Author Topic: EM Drive Developments - related to space flight applications - Thread 2  (Read 2106447 times)

Online Stormbringer

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When antigravity is outlawed only outlaws will have antigravity.

Offline Rodal

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Grenade!

http://phys.org/news/2015-03-theorist-gravitational-casimir.html
I attach the actual paper (available at arXiv) by James Quach on the Gravitational Casimir effect for those interested to read it for personal research purposes.  All others should access it through the American Physical Society at http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.081104

@NOTSOSUREOFIT: Notice that the paper begins with a Maxwell-equation-like formulation of the linearized Einstein field equations known as gravitoelectromagnetism

Quote from: James Quach
if experiments show the Casimir pressure to be an order of magnitude larger than that predicted from the photonic contribution alone, this would be the first experimental evidence for the validity of the H-C theory and the existence of gravitons. This would open a new field in the way of graviton detection.
« Last Edit: 03/04/2015 02:10 PM by Rodal »

Offline Notsosureofit

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Grenade!

http://phys.org/news/2015-03-theorist-gravitational-casimir.html

Hmm, one might suppose that if the graviton interaction is enhanced by the superconducting currents, then perhaps the graviton interaction is also enhanced by the existence of RF induced currents ??

Offline aero

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Thank you Dr. Rodal - So here is the complete set for some magnetic source run. I didn't record any details except I can see  that the antenna in in the location of the magnetic antenna I use.  Is it possible that all of the images are correct? If so that would increase my confidence in the meep output.
Yes, they can all be correct.  But we need your help in identifying the images you posted.  The electric and magnetic fields are vectors in 3-D space, with orthogonal base vector components.


For example, what does this represent? Is this a contour plot of the electric field component oriented along the axial direction  (the vector component oriented along the "y" axis)? The reason why I think it is the axial component is because the axial component should be symmetric about the "y" axis (which it is)

Notice how although you impose flat faces, the electromagnetic field inside the cavity wants to be spherical (thus the 2 curved boundaries between the 3 contour regions).  Left to its own, Nature will do what it wants to do: to propagate as spherical waves.  The radii of the 2 curved boundaries look correct.  The radii of curvature seem to have the same center as the focal point of  intersection of the sides of the truncated cone (the vertex or apex of the cone).



Sorry - I was tired when I posted that.

The file names give the information I have, unless the meep documentation gives more. Meep'c coordinate system is a little confusing. For 2D it is (x, y, no-size). When I place objects in the model, x is the axial direction and y is the in-plane perpendicular. There is no z in the geometry. However, the field you identified is named ez.i.jpeg which means that it is the imaginary component of the electric field in the z, or out of plane direction. Then the fields are identified from the file name as "e" for electric and "h" for magnetic and then "i" for imaginary and "r" for real components of the fields.
As the run is in 2D the other 3 fields can't be generated. That is, no ex, ey or hz.
Retired, working interesting problems

Offline Rodal

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I'm currently trying to finish up the cross section drawing on the flight demonstrator, but i kinda fail to understand how it fits together....

Looking closely (top down wise) at the lower rim it seems to me there is :

-small shiny rim (could be the edge of the alu cone?)
-brownish plate (copper plate?)
-small shiny rim
-thick plate (most probably holding the screw thread)

I'm puzzled about the second small, shiny rim...
Why would you need an additional small slab of alu under the (supposedly) copper plating?
Any one has an idea?

Perhaps it is a compliant (less stiff than the joined flange and the thick flat plate) material to prevent leakage by providing a more uniform stress distribution in the circumferential direction (the screws otherwise produce stress concentrations).  If a gasket, the compliant material would have to satisfy the required electromagnetic properties between the joined components.

But, if the brown material serves as a gasket (whether a soft metal or another material), the flange would have to be unusually thin (which is unlikely in my opinion as it would be difficult to keep the flange flat if it would be that thin).

