Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 1877174 times)

Offline deltaMass

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@The Traveller: For the 3rd time, can you tell me the meaning of the y and x axes here, and the units used

Offline deltaMass

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@The Traveller: For the 3rd time, can you tell me the meaning of the y and x axes here, and the units used

Apologised, didn't see the other requests.

The bottom x axis are the 0.5 units of the black marks on the table the pointer moved over. To gen more data points I estimated when the pointer was midway between the major black marks. The upper y axis are seconds as I frame by frame stepped the video.
Please confirm:

the vertical (y) axis is time in seconds? (so max about 120 secs)
the horizontal (x) axis is distance in tick marks? (so max about 31 marks)

Offline Flyby

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Hmmmm.. can I throw a brick?  ???

Been thinking about the findings of yesterday, while there is still something that is bothering me...

What is nice to see is that dr. Rodal's calculations do also match the graphical recreation i've made of the obtained results. So that confirms for me that the way to calculate the dimensions is most likely a correct one.

What keeps bothering me is the starting values as the calculations do not take the top/bottom cylindrical parts of the cavity into calculation. Consequently, the half cone angle obtained from the drawing is not the one that is calculated.

So.. I've adapted the YANG drawing further to match the calculation method better. What's needed is the angle going from top to bottom, without consideration of cylindrical parts.
I've redone the drawing and added the new half cone angle : 10.8

I do not know if the good doctor would like to check the new angle and see if that would match better or worse ?

Offline TheTraveller

@The Traveller: For the 3rd time, can you tell me the meaning of the y and x axes here, and the units used

Apologised, didn't see the other requests.

The bottom x axis are the 0.5 units of the black marks on the table the pointer moved over. To gen more data points I estimated when the pointer was midway between the major black marks. The upper y axis are seconds as I frame by frame stepped the video.
Please confirm:

the vertical (y) axis is time in seconds? (so max about 120 secs)
the horizontal (x) axis is distance in tick marks? (so max about 31 marks)

My bad incorrect quote. Went back and checked the calcs. Have edited the post.
"As for me, I am tormented with an everlasting itch for things remote. I love to sail forbidden seas.
Herman Melville, Moby Dick

Offline TheTraveller

@The Traveller: For the 3rd time, can you tell me the meaning of the y and x axes here, and the units used

Apologised, didn't see the other requests.

The bottom x axis are the 0.5 units of the black marks on the table the pointer moved over. To gen more data points I estimated when the pointer was midway between the major black marks. The upper y axis are seconds as I frame by frame stepped the video.
Please confirm:

the vertical (y) axis is time in seconds? (so max about 120 secs)
the horizontal (x) axis is distance in tick marks? (so max about 31 marks)

I need to review that chart. Did it when was almost asleep and after a big pain pill. Will do so tomorrow and do the whole sequence as having an early night. Have deleted my earlier reply as it is probably not correct.
« Last Edit: 08/02/2015 09:20 AM by TheTraveller »
"As for me, I am tormented with an everlasting itch for things remote. I love to sail forbidden seas.
Herman Melville, Moby Dick

Offline deltaMass

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@The Traveller: For the 3rd time, can you tell me the meaning of the y and x axes here, and the units used

Apologised, didn't see the other requests.

The bottom x axis are the 0.5 units of the black marks on the table the pointer moved over. To gen more data points I estimated when the pointer was midway between the major black marks. The upper y axis are seconds as I frame by frame stepped the video.
Please confirm:

the vertical (y) axis is time in seconds? (so max about 120 secs)
the horizontal (x) axis is distance in tick marks? (so max about 31 marks)

My bad incorrect quote. Went back and checked the calcs. Have edited the post.
Thanks. It looks vaguely like v = k*x^n where n~=2 maybe. Interesting.
Could you please attach the data file from which you construct the graph (Excel is fine)?

Offline deltaMass

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@The Traveller: For the 3rd time, can you tell me the meaning of the y and x axes here, and the units used

Apologised, didn't see the other requests.

