory agrees with the results of the cannae test as well.

The last picture, also from the Aug. '14 paper shows a negative slope on the baseline position ( no thrust) after each RF pulse.   The first one appears to level off just before the final RF pulse.   After that pulse it heads down again.   I believe the thermally induced change in the CoM of the emdrive causes the balance arm to rotate.   This very slight rotation reduces the reflection distance for the laser beam.
« Last Edit: 02/27/2015 02:28 AM by zen-in »

Offline RotoSequence

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I have some new observations and theory.   I lifted the first picture from the Aug. '14 paper, which shows the linear displacement sensor.   This device tracks the position of a reflected laser dot on a CMOS image sensor.  This is usually done by calculating the center of luminance of the laser dot; a measurement that has an accuracy of a small fraction of the width of a pixel.   The second picture describes a typical LDS that has sub-micron accuracy.

The only control or "NULL" experiment described in the Aug. 14 paper related to the Eagleworks device was when the dummy load was used instead of sending RF into the cavity.   This of course shields the RF very well.   The dummy load is 50 Ohms and so the SWR is 1:1.   However when the cavity is loaded and the dielectric material is inside the cavity it's possible the SWR is much higher.    This would result in RF being reflected back to the amplifier and being radiated from the shield of the RF cable.   This is what happens when the SWR is not 1:1.   It's possible this RF noise is interfering with the LDS.  When the dielectric is not inside the cavity the SWR is lower so no interference takes place.    This theory agrees with the results of the cannae test as well.

The last picture, also from the Aug. '14 paper shows a negative slope on the baseline position ( no thrust) after each RF pulse.   The first one appears to level off just before the final RF pulse.   After that pulse it heads down again.   I believe the thermally induced change in the CoM of the emdrive causes the balance arm to rotate.   This very slight rotation reduces the reflection distance for the laser beam.

Glad to see people still attempting to come up with null-thrust ideas on here.  ;) How does this one account for the measured loss of thrust when the PTFE disk in the resonator cavity came loose after the nylon support bolt melted?

Offline MikeAtkinson

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frobnicat I like your diagrams, very clear.

Note that as the buckling completes the end plate will be at rest with the frustum. This means that there will be an acceleration of the end plate in the opposite direction (at some time after your diagram 4).

After the buckling completes (and all accelerations are zero) the centre of mass will not have changed. However the position of the centre of mass relative to the connection point to the torsion balance may have changed.

From this I think the torsion balance should see a force in one direction, then some time later a force in the other direction. These forces integrated should be zero.

After the buckling has completed the torsion balance should be showing no force, however as the shape of the frustum + end plate has changed the position of the external surfaces has also changed. If the force is being measured as a change in the position of the frustum then a small force would erroneously be shown (I don't think this is the case, but something to check in the experimental set-ups).

Offline Flyby

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What software did you use to do that?

I have in the past used Mathematica to transform images like that but one has to write Mathematica code to get it just right like you did.
While formulating the steps i've used to get to that result, I've concluded I made an error in the last correction step. I took the wrong side for the horizontal (camera yawn distortion) perspective correction.
I'll correct it this evening, local time.. too much to do atm...

Offline Mulletron

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Dr. Rodal & Notsosureofit:

We had an interesting failure in the Eagleworks lab yesterday.  That being I was getting ready to pull a vacuum on our copper frustum mounted in its "reverse" or to the right thrust vector position and ran a preliminary data un to see if it was performing in air as it had two weeks ago just before our last RF amplifier died.  Sadly it wasn't for it was producing less than half of what it did before and in the wrong direction!   

I had Dr. White come in and take a look over my latest test article installation last night and he found that the center 1/4"-20 nylon PE disc mounting bolt that holds the second PE disc to the small OD frustum's PCB endplate was no-longer tensioned as it had been before.  In fact it had partially melted at the interface between the two PE discs thus relieving the strain induced by its bolts threads and nut.  (There are three ~1.00" 1/4-20 nylon bolts mounted on a ~2.00" radius spaced every 120 degrees that hold the first PE disc to the PCB end cap.   There is then a layer of 3/4" wide office scotch tape at the interface between the first and second PE discs and the center 1/4"-20 nylon bolt that hold second PE disc to the first PE disc.) 

Apparently not having the PE discs firmly mounted to the frustum's small OD end cap hindered the thrust producing mechanism that conveys the generated forces in the PE to the copper frustum.  And/or the melted nylon was hogging all the RF energy in the PE discs due to its higher dissipation factor in its semiliquid state.  Either way it looks like there is a high E-field volume where this center nylon bolt hangs out while running in the TM212 resonant mode.  Too bad Teflon bolts are so weak even in comparison to the nylon, for its dissipation factor is at least two orders of magnitude lower than the nylon's.

Best, Paul M.