Perhaps the brown material is later inserted into a thin, shallow, groove in the previously joined and bolted metal flange and plate, that is only then filled with a brown (initially a viscous liquid) adhesive to prevent leakage (and metal conductivity was ensured by the fact that there is metal behind the shallow, thin, brown adhesive).

Whatever it is, it seems to be associated with preventing leaking, as there is a huge number of bolts holding the flange to the flat plate, as if somebody was concerned with leaking and wanted to ensure a uniform fit without leaking.

« Last Edit: 03/04/2015 03:07 PM by Rodal »

Offline Notsosureofit

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FYI

https://www.dropbox.com/s/rtp9gx844yxu6ef/IMAG0372.jpg?dl=0





That one is a 13.25".

See also:



And wire seal dimensions:

http://www.n-c.com/resources/spec/FlangesAndFittings_WireSealFlanges.pdf

The top flange of the cone seems to fit the dimension ratio of a 12.375" (standard) wire seal flange.  The plate on the top end could be just a plate drilled to fit.

Unfortunately, if they used "standard" flanges the cone dimensions are quite a bit larger than what would seem reasonable from the image calculations and Shawyer's numbers.  The wire seal flanges from different manufacturers can vary an enormous amount.  This could easily be someone's "aerospace" version or completely nonstandard to Shawer's specs.

« Last Edit: 03/04/2015 06:22 PM by Notsosureofit »

Offline Rodal

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FYI

https://www.dropbox.com/s/rtp9gx844yxu6ef/IMAG0372.jpg?dl=0
I see the brown reflection of the wood-like table on the left side of the plate, and the shiny rim.

Can't tell whether that is real solid wood, a thin veneer, or Formica laminate countertop   :)
« Last Edit: 03/04/2015 04:02 PM by Rodal »

Offline Notsosureofit

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Doesn't mean that it isn't a copper cone that has been plated on the outside for anti corrosion.  Often this is a Ni coating.

Offline frobnicat

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....
The only thing that I see that can account for the apparent lacking torque is the equilibrating torque induced by the inclination of the plane of rotation of the arm toward the CoM of the rotating assembly, that is equivalent to a hanging pendulum. The way it is used, the balance is more than 90% a hanging pendulum and less than 10% a torsion pendulum driven by flexure stiffness.

If this analysis holds, small changes in stiffness of flexure bearings would make for a minor impact on results. Changes in inclination would be the major way to tune the (linearised hanging pendulum equivalent) stiffness.

A hanging pendulum hangs from a rigid support located above the weight.  Its period depends only on the length of the pendulum's arm (and g , the acceleration of gravity, which is practically constant on Earth).  The flexural stiffness of the pendulum's arm is negligible.

But here nothing is hanging from the stainless steel chamber "rigid ceiling" supported by arms with negligible flexural stiffness.

What I see is the EM Drive weight supported by a frame of Faztek aluminum beams, Faztek beams that are supported from below, not from the stainless steel chamber ceiling.



What rigid support (located above the EM Drive) is the EM Drive hanging from ?  (Where is the "hanging pendulum" rigid support located ?)

What constitutes the arm of the "hanging pendulum"?  Why does it have negligible flexural stiffness? (The flexural stiffness of the aluminum Faztek beams is far from being negligible)

Do you really mean a hanging pendulum (whose period depends only on the length of the arm)?
Or do you mean a flexural pendulum (whose period depends on the stiffness of the arm)?


And if you agree that the flexural stiffness of the arms are not negligible, why take into account only the portion above the weight?  What about the flexural stiffness below the weight? 
Aren't the Faztek beams supported from below?

What I see is your "z" axis going up to a Faztek frame or "bridge" and the "bridge" being supported by two vertical Faztek beams, and those vertical Faztek beams are supported from below, not from above.

Is that then really an inverted flexural/torsional pendulum since it is made by Faztek aluminum beams supported from below?
... pics ...

