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#2080 by Rodal on 14 Oct, 2014 02:00
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Quote
The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work.
The polymath of the 20th Century:
John von Neumann
wrote the above in his essay "Method in the Physical Sciences", in The Unity of Knowledge (1955), ed. L. G. Leary (Doubleday & Co., New York), p. 157
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#2081 by Notsosureofit on 14 Oct, 2014 02:02
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"What if the resonant cavity walls acted like a Hubble horizon, especially for Unruh waves of a similar length..." Why izzat different from asking, what if pigs had wings?
Maybe not a Hubble horizon, but it affects the local impedance of the space around it. Look at the scattering cross-section as a function of wavelength. -
#2082 by aero on 14 Oct, 2014 02:02
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Quote
"What if the resonant cavity walls acted like a Hubble horizon, especially for Unruh waves of a similar length...
Why izzat different from asking, what if pigs had wings?[/quote]
The difference is that he goes ahead and predicts mathematically how well the "pigs" could fly. Then he compares his "flying pigs" to three cases where some strange flying thing was seen, and lo and behold, those strange flying things are flying just about the way the mathematics predicted that pigs with wings could!
"Except for the one case where we could speculate that the pig was injured." -
#2083 by RotoSequence on 14 Oct, 2014 02:15
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QuoteQuote
"What if the resonant cavity walls acted like a Hubble horizon, especially for Unruh waves of a similar length...
Why izzat different from asking, what if pigs had wings?
The difference is that he goes ahead and predicts mathematically how well the "pigs" could fly. Then he compares his "flying pigs" to three cases where some strange flying thing was seen, and lo and behold, those strange flying things are flying just about the way the mathematics predicted that pigs with wings could!
"Except for the one case where we could speculate that the pig was injured."
It's enough to drive interest, that's for sure! Still, I really need to see the theory applied to new experiments to remove doubts about the physics of EM drives. Since those experiments are already being performed, I guess it's time to hurry up and wait.
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#2084 by Rodal on 14 Oct, 2014 02:25
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@RotoSequence, I completely agree with you. That's exactly what I was taught at MIT. The "model" stands only as long as experiments verify it. The "model" falls immediately when experiments fail to verify it.QuoteQuote"What if the resonant cavity walls acted like a Hubble horizon, especially for Unruh waves of a similar length...
Why izzat different from asking, what if pigs had wings?
The difference is that he goes ahead and predicts mathematically how well the "pigs" could fly. Then he compares his "flying pigs" to three cases where some strange flying thing was seen, and lo and behold, those strange flying things are flying just about the way the mathematics predicted that pigs with wings could!
"Except for the one case where we could speculate that the pig was injured."
It's enough to drive interest, that's for sure! Still, I really need to see the theory applied to new experiments to remove doubts about the physics of EM drives. Since those experiments are already being performed, I guess it's time to hurry up and wait.
The model falls if another model with the same number or smaller number of parameters does a better job at explaining the experimental data.
Excellent wording "It's enough to drive interest. We need to see the theory applied to new experiments to remove doubts about the physics of EM drives"
I couldn't have said it better. The model has to be further explored regarding a larger range of Q, a much larger range of frequency, and a much larger geometrical range. The power range (a factor of 6000 from minimum to maximum power modeled) is already very interesting. -
#2085 by Rodal on 14 Oct, 2014 02:33
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The next step that could be done is:
are there other physical models that result in the same (or better) formula to explain the experimental data ?
They don't need to be physical models that make the EMDrive fly, they can be physical models that explain the experimental data as an artifact. For example the "magnetic" explanation as an artifact (and other explanations ) are also expected to be related to the input power. But the trick is to find other physical explanations that predict all these data as well or better. The interesting thing is the dependence on Q and frequency, and on the inverse of the flat surface diameters. -
#2086 by JohnFornaro on 14 Oct, 2014 02:43
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Quote from: McCulloch
"What if the resonant cavity walls acted like a Hubble horizon, especially for Unruh waves of a similar length...
Quote from: JFWhy izzat different from asking, what if pigs had wings?