This was probably one of the most important revelations to come out of Eagleworks yet, other than it works in vacuum. For those who are trying to figure out how it works, wow. It has really gotten my gears turning over the last few days. I hope Paul comes back with more about this, like what happens if a tiny gap is intentionally placed between the PE and copper. The PE and copper should be Casimir attractive while in close contact, but it looks like it became repulsive? somehow upon introduction of the tiny gap introduced by the bolt not holding. This is a significant discovery if it can be repeated, and even better......explained. It has really had me scratching. I don't get the reverse part. What does this mean!??

This link got me chasing down leads. I wish MIT would have provide a reference to what they're talking about, top image: http://www.mit.edu/~kardar/research/seminars/Casimir2010/talks/MITlunch/OffEquil.html

There's a lot of similar stuff out there about this kind of "induced repulsion" like this:
http://arxiv.org/find/quant-ph/1/au:+Chen_F/0/1/0/all/0/1 and this
http://arxiv.org/pdf/1201.5585.pdf refs 27,28

But so far nothing that seems to fit the conditions described within emdrive.
« Last Edit: 02/26/2015 09:28 PM by Mulletron »
Challenge your preconceptions, or they will challenge you. - Velik

Offline Mulletron

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It was never explicitly stated why Shawyer got rid of the dielectric section. Thinking about it tells me it was probably due to heat. And the thruster still works without it.
I've been reading up more on Cr2O3 lately due to its magnetoelectric properties and mention throughout the literature. I discovered that it can withstand really high temperatures. I wonder if this material would help improve the thrust.
http://en.wikipedia.org/wiki/Chromium(III)_oxide
Challenge your preconceptions, or they will challenge you. - Velik

Offline zen-in

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I have some new observations and theory.   I lifted the first picture from the Aug. '14 paper, which shows the linear displacement sensor.   This device tracks the position of a reflected laser dot on a CMOS image sensor.  This is usually done by calculating the center of luminance of the laser dot; a measurement that has an accuracy of a small fraction of the width of a pixel.   The second picture describes a typical LDS that has sub-micron accuracy.

The only control or "NULL" experiment described in the Aug. 14 paper related to the Eagleworks device was when the dummy load was used instead of sending RF into the cavity.   This of course shields the RF very well.   The dummy load is 50 Ohms and so the SWR is 1:1.   However when the cavity is loaded and the dielectric material is inside the cavity it's possible the SWR is much higher.    This would result in RF being reflected back to the amplifier and being radiated from the shield of the RF cable.   This is what happens when the SWR is not 1:1.   It's possible this RF noise is interfering with the LDS.  When the dielectric is not inside the cavity the SWR is lower so no interference takes place.    This theory agrees with the results of the cannae test as well.

The last picture, also from the Aug. '14 paper shows a negative slope on the baseline position ( no thrust) after each RF pulse.   The first one appears to level off just before the final RF pulse.   After that pulse it heads down again.   I believe the thermally induced change in the CoM of the emdrive causes the balance arm to rotate.   This very slight rotation reduces the reflection distance for the laser beam.

Glad to see people still attempting to come up with null-thrust ideas on here.  ;) How does this one account for the measured loss of thrust when the PTFE disk in the resonator cavity came loose after the nylon support bolt melted?

I haven't seen the data from that experiment so am not able to comment on it.   The laser distance sensor has a very high resolution and an event like that would be difficult to interpret if a plot was disclosed.

I think the LDS is probably an interferometer as diagrammed below.    For red light (650 nM) it would take a movement of just 325 nM for each peak of the fringe.  For a slowly moving TP the interferometer's output sine wave would be in the audio region.  However a simple interferometer is not able to detect what direction the mirror is moving.   Another LDS uses different waveforms and a lot of post processing to get direction of movement as well as relative distance.   Both use transimpedance amplifiers that are sensitive to interference.   If RF interference is the explanation for this anomalous force one would expect the force indication to be in both directions.   However there may be some aspect of the experimental setup or the post processing inside the LDS that precludes this.    Since there are so few experimental results disclosed (waveforms), it's difficult to know what is happening.
« Last Edit: 02/27/2015 03:03 AM by zen-in »

Online aero

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It's to bad that we can't find a way that one of the little known or unknown solutions to Maxwell's equations can cause  a momentum. Meep indicates that it does, and if we had a mechanism then it would be straight forward to design more effective thrusters using meep. For example, I modified the Copper Kettle only a little and meep got a 100 times increase in the force over the design tested. The cavity drawing is attached as is the force/power curve for gaps ranging from 1% down to 0.2% of the cavity height, not counting the added height from the pipes.

Note that the "Rim gap" line on the force/power curve is the same one I showed before for the Copper Kettle as Paul presented it. The "pipe" force is about 100 times larger, so the rim gap force plots as a straight line at zero by comparison. Oh, and I didn't just accidentally arrive at the pipe design, I have seen this and similar results for some time. It's now just a good time to share.