It's not about faztek beams compliance. It's about introducing a tilt in the Z axis of rotation (the tilt is around the Y axis) so that the CoM Centre of Mass of the whole rotating assembly, which is not exactly on the Z axis (from the values given by Paul March) but behind the axis (X-) will be lowest when at rest equilibrium position and will have to climb the gravitational potential (ie work against) if it is to deviate from this position (by rotating around the Z axis).

This could be analysed in terms of potential energy, but my Newtonian bias is toward forces and accelerations, see attached picture : movements in a sloped plane XY with theta the angle of slope (0 for horizontal, pi/2 for vertical) and assuming the forces in Z all cancel (since trajectories don't depart from XY) and don't couple to forces on X or Y (no friction) are equivalent to movements in XY plane that would be vertical in a reduced gravity of g sin(theta). This equivalence is used for instance with inclined air cushioned tables frictionless dynamics.

So in the end we have a position restoring torque that is dcom mcom g sin(theta) sin(alpha). For small deviations alpha (and indeed we know they are small), this can be linearised
torque/alpha = dcom mcom g sin(theta)
This behaves like an added spring constant of dcom mcom g sin(theta) [Nm/rad] to the stiffness of the flexure bearings 9.06e-2 [Nm/rad]

But, there is a very strange thing happening with this line of reasoning, when I do quantitative comparison, if flexure bearings really are .007Lb-in/degree each = total 9.06e-2 Nm/rad then it is so low under the required stiffness (in some charts, only 1m measured linear displacement for 29.1N cal. pulses) that it would require an added stiffness equivalent (from this pseudo-hanging pendulum effect) that amounts to an inclination angle theta up to 25 (degrees). Wow ! This would certainly not have remained unnoticed in the pictures ! I'm puzzled.

@ Star-Drive : you say you haven't really controlled the amount of tilt used to "stabilize" the pendulum, can you confirm that it is indeed tilted with the frustum (X+) getting higher and the electronic stack (X-) going lower, that is when looking in front of the vacuum chamber the downward slope would be from the front to the back ? Do you have an upper bound for the slope introduced ? Do you see why there would be such a huge disparity between the low stiffness of flexure bearings given at .007 In-Lb/degree each, that would allow for a reading of .353*(29.1e-6* 0.286)/9.06e-2 = 32.4m in response to 29.1N cal. pulses and the apparent higher stiffness of between 1m to 2.5m response to cal. pulses (depending on the charts) ?

Thank you for the latest complement of informations. For confirmation : 7.64118 kg + 0.200 kg mass is the mass of the complete electronic stack on the back of pendulum's arm ? Mass of small diameter dielectric would be around 1kg ? Total mass of rotating assembly, with dielectric, would be just a bit above 25Lb ?
« Last Edit: 03/04/2015 04:51 PM by frobnicat »

Offline sghill

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That thick bottom-most plate looks like its a painted rubber or silicon footplate to me.  The cracks in the paint are a dead giveaway that the thick bottom footer is some sort of flexible material that's been painted and then cracked after it flexed. 

It makes sense to have a flexible footer to avoid any sort of damage when handling the thing from time to time.

Here's an example:
« Last Edit: 03/06/2015 05:31 PM by sghill »
Bring the thunder Elon!

Offline Rodal

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....
It's not about faztek beams compliance. It's about introducing a tilt in the Z axis of rotation (the tilt is around the Y axis) so that the CoM Centre of Mass of the whole rotating assembly, which is not exactly on the Z axis (from the values given by Paul March) but behind the axis (X-) will be lowest when at rest equilibrium position and will have to climb the gravitational potential (ie work against) if it is to deviate from this position (by rotating around the Z axis). ....
Thank you for taking the time to draw these excellent pictures.  A picture is worth 1000 words.

What compliance is responsible for the tilt in the Z axis of rotation around the Y axis) ?  You state that the tilt is not due to the Faztek beam compliance (although if the Faztek beam would be compliant enough it certainly would tilt).

If it is not due to the Faztek beam compliance, then my understanding is that you are saying that it is due to the compliance of the Riverhawk bearing.  I had interpreted what was written about the Faztek bearings as providing a clamp condition (no tilt). 

