What I told prof mike is 18.4 mN was achieved (best result) with 1701A based on ~750W into a Q of ~10K. Both power and Q had a margin of error of 5-6%, displacement force is tighter at 2%. So it went with my home lab setup...Q was measured on a VNA, Power was based on factory specs with new, conventional magnetron directly coupled into cavity, centered on large diameter plate. Note that the mag pulled down from 2455 to 2440 MHz only a few times before thermal runaway and mag degradation (about 7 or 8 test runs). After this, I ended my testing in the summer as mag dropped both in core temp and relative (spec an) output. This is what I had; to few data points to compile a formal test report, but enough to know what my ideal displacement force was when mag was passing thru resonance at full power.
What I told prof mike is 18.4 mN was achieved (best result) with 1701A based on ~750W into a Q of ~10K. Both power and Q had a margin of error of 5-6%, displacement force is tighter at 2%. So it went with my home lab setup...Q was measured on a VNA, Power was based on factory specs with new, conventional magnetron directly coupled into cavity, centered on large diameter plate. Note that the mag pulled down from 2455 to 2440 MHz only a few times before thermal runaway and mag degradation (about 7 or 8 test runs). After this, I ended my testing in the summer as mag dropped both in core temp and relative (spec an) output. This is what I had; to few data points to compile a formal test report, but enough to know what my ideal displacement force was when mag was passing thru resonance at full power.
Dave:
To clarify what I said was that tens of mN have to be demonstrated in a hard-vacuum that shows input power to thrust output scaling over at least a 20-to-1 RF input power range without a lot of confounding thermal artifacts in the thrust traces to muddy the observational waters. Doing EMdrive experiments in-air over a narrow RF power input range as you have done are the first steps, but they are not conclusive enough for those who make a living by doubting everything and who sadly control the R&D purse-strings in the USA, at least in the halls of academia and government. So I'm glad you found a commercial venture that had different standards than this set, but it is the reality for most R&D shops.
Best, Paul M.
FYI - This "super conductive paint" as a substrate for electroplating 3d printed parts comes highly recommended on the 3d printing subreddit. Apparently it works better than the graphite paint sold by most electroplating shops.
http://www.mgchemicals.com/products/emi-and-rfi-shielding/other-coating-systems/super-shield-nickel-841
... in my opinion, both the EMdrive and MEGA drives will be found to be creating and using high energy intensity, fast (nanosecond or less) time-varying E&M fields to entrain, compress and accelerate a confined volume of the cosmological gravitational field, AKA spacetime, AKA the quantum-vacuum..
Paul & Todd,
What I told prof mike is 18.4 mN was achieved (best result) with 1701A based on ~750W into a Q of ~10K. Both power and Q had a margin of error of 5-6%, displacement force is tighter at 2%. So it went with my home lab setup...Q was measured on a VNA, Power was based on factory specs with new, conventional magnetron directly coupled into cavity, centered on large diameter plate. Note that the mag pulled down from 2455 to 2440 MHz only a few times before thermal runaway and mag degradation (about 7 or 8 test runs). After this, I ended my testing in the summer as mag dropped both in core temp and relative (spec an) output. This is what I had; to few data points to compile a formal test report, but enough to know what my ideal displacement force was when mag was passing thru resonance at full power.
those who make a living by doubting everything
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According to my model, the thrust will depend on which direction most of the magnetic flux is escaping into the copper. In that regard, this design should outperform the pointier cones. Just my gut instinct, assuming it will accelerate with the big end leading.Why the "gut instinct" instead of a calculation based on your model ?
Because actual power dissipation and conduction losses are unknowns to me. I don't know how to estimate them based on these models (yet), but logically thinking, the "exhaust" would be best pointed out the small end, not out the side walls.
Paul & Todd,
What I told prof mike is 18.4 mN was achieved (best result) with 1701A based on ~750W into a Q of ~10K. Both power and Q had a margin of error of 5-6%, displacement force is tighter at 2%. So it went with my home lab setup...Q was measured on a VNA, Power was based on factory specs with new, conventional magnetron directly coupled into cavity, centered on large diameter plate. Note that the mag pulled down from 2455 to 2440 MHz only a few times before thermal runaway and mag degradation (about 7 or 8 test runs). After this, I ended my testing in the summer as mag dropped both in core temp and relative (spec an) output. This is what I had; to few data points to compile a formal test report, but enough to know what my ideal displacement force was when mag was passing thru resonance at full power.And as you always forget to include, you know that you got a comparable displacement when you did a run with broken RF equipment. Ignoring some of the available data because it is inconvenient does no one any good.