The difference is that he goes ahead and predicts mathematically how well the "pigs" could fly. Then he compares his "flying pigs" to three cases where some strange flying thing was seen, and lo and behold, those strange flying things are flying just about the way the mathematics predicted that pigs with wings could!
That's too facile an explanation, particularly when depending upon the hypothetical Unruh effect.
Without being snarky, but trying to follow the winged pig analogy a mite further, it's like saying: Let's assume these dimensions for the Unruh pig wings, and lo, they accomodate the reported data. Remember too, that no "strange flying thing was seen", by the community in general. What has happened so far is only that some strange flying thing was thought to be seen.
Plus, typically Unruh pig wings are only found in integral divisions of the friggin' Hubble distance, a huge number of meters. We have some experimentors claiming that there is cupric Unruh pig's wing effect at the boundary of a very small pig's wing of a specific geometry. McCulloch the theoretician acknowledges this: "What if the resonant cavity walls acted like a Hubble horizon, especially for Unruh waves of a similar length"
No actual pigs were harmed in this analogy.Q = quality factor
Which sounds like a tunable parameter, by this wording. McCulloch calls the Q factor, the "number of photon 'bounces'", so now I'm having a terminology tantrum. I thought that tunable parameters, aka 'fudge factors' were frowned upon. So what is it, quality? or a specific number of 'bounces' which seem to be linearly related to the power input?
This device, should it work as hypothesized, has no pragmatic value when the power going in is compared to the thrust that they think they get out of the device. -
#2087 by aero on 14 Oct, 2014 02:56
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Q is defined as:
Q = stored energy/energy lost per cycle.
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#2088 by Rodal on 14 Oct, 2014 03:00
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Q is defined as:
Q = stored energy/energy lost per cycle.
Yes, that is one of several (completely identical to each other definitions of Q). A standard, universally accepted definition for all kinds of mechanical vibrations and electromagnetic oscillations to characterize damping. A very well defined mathematical variable, that is completely independent from McCulloch's theory. All three laboratories that did the testing (in USA, UK and China) were completely aware of the importance of Q and went through the trouble of measuring and reporting Q (the table of values contains the experimentally reported values of Q, and those were the values used in the formula for predictions, without any changes). -
#2089 by Mulletron on 14 Oct, 2014 11:26
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Until it is recognized that conservation of momentum has to be satisfied both locally and globally, no more progress can be made. One cannot pick or choose which.
The report also clearly stated the importance of the dielectric.
Page 18 clearly shows that thrust does not scale with Q.
Ignoring data and physical law puts wings on pigs.
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#2090 by Rodal on 14 Oct, 2014 14:09
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The following study (and similar studies on the other experimental variables) is trivial to do, but I enclose it as a service to readers that may not have had the time to do a statistical exploration of the data, to notice the significance of the variables and McCulloch's formula.
The language of engineers and scientists is mathematical formulas, numbers, graphs and not words. Professional engineering and scientific discourse uses such exploration of data and not words like "pigs", "the cake is a lie", and personalization words like "you" and "I".
I enclose a plot of experimental and predicted Q, for the EMDrive experiments conducted in the US, UK and China, and reported in my my last post with data (please refer to: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1270264#msg1270264 ).
The horizontal axis shows the experimentally measured Q.
The vertical axis shows the predicted Q from McCulloch's formula (inverted to express Q as a function of the other variables), using experimentally-measured forces, and expressed as follows:
PredictedQ = (ExperimentalForce)*Frequency/((PowerInput)*(1/Dsmall-1/Dbig))
It is obvious from the plot that:
1) There is a significant experimental dependence on Q, the R^2 value is statistically significant: 81% (and this is including the outlier data: the very anomalous test reported by Brady et.al at a frequency of 1.937 GHz).
2) The actual Q dependence is linear as predicted by McCulloch's formula, as shown by the least squares formula shown in the box. It is certainly linear within the (obvious from plotting the data) experimental uncertainty in the measurements.
