@WarpTech - I looked at your pdf.Einstein's ghost will bite you in the neck while you sleep.Force cannot depend on velocity.

Todd

@Rodal:Is it possible with this data to confirm or deny the correctness of 2*P/c versus 2*P/v_{g}?

Quote from: deltaMass on 07/14/2015 11:59 PM@WarpTech - I looked at your pdf.Einstein's ghost will bite you in the neck while you sleep.Force cannot depend on velocity.Okay, Okay, Okay, I found the confusing part. I hope everyone is listening. I'm sorry that I've probably made the confusion worse, not better. What is causing the confusion (for me anyway) is the reference frame of the problem. The equations I wrote down were all done from the perspective of an observer in the inertial reference frame from where the vehicle started at rest, with a fully charged battery. I did "everything" from that reference frame. However, the value of thrust-to-power in this frame is not what is being specified in the paradox, which was my misunderstanding. What should have been specified explicitly, which I failed to understand, is the use of the rocket equation to calculate k. In that equation k is not arbitrary. It depends on the exit velocity of the propellant in the frame of the rocket! When the problem is formulated as such, the thrust-to-power ratio IS constant, in this frame. See attachment 1.I failed to understand that the thrust depends on the velocity at the exit of the rocket. The c^{2} in the denominator cancels the 16 orders of magnitude that @deltaMass was saying made the power used have negligible mass. On the contrary, the majority of thrust is due to the mass, because the k value is so small! See attachment 2.It is the assumption that is made, where k is arbitrarily large, when it is in fact very small because the exit velocity must be less than c, that causes the over-unity paradox.I got confused by Eout = 0.5*m*v^{2}, because in the frame of the rocket, v=0. So I was thinking that v was measured as the instantaneous velocity in the frame of an inertial observer. It is not. It is measured, as I've been told, as v=a*t, in the frame of the rocket. My mistake.So, thanks for the education. I apologize for confusing people and I hope my mistakes can be forgiven. Live and learn.Todd

We continue the program started with posts ____________________________[img]https://upload.http://forum.nasaspaceflight.com/index.php?topic=37642.msg1403629#msg1403629 http://forum.nasaspaceflight.com/index.php?topic=37642.msg1404000#msg1404000http://forum.nasaspaceflight.com/index.php?topic=37642.msg1404004#msg1404004http://forum.nasaspaceflight.com/index.php?topic=37642.msg1404005#msg1404005http://forum.nasaspaceflight.com/index.php?topic=37642.msg1404006#msg1404006showing for the first time (this has not been previously shown anywhere else) what the stress (force/unitArea) on the Big Base looks like.The stress tensor is obtained using Wolfram Mathematica, post-processed from the transient Finite Difference (using Meep) solution for RF feed ON for an EM Drive.Notice that the stress at the Big Base is pointed in the direction from the small base towards the big base, as required for a recoil motion to take place and accelerate the EM Drive in the opposite direction, towards the small base. This is in accord with Dr. White and Shawyer. (It may also work with conventional microwaving of moist air resulting in plasma ions leaking out of the EM Drive or stressed axionic dark matter for example ) However, the stress is not uniformly distributed through the big base (at least for the mode shape TM11 excited in this example) but instead it is distributed mainly in the circumferential outer periphery of the Big Base.The stress at the Big Base is similar to the one shown at section x=38 near the Big Base, previously shown in this post http://forum.nasaspaceflight.com/index.php?topic=37642.msg1404000#msg1404000, except that the stress is significantly higher and much concentrated at the copper and much less at the center of the Big Base. ... snip ...

Your great enlightenment (what, number ten is it now in the series of consecutive samadhis?) is unfortunately not shared by me, despite its clearly blinding power over the transformation of your logics. It must be fun in there.Look: EmDrive is not a rocket, which is why we call it propellantless. Dear Tsiolkovsky had the right of it when he defined exhaust velocity as an invariant when measured with respect to the rocket. Such luxury you do not have because you have no exhaust to manipulate here.Additional to that misunderstanding (masquerading in your mind, apparently, as a revelation) comes your further misunderstanding that 'v' is relative to the EmDrive. The 'v' used in my proof, clear to most I should have thought, is defined with respect to the original inertial frame in which motion began. In no way should you attempt to interpret it as you now have as relative to the EmDrive itself, for that is not how it is defined in my proof.

