EM Drive Developments - related to space flight applications - Thread 2

[deltaMass]

Consider the typical SRF cavities described in this paper: http://arxiv.org/pdf/physics/0003011.pdf

Each cell in the stack of cavities could be thought of as being two cones arranged back to back: <><><><> (see Figure 5). We would then expect any forces to try and pull the two half-cavities apart.

These were operated at 1.3 GHz, 200 kW CW RF, with a measured Q of ~ 5e9.

Applying the quoted formula of F ~ Po*Q/c, we get a force of 3e6 N.

The cavities have a wall thickness of about 2 mm, and a major radius of ~100 mm, giving a strain of > 2000 MPa in the niobium. The yield strength of niobium is somewhere in the range of 80-150 MPa, depending on temper and annealing. And yet the cavities did not fly apart.

Anyone care to poke holes in this?

It's worse than that because the cavities are niobium-coated copper; copper has a yield strength of 70 MPa.

It's these sorts of observations that keep people grounded in reality.

People will most likely attack your numbers  based on the dissimilarity between these cavities and the EmDrive ones.
The biggest difference I see is that these ones have curved walls. I don't imagine that makes any substantive difference.
Another difference might be the resonant mode choice. Do some modes not "generate thrust"?

[Rodal]

Consider the typical SRF cavities described in this paper: http://arxiv.org/pdf/physics/0003011.pdf

Each cell in the stack of cavities could be thought of as being two cones arranged back to back: <><><><> (see Figure 5). We would then expect any forces to try and pull the two half-cavities apart.

These were operated at 1.3 GHz, 200 kW CW RF, with a measured Q of ~ 5e9.

Applying the quoted formula of F ~ Po*Q/c, we get a force of 3e6 N.

The cavities have a wall thickness of about 2 mm, and a major radius of ~100 mm, giving a strain of > 2000 MPa in the niobium. The yield strength of niobium is somewhere in the range of 80-150 MPa, depending on temper and annealing. And yet the cavities did not fly apart.

Anyone care to poke holes in this?

Holes:

1) "Each cell in the stack of cavities could be thought of as being two cones arranged back to back: <><><><>"

The arrangement presupposed does not have an internal vertical plate at the location of the largest diameter.  It is a symmetrical arrangement without a wall at the biggest diameter.  The EM Drive's are asymmetric configurations.  WarpTech, StrongGR and Notsosureofit's theories for the EM Drive rely on asymmetry which is not present in the configuration you show. 


2) Extrapolating the equation  F ~ Po*Q/c to a Q of  5e9 is way beyond the range of any experimental measurement up to date.  The Q (measured the same way as in the West) of the highest measured EM Drive thrusts ever reported (experiments by Prof. Yang) are only ~10^3, and the Q's reported by NASA are ~10^3 to ~10^4.  Shawyer's Q was 5900 for the Experimental and 45000 for the Demo.  Thus, the experimental formula you are using was not based on any Q's less than 10^5. 

I had an exchange in the forum regarding this: TheTraveller favors using that formula in the Superconducting range (*).  I am on record stating that this does not make sense to me: there is no experimental data to make such an extrapolation (the thrust force of the experiment with Q~10^7 of the Cannae Superconducting was taken apart earlier in the thread -hat tip to zen-in- and it is very much in question: maximum force was less than 10 milliNewtons).  Shawyer has not reported (to our recollection) any thrust force measurements at Q's in the superconducting range.  The formulas advanced by Shawyer, McCulloch and Notsosureofit are also dependent on Q but they are not in a theoretical basis strong enough to warrant extrapolation beyond the range of experimental Q's either.

Using a Q ~10^9 is five orders of magnitude outside the range of an empirical formula based on experiments. 
Not a good thing to do (to extrapolate a formula much beyond the region where one has experimental points).

Just using your figures, but this time within the range of validity of the Q's experimental formula:

200MPa/10^5 = 2*10^-4 MPa

200 MPa/10^6 = 2*10^-5 MPa

both orders of magnitude smaller than 80-150 MPa.

NOTE: (*) If anything your example (when ignoring point #1 above) can be taken as a Reductio ad absurdum demonstrating that Todd (WarpTech) theory is correct (that Q shouldn't be too large)


Minor points:

3) " giving a strain of > 2000 MPa" . MegaPascals are a measure of stress and not strain.  Strain is a dimensionless quantity.
4) I won't go over into further detail on your stress analysis because it is not warranted, because the calculated force (see #2) is so many orders of magnitude outside of its experimental range.