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Because actual power dissipation and conduction losses are unknowns to me. I don't know how to estimate them based on these models (yet), but logically thinking, the "exhaust" would be best pointed out the small end, not out the side walls.
I still think that your theory's main flaw is that you take portions of your equations and decide that they are have a specific meaning just because the units match, with no other justification. If you had properly mathematically defined the physical quantities first, you shouldn't run into issues where you can't calculate their values. In this case "power dissipation" is ambiguous, because EM energy is being "dissipated" into heat, but, the energy is still there just in a different form, so it wasn't dissipated out of the frustum. Since you didn't start your derivation with a full definition of power dissipation, there is no way to know if it should be dissipation of EM energy into another form, or dissipation of the energy from the frustum all together. The second one is the one that seems more compelling as a general concept to me, but that value is 0 (until thermal radiation kicks in.)
I can help you with calculating some of these values though, so that you can at least make numerical predictions, and we can see what the numerical results of your theory are.
For calculations of the power dissipation due to currents, you can use the same methods Egan did in his calculations here. You should be able to get answers based on his other equations on that page. (some work is required to get the values of parameters like n and k for different cavity sizes)
You also previously have said you didn't know how to calculate the magnetic flux inside the frustum. There are an infinite number of ways to define it, but I can give you 2 of the better ones I can thin of, though these definitions are relative to you being inside frustum, and therefore are essentially meaningless without a frustum to refer to. (Again, your lack of definition of the terms you use is a problem with this theory, as is using something that isn't defined in a general case and using that as a basis for a general theory.)
Definition 1: Flux inside a circle defined at the sidewall
Φ(r) = ∫0θ0∫02πBr(r,θ,φ) r2 sin(θ)dφdθ
Where θ0 is the cone half angle, and Br is the component of B in the rhat direction. (result of B · rhat) note that the flux would be equally well defined by B · -rhat, so you can get 2 more definitions, just by taking the negative of these 2.
Definition 2: Flux inside a circle intersecting the current point:
Φ(r,θ) = ∫0θ∫02πBr(r,θ',φ) r2 sin(θ')dφdθ'
Where I defined θ' as a temporary variable for the integration.
Both of these definitions are written in spherical coordinates so you can use them with Egan's results. They could be defined basically equivalently in cylindrical coordinates for use with Rodal's flat endplate solution. (The simplest cylindrical version of definition 1 would not be exactly equivalent)
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Because actual power dissipation and conduction losses are unknowns to me. I don't know how to estimate them based on these models (yet), but logically thinking, the "exhaust" would be best pointed out the small end, not out the side walls.
I still think that your theory's main flaw is that you take portions of your equations and decide that they are have a specific meaning just because the units match, with no other justification. If you had properly mathematically defined the physical quantities first, you shouldn't run into issues where you can't calculate their values. In this case "power dissipation" is ambiguous, because EM energy is being "dissipated" into heat, but, the energy is still there just in a different form, so it wasn't dissipated out of the frustum. Since you didn't start your derivation with a full definition of power dissipation, there is no way to know if it should be dissipation of EM energy into another form, or dissipation of the energy from the frustum all together. The second one is the one that seems more compelling as a general concept to me, but that value is 0 (until thermal radiation kicks in.)
I can help you with calculating some of these values though, so that you can at least make numerical predictions, and we can see what the numerical results of your theory are.
For calculations of the power dissipation due to currents, you can use the same methods Egan did in his calculations here. You should be able to get answers based on his other equations on that page. (some work is required to get the values of parameters like n and k for different cavity sizes)
You also previously have said you didn't know how to calculate the magnetic flux inside the frustum. There are an infinite number of ways to define it, but I can give you 2 of the better ones I can thin of, though these definitions are relative to you being inside frustum, and therefore are essentially meaningless without a frustum to refer to. (Again, your lack of definition of the terms you use is a problem with this theory, as is using something that isn't defined in a general case and using that as a basis for a general theory.)
