The voltage and current "from the supply" is NOT the voltage and current stored in the LC oscillator or inside the frustum. The Supply current is not the Circulating current, they are two different loops in the Mesh diagram. The LC oscillator is NOT a resistor. You are confusing the voltage and current "from the supply", with the voltage and current "inside the oscillator". Inside the oscillator, they are 90 deg out of phase if resistance losses are neglected.
At resonance there are no external reactive components of the load and the LC circuit looks to the generator as a resistor.
The Eagleworks torsion pendulum
Doing some calculations, I realised how little we know about the measurement device the Eagleworks team used. Below, I do some estimations and calculations.
What I should like to know, are: moment of inertia, resonant frequency, how much does the frustum moves at a given force, dynamic response.
Information we have: internal dimensions of the vacuum vessel (914 mm long) [Brady et al., 2014; White et al., 2016], mass of the complete frustum system (9.3 kg) and figures from which we can estimate the frequency of the pendulum.
Calculation of the moment of inertia (MoI):
- the pendulum arm, if symmetrical, can be at most ~ 900 mm long. But you have to subtract at least the radius of the frustum (including flange ~160 mm), so the centre-of-gravity of the frustum is then at 900-160)/2 = 370 mm mm from the centre of rotation.
- The mass of the frustum and counterweight are given, e.g., in the attached figure [1]: 9.3 kg with a counterweight of 8 kg (OK, it is probably a bit asymmetrical, but we need only orders of magnitude).
⇨ I = 2 x (0.37^2 x 9.3) ≈ 2.5 kg m^2
the torsion pendulum beam and several parts will give a little contribution, maybe 0.1 kg m^2 in total, so say
I total = 2.6 kg m^2
In the first figure a number of calibration pulses are given [F1]. It can be seen that in this configuration the system is a little overdamped (bigger damping than critical, because it has no ‘overshoot’).
In some other figures overshoots after a stepfunction force can be seen. [F2] for instance, a measurement with a dummy load, shows some ringing which points to a slightly underdamped system. Probably this is because the MoI of the pendulum was less than in the configuration with the full frustum.
From this figure [2] a period of ~ 4 s can be estimated (neglecting the influence of damping).
However, in this configuration the frustum seems to be not present, only a big fat dummy load and a weight (1 kg?). So let’s suppose on both sides there is a mass of 3 kg (at distances of 0.4 m from the centre of rotation), this gives a MoI:
I = 2 x (0.37^2 x 3.0) = 0.8 N m rad^-1
Together with the calculated MoI above, the torsion constant can be calculated:
K = 2.0 N m rad^-1. From some other figures [e.g., F3], the pendulum frequency seems to be closer to 5 s, then I = 1.3 N m rad^-1, so let’s say
K (the torsion constant) = 1.7(3) N m rad^-1 .
This torsion constant corresponds to a steel wire of 5 mm diameter (k = πGd^4 / 32l [ref?]). Quite a thick ‘torsion wire’, but White et al. refer to it as a ‘flexure bearing’, which seems quite justified.
angle of rotation = force x arm length/K, approx. angle = tan(angle) = displacement/arm length
⇨ displacement @ a force of 65 µN ≈ 5 µm
That aint much. I guess (from the figures) the optical displacement sensor has submicrometer resolution (but we don’t know the type).
Are these numbers approximately correct, Paul?
References
Brady et al., 2014.
White et al., 2016.
Attached figures (I think they all come from Paul March / Star-Drive)
[F1] August 18, 2015_Copper Frustum Forward & Reverse Tests_9.3kg Integrated Copper Frustum Test Article with 8kg Counter Balance Force Calibrations.jpg
[F2] Eagleworks_dummyloadtest.jpg
[F3] TE012NoDielectric.jpg
As many of you know, SSI hosted the Estes Park Breakthrough Propulsion Workshop last September 20-22, 2016. At that time we said that videos and presentation materials would be available at the SSI site and on YouTube in early December. Thanks to the efforts of our volunteer audio-visual team (Robert Smith, SSI Chief Archivist and Evangelist and Robin Snelson, SSI Executive Director), plus Drs. Heidi Fearn and Lance Williams, among others, we have met that self-imposed deadline. Thanks to all concerned!