[aero]

I'm incredibly appreciate of all the work that went into the dimensional estimates of the various drives but I'm having some difficulty understanding where the dimensional values came from regarding the attached image:

Shawyer reported a large plate diameter of .28m - so using that as a given.

Going straight off the image (not taking into account perspective) at the junction of the cone and the cylinder I get about .169m for the small plate diameter. This is a difference of 40mm with what was originally estimated and about 73mm from Dr. Rodal's calculation (96.13) of the small plate diameter.  This is an enormous difference and I can't believe it. I'm going to model this and lay it on top of the photo in perspective so I can find out what the numbers are closer to.

Also the cone length was estimated to be .345m - which is larger than the plate diameter. Between which two points is this measurement for?

That one was a challenge. Note the geared mechanism at the small end, end of the cylinder. It was considered that this mechanism drove a plunger that changed the length of the cavity in order to adjust the resonance frequency. Hence there needed to be some part of the diameter of the interior of the cylinder section devoted to supporting and guiding this plunger. How much was just a guess, but as I recall, I assumed that the actual small end of the resonant cavity was likely located about midway between the ends of the cylinder.

I think we have better information now so revisiting this estimate is warranted.

[StrongGR]

As promised I am posting the latest draft about general relativity and electromagnetic field. The relevant conclusion is that there is thrust. Thanks to the comments by Jose Rodal, it can be shown that this can be meaningful and the best geometry is that of the frustum tending to a cone. There is no violation of conservation law due to the presence of the gravity that can escape the device producing a reaction.

I post it here for your comments that are very welcome as usual. You can find the final equation at page 12 for your evaluations. Later on, I will post a version with a somewhat different presentation to arxiv.

I like you paper but have a request for a point of clarification. I got really confused when you went from equation 55 to equation 56. Why did you invert the c⁴/G term? (Actually I got confused way before that but I won't go there.

I have taken out a l0^-1 that so becomes l0^-2.

[StrongGR]

r2=10^5.5
r1=1
is a correct example.

It is my approximation: r2 increasingly large and r1 decreasing toward zero otherwise one should change the final formula. So, in your example it would be better to have r2=10 m and r1=10^-3 m and so on. This is a cone.

Yes. But the dependence on r2 is stronger than the one on r1, because r2 is to the sixth power whereas r1 is just squared.
So: if you keep r1 constant and vary r2, you don't need many orders of magnitude to have a reasonable effect; if you keep r2 constant and vary r1, you need to go down a lot of orders of magnitude.

If we have an r2 of one meter, r1 must be 10^-16, which is a tenth of a femtometer, which is less than the size of a proton. We cannot possibly manufacture such a cone and I think it would not work anyway because the resulting "small end plate" doesn't have enough electrons to behave like an ideal EM-reflecting plate. Although maybe it doesn't need to and it's just the cavity shape that matters.

What if we considered other shapes? We started with the truncated cone because of the EmDrive, but what if we considered a pillbox cavity (which is basically a rounded cone...)? All the equations would be different, for sure, but it might be worth exploring. Maybe in another thread.

Another way around, as suggested above, is to fill with some material the cavity. The formula goes like mur^-2 and mur much smaller than 1.

Yes, varying mu may be profitable too.

But then you have that U_0^4 that depends on Q^2 and P^2. As said before, I am not certain that I get a really macroscopic effect even if an interferometric device, sensible enough, can grant observation of the effect. I have to work out some numerics to see really what is going on. There is also the contribution coming from the square of the mode that can take the effect down.

[deltaMass]

You could always do a spot of partial differentiation to find the multidimensional optimum, if such exists.

[aero]

As promised I am posting the latest draft about general relativity and electromagnetic field. The relevant conclusion is that there is thrust. Thanks to the comments by Jose Rodal, it can be shown that this can be meaningful and the best geometry is that of the frustum tending to a cone. There is no violation of conservation law due to the presence of the gravity that can escape the device producing a reaction.

I post it here for your comments that are very welcome as usual. You can find the final equation at page 12 for your evaluations. Later on, I will post a version with a somewhat different presentation to arxiv.

I like you paper but have a request for a point of clarification. I got really confused when you went from equation 55 to equation 56. Why did you invert the c⁴/G term? (Actually I got confused way before that but I won't go there.

I have taken out a l0^-1 that so becomes l0^-2.

Sorry, but I still don't understand how that converts c⁴/G to (c⁴/G)^-1.

I suspect that there is a transcription error somewhere, and that (c⁴/G)^-1 was intended all along.

[ThereIWas3]

A search of YouTube for the term "emdrive" turns up a bunch of interesting presentations, including by a "iulian" dated two days ago, showing his test setup and the measurement of thrust.