The bottom x axis are the 0.5 units of the black marks on the table the pointer moved over. To gen more data points I estimated when the pointer was midway between the major black marks. The upper y axis are seconds as I frame by frame stepped the video.
Please confirm:

the vertical (y) axis is time in seconds? (so max about 120 secs)
the horizontal (x) axis is distance in tick marks? (so max about 31 marks)

I need to review that chart. Did it when was almost asleep and after a big pain pill. Will do so tomorrow and do the whole sequence as having an early night. Have deleted my earlier reply as it is probably not correct.
Thank you. You are welcome to send the raw data anytime

Offline flux_capacitor

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Yang's frustum has the following dimensions:

- cavity length (m): 0.24
- big diameter (m): 0.201
- small diameter (m): 0.1492

In particular, the big end is smaller than the height, not larger.

There is no resonance I can find for those dimensions at 2.45GHz. Can get TE012 resonance at 2.51GHz

They were surely wrong dimensions, based on the assumption Yang's drawings had the correct proportions. But what is your analysis of Rodal's revised numbers for Yang's frustum having TE012 resonance at 2.45 GHz:

Db = 0.247 m

Ds  = 0.114425 m

L = 0.24 m


r1= 0.211022 m

r2= 0.455515 m

Cone half-angle = 15.44 degrees

According to you, the cutoff dimension, just below the guide wavelength for TE01 mode at 2.45GHz = 148.7 mm
But Rodal's small end for Yang's frustum is now at 114.42 mm.
Your advice?
« Last Edit: 08/02/2015 10:58 AM by flux_capacitor »

Offline rfmwguy

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NSF-1701 3rd static temp test video. I learned the IR gun is not useful at 3 feet. Also the quick drop of temp when mag cycles off is false reading. Regardless, saw some interesting arcing at full power at 1 minute duration. Frustum itself remained at low temp. Mag went to about 160C.



Digital cameras can be modified to record in the IR spectrum.  http://www.lifepixel.com/  IR is normally filtered out so that you can't go peaking under peoples clothes.
Way cool...oh how I wish I had real funding ;)
« Last Edit: 08/02/2015 12:47 PM by rfmwguy »

Online Rodal

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Hmmmm.. can I throw a brick?  ???

Been thinking about the findings of yesterday, while there is still something that is bothering me...

What is nice to see is that dr. Rodal's calculations do also match the graphical recreation i've made of the obtained results. So that confirms for me that the way to calculate the dimensions is most likely a correct one.

What keeps bothering me is the starting values as the calculations do not take the top/bottom cylindrical parts of the cavity into calculation. Consequently, the half cone angle obtained from the drawing is not the one that is calculated.

So.. I've adapted the YANG drawing further to match the calculation method better. What's needed is the angle going from top to bottom, without consideration of cylindrical parts.
I've redone the drawing and added the new half cone angle : 10.8

I do not know if the good doctor would like to check the new angle and see if that would match better or worse ?

0) Given L=24 cm and f=2.45 GHz from Yang's paper, we are at liberty to choose only one additional parameter to ascertain Yang's dimensions: for example, the small diameter (obtained from the cut-off condition), or the cone half-angle, or the ratio D/L.  Only one parameter, that's it.  To consider more than one parameter, we have to drop L=24 cm as a condition.  (We are not going to drop f=2.45 GHz, are we?)

1) I obtained the previous estimates for Yang's dimensions assuming the cut-off condition for the small diameter at 2.45 GHz.  That set the dimension of the small diameter.  Everything else flowed from there.

2) Since setting the small diameter for Yang to be governed by the cut-off condition resulted in a cone half angle of 6 degrees which is ridiculously small, we decided to drop the cut-off condition and adopt as the parameter the cone half-angle.  The cone half-angle is a much more important variable in the solution of the problem.  The cut-off condition does not apply to tapered cavities (this has been well known in the peer-reviewed resonant cavity literature for several decades).  The cone half-angle was determined to be 15 degrees both by you and Shell independently.  The cone half-angle is a most important boundary condition for the physical problem.  You cannot substitute it with an average cone half-angle (10.8 degrees) based on the distorted ends.  That goes against the physics of the problem.  Modifying the ends are much less important than the sides for this problem.  This can be shown mathematically.  Those modifications at the ends make the geometry not longer a truncated cone.  One has to respect what is conical in the geometry: the angle between the conical sides and the axis of axi-symmetry of the cone.