Do you have quantitative information from the Riverhawk bearing manufacturer as to what is the magnitude of the torsional stiffness for a rotation around the Y axis provided by two Riverhawks that would allow such a tilt around the Y axis?

NOTE: if such a tilt occurs, due to compliance of the Riverhawk bearings around the Y axis, it would be analogous to a flexural pendulum, with flexural stiffness given by the magnitude of the Riverhawk torsional stiffness for a rotation around the Y axis.   
« Last Edit: 03/04/2015 05:16 PM by Rodal »

Offline Flyby

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The "Copper" is just the reflection of the floor from the side of the flange.  The 2 bright lines are reflections from the edge bevels.  If they used the Copper CF (or wire) seals they are located inside of the bolt line.

Assuming they are indeed the beveled edges, like you say, the second rim should then be the top bevel of the screw thread holding plate. That could indeed make sense then...

But as you got all the dimensions figured out already, I'll rest my case and switch back to observer modus... :-X
« Last Edit: 03/04/2015 05:44 PM by Flyby »

Offline Rodal

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Do you have a reference giving frequency, Q, power and thrust measurements for the Flight Thruster?

This is the only reference I have for data for the Flight Thruster: http://emdrive.com/flightprogramme.html,  I can't find a Q reported.

Several of them for the "Flight Thruster Programme":

Shawyer's CEAS 2009 paper stated, page 9:
Quote
The Flight thruster programme covers the design and development of a 300 Watt C Band flight thruster. This has a specified thrust of 85 mN, and a mass of 2.92Kg. Overall dimensions are 265mm diameter at the baseplate and a height of 164mm.

Then in the 2010 Toulouse TECHNO DIS paper, page 8:
Quote
Development testing of the unit, up to a power of 600 W, is under way, and to date, has given a mean specific thrust of 330 mN/kW.
[]
This is needed to ensure the input frequency matches the resonant frequency of the high Q (60,000) cavity, over the full input power range and the qualification temperature specification.

And in the IAC 2013 paper, page 4:
Quote
The Dynamic performance of the non superconducting Flight Test model, manufactured and tested by SPR Ltd, and described in REF 3 [N.B.: 2010 Toulouse TECHNO DIS paper] was modeled with a cavity Qu = 50,000 and Fres=3.85 GHz.

Finally the mean specific thrust of 326mN/kW over 19 test runs of up to 90 secs duration from 150 W to 450 W was found on the web page http://emdrive.com/flightprogramme.html
As well as the diagram which shows the maximum thrust achieved @ 450 W:


If the 265mm base diameter that Shawyer gave does in fact refer the the exterior diameter of the base plate and if the height is measured from the yellow arrows indicated in the aforementioned photo, which is the only way I can reconcile his figures with the photo, then my best guess for the inner resonance cavity is:

224mm base diameter
145mm top diameter
164mm height (given by Shawyer).

Here's the chart if anyone is interested, cluttered though it has admittedly become.

Thanks!  That brings that X number down to ~55.  Still a very high mode, but 3.85GHz !


McCulloch's equation gives 148 milliNewtons for Shawyer's demo, comparing pretty well with Shawyer's reported measurements of 80 to 214 millinNewtons, see:

http://physicsfromtheedge.blogspot.com/2015/02/mihsc-vs-emdrive-data-3d.html

I understand that you need to use X=26 in your equation for Shawyer's Demo, also a high mode.

On the other's hand McCulloch's equation is off by a factor >10 for NASA Eagleworks test results.

That is an interesting fit.

Of course I havn't seen Mike's derivation in 3D.  I only follow the Equivalence argument the best I can w/o fudge factors and see what comes out.  At the moment I think these are maximums if you have all the parameters and I like the NASA results because they seem to have eliminated more sources of error.  Still, it may all be fiction which is what we want to find out.