And yes, the force indicated by meep is 70 muN/Watt. That is about 21,000 times 1/c, a photon rocket. The cavity was simulated in a space environment, nothing near to interact with except vacuum.

I know people don't like the idea of evanescent waves causing the thruster force, and by looking at the field patterns it seems that the fields exterior to the cavity extend well beyond 1/3 wavelength. Maybe it is something else but still a solution to Maxwell's equations. I can't guess what that might be.

Unless of course it is surface electrons excited by the high power resonant RF, tunnelling through the 35 micron copper ends.
« Last Edit: 02/27/2015 06:19 AM by aero »
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Offline JPLeRouzic

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It's to bad that we can't find a way that one of the little known or unknown solutions to Maxwell's equations can cause  a momentum.
There is obviously momentum in electromagnetic waves. There are also some little known electromagnetic effects that create torque.

Quote
Unless of course it is surface electrons excited by the high power resonant RF, tunnelling through the 35 micron copper ends.
Yes, and many other things may happen were not tested nor even proposed. I wonder how people can know that a lot of energy is pumped in this device and imagine nothing will get out. At the very least thermal effects should happen. Testing it in (near) vacuum doesn't eliminate the thermal hypothesis. Even Pioneer's acceleration that was due to thermal effects after all: http://spectrum.ieee.org/aerospace/astrophysics/finding-the-source-of-the-pioneer-anomaly
Another thing that strikes me is that people search for a unique cause explaining everything, which is a bit unlikely.

One last thought: If a simulator shows results, build this device and publish results in a mainstream conference. Interesting things may happen ;-)

Offline frobnicat

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I have some new observations and theory.   I lifted the first picture from the Aug. '14 paper, which shows the linear displacement sensor.   This device tracks the position of a reflected laser dot on a CMOS image sensor.  This is usually done by calculating the center of luminance of the laser dot; a measurement that has an accuracy of a small fraction of the width of a pixel.   The second picture describes a typical LDS that has sub-micron accuracy.

I thought the linear displacement sensor was based on photons time of flight of reflected light rather than parallax of diffused light dot position :
Quote from: anomalous thrust page 3...
Displacement of the pendulum arm is measured via a Linear Displacement Sensor (LDS). The primary LDS components consist of a combined laser and optical sensor on the fixed structure and a mirror on the pendulum arm. The LDS laser emits a beam which is reflected by the mirror and subsequently detected by the optical sensor. The LDS software calculates the displacement (down to the sub-micrometer level) based upon the beam reflection time. Prior to a test run data take, the LDS is positioned to a known displacement datum (usually 500 micrometers) via mechanical adjustments to its mounting platform. Gross adjustments are performed via set screws. Fine adjustments are performed using manually - operated calibrated screw mechanisms and a remotely controlled motorized mechanism that can be operated with the chamber door closed and the chamber at vacuum. The remote adjustment capability is necessary since the LDS datum will change whenever a change to the test facility environment affects the roll - out table or the chamber e.g., whenever the chamber door is closed or latched and whenever the chamber is evacuated. Once the LDS displacement is adjusted in the final test environment, further adjustment between test run data takes is usually not required.

Do we have other precisions concerning the type of LDS used ? If is ToF (time of flight) reaching sub-micrometer would mean interferometry of some sort ? I see zen-in you have same conclusion in latest post.

Quote
The only control or "NULL" experiment described in the Aug. 14 paper related to the Eagleworks device was when the dummy load was used instead of sending RF into the cavity.   This of course shields the RF very well.   The dummy load is 50 Ohms and so the SWR is 1:1.   However when the cavity is loaded and the dielectric material is inside the cavity it's possible the SWR is much higher.    This would result in RF being reflected back to the amplifier and being radiated from the shield of the RF cable.   This is what happens when the SWR is not 1:1.   It's possible this RF noise is interfering with the LDS.  When the dielectric is not inside the cavity the SWR is lower so no interference takes place.    This theory agrees with the results of the cannae test as well.

If condition for the hypothesis is : amount of RF power radiated from the feed cable interferes with LDS values, then we need to know some precise details on LDS and how such interference could take place.

Also, do we know how the RF amplifier deals with varying degrees of back reflected power. Could it be conceivable that this back reflected power generates or modifies some current DC component somewhere and that this DC components push to a varying degree on damper's magnetic field ?

We know of at least one significant DC current component interaction with the damper's magnetic field : around 10N upward (increasing distance) due to 5.6 A DC current in RF amplifier's power cable. Could this drawn DC current be changed (in significant ratio) due to reflected RF power levels ?

Another thing, those reflected power levels of varying degrees could change the heating rates of RF amplifier radiators, that are known to IR heat the flexure bearing and change the rest equilibrium point of balance. Albeit slowly.