3) From the drawings one cannot obtain dimensions, one can only obtain dimensionless ratios.  That's why I had asked for the angle and the ratios.  Shell answered that determining the ratios was arbitrary because of the end condition not being a truncated cone.  She is correct.  Now, if you want, we can proceed as follows:

a) cone half-angle = 15 degrees
b) determine the ratio of the average diameter to the length:  D/L = (Db/L +Ds/L)/2  and use this ratio D/L to obtain the dimensions from Yang's paper (which is posed in terms of D/L).  Doing so means to drop L=24 cm (given by Yang's paper) as a reliable number and considering D/L to be more robust than L=24 cm

So, do you think that you can provide the ratio D/L = (Db/L +Ds/L)/2 with more confidence than our reliance on Yang providing L=24 cm, and do you think that we should substitute L=24 cm with this ratio D/L? and then I can proceed to determine the dimensions based on the cone half angle = 15 degrees and this ratio D/L ?

If so, what is your robust estimate of the ratio  D/L = (Db/L +Ds/L)/2  ?

Db = diameter of the big base
Ds = diameter of the small base
L = distance between bases measured perpendicular to both bases
« Last Edit: 08/02/2015 02:02 PM by Rodal »

Offline leomillert

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Shawyer's frustum design rules are:

1) Small end to be as small as possible to have cutoff just below it's guide wavelength. For TE01 mode and 2.45GHz the min small in diameter, in air, is 148.7m diameter. As you can see the Prof Yang small end diameter at 149.2mm is 0.5mm bigger than the minimum. That gives the frustum a bit of breathing room if the external freq needs to increase for tracking or a wide magnetron output bandwidth.

Yes, that is Shawyer's rule.
But it makes no sense.
It has been known for over 2 decades that

"Due to the absence of sharp cut-off frequencies ..., the interior of the frustum can support nontrivial field amplitudes, even in regions of relatively small electrical cross section"
Electromagnetic plane wave excitation of an open-ended conducting frustum, IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 42, NO. 5, MAY 1994. 699

I also have attached Doctor Rodal's report on the matter that should make your mind once and for all, as it is made obvious that truncated cones show an absence of sharp cut-off frequencies and that continuing the cone beyond the small diameter at which cut-off would occur (according to the cylindrical formula with is inapplicable to the cone) leads to significantly higher amplitudes of the electromagnetic fields.

To everyone reading this,  don't take Shawyer's rules as actual rules. Take them with a pinch of salt and research before trusting what he says.
This particular rule, which is nonsensical, has hindered development, because people wouldn't test lower small diameters (which are good) just because Shawyer claimed without any basis that it wouldn't work.

Offline rfmwguy

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weekly interactive particle
you can't go peaking under peoples clothes.

Sometimes poor spelling is an advantage  8)
Nuthing gits bye you DM, I need to keep watching my Pees and Qs with u around ;)

Online Rodal

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Yang's frustum has the following dimensions:

- cavity length (m): 0.24
- big diameter (m): 0.201
- small diameter (m): 0.1492

In particular, the big end is smaller than the height, not larger.

There is no resonance I can find for those dimensions at 2.45GHz. Can get TE012 resonance at 2.51GHz

They were surely wrong dimensions, based on the assumption Yang's drawings had the correct proportions. ..

No, they were the dimensions that I had correctly based on the assumption that the small diameter for Yang was obtained based on the cut-off condition for the small end.  And TheTraveller's calculation actually confirms it:

<<There is no resonance I can find for those dimensions at 2.45GHz. Can get TE012 resonance at 2.51GHz>>

The 2% difference between 2.45 GHz and 2.51 GHz is completely and utterly negligible compared to the other differences we are talking about: compared to the difference between 6 degrees and 15 degrees for the cone half-angle or compared to the uncertainties in having to eyeball the dimensionless ratio equations from Yang's chart.

On top of that, the result TE012 resonance at 2.51GHz is obtained by TheTraveller from an Excel spreadsheet using very simplified ad-hoc approximate formulas that do not respect the boundary conditions of the problem while the solution for TE012 2.45GHz resonance uses Wolfram Mathematica to solve the exact solution to the problem using Legendre Associated Functions and Spherical Bessel functions.

Taking into account the above considerations, the 2% different ad-hoc TE012 resonance at 2.51GHz means a complete agreement with the dimensions provided, because the 2% difference is completely within bounds.