3) The fact that the predicted curve (in red) is off by a factor of ~34%, as I have previously addressed in Prof. McCulloch's blog is expected, since McCulloch's formula is a 1 Dimensional simplification of the full 3-D Modified Inertia formulation: as the simplified formula neglects the Unruh wave contribution from the sides of the cone (the simplified formula only uses the flat areas into consideration).
Concerning the dielectric:
Brady et. al. state is
<<There appears to be a clear dependency between thrust magnitude and the presence of some sort of dielectric RF resonator in the thrust chamber. The geometry, location, and material properties of this resonator must be evaluated using numerous COMSOL® iterations to arrive at a viable thruster solution. We performed some very early evaluations without the dielectric resonator (TE012 mode at 2168 MHz, with power levels up to ~30 watts) and measured no significant net thrust.>>
So, some "very early tests" at a significantly higher frequency with non-reported Q. Not much one can do regarding Q with this statement for which Q is not reported (we don't know whether it was even measured for this case).
Given the fact that they have outlier data (included in the attached plot and taken into account to compute R^2) showing one experiment given 10% less thrust with 6 times higher input Power, this "dielectric" statement with an unreported Q is not that relevant.
Also, the information from @wembley is that Shawyer no longer uses any dielectric. Shawyer's started using ferrites, then he switched to dielectric materials and according to the latest information he no longer uses dielectric. Shawyer's reference to dielectric is several years old.
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#2091 by Notsosureofit on 14 Oct, 2014 14:42
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Just for fun, let's say the prediction curve is absolutely accurate and based on 70 years of experience w/ copper waveguides and resonators. Then the difference w/ these tapered chambers represent a loss of power which is going somewhere
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#2092 by Rodal on 14 Oct, 2014 14:45
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Just for fun, let's say the prediction curve is absolutely accurate and based on 70 years of experience w/ copper waveguides and resonators. Then the difference w/ these tapered chambers represent a loss of power which is going somewhere
Yes, good point. I also noticed that early on. My take on that is the following:
The fact that the predicted curve (in red) is off by a factor of ~34%, as I have previously addressed in Prof. McCulloch's blog is expected, since McCulloch's formula is a 1 Dimensional simplification of the full 3-D Modified Inertia formulation: as the simplified formula neglects the Unruh wave contribution from the sides of the cone (the simplified formula only uses the flat areas into consideration).
The simplified 1 Dimensional formula of McCulloch's full theory is obviously an approximation since it leads to an infinite predicted force for the diameter of the smaller flat surface going to zero. So the 1D formula overpredicts the force (because it does not take into account the Unruh wave contribution from the curved surface of the cone). -
#2093 by Notsosureofit on 14 Oct, 2014 14:48
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Just for fun, let's say the prediction curve is absolutely accurate and based on 70 years of experience w/ copper waveguides and resonators. Then the difference w/ these tapered chambers represent a loss of power which is going somewhere
Yes, good point. I also noticed that early on. My take on that is the following:
The fact that the predicted curve (in red) is off by a factor of ~34%, as I have previously addressed in Prof. McCulloch's blog is expected, since McCulloch's formula is a 1 Dimensional simplification of the full 3-D Modified Inertia formulation: as the simplified formula neglects the Unruh wave contribution from the sides of the cone (the simplified formula only uses the flat areas into consideration).
It would be nice to have the COMSOL prediction for these chambers.
Edit: Forgot they use a simplified chamber wall. -
#2094 by JohnFornaro on 14 Oct, 2014 14:49
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Just for fun, let's say the prediction curve is absolutely accurate and based on 70 years of experience w/ copper waveguides and resonators. Then the difference w/ these tapered chambers represent a loss of power which is going somewhere
Yes, good point. I also noticed that early on. My take on that is the following:
The fact that the predicted curve (in red) is off by a factor of ~34%, as I have previously addressed in Prof. McCulloch's blog is expected, since McCulloch's formula is a 1 Dimensional simplification of the full 3-D Modified Inertia formulation: as the simplified formula neglects the Unruh wave contribution from the sides of the cone (the simplified formula only uses the flat areas into consideration).