[StrongGR]

As promised I am posting the latest draft about general relativity and electromagnetic field. The relevant conclusion is that there is thrust. Thanks to the comments by Jose Rodal, it can be shown that this can be meaningful and the best geometry is that of the frustum tending to a cone. There is no violation of conservation law due to the presence of the gravity that can escape the device producing a reaction.

I post it here for your comments that are very welcome as usual. You can find the final equation at page 12 for your evaluations. Later on, I will post a version with a somewhat different presentation to arxiv.

I like you paper but have a request for a point of clarification. I got really confused when you went from equation 55 to equation 56. Why did you invert the c⁴/G term? (Actually I got confused way before that but I won't go there.

I have taken out a l0^-1 that so becomes l0^-2.

Sorry, but I still don't understand how that converts c⁴/G to (c⁴/G)^-1.

I suspect that there is a transcription error somewhere, and that (c⁴/G)^-1 was intended all along.

Thanks for pointing out this. I will check all tomorrow. Please, consider that a term c^4/G is coming out from the construction of the tensor in eq.(46). I have checked physical dimensions step by step by I'll redo it for sure.

[phaseshift]

I'm incredibly appreciate of all the work that went into the dimensional estimates of the various drives but I'm having some difficulty understanding where the dimensional values came from regarding the attached image:

Shawyer reported a large plate diameter of .28m - so using that as a given.

Going straight off the image (not taking into account perspective) at the junction of the cone and the cylinder I get about .169m for the small plate diameter. This is a difference of 40mm with what was originally estimated and about 73mm from Dr. Rodal's calculation (96.13) of the small plate diameter.  This is an enormous difference and I can't believe it. I'm going to model this and lay it on top of the photo in perspective so I can find out what the numbers are closer to.

Also the cone length was estimated to be .345m - which is greater than the large plate diameter. Between which two points is this measurement for?

I'm almost certain that the small plate diameter is close to .17m. This produces a design factor of .4853.  Where did you (Rodal) get the design factor of .844 that you used in calculating the small diameter of .09613m?

[Rodal]

Where did you (Rodal) get the design factor of .844 that you used in calculating the small diameter of .09613m?

Take a gander again  : I had meticulously answered that question in my message http://forum.nasaspaceflight.com/index.php?topic=36313.msg1376720#msg1376720 which you (phaseshift) quoted verbatim in your own message http://forum.nasaspaceflight.com/index.php?topic=36313.msg1376723#msg1376723

[phaseshift]

..Shawyer reported a large plate diameter of .28m - so using that as a given...
I'm almost certain that the small plate diameter is close to .17m. This produces a design factor of .5197. ...

No, it is even worse, using that value for the small diameter (0.17 m), the DesignFactor (calculated with this equation http://forum.nasaspaceflight.com/index.php?topic=36313.msg1374110#msg1374110 )  is even smaller:

smallDiameter = 0.17 m;
bigDiameter = 0.28 m;
f = 2.45*10^9 Hz;
cst = 1.7062895542683174;
cM = 299705000 m/s (speed of light in air);

results in the following DesignFactor

Design Factor = 0.4853 (instead of the 0.5197 value you quoted above)

Yes, I caught that just a minute ago.  its .4853

[phaseshift]

..Shawyer reported a large plate diameter of .28m - so using that as a given...
I'm almost certain that the small plate diameter is close to .17m. This produces a design factor of .5197. ...

No, it is even worse, using that value for the small diameter (0.17 m), the DesignFactor (calculated with this equation http://forum.nasaspaceflight.com/index.php?topic=36313.msg1374110#msg1374110 )  is even smaller:

smallDiameter = 0.17 m;
bigDiameter = 0.28 m;
f = 2.45*10^9 Hz;
cst = 1.7062895542683174;
cM = 299705000 m/s (speed of light in air);

results in the following DesignFactor

Design Factor = 0.4853 (instead of the 0.5197 value you quoted above)

Which is interesting given that his experimental thruster had a DF of .497.  So I don't know if he incorrectly reported .844 or the equation is wrong.  I can say for certain that the small plate diameter in the photo is not even close to 96mm - I couldn't be that much off with my eyes closed lol

[phaseshift]

..Shawyer reported a large plate diameter of .28m - so using that as a given...
I'm almost certain that the small plate diameter is close to .17m. This produces a design factor of .5197. ...