Quote
The last picture, also from the Aug. '14 paper shows a negative slope on the baseline position ( no thrust) after each RF pulse.   The first one appears to level off just before the final RF pulse.   After that pulse it heads down again.   I believe the thermally induced change in the CoM of the emdrive causes the balance arm to rotate.   This very slight rotation reduces the reflection distance for the laser beam.

When integrating the momentum needed to keep the balance away from it's rest equilibrium point you see that relative movement a part's CoM relative to fixation point would have to be huge to account for such long term drift against a fixed rest equilibrium point. The most obvious explanation for those drifts is a change of rest equilibrium point of the balance (heating of flexure bearing blocks).

If we have  very roughly an apparent force drift of 30N during 30s, that's 1N/s, then F(t) = - 1e-6*t
If such F(t) is to be explained by a recoil of a moving part, such moving part of mass m would have to be accelerated (in the opposite direction, to the left) at  a(t) = -F(t) / m   that's v(t)=5e-7/m t  and  x(t)= 1.7e-7/m t^3
The moving part's CoM would have to change position as the cube of time to explain such drifting force (against a stable equilibrium rest position of balance) as a recoil effect.
x(t)*m = 1.7e-7 t^3 = 5.6e-3 kg m at t=30s,  that is 1kg moving 5.6mm  or  5.6kg moving 1mm, at least (the drifting baseline shows now sign of reversing...) if rest equilibrium position is supposed stable.

So the most obvious explanation so far (as first given by Paul March) is that this drifting component of measured distance  is not due to a varying force but due to a varying equilibrium rest position (like tuning or detuning a scale when nobody is on it moves the readings).

Edits in blue, for clarification.
« Last Edit: 02/27/2015 12:31 PM by frobnicat »

Offline Notsosureofit

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Weekend coming:

Where do we stand on the frequency, dimensions, power, mode and Q for the Shawyer cavity discussed above ?

Offline frobnicat

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frobnicat I like your diagrams, very clear.

Note that as the buckling completes the end plate will be at rest with the frustum. This means that there will be an acceleration of the end plate in the opposite direction (at some time after your diagram 4).

Yes, for a buckling of the right plate to the right (outward) there would be initially an impulse to the left (as seen from the rest of the frustum) then an impulse of equal but opposite momentum to the right when the buckling slows and stops. See attached charts.

Quote
After the buckling completes (and all accelerations are zero) the centre of mass will not have changed. However the position of the centre of mass relative to the connection point to the torsion balance may have changed.

The CoM of the whole system will not have changed for a free floating system, yes. Maybe it's better then to see the other way around since the whole system's CoM is immobile it can play a role of reference : the position of the connection point to the torsion balance relative to the centre of mass may have changed.
But the system's CoM is inertial (not changing) only if the system is isolated (free floating)

Quote
From this I think the torsion balance should see a force in one direction, then some time later a force in the other direction. These forces integrated should be zero.

Yes the force (kg m/s) when integrated is the momentum (kg m/s) and there can be no net momentum difference in total between initial and final immobile positions of the frustum. Again, this is only valid for free floating system.

The balance arm experiences a recoil force, but we don't see a force, only a deviation in position caused by force. I'm not sure the deviation has to integrate to 0 (so we have to remember that deviation != force).

Quote
After the buckling has completed the torsion balance should be showing no force, however as the shape of the frustum + end plate has changed the position of the external surfaces has also changed. If the force is being measured as a change in the position of the frustum then a small force would erroneously be shown (I don't think this is the case, but something to check in the experimental set-ups).

Given the rest position restoring spring of the balance, a moving part can only impart a transient signal, when the moving part stops moving (relative to rest of system), the balance will restore to it's rest state equilibrium, ie showing a 0 force reading. There is no way for an ended (non longer evolving) deformation in the system on top of the balance arm to make a long lasting deviation from rest equilibrium.

It can be modelled as a part of mass m (green disc) being driven at varying distance L(t) relative to rest of the system of mass M (blue square), rest of the system being linked by a spring and damper to inertial rest frame of infinite mass (earth).

In the charts,
horizontal axis : time
vertical axis magenta : force of mass m on mass M
vertical axis black : distance between mass m and mass M,  L(t) that drives the excitation
vertical axis blue : acceleration of mass M
vertical axis green : velocity of mass M
vertical axis red : position of mass M, what would be measured as a result

Deviations upward correspond to movements to the left. All scales arbitrary at the moment (for illustration purpose only). At same scale, with m<<M the black step on L(t) would appear much greater than the resulting steplike response of position of arm (rpos, in red). For instance it would take a step of 10cm to the left of a mass m=100g to make a mass M=1kg to step to the right by 1cm.

cap1 : stiffness and damping to 0 (free floating)
cap2 : some stiffness (position restoring spring) but no damping
cap3 : slightly underdamped system
cap4 : slightly overdamped system

Note in the last case how it's not obvious that the integrated surface between red curve (positions readings) and the 0 axis (not shown, sorry) is indeed 0. I'll need to check. But if one is to interpret naively the red curve (position of balance arm) directly as force it would be tempting to say there is a net leftward average force. I will try to calibrate my model on the real values of the experiment.

