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#160 by Star One on 09 Aug, 2015 19:31
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Also that they've now built an experiment to help prove the theory to detect an effect people might have never imagined before this could have existed.
I can't find any details on such an experiment. Link, please?
It's in the link I originally posted on this topic up thread.
Posted again for ease of reference.
http://motherboard.vice.com/read/there-is-growing-evidence-that-our-universe-is-a-giant-hologramQuoteThe actual experiment that will decipher this involves measuring the relative positions of large mirrors separated by 40 meters, using two Michelson laser interferometers with a precision 1 billion times smaller than an atom. If, as according to the holographic noise hypothesis, information about the positions of the two mirrors is finite, then the researchers should ultimately hit a limit in their ability to resolve their respective positions.
“What happens then?” Lanza said. “We expect to simply measure noise, as if the positions of the optics were dancing around, not able to be pinned down with more precision. So in the end, the experimental signature we are looking for is an irreducible noise floor due to the universe not actually storing more information about the positions of the mirrors.”
The team is currently collecting and analyzing data, and expects to have their first results by the end of the year. Lanza told me they are encouraged by the fact that their instruments have achieved by far the best sensitivity ever to gravitational waves at high frequencies.
“The physics of gravitational waves is unrelated to holographic noise, however, the gravity wave results demonstrate that our instrument is operating at top notch science quality, and we are now poised to experimentally dig into the science of holographic noise,” Lanza said.
You can find more details & relevant links here.
http://www.sciencedaily.com/releases/2015/04/150427101633.htm
Here's the paper.
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.111602 -
#161 by X_RaY on 09 Aug, 2015 19:37
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The russian patent is hard to read even with automatic translation, but quite interestingJust to bring it back to the surface : is any one going to try with Matglas 2714A at the big end?
To see if extreme magnetic permeability has any impact on EMdrive performances?
If too expensive, a second option would be an iron plate ( as noted on the wiki list : (99.95% pure Fe annealed in H) )
This is particularly suitable for TE (transverse electric) modes, because they have a magnetic field in the axial direction. Thus it may be something that SeeShells may want to consider if she succeeds in exciting a TE mode.
TE modes ==> particularly suitable to a ferromagnetic end
TM modes ==> particularly suitable to a dielectric end (as used for example by NASA Eagleworks)
µ, epsilon dependence make sense
The same like in the picture for the E-field is true for the H-field using high µ_r
I remember there was a discussion based on permeability and susceptibility and losses in the last thread.
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#162 by Rodal on 09 Aug, 2015 19:56
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You have the exact solution for E and H in a frustum cavity. Simply plug in the E vector into equation 9,
kr = j*(1/E)*dE/dr
where E is the electric field vector, all 3 components, which you already have in Mathematica. I think it should be just a few lines of code to take the derivative of a vector you already have, and multiply by the inverse.
My solution is in terms of real valued functions (Spherical Bessel functions), while Zeng and Fan used the complex-valued spherical Hankel functions (or Spherical Bessel functions of the third kind -same thing-).
A complex valued solution is needed to separate the real and imaginary terms alpha and beta. So I would need to spend the time to re-cast the solution in terms of complex-valued Spherical Hankel functions (or Spherical Bessel functions of the third kind -same thing-). To do this I would need to review Hankel functions (I think that they are usually used for theoretical work to express outward- and inward-propagating wave solutions of the wave equation) and make sure that all the terms are correct, including defining factors.
***************
I still think that you can use Zeng and Fan's results, the only difference is that you have to multiply the results in Fig 2 and Fig 3 by Sin[θ] to get the momentum component in the longitudinal direction, but I haven't checked this. -
#163 by Ricvil on 09 Aug, 2015 20:26
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In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because Sr = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the k-vector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to re-derive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
Yes Dr Rodal, to me Zeng and Fan don't write the correct expressions for the problem of propagation on a tapered conical waveguide.
One way is solve the helmoltz equations respecting directly the physical boundary conditions under the geometry of problem.
This will implies that standard solutions of wave equation in spherical coordinates ( in general, bessel and legendre functions of integer order), must be subtituted by specific solutions with fractionary order legendre/ bessel functions.