No, it is even worse, using that value for the small diameter (0.17 m), the DesignFactor (calculated with this equation http://forum.nasaspaceflight.com/index.php?topic=36313.msg1374110#msg1374110 )  is even smaller:

smallDiameter = 0.17 m;
bigDiameter = 0.28 m;
f = 2.45*10^9 Hz;
cst = 1.7062895542683174;
cM = 299705000 m/s (speed of light in air);

results in the following DesignFactor

Design Factor = 0.4853 (instead of the 0.5197 value you quoted above)

Which is interesting given that his experimental thruster had a DF of .497.  So I don't know if he incorrectly reported .844 or the equation is wrong.  I can say for certain that the small plate diameter in the photo is not even close to 96mm - I couldn't be that much off with my eyes closed lol

I can see people next stating that Shawyer just transposed the numbers: he meant to write

DesignFactor = 0.484 (which gives a sD = 0.17027 m)

but he wrote instead

DesignFactor =0.844   

Yes, good possibility - I did the EXACT same thing about 10 minutes ago.

[Rodal]

...
I can see people next stating that Shawyer just transposed the numbers: he meant to write

DesignFactor = 0.484 (which gives a sD = 0.17027 m)

but he wrote instead

DesignFactor =0.844   

Yes, good possibility - I did the EXACT same thing about 10 minutes ago.

I suggest that we wait for the person who has read most of Shawyer's papers (TheTraveller).  Perhaps TheTraveller can find another paper on the Demonstrator Engine by Shawyer besides the one I quoted, and check whether Shaywer quotes the same DesignFactor 0.844 or the more sensible number 0.484

[deltaMass]

I don't get it. Why would anyone use a Design Factor that wasn't (near as dammit) unity, since one has complete design freedom to do that?

[phaseshift]

I suggest that we wait for the person who has read most of Shawyer's papers (TheTraveller).  Perhaps TheTraveller can find another paper on the Demonstrator Engine by Shawyer besides the one I quoted, and check whether Shaywer quotes the same DesignFactor 0.844 or the more sensible number 0.484

This is my source: http://www.emdrive.com/IAC-08-C4-4-7.pdf

[Rodal]

I suggest that we wait for the person who has read most of Shawyer's papers (TheTraveller).  Perhaps TheTraveller can find another paper on the Demonstrator Engine by Shawyer besides the one I quoted, and check whether Shaywer quotes the same DesignFactor 0.844 or the more sensible number 0.484

This is my source: http://www.emdrive.com/IAC-08-C4-4-7.pdf

Meanwhile, if you have the time and find it worthwhile to do so, perhaps you could ascertain whether the following dimensions make sense

(* Shawyer Experimental *)
rfFrequency=2.45*10^9;
cavityLength=0.156;(estimated from photographs)
bigDiameter=0.16; (given by Shawyer)
smallDiameter=0.1025; (obtained from the Design Factor, bigDiameter and frequency provided by Shawyer)
Design Factor = 0.497;

[phaseshift]

I also think the cavity length needs to be adjusted on the Demonstrator Thruster to .187m.

My reasoning and measurements:

I believe Shawyer angled the cone to his expectation of where the small diameter plate will be.  When the device is turned on the plate is slightly back inside the cylinder and gradually moved forward until there is phase lock. The length of the cylinder, in part, is to accommodate the movement mechanism and the volume of the small plate.

In my recent model the cone length is exactly .187m (from the face of the small plate to the face of the large plate). Slightly longer than the .183m calculated from 3 * .123m / 2 - based on .2450Ghz. I think 4mm is ample distance to move the small plate to achieve phase lock as I described above.

Did I do the math right?

[hhexo]

But then you have that U_0^4 that depends on Q^2 and P^2. As said before, I am not certain that I get a really macroscopic effect even if an interferometric device, sensible enough, can grant observation of the effect. I have to work out some numerics to see really what is going on. There is also the contribution coming from the square of the mode that can take the effect down.

Let's keep working this out.

Hm... from equation (22) I get that a volume integral of the square of the mode times U0/2mu0 is equal to QP/omega. Omega is the resonant angular frequency (which I think is the linear frequency divided by 2pi).
Q is about 10^4 (for the devices we've seen).
Let's say P is about 10^3 (1KW).
omega is about 10^9 (because gigahertz).
mu0 is still about 10^-6.

I don't know about that volume integral, but mu0*QP/omega is about 10^-8. Unless the volume integral is a substantially negative power of ten, this isn't helping much. Also, it looks like increasing the resonance frequency actually makes things worse (is that right?!).
U0^4 becomes about 10^-32 divided by the fourth power of that volume integral.

This effect is starting to become too small.
Still, these are just back-of-the-envelope ballpark calculations, and I can't figure out all those integrals as my maths isn't good enough. So, as you say, we need proper numerics.
I'm just not too hopeful.