Offline Rodal

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I like your drawings with the buckled condition idealized as a beam with three hinges: one hinge at the center and a hinge at each end. :)

Thank you very much for taking the time to make those drawings.   :)

I should have looked at that initially. I agree with your drawing.  To the extent that my prior wording disagreed with your drawing, my prior words were incorrect, when and if they referred to the thermal force Fpr.

Let's then address what happens in the opposite case that the plate instead buckles to the right:

The flat plate can theoretically buckle towards the left or towards the right (if the copper is thin enough) depending on initial imperfectionsIf when the buckled plate moves towards the left it gives a force towards the right then  if the plate buckles towards the right it would produce a force towards the left, in the same direction as the EM Drive's motion, do you agree?.

Then, if this buckling analysis is correct, it gives transient force that is towards the left when the plate buckles towards the right and it gives a transient force to the right when the plate buckles towards the left.

Now I have to give further thought to which direction the plate buckles when heated.  The real plate has a neutral surface that is not at the middle of the cross-section.  It is really a bi-material thermostat: with the epoxy expanding much more than the very thin copper coating.   If this unsymmetric laminate would be exposed to a uniform temperature it would expand towards the outside, producing a force towards the left, like the EM Drive force.  The question is what happens under the superposed thermal gradient through the thickness. The IR Camera shows very pronounced heating on the outside surface....
I have calculated the variables that govern which way the circular plate will buckle.

Using S. Timoshenko's classic solution to the bimaterial thermal expansion problem (Journal of the Optical Society of America, JOSA, Vol. 11, Issue 3, pp. 233-255 (1925) ) the radius of curvature can be expressed as:

radiusOfCurvature = (t1+t2)*(3(1+m)+(1+m*n)(m^2 +1/(m*n)))/(6*deltaAlpha*deltaT*((1+m)^2))

where I have expressed the following variables as non-dimensional ratios (allowing use of any consistent system of units, and revealing the important parameters, instead of the expression in Wikipedia that is awkwardly expressed in dimensional units, and expressed for the curvature instead of its reciprocal):

m=t1/t2  Thickness ratio
n=E1(1-nu1^2)/(E2(1-nu2^2))  Plate stiffness-ratio

and I have used the (plates and shells) stifness E1(1-nu1^2) taking into account the Poisson's ratio, since we are dealing with a plate instead of an uniaxial beam (this makes practically no difference for this case due to the very small values of the Poisson's ratio involved for FR4 and the very thin layer of copper).

and the differences in thermal expansion and temperature:

deltaAlpha=alpha2 - alpha1 
deltaT=T - To

t1 and t2 are the thicknesses of the layers
E1 and E2 are the Young's modulii
nu1 and nu2 are the Poisson's ratios

From Paul March we know:

t1=0.00138 inches
t2=0.063 inches

the material "1" is copper

Wikipedia and Engineering Toolbox give E1=17*10^6 psi

Wikipedia, NBS (Hidnert &Krider's classic article) and Engineering Toolbox give alpha1= 17*10^(-6) 1/degK 

and Wikipedia gives nu1=0.33

and that the material "2" is FR4

The following references give:

Wikipedia
ECW = 3*10^6 psi   alphaCW= 14*10^(-6) 1/degK   nuLW=0.136
ELW = 3.5*10^6 psi alphaLW= 12*10^(-6) 1/degK  nuCW=0.118

P-M Services (UK)
                               alphaCW= 15*10^(-6) 1/degK
                               alphaLW= 11*10^(-6) 1/degK

Leiton (Germany)
                               alphaCW= 17*10^(-6) 1/degK
                               alphaLW= 12*10^(-6) 1/degK

It is trivial to show that the sign of the curvature (which way the plate is going to buckle) is governed only by the difference in thermal expansion coefficients between the two layers (and of course whether deltaT is positive or negative).

Bimaterial thermal bending will take place along the anisotropic in-plane direction with the highest thermal expansion and lowest modulus.  It is obvious that this is the CW direction.

It is immediately obvious, that using Leiton's (Germany) coefficient of thermal expansions, the copper/FR4 laminate circular plate will not experience any bimaterial bending whatsoever because according to Leighton alphaCW of FR4 is exactly the same as the universally accepted alpha1 of copper.

The thermal IR camera shows temperature readings ranging from below 79 deg F to a concentrated maximum at certain small spots of 94.3 deg F.

Using Wikipedia's properties, the plate will experience an extremely small amount of bimaterial bending towards the inside, for a temperature increase from 68 deg F to 79 deg F, with a huge radius of curvature exceding 7000 inches (practically flat, in relation to the thickness of only 0.064 inches).