Other way, more complicated, is find solutions using the called "coupled-mode theory in instantaneous eigenmode (quasimode) basis ", where one can use a superposition cilindrical modes, evolving a coupled-mode equation along the longitudinal axis of propagation, where each cilindrical mode has a instantaneous dependence on the radii of tapered section of conical waveguide.
Of course, there are many others forms to solve this problem.
I set to bold because, to my understanding, this is precisely what they did. Look at equations 2 & 3, and the associated text that follows it, through to equation 8. This part of their work is not that difficult to follow, so I don't see precisely where they make any error or assumptions that would cause it to be wrong. Their answer includes everything you just said, and the derivatives are Hankel functions of "fractional order". Where is the error?
Todd
Sorry Todd, Dr Rodal and all people from this forum.
My fault. The zeng and fan field solutions are correct and the table 1 shows the order of associated legendre/bessel functions for some values of cone angle thetazero.
But together,the definitions in ( 8 ), (9) , (10), (11), (12), (13), and (14) make no sense to me.
A "constant" kr while defining the exponential in ( 8 ) and (9) , or in other words, kr is not a function of any spatial variable at this point, but becomes a function of r later.
The same for "constant" gamma definition in (10) and (11).
Suddenly, these "constants" becomes functions in (12), (13) and (14).
Magic? -
#164 by rfmwguy on 09 Aug, 2015 21:37
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Its possible oam is the reason for force variants in different orientations. IOW cosmic speed limit might create a localized force to shed photon speed. Obviously not sure but the brick wall of C is there in our reference frame...in which we are in orbital motion...something to ponder perhaps.
If you really want to dive deep, look at Orbital Angular Momentum of circular radiation:
http://arxiv.org/ftp/arxiv/papers/0905/0905.0190.pdf
You think it is converting OAM to LM in there?
Didn't someone detect rotation in MEEP a few pages back? -
#165 by leomillert on 09 Aug, 2015 21:51
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http://arxiv.org/abs/1508.00626
The Reality of Casimir Friction
K. A. Milton, J. S. Høye, I. Brevik
Theoretical consensus is emerging.
Thank you for posting this reference. It would be very much appreciated any other references you may find on this subject (Casimir friction)
Found some.
Casimir friction force and energy dissipation for moving harmonic oscillators - J. S. Høye; I. Brevik
Casimir friction at zero and finite temperatures - Høye, Johan S.; Brevik, Iver (2014)
Macroscopic approach to the Casimir friction force - V. V. Nesterenko,A. V. Nesterenko (2014)
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#166 by deltaMass on 09 Aug, 2015 22:07
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I can understand the attraction of taking the idea of Casimir friction in order to explain an EmDrive as some sort of Zero-Point Dean Drive. A pawl and ratchet into spacetime. What I don't understand is how people can make such a proposal when there is no Casimir effect in an EmDrive in the first place.
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#167 by WarpTech on 09 Aug, 2015 23:58
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In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because Sr = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the k-vector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to re-derive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
Yes Dr Rodal, to me Zeng and Fan don't write the correct expressions for the problem of propagation on a tapered conical waveguide.
One way is solve the helmoltz equations respecting directly the physical boundary conditions under the geometry of problem.
This will implies that standard solutions of wave equation in spherical coordinates ( in general, bessel and legendre functions of integer order), must be subtituted by specific solutions with fractionary order legendre/ bessel functions.
Other way, more complicated, is find solutions using the called "coupled-mode theory in instantaneous eigenmode (quasimode) basis ", where one can use a superposition cilindrical modes, evolving a coupled-mode equation along the longitudinal axis of propagation, where each cilindrical mode has a instantaneous dependence on the radii of tapered section of conical waveguide.
Of course, there are many others forms to solve this problem.
I set to bold because, to my understanding, this is precisely what they did. Look at equations 2 & 3, and the associated text that follows it, through to equation 8. This part of their work is not that difficult to follow, so I don't see precisely where they make any error or assumptions that would cause it to be wrong. Their answer includes everything you just said, and the derivatives are Hankel functions of "fractional order". Where is the error?
