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#2760 by JohnFornaro on 29 Oct, 2014 00:25
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There is no explicit mating shown in the referenced picture (reproduced below), and again you are considering the lip from only one side.
Not quite sure I unnerstand ya, doc. Here's my guess as to what the section thru the completely fabricated round thing is.
So I reckon that you came up with the same cavity height: 3 cm (three centimeters), partner
Thanks
Yahbut, as you see, I said, 0.5 + 0.5 for those fractional dimensions. Never could figger out how you got 0.4 + 0.6, but never mind. Notice how many of the dimensions are estimates. -
#2761 by Rodal on 29 Oct, 2014 00:36
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Yahbut, as you see, I said, 0.5 + 0.5 for those fractional dimensions. Never could figger out how you got 0.4 + 0.6, but never mind. Notice how many of the dimensions are estimates.
Walkin' in Tall Cotton - Doin' Aw'right -
#2762 by JohnFornaro on 29 Oct, 2014 00:52
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Walkin' in Tall Cotton - Doin' Aw'right
Watch out my man, the trolls'll gitcha.
Ise .
Dr. John signin' out. -
#2763 by Rodal on 29 Oct, 2014 02:11
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All right. I'm a bit surprised then. Maybe not 7s but 2s seemed like possible to me (with eyeballs used to look at basic second order ringing oscillators).
Eagleworks inverted torsional pendulum response to exponentially decaying forcing functions (force in Newtons)
© Rodal 2014
The previous plots showed the torsional angular motion due those purely torsional forcing functions .
It is interesting to look at the chaotic motion of the swinging angular motion of the pendulum for the lower moment of inertia motion, due to coupled nonlinearity for the following case:
Forcing function for torsional force:
Piecewise[{{(80*10^(-6))*(1-Exp[-t/tau]),t<30},{0,t>= 30}}],tau=0.000001
Forcing function for swinging force excitation (lower moment of inertia angular direction)
Piecewise[{{(80*10^(-6))*(1-Exp[-t/tau]),t<30},{(80*10^(-6))*(Exp[-(t-30)/tau]),t>= 30}}],tau=0.000001
NOTE: the amplitude is about 1% of the previous motion, so the chaotic motion is not noticeable for this forcing function during this time period. Notice that the chaotic motion persists long after the forcing excitation has died out: a chaotic artifact due to the nonlinear equations of motion ..
...
It is fascinating that the (for the above forcing functions and time period very small amplitude ) nonlinear chaotic vibration due to nonlinear coupling of swinging with torsional modes of the Eagleworks inverted torsional pendulum (see above description and plot attached again below) resembles the chaotic calls of the the 7 years old female dog "Schaka" in this study (but with different frequencies): http://edoc.hu-berlin.de/dissertationen/riede-tobias-2000-06-26/HTML/riede-ch3.html
"Nonlinear systems display a number of typical phenomena which are briefly described here. Aperiodic (or chaotic) oscillations are characterized by irregularity, and in extreme cases there are no repeating periods at all. Period doubling (subharmonic regime) is another characteristic of nonlinear dynamical systems. It is characterized by a sudden change in the frequency of the oscillations, such that the spacing between spectral components is halved."
Eagleworks inverted pendulum time series displays similar high amplitude during the chaotic and biphonic episode of the dog:
It is interesting that Brito, Marini and Galian, in (default) Argentina, with much less money than NASA in the USA to perform their tests understood these issues (using instead an oil-damped Cavendish pendulum) when they nullified the Mach Lorentz effec Thruster. Well, hopefully Johns Hopkins will test these EM Drives with their Cavendish balance.