The simplified 1 Dimensional formula of McCulloch's full theory is obviously an approximation since it leads to an infinite predicted force for the diameter of the smaller flat surface going to zero. So the 1D formula overpredicts the force (because it does not take into account the Unruh wave contribution from the curved surface of the cone).
Which, I might point out, is a number of words, and not an actual 3d formula which accurately portrays the contribution of the hypothetical Unruh wave.
Which is not saying that I already understand that 3D equation. I do understand the 1D equation. Up to a point. Not the one at the top of my head, you wisecracks. -
#2095 by Rodal on 14 Oct, 2014 14:54
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Engineers and Scientists understand the usefulness of 1 Dimensional approximation of fully 3D theories to obtain closed-form solutions. This is understood by any structural engineer using beam equations instead of fully 3-D equations that are unsolvable without numerical analysis. The usefulness of closed-form solutions is understood in fluid mechanics, heat transfer, solid mechanics, and just about every engineering and scientific discipline. The usefulness of closed-form solutions (always an approximation of full 3D solutions of course) is certainly understood by Aerospace Engineers.
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#2096 by Rodal on 14 Oct, 2014 18:19
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I enclose plots of experimental and predicted frequency, for the EMDrive experiments conducted in the US, UK and China, and reported in my my last post with data (please refer to: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1270264#msg1270264 ).
The horizontal axis shows the experimentally measured frequency.
The vertical axis shows the predicted frequency from McCulloch's formula (inverted to express the frequency as a function of the other variables), using experimentally-measured forces, Q, power input and geometry, and expressed as follows:
PredictedFrequency =(PowerInput)*Q*(1/Dsmall-1/Dbig) / (ExperimentalForce)
It is obvious from the plot that:
1) The experiments in the US, UK and China did not peform a satisfactory exploration of frequencies. Basically only two frequency ranges have been explored: ~1.9 GHz in the US and ~2.5 GHz in the UK and China
2) The uncertainty experimental bars are very large and they overwhelm the very small frequency range that was explored.
3) There is a clear statistical outlier (Brady et.al. at 1.937 GHz) that I have repeatedly pointed out. The fact that this is a statistical outlier is evident from the plot.
4) The data with the statistical outlier included gives a very poor R^2 = - 12%. Essentially, including the statistical outlier indicates that the uncertainty overwhelms the power to conclude anything concerning frequency dependence.
5) Considering the data without the outlier gives a weak statistical dependence: R^2 = 22%. Essentially inversely proportional to the frequency, as predicted by McCulloch, but again there is not enough statistical data to make any statistical conclusion regarding frequency dependence.
6) The fact that the predicted curve (in red) is below the experimental curve, as I have previously addressed in Prof. McCulloch's blog is expected, since McCulloch's formula is a 1 Dimensional simplification of the full 3-D Modified Inertia formulation: as the simplified formula neglects the Unruh wave contribution from the sides of the cone (the simplified formula only uses the flat areas into consideration), hence it overpredicts the force. Since frequency and force appear as inverse to each other, an overprediction of force means an undeprediction of frequency based on experimentally measured force.
7) A very important issue is the fact that resonance amplitude is a very nonlinear function of frequency. Besides this being expected, such resonance amplitude nonlinear dependence on frequency is shown in the S22 plots. Hence it is not surprising that a formula that is inversely proportional to frequency cannot possibly reflect the huge changes in amplitude resonance emanating from small changes in frequency (for example for Brady et.al. at 1.88, 1.933 and 1.937 GHz), particularly when experimenters deliberately chose to conduct their experiments at frequencies close to resonance.
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#2097 by Rodal on 14 Oct, 2014 18:43
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Also, one can follow the pertinent arguments brought up by @aero concerning the axial wavelength, regarding frequency dependence in the simplified formula: http://physicsfromtheedge.blogspot.it/2014/10/mihsc-vs-emdrive-data-1.html .
Thanks @aero for continuing a professional engineering/scientific exploration of the EMDrive experimental data
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#2098 by aero on 14 Oct, 2014 20:13
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I'm not sure what your frequency-frequency curves signify.