@ RODAL

Still have question about the Shawyer "Demo" cavity w/ 174mN.  What are the current estimates of the cone dimensions, frequency (3.85GHz?), and Q (6000 est?).  When I put in TM02 and 450W, I get 174.8microN, rather than the 174milliN reported.  I would like to recheck those numbers.

Even w/ Q=45000, I need to get X up around (65 Very high mode) to get those numbers.  Is that possible w/ 3.85GHz ??

Thanks

Using the geometrical dimensions for Shawyer's flight thruster:

Big Diameter = 224 mm
Small Diameter = 145 mm
Axial Length = 164 mm height (given by Shawyer)

Having successfully compared my exact solution results with the COMSOL's Finite Element Analysis by NASA and thermal IR camera imaging results  and to the exact solution results of Greg Egan, I now calculate some Mode Shapes and associated frequencies (in vacuum with NO dielectric) for Shawyer's flight thruster, for comparison with @Notsosureofit's formula

TM551 4.10811 GHz
TM552 4.76536 GHz
TM553 5.25893 GHz

TM441 3.57892 GHz
TM442 4.20942 GHz

TM443 4.67270 GHz

TM331 3.03740 GHz
TM332 3.63559 GHz
TM333 4.05446 GHz


TM011 1.23005 GHz
TM012 1.63637 GHz
TM013 2.24872 GHz

And for @Notsosureofit's comparison, here are the first m to 10, n to 5 Bessel zeros and Bessel derivative zeros up to 15 digits:  http://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlx, therefore we get:

TM55 --> X55=22.2177998965612
TM44 --> X44=17.6159660498048
TM33 --> X33=13.0152007216984
« Last Edit: 03/04/2015 06:28 PM by Rodal »

Offline frobnicat

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....
It's not about faztek beams compliance. It's about introducing a tilt in the Z axis of rotation (the tilt is around the Y axis) so that the CoM Centre of Mass of the whole rotating assembly, which is not exactly on the Z axis (from the values given by Paul March) but behind the axis (X-) will be lowest when at rest equilibrium position and will have to climb the gravitational potential (ie work against) if it is to deviate from this position (by rotating around the Z axis). ....
Thank you for taking the time to draw these excellent pictures.  A picture is worth 1000 words.

What compliance is responsible for the tilt in the Z axis of rotation around the Y axis) ?  You state that the tilt is not due to the Faztek beam compliance (although if the Faztek beam would be compliant enough it certainly would tilt).

If it is not due to the Faztek beam compliance, then my understanding is that you are saying that it is due to the compliance of the Riverhawk bearing.  I had interpreted what was written about the Faztek bearings as providing a clamp condition (no tilt). 

Do you have quantitative information from the Riverhawk bearing manufacturer as to what is the magnitude of the torsional stiffness for a rotation around the Y axis provided by two Riverhawks that would allow such a tilt around the Y axis?

NOTE: if such a tilt occurs, due to compliance of the Riverhawk bearings around the Y axis, it would be analogous to a flexural pendulum, with flexural stiffness given by the magnitude of the Riverhawk torsional stiffness for a rotation around the Y axis.

And a thousand English words is a lot of sweat for me  :)
To answer your questions : while I consider looking for compliance aspects, both for faztek structural elements and for the bearings, there is no compliance implied by my latest post, the tilt would be voluntarily introduced for the whole experiment platform, including the bearing supporting fixed parts (the supporting axis is tilted, not just the arm or arm's rotation axis). That's how I read the answer of Star-Drive :

...
While I'm at it : is the plane in which the arm rotates kept as horizontal as possible (ie the axis of rotation as vertical as possible) or is there a small slope voluntarily introduced leading to some pendulum effect against g (for stabilisation or tuning purpose) ? That could explain the varying deviation (in m) for the same calibration pulses thrusts. Also wondered if this is what was implied in this post :
Quote from: Star-Drive
...
These thermally induced actions to the left requires the torque pendulum's arm to move to the right to maintain the balance of the torque pendulum's arm in the lab's 1.0 gee gravity field, since we also use the Earth's g-field to help null the pendulum's movements.
...