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#2764 by zen-in on 29 Oct, 2014 04:30
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There is no explicit mating shown in the referenced picture (reproduced below), and again you are considering the lip from only one side. There is also a contacting lip on the other side that I took into account as well as the curved recess from the other side. There is no penetration shown in this picture so you have 1 cm + 0.4 cm lip + 0.6 lip + 1cm = 3 cm depth of cavity (measured in vertical direction)
The two halves would each need an O-ring channel and some means of fastening them together if they ever hoped to pump it down to just 50 Torr, as claimed. So maybe they have two sets of drawings: One set that were used to fabricate the device and this set that appears to be fictional. -
#2765 by ThinkerX on 29 Oct, 2014 05:03
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Zen-in:
Step by step photo's with explanations as to how this device was fabricated:
http://web.archive.org/web/20121005004712/http://www.cannae.com/proof-of-concept/experimental-results/2-uncategorised/30-appendix-d
And:QuoteThe QDrive POC cavity demonstrated an unbalanced force that was approximately 2-3% of numerical method predictions for peak-force generation of the design. The POC cavity did not develop full thrust due to power limitations into the cavity. The low field energy in the cavity is related to low cavity Q and power losses in the cavity that are not related to Niobium BCS losses. The likely cause for this power loss in the cavity is related to signal-port design and port placement on the cavity.
If that helps anybody.
Does this make sense?
http://web.archive.org/web/20121102083203/http://www.cannae.com/theory-of-operation/principles-of-operationQuoteThis section will show that a radially-asymmetric, equatorially-asymmetric resonating cavity can generate a time-averaged MFF that is not counterbalanced by an equal and opposite time-averaged EFF. This imbalance in the combined MFF and EFF yields a time-averaged net imbalance in the total Lorentz force exerted on the cavity. An unbalanced force is generated.
The resonating cavity depicted in Figure 1 below is a QDrive resonating cavity capable of generating a time-averaged linear imbalance in the net Lorentz forces exerted on the cavity by operation of a TM010 EM wave within the cavity. The linear unbalanced-force vector on the cavity of Figure 1 is coincident with the z-axis of the cavity.
There are 60 identical slots located on the bottom plate of the cavity of Figure 1. The slots are located in areas of the resonating cavity that experience strong magnetic fields and weak electric fields.
figure 1
Figure 1
On the top plate of the cavity, above the slots of the bottom plate, Lorentz forces generated on the cavity walls by the magnetic field of the EM wave point in the positive z-direction. On the bottom plate, on areas of the cavity wall located between the slots (called bridges), Lorentz forces generated by the magnetic field of the EM wave point in the negative z-direction.
When operated with a TM010 EM wave, the cavity generates a time-averaged net imbalance in Lorentz forces on the cavity. The imbalance in Lorentz forces occurs because the magnetic-field, Lorentz-force pressure in the positive z-direction on the top plate is greater than the negative z-directed, magnetic-field, Lorentz-force pressure on the bottom plate.
The EFF generated by the TM010 wave operating in the cavity does not counterbalance the positive z-directed MFF. In the areas of the cavity where strong electric fields occur, the cavity is symmetrical with respect to z-directed, electric-field Lorentz forces. The cavity asymmetries occur in areas of weak electric field and strong magnetic field, meaning that the imbalance in EFF generated by these asymmetries (the slots located on the bottom plate) is negligible compared with the MFF imbalance generated by these asymmetries.
In the cavity of Figure 1, the differential in magnetic-field Lorentz forces is not counterbalanced by the differential in electric-field Lorentz forces. A time-averaged, net-unbalanced Lorentz force is generated on the cavity by operation of a TM010 EM wave within the cavity.
This one gave me a headache:
http://web.archive.org/web/20121107172136/http://www.cannae.com/theory-of-operation/conservation-laws
Part lecture in basic physics, part equations I can't grasp.
I'll finish with this:
http://web.archive.org/web/20121107172131/http://www.cannae.com/theory-of-operation/appendices
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#2766 by frobnicat on 29 Oct, 2014 09:58
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I'm assuming this was tested with internal vacuum. Or was it just frozen air that was vaporized by RF energy?Quotethe POC cavity and attached vacuum tubing are only supported by the central vacuum pipe depicted in Figure 4. The central vacuum pipe is attached to a support arm depicted in Figure 4. During experimental runs, the cavity and attached vacuum tubes are supported by two Cooper Instruments LFS 210 load cells.