___________________________________________

The issue at hand (determination of Yang's geometry) has to do with whether L=24cm provided by Yang in her paper is correct, and if so, whether the other (one and only one available to choose) parameter to consider should be the small diameter (based on cut-off), or the cone half-angle (determined from drawings), or some other parameter like D/L (determined from drawings), etc.

One cannot obtain dimensions from Yang's schematic drawings, one can only obtain dimensionless ratios: angles and ratios, that's it.

For L=24 cm and f=2.45 GHz, you cannot satisfy both that the diameter of the small base be above cut-off for an open waveguide AND satisfy the cone half-angle from Yang's drawings .  They are in violent conflict with each other.  Something got's to give.

This has to be clearly understood:  we have mathematical relations to satisfy here, they are mathematical constraints.  You cannot satisfy all the dimensionless ratios from Yang's drawings and simultaneously satisfy the cut-off condition at the small end and simultaneously satisfy L=24 cm and simultaneously satisfy the D/L vs frequency relation.
« Last Edit: 08/02/2015 01:58 PM by Rodal »

Offline Silversheep2011

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For the Labs with the Big money! 

I enjoyed this paper on the direction where our microwave technology is going these days.
and found it easy enough to read for us  'Joe normal' types to see some of the important things going on in the thread and why some of those interrelationships like cavity shape and multi antenna are so important.

Seems it could offer better control of space and control of frequency, phase,  power and feedback shaping.
start by look at first figure on second page and see the variation going on with the same machine, with  3x 30 second blasts - I would be worried about validation aspects long term when this looks over the 10% mark.
 
P.S. I have no connection to this company,  this is for information and discussion only.

[edit note: figure is on second page]
« Last Edit: 08/02/2015 01:39 PM by Silversheep2011 »

Offline TheTraveller

Shawyer's frustum design rules are:

1) Small end to be as small as possible to have cutoff just below it's guide wavelength. For TE01 mode and 2.45GHz the min small in diameter, in air, is 148.7m diameter. As you can see the Prof Yang small end diameter at 149.2mm is 0.5mm bigger than the minimum. That gives the frustum a bit of breathing room if the external freq needs to increase for tracking or a wide magnetron output bandwidth.

Yes, that is Shawyer's rule.
But it makes no sense.
It has been known for over 2 decades that

"Due to the absence of sharp cut-off frequencies ..., the interior of the frustum can support nontrivial field amplitudes, even in regions of relatively small electrical cross section"
Electromagnetic plane wave excitation of an open-ended conducting frustum, IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 42, NO. 5, MAY 1994. 699

I also have attached Doctor Rodal's report on the matter that should make your mind once and for all, as it is made obvious that truncated cones show an absence of sharp cut-off frequencies and that continuing the cone beyond the small diameter at which cut-off would occur (according to the cylindrical formula with is inapplicable to the cone) leads to significantly higher amplitudes of the electromagnetic fields.

To everyone reading this,  don't take Shawyer's rules as actual rules. Take them with a pinch of salt and research before trusting what he says.
This particular rule, which is nonsensical, has hindered development, because people wouldn't test lower small diameters (which are good) just because Shawyer claimed without any basis that it wouldn't work.

Shawyers claim is not without basis, it is based on microwave industry experience. A waveguide operated below cutoff will not propagate an EM wave.

If the small end operates below cutoff there is no EM wave to bounce off the small end, then the big end, then the small end, then the big end, etc.

But please yourself and ignore microwave industry practice, Shawyer & Prof Yang.
"As for me, I am tormented with an everlasting itch for things remote. I love to sail forbidden seas.
Herman Melville, Moby Dick

Offline TheTraveller

Yang's frustum has the following dimensions:

- cavity length (m): 0.24
- big diameter (m): 0.201
- small diameter (m): 0.1492

In particular, the big end is smaller than the height, not larger.

There is no resonance I can find for those dimensions at 2.45GHz. Can get TE012 resonance at 2.51GHz

They were surely wrong dimensions, based on the assumption Yang's drawings had the correct proportions. But what is your analysis of Rodal's revised numbers for Yang's frustum having TE012 resonance at 2.45 GHz:

Db = 0.247 m

Ds  = 0.114425 m

L = 0.24 m


r1= 0.211022 m

r2= 0.455515 m

Cone half-angle = 15.44 degrees

According to you, the cutoff dimension, just below the guide wavelength for TE01 mode at 2.45GHz = 148.7 mm
But Rodal's small end for Yang's frustum is now at 114.42 mm.
Your advice?