The link: http://ssi.org/ssi-releases-bpw2016-videos/
Videos will be posted in sequence over the next few days. PDFs of papers and presentations will be available on the SSI site in a few weeks, and we should be able to generate hardcopy books of the proceedings by early next year for those who are interested.
Thanks again for your patience. I hope Chris Bergin will forgive a minor plug for SSI donations, as well. For those who are interested, go to our home page at www.ssi.org and select your favorite project from the sidebar.Thank you for hosting the Advanced Propulsion workshop, Thank you for inviting me.
It took me a week, to calm down and be able to sleep all night without waking up at 3AM and going, "OMG, it makes sense". Quite sure after refreshing and renewing my memory with your videos, I'll be in the same pattern for another week. Not complaining, but thanking you for being hosts for a fantastically brilliant group dedicated to the next giant leap for mankind.
My Very Best,
Shell
Your not holding constant the power your feeding in which equals the losses. I thought the point of using a superconducting cavity was to store more power for the same amount of power fed in.
If you change your input power when you change Q then your stored power Energy may stay the same. Power loss=power supplied [Q(w)*9]*[power_supplied*(1/9)]/w=(Maximum_Energy_Stored)
Dustin,
Cavities store energy and not power.
...
Well, I wouldn’t bet on that. All the em wave models up to now are based on E and B alternatively shaking hands in a perfectly “empty” vacuum. Now, we know better. The vacuum is an electromagnetic tissue, a medium. It is therefore more likely that the em waves are actually gliding as a travelling variation in one property of the medium, like all the other waves we know. .. Time to update the model to fit Casimir and all other clues we have about this medium.
From the start I knew the vacuum was not empty. Logically, how can “nothing” have properties like permeability and permittivity? (and half a dozen more properties..)
Food for thought...
2b. A = Grad(Phi). We don't know what the Grad(Phi) is, inside the frustum as a function of time or position. I can't say it is a solution or not since I don't have a function for it, only that this is the type of solution we are looking for. I can assume that over a small enough region, it will hold but I don't have an exact solution. Only these general equations.
Ok. And how is the magnetic field related to A?
"A" can be a superposition of vector fields, both rotational and non-rotational. "B = curl(A)", "E = -dA/dt". "Phi = Integral(A)ds", where "s" is a closed path around the flux being measured. There are many ways the field "A" can be expressed. From the color plots produced by the modelers, we can estimate "A" from "E". That is the easiest way to visualize it for me. In QM, the 4-vector field Au is the EM field, and Maxwell's equations are derived from it. In the Lorenz gauge, <|duAu|> = 0, is generally covariant.
I don't know your level of understanding of these things. Some of your statements imply you are well versed in Maxwell's equations, but others show you're not so familiar with the electrical engineering terms that I use. What is your level of EM Theory and QM comprehension? I do not consider myself an expert, but rather someone with a good intuition and knows just enough of the Math to be dangerous.
If B=curl(A) and A=Grad(\Phi), then B=0 (this is just a vector calculus identity which holds for any twice differentiable scalar field \Phi).
I'm (astro)physicist so engineering terms and to some extent notation is unfamiliar to me.
The Eagleworks torsion pendulum
Doing some calculations, I realised how little we know about the measurement device the Eagleworks team used. Below, I do some estimations and calculations.
....
K (the torsion constant) = 1.7(3) N m rad^-1 .
This torsion constant corresponds to a steel wire of 5 mm diameter (k = πGd^4 / 32l [ref?]). Quite a thick ‘torsion wire’, but White et al. refer to it as a ‘flexure bearing’, which seems quite justified.
angle of rotation = force x arm length/K, approx. angle = tan(angle) = displacement/arm length
⇨ displacement @ a force of 65 µN ≈ 5 µm
....