Based on this from Prof. M:QuoteWhat if the resonant cavity walls acted like a Hubble horizon, especially for Unruh waves of a similar length (as they are in this case)? Then the inertial mass of the photons would increase towards the cavity's wide end, since more Unruh waves would fit there, since mi=m(1-L/2w), where w is the cavity width. The force carried by the photons then increases by this factor as they go from the narrow end (width w_small) towards the wide end (width w_big). The force difference between ends is
dF = (PQ/c)*((L/w_big)-(L/w_small)) = (PQ/f)*((1/w_big)-(1/w_small)).
From this it is clear that L is the Unruh wave length and that the cavity walls act like a Hubble horizon. Therefore L/c is the Unruh frequency. Resonance of the Unruh waves within the cavity is not required, they are driven by the RF waves which do resonate however. Therefore, acceleration within the cavity walls is driven by the RF waves which in turn drive the Unruh waves.
But the Unruh frequency need not be the same as the RF frequency. They need only be some frequency that is sustained by the cavity height and the RF wave induced accelerations. I have calculated that the cavity height constrains wavelength, lamda, to 6, 9 or 18 inches. (2d = n lamda) so lamda = 2d/n. Here d is the cavity height = 9 inches so lamda = 18(n=1), = 9(n=2) = 6(n=3).
But there is another important consideration. That is that within the big and small end of the cavity, the Unruh waves reflections are separated in time by d/c and by the choice of the driving RF frequency there are acceleration pulses to driving Unruh waves just exactly in synchronization with that time difference or wavelength which is 9 inches. I don't know of any reason that the Unruh waves would prefer a higher frequency, shorter wavelength.
I can't justify the Unruh waves selecting a higher energy state when there is a lower energy state available. -
#2099 by Rodal on 14 Oct, 2014 20:16
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I received the attached e-mail from Robert Ludwick that explains the anomalous outlier in NASA's Brady et. al. report as well as bringing up excellent questions regarding the curious choice of testing frequencies pursued by NASA's Brady et.al. (curious since not only did they have COMSOL Finite Element calculations of resonance but they actually had the S22 plot for actual measured resonance) and their use of a Voltage Controlled Oscillator (VCO).
This is an outstanding contribution by Robert Ludwick that I reproduce in its entirety. A professional examination of the data, that serves to clarify and understand it.
I added Bolding and color for emphasis [not present in his original e-mail] to the sections that I found most attention calling.
From: Robert Ludwick
Sent: Tuesday, October 14, 2014 12:27 PM
To: [email protected]
Subject: Re: EM Drive Developments « Reply #2082 on: Today at 12:30 AM
Hello Dr. Rodal,
I apologize for using email for this, rather than the forum, but I am not a
member and can’t post there—I think.
I was reading the ongoing discussion re Shawyer’s EmDrive and came across the
subject comment by you.
At the end of the data table showing the measured thrust vs the MiHsC thrust
prediction, you said this:
"The following experiment is very anomalous:
Brady et al. (2014) b " " 18100 16.7 1.937 0.315 0.0501
because:
1) An increase in Q from Brady et al. (2014) a, from Q=7320 to Q=18100 (a
factor 2.5 times) results in a smaller experimentally measured force
(practically 50% of the force with the much lower Q)
2) An increase in Power Input from Brady et al. (2014) c, from 2.6 Watts to
16.7 Watts (a factor 6 times) results in a smaller experimentally measured
force (10% smaller)
3) It was conducted at a frequency only 0.3% different than Brady et al.
(2014) a"
First of all, I don’t know what Brady was using as a source.
That said, there are several trivial explanations for the anomalous test
results (all of which Brady may have already accounted for—I don’t know).
The bandwidth of the widget is Resonant Frequency/Q.
If you increase the Q the bandwidth decreases.
Using the data provided for the three Brady tests:
Freq (MHz) Q Power (W) Bandwidth (MHz) Bandwidth (% of Test Freq)
1933 7320 16.9 .264 0.014
1880 22000 2.6 .085 0.0045
1937 18100 16.9 .107 0.0055
(The quoted dimensions for the thruster were the same for all three tests, so
why was the test frequency varied by +/- 1.5%, when the broadest bandwidth,
based on the measured Q, was +/- 0.007 %?)