...
The design of our Torque pendulum follows what JPL and Busek Co did at their respective facility, see attached report from Busek.  We found that if we tried to keep the arm completely horizontal though that the pendulum's neutral point would wonder erratically and make alignments near impossible. So yes I balance the pendulum arm so there is always a slight tilt in it, however this tilt angle magnitude is not controlled as well as it probably should.

Best, Paul M.

Just tilting the arm relative to a still vertical axis Z would introduce no stabilization, for stabilization the axis of rotation itself has to be tilted (to some degree) at the level of the fixed support. I suppose this is done by raising or lowering the 3 (?) base damped platforms against which the whole experiment weight rests. Hope I'm not misinterpreting...

Offline Rodal

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....
It's not about faztek beams compliance. It's about introducing a tilt in the Z axis of rotation (the tilt is around the Y axis) so that the CoM Centre of Mass of the whole rotating assembly, which is not exactly on the Z axis (from the values given by Paul March) but behind the axis (X-) will be lowest when at rest equilibrium position and will have to climb the gravitational potential (ie work against) if it is to deviate from this position (by rotating around the Z axis). ....
Thank you for taking the time to draw these excellent pictures.  A picture is worth 1000 words.

What compliance is responsible for the tilt in the Z axis of rotation around the Y axis) ?  You state that the tilt is not due to the Faztek beam compliance (although if the Faztek beam would be compliant enough it certainly would tilt).

If it is not due to the Faztek beam compliance, then my understanding is that you are saying that it is due to the compliance of the Riverhawk bearing.  I had interpreted what was written about the Faztek bearings as providing a clamp condition (no tilt). 

Do you have quantitative information from the Riverhawk bearing manufacturer as to what is the magnitude of the torsional stiffness for a rotation around the Y axis provided by two Riverhawks that would allow such a tilt around the Y axis?

NOTE: if such a tilt occurs, due to compliance of the Riverhawk bearings around the Y axis, it would be analogous to a flexural pendulum, with flexural stiffness given by the magnitude of the Riverhawk torsional stiffness for a rotation around the Y axis.

And a thousand English words is a lot of sweat for me  :)
To answer your questions : while I consider looking for compliance aspects, both for faztek structural elements and for the bearings, there is no compliance implied by my latest post, the tilt would be voluntarily introduced for the whole experiment platform, including the bearing supporting fixed parts (the supporting axis is tilted, not just the arm or arm's rotation axis). That's how I read the answer of Star-Drive :....


OK, let's say that you tilt the axis Z axis by rotating it around the Y axis, and that you meet no resistance torque whatsoever in doing so.... Mmmmm... hard to believe particularly when we are discussing microNewton forces (less than the weight of a grain of sand).... hard to believe that there is no torque resistance

But for discussion's sake, if there is no resistance met in rotating the Z axis around the Y axis as you posit, what prevents the axis from continuously rotating to an arbitrary angle (if there is no resistance) ?

If it is posited that it is "balanced" ....Mmmmm.... it maybe balanced statically, but is it stable ?
is the position neutrally stable?
and what about dynamics?  wouldn't you get dynamic oscillations? maybe that's what you meant by hanging pendulum?
and how do we know whether it is dynamically stable ?  (it maybe statically neutrally stable but dynamically unstable)

If this is the reason for the baseline's slope, why does it slowly creep ? what governs the speed of movement of the slope? is there damping of this rotation? what is the source of this rotation's damping?

Is it being proposed that pendulum oscillations for Z axis rotation around the Y axis that are only governed by the length of the arm ?

Would like to have more input from Paul March about this....QUESTION TO PAUL: what keeps the Z axis stable at a given angle?  Is it just weight distribution? Or is there a stiffness associated with it?. Is there damping associated with this rotation? if so, what is the source of the damping?   Why is it that the Riverhawk bearings don't prevent this rotation? Can one adjust the Riverhawk bearing settings to decrease or eliminate this movement?  Can one increase the stiffness of the Riverhawk bearings to accomplish this?
« Last Edit: 03/04/2015 07:52 PM by Rodal »

Offline frobnicat

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@ Rodal :
See attached picture to share my mental image. Tilt over-exaggerated for illustration.