Todd
Sorry Todd, Dr Rodal and all people from this forum.
My fault. The zeng and fan field solutions are correct and the table 1 shows the order of associated legendre/bessel functions for some values of cone angle thetazero.
But together,the definitions in ( 8 ), (9) , (10), (11), (12), (13), and (14) make no sense to me.
A "constant" kr while defining the exponential in ( 8 ) and (9) , or in other words, kr is not a function of any spatial variable at this point, but becomes a function of r later.
The same for "constant" gamma definition in (10) and (11).
Suddenly, these "constants" becomes functions in (12), (13) and (14).
Magic?
Agreed, they misuse the word "constant" when pertaining to the variables, alpha and beta. It is a terminology issue though, not math that is incorrect.
It is not magic. Equation 12 is the derivative of equation 2, per equations 9 and 10, for TE modes. Equations 13 and 14 are the derivatives of equation 5, for TM modes. Since there is no component of Er in equation 2, there is no radial component of attenuation for the E field in the r direction. But there is for the TM mode, in equation 5 to give equation 14.
Todd -
#168 by Rodal on 10 Aug, 2015 01:12
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Agreed, they misuse the word "constant" when pertaining to the variables, alpha and beta. It is a terminology issue though, not math that is incorrect.
It is not magic. Equation 12 is the derivative of equation 2, per equations 9 and 10, for TE modes. Equations 13 and 14 are the derivatives of equation 5, for TM modes. Since there is no component of Er in equation 2, there is no radial component of attenuation for the E field in the r direction. But there is for the TM mode, in equation 5 to give equation 14.
Todd
It may be interesting to plot the γ function, the logarithmic gradient of the electric field:
γ = - dLog[E]/dr = - (1/E)*dE/dr
defined by Zeng and Fan, and apply it to the case of standing waves in a closed resonant cavity: Yang/Shell for TE011 and TE012, to see what it looks like.
In this case γ = γθ = γφ
γθ = - (1/Eθ)*dEθ/dr = γφ = - (1/Eφ)*dEφ/dr
γ is real, these are standing waves hence there is no imaginary component of γ.
γ grows without bounds, to Infinity, at each end because the transverse electric fields are zero at the big base and at the small base in order to satisfy the boundary condition that electric fields parallel to a metal boundary must be zero. Since γ is defined as the ratio of the gradient of the electric field with respect to r, divided by the electric field, when the field is zero at the bases, while the numerator is maximum, γ is infinite at the boundaries.
For TE012, γ also grows without bounds at the middle node of the two half-wave patterns because at that point the transverse electric field is zero while its gradient with respect to r is maximum.
Notice that γ is negative at the small base (small r) and positive at the big base (large r).
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#169 by Ricvil on 10 Aug, 2015 01:38
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...
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because Sr = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the k-vector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to re-derive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
Yes Dr Rodal, to me Zeng and Fan don't write the correct expressions for the problem of propagation on a tapered conical waveguide.
One way is solve the helmoltz equations respecting directly the physical boundary conditions under the geometry of problem.
This will implies that standard solutions of wave equation in spherical coordinates ( in general, bessel and legendre functions of integer order), must be subtituted by specific solutions with fractionary order legendre/ bessel functions.
Other way, more complicated, is find solutions using the called "coupled-mode theory in instantaneous eigenmode (quasimode) basis ", where one can use a superposition cilindrical modes, evolving a coupled-mode equation along the longitudinal axis of propagation, where each cilindrical mode has a instantaneous dependence on the radii of tapered section of conical waveguide.
Of course, there are many others forms to solve this problem.
I set to bold because, to my understanding, this is precisely what they did. Look at equations 2 & 3, and the associated text that follows it, through to equation 8. This part of their work is not that difficult to follow, so I don't see precisely where they make any error or assumptions that would cause it to be wrong. Their answer includes everything you just said, and the derivatives are Hankel functions of "fractional order". Where is the error?
Todd
Sorry Todd, Dr Rodal and all people from this forum.
My fault. The zeng and fan field solutions are correct and the table 1 shows the order of associated legendre/bessel functions for some values of cone angle thetazero.