Also, using Wikipedia's properties, the plate will experience an extremely small amount of bimaterial bending towards the inside, for a temperature increase from 68 deg F to 94.3 deg F, with a huge radius of curvature exceeding 3000 inches (practically flat, in relation to the thickness of only 0.064 inches).

CONCLUSION: due to the fact that FR4 has a coefficient of thermal expansion very similar to the one of copper, and that the thickness of the copper is extremely small compared to the thickness of FR4, the circular plate will experience either no bimaterial thermal bending whatsoever, or it will be extremely small (will stay practically flat) under the measured changes in temperature.  Therefore, bi-material bending due to a change in temperature is irrelevant to the buckling problem.  Buckling is instead governed by the plate's initial imperfect flatness

« Last Edit: 02/27/2015 06:04 PM by Rodal »

Offline Rodal

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I like your drawings with the buckled condition idealized as a beam with three hinges: one hinge at the center and a hinge at each end. :)

Thank you very much for taking the time to make those drawings.   :)

I should have looked at that initially. I agree with your drawing.  To the extent that my prior wording disagreed with your drawing, my prior words were incorrect, when and if they referred to the thermal force Fpr.

Let's then address what happens in the opposite case that the plate instead buckles to the right:

The flat plate can theoretically buckle towards the left or towards the right (if the copper is thin enough) depending on initial imperfectionsIf when the buckled plate moves towards the left it gives a force towards the right then  if the plate buckles towards the right it would produce a force towards the left, in the same direction as the EM Drive's motion, do you agree?.

Then, if this buckling analysis is correct, it gives transient force that is towards the left when the plate buckles towards the right and it gives a transient force to the right when the plate buckles towards the left.

Now I have to give further thought to which direction the plate buckles when heated.  The real plate has a neutral surface that is not at the middle of the cross-section.  It is really a bi-material thermostat: with the epoxy expanding much more than the very thin copper coating.   If this unsymmetric laminate would be exposed to a uniform temperature it would expand towards the outside, producing a force towards the left, like the EM Drive force.  The question is what happens under the superposed thermal gradient through the thickness. The IR Camera shows very pronounced heating on the outside surface....
I have calculated the variables that govern which way the circular plate will buckle.

Using S. Timoshenko's classic solution to the bimaterial thermal expansion problem (Journal of the Optical Society of America, JOSA, Vol. 11, Issue 3, pp. 233-255 (1925) ) the radius of curvature can be expressed as:

radiusOfCurvature = (t1+t2)*(3(1+m)+(1+m*n)(m^2 +1/(m*n)))/(6*deltaAlpha*deltaT*((1+m)^2))

where I have expressed the following variables as non-dimensional ratios (allowing use of any consistent system of units, and revealing the important parameters, instead of the expression in Wikipedia that is awkwardly expressed in dimensional units, and expressed for the curvature instead of its reciprocal):

m=t1/t2  Thickness ratio
n=E1(1-nu1^2)/(E2(1-nu2^2))  Plate stiffness-ratio

and the differences in thermal expansion and temperature:

deltaAlpha=alpha2 - alpha1 
deltaT=T - To

t1 and t2 are the thicknesses of the layers
E1 and E2 are the Young's modulii
nu1 and nu2 are the Poisson's ratios

From Paul March we know:

t1=0.00138 inches
t2=0.063 inches

the material "1" is copper

Wikipedia and Engineering Toolbox give E1=17*10^6 psi

Wikipedia, NBS (Hidnert &Krider's classic article) and Engineering Toolbox give alpha1= 17*10^(-6) 1/degK 

and Wikipedia gives nu1=0.33

and that the material "2" is FR4

The following references give:

Wikipedia
ECW = 3*10^6 psi   alphaCW= 14*10^(-6) 1/degK   nuLW=0.136
ELW = 3.5*10^6 psi alphaLW= 12*10^(-6) 1/degK  nuCW=0.118

P-M Services (UK)
                               alphaCW= 15*10^(-6) 1/degK
                               alphaLW= 11*10^(-6) 1/degK

Leiton (Germany)
                               alphaCW= 17*10^(-6) 1/degK
                               alphaLW= 12*10^(-6) 1/degK

It is trivial to show that the sign of the curvature (which way the plate is going to buckle) is governed only by the difference in thermal expansion coefficients between the two layers.

Bimaterial thermal bending will take place along the anisotropic in-plane direction with the highest thermal expansion and lowest modulus.  It is obvious that this is the CW direction.

It is immediately obvious, that using Leiton's (Germany) coefficient of thermal expansions, the copper/FR4 laminate circular plate will not experience any bimaterial bending whatsoever because according to Leighton alphaCW of FR4 is exactly the same as the universally accepted alpha1 of copper.

The thermal IR camera shows temperature readings ranging from below 79 deg F to a concentrated maximum at certain small spots of 94.3 deg F.