At TE012 and 2.45GHz the small end diameter I gave was the smallest that will allow operation just above cutoff. Anything smaller will not, according to what the SPR method predicts, work.
"As for me, I am tormented with an everlasting itch for things remote. I love to sail forbidden seas.
Herman Melville, Moby Dick

Online Rodal

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But please yourself and ignore microwave industry practice, Shawyer & Prof Yang.
Prof. Yang starts her papers by first briefly discussing Shawyer's theory and conjectures (just like Tajmar) does.
This brief introduction to Shawyer's theory is standard academic practice.  It should not be confused by Yang adopting Shawyer's theory, which she clearly does not. Then she goes to  her own formulation. Yang's own formulation is  different from Shawyer: Yang uses a Finite Element Analysis Formulation to calculate the Stress Tensor and hence the thrust force.  Look at the equations she uses in her Finite Element Analysis: they are not Shawyer's equations.  Shawyer never calculates the stress tensor like Yang does.

Shawyer claims that there are no stresses, no pressure and no force on the lateral conical sides.  Yang does all the opposite: she calculates the stresses and forces on the lateral conical sides and shows that these forces are quite considerable.  Here is an image from Yang showing the pressure on the conical lateral sides, that Shawyer ignores:



Let's give credit to Yang where it is due: Yang developed her own formulation and her own different experimental set-up and different EM Drive design.  She is not a copy-cat of Shawyer.  She has a different formulation than Shawyer, and she reported much higher thrust forces and specific forces (force per InputPower) than Shawyer.

Objective readers: make up your own mind on this: read Yang's formulation and see the difference.
« Last Edit: 08/02/2015 03:48 PM by Rodal »

Offline SeeShells

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Yang's frustum has the following dimensions:

- cavity length (m): 0.24
- big diameter (m): 0.201
- small diameter (m): 0.1492

In particular, the big end is smaller than the height, not larger.

There is no resonance I can find for those dimensions at 2.45GHz. Can get TE012 resonance at 2.51GHz

They were surely wrong dimensions, based on the assumption Yang's drawings had the correct proportions. ..

No, they were the dimensions that I had correctly based on the assumption that the small diameter for Yang was obtained based on the cut-off condition for the small end.  And TheTraveller's calculation actually confirms it:

<<There is no resonance I can find for those dimensions at 2.45GHz. Can get TE012 resonance at 2.51GHz>>

The 2% difference between 2.45 GHz and 2.51 GHz is completely and utterly negligible compared to the other differences we are talking about: compared to the difference between 6 degrees and 15 degrees for the cone half-angle or compared to the uncertainties in having to eyeball the dimensionless ratio equations from Yang's chart.

On top of that, the result TE012 resonance at 2.51GHz is obtained by TheTraveller from an Excel spreadsheet using very simplified ad-hoc approximate formulas that do not respect the boundary conditions of the problem while the solution for TE012 2.45GHz resonance uses Wolfram Mathematica to solve the exact solution to the problem using Legendre Associated Functions and Spherical Bessel functions.

Taking into account the above considerations, the 2% different ad-hoc TE012 resonance at 2.51GHz means a complete agreement with the dimensions provided, because the 2% difference is completely within bounds.

___________________________________________

The issue at hand (determination of Yang's geometry) has to do with whether L=24cm provided by Yang in her paper is correct, and if so, whether the other (one and only one available to choose) parameter to consider should be the small diameter (based on cut-off), or the cone half-angle (determined from drawings), or some other parameter like D/L (determined from drawings), etc.

One cannot obtain dimensions from Yang's schematic drawings, one can only obtain dimensionless ratios: angles and ratios, that's it.

For L=24 cm and f=2.45 GHz, you cannot satisfy both that the diameter of the small base be above cut-off for an open waveguide AND satisfy the cone half-angle from Yang's drawings .  They are in violent conflict with each other.  Something got's to give.

This has to be clearly understood:  we have mathematical relations to satisfy here, they are mathematical constraints.  You cannot satisfy all the dimensionless ratios from Yang's drawings and simultaneously satisfy the cut-off condition at the small end and simultaneously satisfy L=24 cm and simultaneously satisfy the D/L vs frequency relation.