Peter,
In response to a previous post of mine, Paul posted a pdf datasheet for the Bendix style flexures. The spring constant is listed at 0.007 lb-in/deg. I assumed that EW used two of them, one at the top and one at the bottom, for a combined spring constant of 0.014 lb-in-deg. With this in mind I used the EW calibration pulse of 29 Newtons and the resultant displacement of 2 uM to determine the achieved spring rate. My result was 0.32 lb-in/deg which disagreed significantly with the flexure assumption. I concluded that I either made a mistake or that the purposeful gravity pendulum that EW set-up to "stabilize" the apparatus was the majority contributor to the system's torsional response. I considered the magnetic damper's effect but since the cal pulse appeared to reach its final flat-top value, the damper's contribution was negligible.
Dan
Per request by Harold White, they will not be presenting a video by Paul March. Go figure...
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All of the operators in your diagram must send the cue balls back to their original position. Maybe you could provide a sketch showing how they do this while "deliberately not scattering" the momentum of the cue balls on the return trip.
I don't think it can be done.
Something you need to understand, is that the definition of conservation of momentum means that any time you get net motion through a setup like this, it means you made a mistake.
In this case, it seem that you don't understand that momentum is a vector quantity. When the ball with momentum X hits the 2 balls and send them off at 45 degree angles, each of the other 2 balls will have momentum X/sqrt(2), not X/2. This is because the horizontal component of momentum for each is X/2 in order to conserve momentum in that direction. Work this through to the end, and you'll see no pressure difference.
(To determine the angles they will go at, you need to apply energy conservation, in this case with equal mass balls, opposing 45 degrees angles with the original ball coming to a complete stop is the right answer for a perfectly elastic collisionn.)
IAC, Adelaide, Australia, Sept, 2017
Hi Guys,
I'm very seriously considering setting up an exhibit booth, so to demo my non cryo S band thruster happily spinning and accelerating on a rotary test rig during the conference.
Will any of you guys be going and/or will any of you have a product in the market by then?
All the best,
Phil
of course assuming my health will support that plan
A photon rocket is not a gradient in an effective potential energy per kg of field mass. So I'd have to say, no. Thrust in this theory depends on the field mass and the potential gradient it can fall through from one end to the other, and/or from one time to another.
If you find my use of the term "momentum" wrong because I pair it with a direction and that sounds redundant because momentum includes a direction, then I see lots of sources using phrases like "forward momentum", even physics lessons; but if that's not enough for you, then please feel free to substitute in the word "push" or something like that where I use "momentum". If "X/sqrt(2)" means "divide X by 1.41...", then my point will remain the same, since the quotient will still be smaller than X. ...
-- those two balls inevitably took that momentum away from the cue ball's momentum, and, if conservation of energy is to hold, then rightward momentum has overall been reduced?
(To determine the angles they will go at, you need to apply energy conservation, in this case with equal mass balls, opposing 45 degrees angles with the original ball coming to a complete stop is the right answer for a perfectly elastic collision.)
This sounds like what my example says (and then those two balls travelling in opposing 45 degree angles likewise hit two more balls each, which are in turn likewise positioned so they travel in opposing 45 degree angles to the trajectories of the balls which hit them). If you ddin't intend it to concur with my example, then could you please provide more detail, maybe a diagram?
Two important news announced publicly by Dave elsewhere.
First, the sad news:Quote from: rfmwguyPer request by Harold White, they will not be presenting a video by Paul March. Go figure...
By "they" Dave means the Space Studies Institute and by the "video" he means Paul's presentation at the Estes Park Breakthrough Propulsion Workshop on 21 September 2016.
Paul retired from Eagleworks at the end of September. Before or after the workshop?

Two important news announced publicly by Dave elsewhere.
First, the sad news:Quote from: rfmwguyPer request by Harold White, they will not be presenting a video by Paul March. Go figure...
By "they" Dave means the Space Studies Institute and by the "video" he means Paul's presentation at the Estes Park Breakthrough Propulsion Workshop on 21 September 2016.
Paul retired from Eagleworks at the end of September. Before or after the workshop?
The video will be available, but our disclaimer is it represents Paul's personal views and not NASA's. No JSC Eagleworks endorsement is expressed or implied.