Using Wikipedia's properties, the plate will experience an extremely small amount of bimaterial bending towards the inside, for a temperature increase from 68 deg F to 79 deg F, with a huge radius of curvature exceding 7000 inches (practically flat, in relation to the thickness of only 0.064 inches).

Also, using Wikipedia's properties, the plate will experience an extremely small amount of bimaterial bending towards the inside, for a temperature increase from 68 deg F to 94.3 deg F, with a huge radius of curvature exceeding 3000 inches (practically flat, in relation to the thickness of only 0.064 inches).

CONCLUSION: due to the fact that FR4 has a coefficient of thermal expansion very similar to the one of copper, and that the thickness of the copper is extremely small compared to the thickness of FR4, the circular plate will experience either no bimaterial thermal bending whatsoever, or it will be extremely small (will stay practically flat) under the measured changes in temperature.  Therefore, bi-material bending due to a change in temperature is irrelevant to the buckling problem.  Buckling is instead governed by the plate's initial imperfect flatness
Therefore, since the bimaterial thermal bending is either non-existent (according to Leiton-Germany properties) or completely negigible (according to Wikipedia thermal expansion properties for FR4), it is obvious that buckling of the circular plate will be governed by initial imperfections.

In this case, initial imperfections are most likely the result of manufacturing (due to small unsymmetric differences in the FR4 laminate cross-section fiberglass reinforcement, or to the residual stresses from deposition of the copper).

Therefore, the circular plate will buckle either:

A) inwards in which case the force will be to the right
or
b) outwards, in which case the force will be to the left, in the same direction as the EM Drive measured force

There is no basis at this point to decide whether the force will be towards the left (same as the measurement) or towards the right (opposite to the measurement).  It is entirely dependent on the initial non-flatness of the plate..

Statements that the buckling force will be in the same or opposite direction as the measured EM Drive's force are dependent on the unjustified assumption that the buckling will be in a given direction (outwards or inwards, respectively).  That is unsupported by the facts.  The plate can buckle outwards or inwards, depending on the initial imperfect flatness.  Therefore the force can be towards the left (same direction as the EM Drive's measured force) or in the opposite direction.

ANOTHER ARTIFACT BITES THE DUST, and another one, and another one   :)

Therefore the buckling force explanation for the measured EM Drive's thrust is nullified on two accounts:

A) It could only explain the magnitude of the initial transient force but not the longer duration (40 sec) force

B) The direction of the buckling  force can be either in the same direction as the measured EM Drive's force or in the opposite direction, dependent on the initial imperfect flatness of the circular plate.  Since this imperfect flatness should be random for different plates used in the US, UK and China, one must conclude that it would be an unlikely coincidence that all measurements were conducted with plates that were originally imperfect in such a way as to produce buckling forces in the same direction as measured.



Furthermore, to avoid confusion, it should be pointed out again that the buckling force effect cannot be used for propellant-less propulsion. It was submitted only as an explanation for an experimental artifact. The center of mass of an EM Drive free in space should not move during or after buckling.  The center of mass of an EM Drive free in space should be completely unaffected by any buckling .
« Last Edit: 02/27/2015 08:47 PM by Rodal »

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FYI

Found my Gunn Oscillator !!

Offline Rodal

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FYI

Found my Gunn Oscillator !!
Where was it hidden? Inquiring minds would like to know... :)

Offline Notsosureofit

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FYI

Found my Gunn Oscillator !!
Where was it hidden? Inquiring minds would like to know... :)

On the back of a variable attenuator. ( ~50mW)
https://www.dropbox.com/s/vdueo9mi6l3s4kb/2015-02-27%2011.18.24.jpg?dl=0

"CAVITY" is on the way !
http://www.ebay.com/itm/201065780928?_trksid=p2059210.m2749.l2649&ssPageName=STRK%3AMEBIDX%3AIT

Looks like short WR90 to WR75 that can be machined. (Any short WR51 to WR90 would also work if anyone has one around)
« Last Edit: 02/27/2015 03:45 PM by Notsosureofit »

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Here is another bit of data from meep that I found interesting. This was from very early on so the gap used (2% base radius) was larger than ideal. The curve shows the Force/Power generated with a gap in the base plate, as the gap moves from the center of the base to the edge of the base. As you can see, whatever it is that causes the thrust effect as detected by meep is concentrated at the edge, in the corner of the cavity between the base and the cone body.

Speaking to the magnitude of the force on this graph. At the time I took this data I was using gaps only in the large end of the cavity. Later data shows that gaps in both ends of the cavity multiplies the detected force by a large factor.

As for what is causing the force? Don't know but this drawing indicates that the copper only needs to be thin or non-existent at the edge of the base. Elsewhere it can be thick with little effect.

Oh - and I should mention that on my cavity with the pipes extending axially from the ends, the drawing scale shows those pipes to be 1 inch long from the interior of the cavity. What I should mention is that length doesn't matter. Changing the length of the pipe (1" to 1/4") only changes the Force/Power calculated by meep in the third or fourth decimal place. A simple gap in the thin 35 micron copper works almost as well.