Grey : solid rotating assembly (no deformation implied)
Orange/brown : fixed assembly (no deformation implied)
Blue : the ground slab of the vacuum chamber (no deformation implied)

For now, assume a perfect axis of rotation around Z : only one degree of freedom of Grey relative to Orange, the "official" rotation around Z, no compliance implied, Grey kept in the XY plane, plane has same tilt as Orange (XY parallel to Orange platform).

@Star-Drive
Can you confirm this is a correct way to understand that there is a tilt in the axis of rotation ?

Offline frobnicat

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Follow-up on the apparent higher stiffness of balance (displacement against a given force) than due to the tandem of .007 Lb-in/degree flexure bearings. One set of robust measures are the mass distributions (as per latest Star-Drive precisions) and the oscillation pseudo-period of around 4.5s clearly visible in Fig. 19 page 20 of Brady et al anomalous...

All those figures show a linear displacement reading of approximately 1m for the calibration pulses at 29.1N, some other charts show between 1m to 2.5m for the same calibration force, the charts like those of fig. 19 are the "stiffer" to explain, but the following argument does not depend on this apparent sensitivity (ie would be the same even if calibrations pulses and reading magnitudes where completely off scale)

If we assume the pseudo-period of 4.5s as the result of a underdamped rotating harmonic motion (around Z), the same period (well, almost the same) could be observed from an undamped rotating harmonic motion :
 I * alpha_dot_dot= -k * alpha  where the right term is a linear restoring torque (proportional to angular deviation alpha) and I is the moment of inertia around Z. Pulsation omega of that harmonic oscillator is such that  omega = sqrt(k/I) = 2pi/T   or T (period) = 2pi sqrt(I/k)   but since I'm interested in the value of k (stiffness around Z)   k = 4 pi I / T

Rough estimation of I around Z axis (assuming frustum and electronic stack as punctual mass and faztek arm as a thin element) :
Frustum with dielectric : 2.60*0.286 =   8.18e-2
Front Faztek arm part : 0.567*0.375/3 = 2.66e-2
Back Electronic stack : 7.84*0.190 =   3.61e-2
Back Faztek arm part : 0.356*0.235/3 =0.65e-2
Total I=0.151 kg m

with T=4.5s  =>  k = 0.294  Nm/rad

Independently : for a deflection of 1m @ .353m (LDS distance from Z) that is 2.83e-6 rad,  as a result of 29.1N @ .286m (cal. force distance from Z) that is 8.32e-6 Nm, needs a restoring torque with a stiffness of 8.32e-6/2.83e-6 = 2.94 Nm/rad

Surprisingly 10 times more than the previous. Have I skipped a power of 10 somewhere ??

And two .007 Lb-in/degree flexure bearings make for only 0.0906 Nm/rad

I'm lost in conjectures...

Offline Notsosureofit

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 Trying to post emdrive5.xls
« Last Edit: 03/04/2015 11:52 PM by Notsosureofit »

Offline Rodal

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Trying to post emdrive5.xls

I yellowed the frequencies closest to operating frequency (reported as 3.85GHz ) showing @Notsosureofit's formular results from 19 to 52 mN/kW for Shawyer's Flight Thruster

Shawyer reported 326mN/kW.
« Last Edit: 03/05/2015 12:40 AM by Rodal »

Offline Notsosureofit

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The flight thruster is shown as what appears to be an oscillator configuration, so it is still possible that the loaded Q is higher than the unloaded Q.  But that is speculation.  I do worry about his concept of "no static thrust" as well.

(and yes the simple dispersion relation drops dependence on "p".  Maybe we can get that in there w/ your exact solution ??)
« Last Edit: 03/05/2015 12:37 AM by Notsosureofit »

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