The group velocity in a waveguide is by definition; vg = dw/dk, correct?

In other words, apparently EM waves in a waveguide behave differently than matter in a rocket, in this regard.Or am I botching it again? Todd

We are seeing evanescent waves in these images! The power diminishes (exponentially?) as the waves move from front to back. After each reflection, the poynting vectors that hit the wall give up some momentum to the frustum pushing it forward, and redirect themselves more toward the x direction. After each bounce, the vector loses momentum and energy due to heat from copper losses. The less energy and momentum it has when it arrives at the big end plate, and the lowest angle of incidence that can be achieved, the more thrust will be harnessed. Makes me think that "Brass" used by Juan Yang may be better than copper. It's resistivity is 5x higher, and a superconductor may not work as well. Based on this, longer and less taper is better, but I have not calculated an optimum design factor yet.Todd

Even with very modest k (say 10^{-6} N/W) one can achieve excellent mission performance when lots of power is available. Let's go to Pluto (40 AU, 100 Kg). With 1 MW power it takes 1.1 years and maximum speed is 0.1%c.

Because of the waveguide's taper, the expanding wavefront's frequency drops with each consecutive reflection. As the frequency shifts, that extra momentum is once again transferred into the frustum in the form of Radiation Pressure By Reflection.

The Group Velocity and Guide wavelength change as the tapered waveguides diameter changes. The EM waves frequency (Guide Wavelength) doesn't change because of the end plate bounce.

Quote from: TheTraveller on 07/15/2015 06:29 AMThe Group Velocity and Guide wavelength change as the tapered waveguides diameter changes. The EM waves frequency (Guide Wavelength) doesn't change because of the end plate bounce.WarpTech's frustum doesn't have an end plate.

Quote from: tleach on Today at 06:22 AMBecause of the waveguide's taper, the expanding wavefront's frequency drops with each consecutive reflection. As the frequency shifts, that extra momentum is once again transferred into the frustum in the form of Radiation Pressure By Reflection.

This Redot model is the 5011 (specifically for 2.4 GHz), not the 1050A (specifically for 100 - 500 MHz).

Quote from: SeeShells on 07/14/2015 11:58 PMWould anyone be interested that would model a perforated copper sheet for me in meep?I'll post the specs of the sheets and angles to run at.ShellExcellent point. There is no fundamental problem whatsoever in modelling this in Meep. This is what FD and FE programs are for. It is a pre-processing problem. It requires for somebody to write a pre-processing mesh routine to locate copper and holes in a grid with holes in them. The number of nodes required to do this will be much, much larger than the present number of nodes used, and therefore the amount of computer memory and computer time will be much larger.Another way to handle this (not requiring a different mesh than presently used) would be to use an equivalent constitutive model for the copper with holes (letting wavelengths small enough pass through holes and large wavelengths not pass through, and distributing this wavelength dependence at every node in an average sense). For example, one may start by modeling a problem with a known exact solution, either a rectangular or cylindrical cross-section cavity of smaller dimensions, modeled with and without the perforated holes to see what difference it makes if any, and if it makes a difference, work out a model for the copper with holes using an equivalent model with copper with no holes for the truncated cone. Theoretical and/or experimental papers on the effect of perforation on microwaves waveguides would be very helpful for this. The simplest thing is to refer to papers and ascertain whether the effect of the small wavelength is negligible and henceforth deduce that the effect of the holes is negligible.The practical problem of holes is lack of stiffness, and this compliance leading to distortion that may affect the Q. If these effects are of interest, I would start by modeling the hexagonal cross-section and see what difference that makes. (The hexagonal model will take much less computer resources than modeling the holes).

Would anyone be interested that would model a perforated copper sheet for me in meep?I'll post the specs of the sheets and angles to run at.Shell

since we know that the total power transmitted through the waveguide is P = vg U / L (vg is the group velocity, L is the waveguide length and U is defined as before [ U is the total energy of the electromagnetic fields])