....
the helium dewar depicted in Figure 4 is vacuum sealed. Pressure over the liquid helium is reduced to 50 Torre reducing its temperature to 2.3 K. Prior to experimental runs, the vacuum seal on the helium vessel is broken, bringing pressure above the liquid helium to atmospheric pressure. Tests on the cavity were then run while the liquid helium bath was below its atmospheric boiling temperature. The helium pump-down procedure eliminated boiling helium buoyancy beneath the cavity as a potential cause of false-positive experimental results.
Frobnicat: your comments would be appreciated whether the heated air artifact would be nullified by this test
I agree with Aero that it is reasonable to think the resonant cavity is evacuated, that is sealed, obviously there can't be "warm jet leaks" in such a configuration. If it wasn't sealed relative to atmosphere (eg through the innermost tubing (that also serves as the microwave power wire ?) , then the outside air would rush to condensate and fill the cavity (and give quite a lot of heat to the helium bath...)
Overall, playing with low temperatures, any dynamics in "differential temperature that creates differentials on pressures and movements of fluids, jets or otherwise" would give stronger spurious signals. A 1K temp differential would give on the order of 100 more thrust or momentum working at 3K than at 300K.
So my humble opinion : yes it would nullify a "heated air artifact" hypothesis, but at the condition it was conducted in a sensible way. And I see a lot more way to introduce hard to find artifacts by conducting those experiments tinkering with cryogenic fluids rather than in lab ambient conditions. A much much simpler way to get rid of the "warm jet hypothesis" is to make the cavity sealed (and able to withstand the few hundreds of Pascals differential the heated gas will put). I already said that (at the beginning of this thread) : as simple as possible clean setup, even with lousy thrust/power ratio (but still better than 1/c) is just the experiment all "classically educated" scientists are waiting for to give any credibility to those results. This is supposed to work at room temperature, so let's prove it does really work at room temperatures. Adding more bells and whistles to improve the thrust/power is just adding more ways to fool ourselves (well, experimenters in this case).
I won't comment anymore on this superconducting device before I see where the warm jet hypothesis is leading with Brady's report. I'm on heat propagation transients, rewriting my equations with Hagen-Poiseuille flow (leaks probably longer than wider, so orifice in thin plate is not good), trying to elucidate the microwave/water vapor coupling, and scraping the thrust vs time graphs to do some further dynamics studies (and share with anybody).
In vacations with limited connectivity, all this will take a few days.
Questions about brady's devices (anomalous...) : what was the best guests as to the thickness of copper for the walls ? what was the best guess for the thickness of copper and epoxy(?) for the PCBs closing the ends ? is it specified anywhere in those reports if the cavity is hermetically sealed or not (by hermetic I mean : should you put some soda in it, close, shake, wait an hour, open, you should hear a pshhit) ? in a cavity excited at resonance, would some parts of the walls see more power dissipated by area than others or would the power distribute evenly on all inner surfaces ?
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#2767 by frobnicat on 29 Oct, 2014 10:44
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Shawyer made an explanation years ago about how the thruster would develop less and less thrust the faster it was going, but the mechanism made no sense, and it still proposed to violate conservation, and the whole notion of velocity changing thrust is again, a violation of relativity. Velocity relative to what exactly? Made no sense and that was just before they cut his funding in Great Britain, IIRC.
Yes I saw that too on one of his papers, and then again on the latest presentation there is mention to "energy conservation" but his "efficiency decay" with speed has
1/ indeed a problem of definition (as you and aero notice : speed relative to what ?)
2/ indeed a violation of Lorentz invariance (very accurately checked so far, in lab or with astronomical sources)
3/ seemingly not much impact on his mission profiles that still give more kinetic energy at the end than was put into, by a wide margin
Handwaving "energy conservation" away that way is less than satisfying. I won't comment anymore on Shawyer's theories or mission profiles.
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#2768 by Rodal on 29 Oct, 2014 10:54
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....