The force calculated is more strongly dependent on the direction of the pipes, however. From looking at the data I have posted you can see that the force is reduced from 70 to 0.08 as the angle changes from axial to outward horizontal. I did calculate one intermediate angle and found that the force seems to reduce as the cosine of the angle off vertical in the outward direction. I have yet to angle the pipes inward so no data for that instance.
« Last Edit: 02/27/2015 06:58 PM by aero »
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While looking into the tunnelling of electrons through a barrier, I observe that the mathematics for tunnelling of electrons is very similar to the mathematics presented for propagation  evanescent waves through a restriction in an RF wave-guide. See page 15, here http://wwwsis.lnf.infn.it/pub/INFN-FM-00-04.pdf for evanescent wave propagation and sheet 8, here http://tuttle.merc.iastate.edu/ee439/topics/tunneling.pdf for tunnelling of electrons through a barrier. (I would paste the math here, but both papers are PDF's, so I can't.)

I guess I shouldn't be surprised that the math is similar, if not the same, as tunnelling electrons are evanescent matter waves so the math should be similar. The big difference in the two math formulations is that the author of the first paper, evanescent wave propagating through a restriction in the wave guide, relies on extended special relativity to keep the exp (+term) in the wave equation while the author of the electron tunnelling paper relies on a physical observation to retain that term.

This brings up a question. "Since we are concerned with the mass of the thruster, why isn't it made from a light metal, aluminium for example?" The work function of aluminium is very close to that of copper, is all metals. Granted that aluminium oxidized when exposed to air so that its work function more than doubles after exposure, but a very thin layer of gold electro deposited on both sides would eliminate that problem with the result of a much less massive thruster.

Can anyone suggest a reason that an aluminium cavity would not work?
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Offline Rodal

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While looking into the tunnelling of electrons through a barrier, I observe that the mathematics for tunnelling of electrons is very similar to the mathematics presented for propagation  evanescent waves through a restriction in an RF wave-guide. See page 15, here http://wwwsis.lnf.infn.it/pub/INFN-FM-00-04.pdf for evanescent wave propagation and sheet 8, here http://tuttle.merc.iastate.edu/ee439/topics/tunneling.pdf for tunnelling of electrons through a barrier. (I would paste the math here, but both papers are PDF's, so I can't.)

I guess I shouldn't be surprised that the math is similar, if not the same, as tunnelling electrons are evanescent matter waves so the math should be similar. The big difference in the two math formulations is that the author of the first paper, evanescent wave propagating through a restriction in the wave guide, relies on extended special relativity to keep the exp (+term) in the wave equation while the author of the electron tunnelling paper relies on a physical observation to retain that term.

This brings up a question. "Since we are concerned with the mass of the thruster, why isn't it made from a light metal, aluminium for example?" The work function of aluminium is very close to that of copper, is all metals. Granted that aluminium oxidized when exposed to air so that its work function more than doubles after exposure, but a very thin layer of gold electro deposited on both sides would eliminate that problem with the result of a much less massive thruster.

Can anyone suggest a reason that an aluminium cavity would not work?
Their magnetic properties, for example, are opposite: Copper is (weakly) diamagnetic while Aluminum is (weakly) paramagnetic.

What relative magnetic permeability did you input into MEEP for copper? Did you input a value less than one?
  Did you report to us that value?  I don't recall.

Stainless Steel 304L (the material of the vacuum chamber) is weakly paramagnetic (the opposite of copper). What relative magnetic permeability did you input into MEEP for the StSt 304L for the chamber? Did you input a value greater than one? Did you report to us that value?  I don't recall.

These properties (copper diamagnetic, StSt paramagnetic are relevant to the force due to evanescent ineraction problem you are solving with MEEP)

Diamagnetic materials (like copper) create an induced magnetic field in a direction opposite to an externally applied magnetic field, and they are repelled by the applied magnetic field. In contrast, the opposite behavior is exhibited by paramagnetic materials (like aluminum): they are attracted to it.

On the other hand, it has been proposed that the best material (just) for the flat big end is a strongly ferromagnetic material: preferably Metglas, or otherwise iron.  This would result in a diamagnetic repellent copper material for the small flat end and the curved conical surfaces and a strongly attractive ferromagnetic material (Metglas thin film coated or just iron) for the big flat end. To my knowledge, this has not been tested.

Since there is really no proven theory of how would an EM Drive generate thrust in space, thereby apparently violating the law of conservation of momentum, and we are still debating whether the experimental measurements are an artifact, the best way to cut to the chase is to test an EM Drive made of Aluminum, and to also test an iron (or a material coated with an interior thin film of Metglas) for the big flat end.

« Last Edit: 02/27/2015 08:13 PM by Rodal »

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