I'd like to insert one other thing here as well, having been in the middle of this as one of the builders. First I understand the why of your calculations and how you arrived at them.

Numbers don't lie, but liars and the deceiving will number. That said I think we need to at least make sure that the cone angle for Yang's frustum is correct, better than just taking it off of Yang's drawings which have been proven to be not quite accurate. How do we know that the drawing wasn't modified to fit the page ie: shortening or lengthening the image changing the cone angle? How can we even know who drew this and in what program? PCPaint? The answer is, we truly cant. That throw the angles and ratios under question as well.

Unless you are aware of a designed numerical conditions and guides that promotes this anonymously vague thing called thrust (don't think any here are) we still are poking the bear in the dark. How can I design something to optimize thrust when we don't even know what causes it and then throw in the misleading facts and figures from other builders and we have a real corundum on our hands. (ack, Shell runs screaming into the woods here) Numbers don't lie, but confusion in reported numbers or intentional misreporting of them makes for bad designing.

I'm not going to throw bricks or mash up my frustum with it but I have much to do in the building of the test stand and I'm gonna sortta float for awhile seeing if better numbers come forth.

Shell





 

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I'd like to insert one other thing here as well, having been in the middle of this as one of the builders. First I understand the why of your calculations and how you arrived at them.

Numbers don't lie, but liars and the deceiving will number. That said I think we need to at least make sure that the cone angle for Yang's frustum is correct, better than just taking it off of Yang's drawings which have been proven to be not quite accurate. How do we know that the drawing wasn't modified to fit the page ie: shortening or lengthening the image changing the cone angle? How can we even know who drew this and in what program? PCPaint? The answer is, we truly cant. That throw the angles and ratios under question as well.

Unless you are aware of a designed numerical conditions and guides that promotes this anonymously vague thing called thrust (don't think any here are) we still are poking the bear in the dark. How can I design something to optimize thrust when we don't even know what causes it and then throw in the misleading facts and figures from other builders and we have a real corundum on our hands. (ack, Shell runs screaming into the woods here) Numbers don't lie, but confusion in reported numbers or intentional misreporting of them makes for bad designing.

I'm not going to throw bricks or mash up my frustum with it but I have much to do in the building of the test stand and I'm gonna sortta float for awhile seeing if better numbers come forth.

Shell
1) Concerning estimation of Yang's dimensions:

Everybody is welcome to come up with their own estimates for Yang's dimensions.  So far, to  my recollection, I'm the only one that estimated Yang's dimensions, with two different and clearly stated assumptions: A) assuming the cut-off condition for the small diameter and alternatively B) assuming the angle from the drawings to be approximately correct.

To all readers disagreeing: what is your estimate for Yang's dimensions and what is it based on?

Let's compare different estimates and the basis for calculating the different estimates.

_____

2) Concerning experiments:

The formulas (Shawyer, McCulloch, Notsosureofit), as well as the Meep results and my computations show that the results based on an approximately cylindrical frustum with 6 degree cone angle are going to be inferior to  one with a larger cone angle.

Concerning the experiments, I very much look forward to have experiments with a frustum having only 6 degree cone half-angle to compare with the experiments with frustum having higher cone angles.

An experiment will really clear this.  Just like Tajmar's experiment with a Q=50 clarified the relationship to Q.

Prior to Tajmar's experiment with Q=50 many people would have expected that Q=50 would result in much lower thrust, but nobody had conducted such experiment.  Now we know.  Ditto for a frustum with 6 degree cone angle, which is very close to a cylinder.  Actually, one might also consider an experiment (without a dielectric) with a cylinder (cone angle=0) and measure the thrust. Conduct an experiment with cone angle =0 (a cylinder), one with cone angle = 6 degrees, and one with cone angle =15 degrees.  That will establish the cone angle dependence. That's what experiments are for.
« Last Edit: 08/02/2015 03:20 PM by Rodal »

Offline SeeShells

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Shawyers claim is not without basis, it is based on microwave industry experience. A waveguide operated below cutoff will not propagate an EM wave.

If the small end operates below cutoff there is no EM wave to bounce off the small end, then the big end, then the small end, then the big end, etc.

But please yourself and ignore microwave industry practice, Shawyer & Prof Yang.

But... what if I don't want to propagate just a EM wave? Evanescent waves are a prime contender in this frustum blender.

Shell

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