This one gave me a headache:
http://web.archive.org/web/20121107172136/http://www.cannae.com/theory-of-operation/conservation-laws
Part lecture in basic physics, part equations I can't grasp.
I'll finish with this:
http://web.archive.org/web/20121107172131/http://www.cannae.com/theory-of-operation/appendices
This stuff from Cannae and from the Chinese, that one can derive from Maxwell's equations a Lorentz force imbalance is erroneous. What it shows is a lack of understanding of the stress tensor.
The paper by Egan correctly solves the problem of force balance not just for a truncated cone, but for any cavity shape (at the end of Egan's paper):
http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html
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#2769 by FITZY on 29 Oct, 2014 10:58
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Re: Frobnicat and his comments on Shawyer's mission profiles. Shawyer's "Energy conservation" attempts will be disproven, with the first free run experiments.
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#2770 by JohnFornaro on 29 Oct, 2014 11:43
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Not sure how they made the thing, but I was figuring the 1cm depth, plus a 0.5cm "lip", visible in the section and the detail. You make two of the round things, and join 'em lip to lip. (don't start with a mating call, pardner) Either you weld them together, or you mechanically fasten them with a 1cm (-) band.
Zen-in:
Step by step photo's with explanations as to how this device was fabricated:
http://web.archive.org/web/20121005004712/http://www.cannae.com/proof-of-concept/experimental-results/2-uncategorised/30-appendix-d
Damn, I'm good.
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#2771 by JohnFornaro on 29 Oct, 2014 11:51
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...as simple as possible clean setup, even with lousy thrust/power ratio (but still better than 1/c) is just the experiment all "classically educated" scientists are waiting for to give any credibility to those results.
Choose one:
1) Well duh.
2) Not gonna happen.
3) Pending weather change in Hades.Quote from: FrobIn vacations with limited connectivity, all this will take a few days.
You do this stuff on vacation? Sheesh.Quote from: Frobwhat was the best guess as to the thickness of copper for the walls?
Well I guessed 1/8".Quote from: Frobyou should hear a pshhit.
Try to express yourself without using profanity.Quote from: Frobwould the power distribute evenly on all inner surfaces?
I don't see how, what with the completely assymetrical location of the M/W feed horn.
Oh. And, nice short post there Fitzy. -
#2772 by JohnFornaro on 29 Oct, 2014 11:55
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"super insulation" is added by SuperGenious:
Me not get it, Kemosabe.
Plus, what is that piece of scientific equipment in the lower right? The black, roughly rectangular object with the light colored cylindrical object. Not sure I recognize it.
Technical note: Reduce the dimensional size of the image. It spanned four screens here at the fornaro compound. -
#2773 by Notsosureofit on 29 Oct, 2014 11:57
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....
This one gave me a headache:
http://web.archive.org/web/20121107172136/http://www.cannae.com/theory-of-operation/conservation-laws
Part lecture in basic physics, part equations I can't grasp.
I'll finish with this:
http://web.archive.org/web/20121107172131/http://www.cannae.com/theory-of-operation/appendices
This stuff from Cannae and from the Chinese, that one can derive from Maxwell's equations a Lorentz force imbalance is erroneous. What it shows is a lack of understanding of the stress tensor.
The paper by Egan correctly solves the problem of force balance not just for a truncated cone, but for any cavity shape (at the end of Egan's paper):
http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html
Yes, that's a really nice exposition. I only wish he had taken it one step further and showed that the imbalance in an accelerating frame of reference is equal to the "weight" of the photon energy. -
#2774 by Ron Stahl on 29 Oct, 2014 12:20
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Dr. White made the same kind of mistake when describing his version of warp. Originally he claimed that his warp notion would essentially provide a "warp boost" that allowed craft to multiply their velocity. So warping spacetime around a craft moving 500 kps could allow it to go 5,000 kps. The trouble came when he was asked what velocity to use. Since velocity is relative, what he was describing was impossible. These kinds of blunders are why you don't want people without adequate training doing your gravity physics for you.Shawyer made an explanation years ago about how the thruster would develop less and less thrust the faster it was going, but the mechanism made no sense, and it still proposed to violate conservation, and the whole notion of velocity changing thrust is again, a violation of relativity. Velocity relative to what exactly? ...snip...