NOTE BY J.RODAL: And for the anomalous test specifically, why did Brady et.al. change the test frequency from 1933 GHz to 1937 GHz, which is only a 0.2% change in frequency or just +/- 0.1%, when the bandwith was 0.0055% ?
If Brady was using a free running VCO, ’tuned’ to the resonant frequency of
the thruster, there is next to zero chance that the VCO, and by extension the
drive power to the thruster, stayed within the bandwidth of the thruster
during the test run OR that, for the high Q thruster, a large percentage of
the source power was within the thruster bandwidth, even if the center
frequency of the source remained centered on the resonant frequency of the
thruster. VCO’s are VERY spectrally dirty and, unless phase locked, very
unstable in relation to the spectral purity required by Brady’s thruster.
NOTE by J.RODAL: Brady's report states:
<<During testing, the Test Engineer controls the RF frequency generation via a 0-to-28 volts dc power input to a voltage-controlled oscillator (VCO). The VCO RF signal output is passed to a variable voltage attenuator (VVA), the output of which is controlled by the Test Engineer via a 0-to-17 volts dc power input. Based upon the VVA output, the amplifier will output up to approximately 28 watts. Amplifier output passes to a dual-directional coupler (DDC), which allows forward and reflected power measurements to be obtained as the power is simultaneously passed to the test article input port. The Test Engineer monitors forward and reflected power and adjusts the input frequency to obtain the desired combination of cavity frequency and power delivery to the cavity.>> p.8
<<The 25 watt amplifier was driven by a Mini-Circuits® voltage controlled oscillator (VCO) passed through a Mini-Circuits® variable voltage attenuator (VVA). The output of the RF amplifier was run through a dual directional coupler (DDC) with power meters positioned to measure forward and reflected power from the test article. For final tuning prior to testing on the rig, typically a stub tuner was placed between the DDC and the test article and the VNA’s Smith Chart and S11 plots were used to optimize coupling with the test article. Figure 17 shows the thruster mounted on the torsion pendulum arm and how it was connected to the RF amplifier.>> p.13
This is the website for the Mini-Circuits® voltage controlled oscillator (VCO)
Mini-Circuits® has over 800 low-noise & wideband models from 3 MHz to 7 GHz:
http://www.minicircuits.com/products/Oscillators.shtml
At any rate, based on the measured frequency and Q of the thruster, the
‘anomaly’ is easily explained (actually, expected) if the drive source
frequency stability and spectral purity were not suited to the requirements of
the thruster. Since test frequencies were only specified to +/- 1 MHz, while
the bandwidth of the thruster required that the source be tunable and stable
in the tens of KHz range, or ideally, less, I suspect that that was the case.
If on the other hand Brady was using a state of the art synthesized signal
source and a ‘clean’ amplifier and ensured that the source was tuned to the
center of the thruster bandwidth during the entire test, never mind.
(All of which calls attention to potential problems with Shawyer’s G2
superconducting thruster. Postulating (and hoping fervently) that the
technology actually works, a superconductor thruster with a Q of 1e9, and a
design frequency of 2 GHz, that implies that the drive source has to be
accurate and stable to within +/- 1 Hz. In other words, that essentially ALL
of the drive power be contained within a bandwidth of +/- 1 Hz, centered on
the resonant frequency of the thruster. That is easily achievable, as very
clean synthesized sources with tuning steps of +/- 0.001 Hz are available in
that frequency range, but magnetrons need not apply unless they are phase
locked to a very stable source. This is possible, but I couldn’t find out
much about their spectral purity within 1 Hz of their nominal output
frequency. Another problem he may have is mechanical stability of the
thruster. It is hard for me to imagine a superconducting thruster whose
resonant frequency (set by physical dimensions) remains stable within +/- 1e9
while undergoing mechanical stresses varying between zero and many tons. But
I suppose that that is JUST engineering. )
Bob Ludwick