Definition 1: Flux inside a circle defined at the sidewall
Φ(r) = ∫0θ0∫02πBr(r,θ,φ) r2 sin(θ)dφdθ
Where θ0 is the cone half angle, and Br is the component of B in the rhat direction. (result of B · rhat) note that the flux would be equally well defined by B · -rhat, so you can get 2 more definitions, just by taking the negative of these 2.
Definition 2: Flux inside a circle intersecting the current point:
Φ(r,θ) = ∫0θ∫02πBr(r,θ',φ) r2 sin(θ')dφdθ'
Where I defined θ' as a temporary variable for the integration.
Both of these definitions are written in spherical coordinates so you can use them with Egan's results. They could be defined basically equivalently in cylindrical coordinates for use with Rodal's flat endplate solution. (The simplest cylindrical version of definition 1 would not be exactly equivalent)
Thanks! Can you also tell us what is the function Br(r,θ,φ), for a TE013 mode, at all points in the frustum, including the antenna feed, so it can be integrated? THAT is the part I don't know, not the integrals. Eagan's equations do not include a source antenna term, and then he hand-waves the answer. As such, he just refers to the solutions as being periodic and therefore, they cancel out over 1 full cycle. That's not very useful unless the equation includes the source terms from the antenna. I don't have that either.
I have done the integral for a simple TM field (not a mode) in a cone, and shown that for a perfect conductor, the field pressure on the inside of the cone SUMs to zero. No problem! But I don't have a source term, or any losses in that integral, and it's not a real mode shape. If I "assume" the surface resistance losses for the applied B field are also uniform, then that integral will SUM to zero as well. But what about when it's not uniform, such as the side walls are made of thick copper, the big end is made of very thin copper on FR4 board which is much hotter, and the small end has a dielectric that keeps it cool? Then what is the Br(r,θ,φ) field to integrate and the surface resistance on all surfaces? I have no idea!
FYI - This "super conductive paint" as a substrate for electroplating 3d printed parts comes highly recommended on the 3d printing subreddit. Apparently it works better than the graphite paint sold by most electroplating shops.
http://www.mgchemicals.com/products/emi-and-rfi-shielding/other-coating-systems/super-shield-nickel-841
If it can be applied with a very thin coat, < .5 mil, then it provides a means to adjust the thickness/transparency of the small end plate. An experiment could be done, varying the thickness of the coat. A thin coat should heat up faster and allow more microwave energy to escape. A thicker coat should heat slower and be less transparent. A loop antenna setup outside that end can tell us the power spectrum of what gets through.
It would be interesting to measure the power spectrum on both sides and from that data, predict the amount of force it will have, then measure it on a thrust balance.
Thanks! Can you also tell us what is the function Br(r,θ,φ), for a TE013 mode, at all points in the frustum, including the antenna feed, so it can be integrated? THAT is the part I don't know, not the integrals. Eagan's equations do not include a source antenna term, and then he hand-waves the answer. As such, he just refers to the solutions as being periodic and therefore, they cancel out over 1 full cycle. That's not very useful unless the equation includes the source terms from the antenna. I don't have that either.
I have done the integral for a simple TM field (not a mode) in a cone, and shown that for a perfect conductor, the field pressure on the inside of the cone SUMs to zero. No problem! But I don't have a source term, or any losses in that integral, and it's not a real mode shape. If I "assume" the surface resistance losses for the applied B field are also uniform, then that integral will SUM to zero as well. But what about when it's not uniform, such as the side walls are made of thick copper, the big end is made of very thin copper on FR4 board which is much hotter, and the small end has a dielectric that keeps it cool? Then what is the Br(r,θ,φ) field to integrate and the surface resistance on all surfaces? I have no idea!The B field for a TE mode is given by Egan's equation of B = (1/ω) curl E = (1/ω) [(1/r) Rα(r) Q1(θ) er + Rα1(r) Q'(θ) eθ ] (see his page for proper formatting).
You can neglect the antenna, because it shouldn't have any effect in steady state if it is ideally designed and positioned, and if the antenna does affect the fields, its effect should be on the order of 1/Q compared to the rest of the fields.
I am not sure what handwaving you are referring to from Egan, but it sounds like you are referring to his general proof of no force, which does not involve any handwaving or have any relevance.