I agree with that. His explanation seemed to me to require the thruster to remember the reference frame at the time of "Power on" and limit itself to accelerations that conserved everything. Maybe he was saying something else but if so, it was very obscure to me.
I don't know about his funding. -
#2775 by zen-in on 29 Oct, 2014 13:01
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Zen-in:
Step by step photo's with explanations as to how this device was fabricated:
http://web.archive.org/web/20121005004712/http://www.cannae.com/proof-of-concept/experimental-results/2-uncategorised/30-appendix-d
Yes, that makes more sense. The diagrams I have seen up til now would not work. But the dewar construction looks like it would result in a low hold time (length of time before all the Helium has evaporated) because there is too much thermal leak from the liquid Nitrogen to the liquid Helium. It's also very hard to differentiate between the thrust created by escaping cryogens and thrust created by an em effect. -
#2776 by frobnicat on 29 Oct, 2014 13:01
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...
Sorry, I re-checked the code because that statement about the 7 sec didn't make sense to me and I found an error on my definition of the exponential function (I had the variable "time" instead of "t" which mean different things in my code. I'll be back with the correct result
Yes, any tau>0.2 sec is clearly discernable.
For tau ~ 1 sec the difference is unacceptable
I'll post some pictures tomorrow after I double check everything. I need to do some work for which I get real $$$ first
All right. I'm a bit surprised then. Maybe not 7s but 2s seemed like possible to me (with eyeballs used to look at basic second order ringing oscillators).
Eagleworks inverted torsional pendulum response to exponentially decaying forcing functions (force in Newtons)
© Rodal 2014
Piecewise[{{(80*10^(-6))*(1-Exp[-t/tau]),t<30},{0,t>= 30}}],tau=0,0.5,1,2,3
Piecewise[{{(80*10^(-6))*(1-Exp[-t/tau]),t<30},{(80*10^(-6))*(Exp[-(t-30)/tau]),t>= 30}}],tau=0,0.5,1,2,3
Piecewise[{{(80*10^(-6))*(1-Exp[-t/tau]),t<30},{(80*10^(-6))*(Exp[-(t-30)/tau]),t>= 30}}],tau=2
Okay, I see, even with short rise times there is not enough "hit" to ring the bell, so to speak.
Note to John: I'm trying hard to express myself without using profanity but remember I'm operating on a non native language here, so my "English emulated mode" is both slower and might appear clumsy, or even "syntax erroneous" at times. I hope the ideas get through.
I still see a qualitative difference in the graphs Obs(t) though : the amplitude of ringing seem to imply a very fast rising time, but we see in your simulated curves that the first ridge of the ringing (the overshoot) is farther to the later stable level of .00001 than the second ridge. First overshoot is .000005 above, second is less than .000003 below (black curve, tau = 0). In the experimental graphs, figure 19, matter is complicated by the drifting baseline but this magnitude difference (relative to the "flat" level after) is not at all seen for the thrust pulses, while it is seen (more or less) for the calibration pulses where we are sure the rise time tau is 0.
If going to the third ridge (sorry this is impractical for me to draw pictures right now) that is the second ringing above (that is, one natural period after the initial overshoot), this second overshoot above is much lower the first (say .000005 for the first, 0.0000015 for the second). Again this is far from obvious in the experimental graphs of figure 19. while it appears more clearly (not perfectly) for the calibration pulses.
On the experimental graphs, If I try visually (I know, this can be misleading) to smooth out the ringing, then I see a ramp-up of the order of one period before reaching the plateau. Hope you see that. How comes ? From the amplitude of ringing, your simulations show we should have a "hit", almost instantaneous excitation to near nominal magnitude. But my visual impression (to be studied more quantitatively) would imply something is rising more slowly, with a tau of 2s or so. Could it be that we have for Fb(t) the sum of a rectangular component of near nominal magnitude (say 75%) + a smaller component (say 25%) of tau =2s ? We already know we have a rectangular pulse component of about 10% with the DC power (at 5.6 Amps)... before we embark on why there would be on top of that a 65% fast rectangle + 25% slower rate "charge/discharge" pulse : I'd like to see, since you have the tools at hand, what shape you have with 0.75*pure_rectangle(t) + 0.25*exp_charge_discharge(t) with various tau as you did (and maybe also trying the relative weights 0.5 0.5 and 0.9 0.1) That would make for 3x5 = 15 curves to sieve through
I owe you abearbeer for the surprise of your simulated results, and learning of the explicit term "dynamic amplification factor"
Concerning the chaotic components, you say that they are 1% of the amplitude of the main modes, do you agree we have quite a lot to explain (in the experimental curves) as main mode responses first before seriously taking that into account ? Also, concerning the principal behaviour of the system (that likely gives 95% of the recorded signal) would you say it is nonlinear ? How far is it from a simple slightly underdamped harmonic oscillator of the form d²x/dt² + 2*damp_ratio*omega0*dx/dt + omega0²*x = 0 ? Would you mind sharing your model's equations ? I'm ready to sign a NDA if you wish...
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#2777 by JohnFornaro on 29 Oct, 2014 13:15
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I'm trying hard to express myself ...
It was an onomatopoetic joke, youngster! You da man! -
#2778 by Rodal on 29 Oct, 2014 13:22
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...
Sorry, I re-checked the code because that statement about the 7 sec didn't make sense to me and I found an error on my definition of the exponential function (I had the variable "time" instead of "t" which mean different things in my code. I'll be back with the correct result
Yes, any tau>0.2 sec is clearly discernable.
For tau ~ 1 sec the difference is unacceptable
I'll post some pictures tomorrow after I double check everything. I need to do some work for which I get real $$$ first
All right. I'm a bit surprised then. Maybe not 7s but 2s seemed like possible to me (with eyeballs used to look at basic second order ringing oscillators).
Eagleworks inverted torsional pendulum response to exponentially decaying forcing functions (force in Newtons)
© Rodal 2014
Piecewise[{{(80*10^(-6))*(1-Exp[-t/tau]),t<30},{0,t>= 30}}],tau=0,0.5,1,2,3
Piecewise[{{(80*10^(-6))*(1-Exp[-t/tau]),t<30},{(80*10^(-6))*(Exp[-(t-30)/tau]),t>= 30}}],tau=0,0.5,1,2,3
Piecewise[{{(80*10^(-6))*(1-Exp[-t/tau]),t<30},{(80*10^(-6))*(Exp[-(t-30)/tau]),t>= 30}}],tau=2
Okay, I see, even with short rise times there is not enough "hit" to ring the bell, so to speak.
Note to John: I'm trying hard to express myself without using profanity but remember I'm operating on a non native language here, so my "English emulated mode" is both slower and might appear clumsy, or even "syntax erroneous" at times. I hope the ideas get through.
I still see a qualitative difference in the graphs Obs(t) though : the amplitude of ringing seem to imply a very fast rising time, but we see in your simulated curves that the first ridge of the ringing (the overshoot) is farther to the later stable level of .00001 than the second ridge. First overshoot is .000005 above, second is less than .000003 below (black curve, tau = 0). In the experimental graphs, figure 19, matter is complicated by the drifting baseline but this magnitude difference (relative to the "flat" level after) is not at all seen for the thrust pulses, while it is seen (more or less) for the calibration pulses where we are sure the rise time tau is 0.
If going to the third ridge (sorry this is impractical for me to draw pictures right now) that is the second ringing above (that is, one natural period after the initial overshoot), this second overshoot above is much lower the first (say .000005 for the first, 0.0000015 for the second). Again this is far from obvious in the experimental graphs of figure 19. while it appears more clearly (not perfectly) for the calibration pulses.