I don't understand why you are asking the questions about the heating not being uniform. Egan shows that the heating isn't uniform, and the parts about if the ends are cooled, or have different heat capacities is for you to answer with your theory. (And your theory being unclear on these things is related to my main issue with it.)
Thanks! Can you also tell us what is the function Br(r,θ,φ), for a TE013 mode, at all points in the frustum, including the antenna feed, so it can be integrated? THAT is the part I don't know, not the integrals. Eagan's equations do not include a source antenna term, and then he hand-waves the answer. As such, he just refers to the solutions as being periodic and therefore, they cancel out over 1 full cycle. That's not very useful unless the equation includes the source terms from the antenna. I don't have that either.
I have done the integral for a simple TM field (not a mode) in a cone, and shown that for a perfect conductor, the field pressure on the inside of the cone SUMs to zero. No problem! But I don't have a source term, or any losses in that integral, and it's not a real mode shape. If I "assume" the surface resistance losses for the applied B field are also uniform, then that integral will SUM to zero as well. But what about when it's not uniform, such as the side walls are made of thick copper, the big end is made of very thin copper on FR4 board which is much hotter, and the small end has a dielectric that keeps it cool? Then what is the Br(r,θ,φ) field to integrate and the surface resistance on all surfaces? I have no idea!The B field for a TE mode is given by Egan's equation of B = (1/ω) curl E = (1/ω) [(1/r) Rα(r) Q1(θ) er + Rα1(r) Q'(θ) eθ ] (see his page for proper formatting).
You can neglect the antenna, because it shouldn't have any effect in steady state if it is ideally designed and positioned, and if the antenna does affect the fields, its effect should be on the order of 1/Q compared to the rest of the fields.
I am not sure what handwaving you are referring to from Egan, but it sounds like you are referring to his general proof of no force, which does not involve any handwaving or have any relevance.
I don't understand why you are asking the questions about the heating not being uniform. Egan shows that the heating isn't uniform, and the parts about if the ends are cooled, or have different heat capacities is for you to answer with your theory. (And your theory being unclear on these things is related to my main issue with it.)
The highlighted statement above shows that you do not yet understand my theory. There is no "steady state", steady state means no thrust. The location of the antenna, the location of the losses, the power that is radiated and what is reflected back or absorbed and dissipated on each cycle has everything to do with it. I can't neglect those things and claim this is a representation of my theory because it isn't. The stored and dissipated energy must be increasing or decreasing. Anything "except" steady state.
those who make a living by doubting everythingNo one does this (how would they?), except maybe some few journalists or something. Certainly not people who are in charge of purse strings.
Please note that in spherical end plate thrusters, the effective resonant length is the frustum height (axial length) and NOT the constant separation between the spherical end plates. Which means the FEKO calculated resonance is not accurate and other means are needed to calculate the resonance freq. The resonant freq of the attached dimensions has been checked.
The resonant frequency has been checked how?
As you will discover the solutions to the guide wavelength terms are very non-linear, which makes the accurate design of a tapered cavity particularly difficult. At SPR Ltd we have developed our own software to give a 2D high resolution numerical solution to the problem. This proprietary design software has been validated for a number of different cavities by ourselves, as well as different research groups operating under commercial agreements with SPR Ltd.
KISS Thruster update:
Latest dimension as attached.
Please note that in spherical end plate thrusters, the effective resonant length is the frustum height (axial length) and NOT the constant separation between the spherical end plates. Which means the FEKO calculated resonance is not accurate and other means are needed to calculate the resonance freq. The resonant freq of the attached dimensions has been checked.
The resonant frequency has been checked how?
Did post this before:QuoteAs you will discover the solutions to the guide wavelength terms are very non-linear, which makes the accurate design of a tapered cavity particularly difficult. At SPR Ltd we have developed our own software to give a 2D high resolution numerical solution to the problem. This proprietary design software has been validated for a number of different cavities by ourselves, as well as different research groups operating under commercial agreements with SPR Ltd.
The KISS Thruster spherical dimensions will resonant in TE013 mode at 2.45GHz, despite what other analytical methods suggest.
As far as I can determine, FEKO, gets thruster resonance wrong. Building a thruster based on its resonance calc could be a bad experience.
our own software to give a 2D high resolution numerical solution to the problem