On the experimental graphs, If I try visually (I know, this can be misleading) to smooth out the ringing, then I see a ramp-up of the order of one period before reaching the plateau. Hope you see that. How comes ? From the amplitude of ringing, your simulations show we should have a "hit", almost instantaneous excitation to near nominal magnitude. But my visual impression (to be studied more quantitatively) would imply something is rising more slowly, with a tau of 2s or so. Could it be that we have for Fb(t) the sum of a rectangular component of near nominal magnitude (say 75%) + a smaller component (say 25%) of tau =2s ? We already know we have a rectangular pulse component of about 10% with the DC power (at 5.6 Amps)... before we embark on why there would be on top of that a 65% fast rectangle + 25% slower rate "charge/discharge" pulse : I'd like to see, since you have the tools at hand, what shape you have with 0.75*pure_rectangle(t) + 0.25*exp_charge_discharge(t) with various tau as you did (and maybe also trying the relative weights 0.5 0.5 and 0.9 0.1) That would make for 3x5 = 15 curves to sieve through
I owe you abearbeer for the surprise of your simulated results, and learning of the explicit term "dynamic amplification factor"
Concerning the chaotic components, you say that they are 1% of the amplitude of the main modes, do you agree we have quite a lot to explain (in the experimental curves) as main mode responses first before seriously taking that into account ? Also, concerning the principal behaviour of the system (that likely gives 95% of the recorded signal) would you say it is nonlinear ? How far is it from a simple slightly underdamped harmonic oscillator of the form d²x/dt² + 2*damp_ratio*omega0*dx/dt + omega0²*x = 0 ? Would you mind sharing your model's equations ? I'm ready to sign a NDA if you wish...
Well, there is a lot to answer there. But what do you think of just modeling the impulse as a trapezoid ?
That means: a linear rise from zero at t=0 to f1 at t=t1, then a slower linear rise from f1 to f2 at t2, and then a linear fall from f2 to zero at t3?
then we can plot several trapezoids, essentially I agree that the rise to f1 is fast, followed by a slower rise to f2
From your writing I think you are seeing actually a more complicated picture, but both of us are patient (unlike others in this forum) so we could try to understand the behavior to this trapezoidal impulse first.
Concerning the chaotic motion, I find that intellectually interesting, perhaps I'll write a paper about it.
Yes, the chaotic motion for the simple impulses we studied so far is only 1%, but it is apparent to me that these researchers (and others in this field) have not taken into account nonlinear dynamics. (If they don't have mathematical model for it, they cannot take it into account).
The interesting thing about a nonlinear dynamic system is that it may show up when people don't expect it (and they will assume that what they measure is real when it may be a "strange attractor" from the nonlinear dynamics of the inverted pendulum). Certainly they don't understand it.
Since this forum is mainly aerospace engineers, a bad (because in this case we have strange attractors and not just instability) analogy would be of an airplane with aluminum wings in a swept-forward design. We know that at certain speeds it is going to experience divergence or flutter instability. The situation with this inverted pendulum would be like such a swept-forward wing airplane flying naively thinking everything is fine because they did preliminary runs and they didn't suffer any instability. -
#2779 by Ron Stahl on 29 Oct, 2014 15:23
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2) NASA Eagleworks, the Chinese, Cannae, and Shawyer (except his demo) have made measurements on constrained systems. None of the researchers have analyzed their measurement systems to analyze whether indeed conservation of momentum is being violated. The closest experiment to a violation of conservation of momentum is Shawyer's demo experiment, but again, the EM Drive demo is restrained and the whole setup is rotating instead of linearly accelerating. No linear acceleration of the center of mass was measured and the measurement system was not analyzed.
It's probably worth noting that Woodward has measured the acceleration of the center of mass in his setup. He did that last Fall when he received feedback from the Aero Corp about their concern that displacing the center of mass could have caused his readings but he and Dr. Heidi Fern showed conclusively this is not true by actually measuring that displacement. He could have done this more accutrately with a laser vibrometer but the method he used was certainly sufficient.