But together,the definitions in ( 8 ), (9) , (10), (11), (12), (13), and (14) make no sense to me.
A "constant" kr while defining the exponential in ( 8 ) and (9) , or in other words, kr is not a function of any spatial variable at this point, but becomes a function of r later.
The same for "constant" gamma definition in (10) and (11).
Suddenly, these "constants" becomes functions in (12), (13) and (14).
Magic?
Agreed, they misuse the word "constant" when pertaining to the variables, alpha and beta. It is a terminology issue though, not math that is incorrect.
It is not magic. Equation 12 is the derivative of equation 2, per equations 9 and 10, for TE modes. Equations 13 and 14 are the derivatives of equation 5, for TM modes. Since there is no component of Er in equation 2, there is no radial component of attenuation for the E field in the r direction. But there is for the TM mode, in equation 5 to give equation 14.
Todd
If one has a function with exponential format F=exp(k.x) and k is a constant then one can write k=(dF/dx)/F.
But if one has a function F=exp(k(x).x) then (dF/dx)/F=k(x) + xdk(x)/dx
If F has no exponential format is worse.
The wave solutions in spherical coodinates are the form exp(+ik.r)/r and exp(-ik.r)/r only when r goes to infinity.
Of couse, the 1/r dependence of the asymptotic fields becomes a 1/r^2 of poynting vector dependence and describes the natural decay/ enhancement of outward/inward spherical waves from/to cone apex, and this factor will cancel with ds=r^2domega infinitesimal area element of a radial power flux calculation, where domega is a infinitesimal solid angle.
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#170 by Rodal on 10 Aug, 2015 01:57
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Yes, basically γ = γ (r) hence it does not make sense that γ is treated as a constant to define
If one has a function with exponential format F=exp(k.x) and k is a constant then one can write k=(dF/dx)/F.
But if one has a function F=exp(k(x).x) then (dF/dx)/F=k(x) + xdk(x)/dx
If F has no exponential format is worse.
The wave solutions in spherical coodinates are the form exp(+ik.r)/r and exp(-ik.r)/r only when r goes to infinity.
E = A e - γ r
γ = - (1/E) dE/dr = α + j β
because this is only true for γ = constant -
#171 by Rodal on 10 Aug, 2015 02:09
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Yes, basically γ = γ (r) hence it does not make sense that γ is treated as a constant to define
If one has a function with exponential format F=exp(k.x) and k is a constant then one can write k=(dF/dx)/F.
But if one has a function F=exp(k(x).x) then (dF/dx)/F=k(x) + xdk(x)/dx
If F has no exponential format is worse.
The wave solutions in spherical coodinates are the form exp(+ik.r)/r and exp(-ik.r)/r only when r goes to infinity.
E = A e - γ r
γ = - (1/E) dE/dr = α + j β
because this is only true for γ = constant
So, really
- (1/E) dE/dr = γ + r dγ/dr
So Zeng and Fan's expression is exact when dγ/dr = 0, that is when γ is constant.
and approximate for dγ/dr ~ 0 (γ nearly constant)
so in the images shown in http://forum.nasaspaceflight.com/index.php?topic=38203.msg1414705#msg1414705 above and in Zeng and Fan's figures, the γ expression is more accurate as a measure of attenuation where γ is flat (where the gradient dγ/dr ~ 0 ) and nearly constant, which is more nearly the case for values such that:
γ = 0 (NO ATTENUATION) -
#172 by aero on 10 Aug, 2015 02:32
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I took a break today and let my computer run 64 cycles of the Shell conic frustum cavity model. The png views and csv data of the final 14 time slices is available here. To me, it does look to be much more "converged" than 32 cycle runs.
https://drive.google.com/folderview?id=0B1XizxEfB23tfmVCZlhnNUVtTGRoTTlZSGJiT3ZfSHBvYnNELUc1WlN0Sk15ZDZud3pSWmM&usp=sharing
Please read the data description file for the details of the run. -
#173 by Ricvil on 10 Aug, 2015 02:37
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Yes, basically γ = γ (r) hence it does not make sense that γ is treated as a constant to define
If one has a function with exponential format F=exp(k.x) and k is a constant then one can write k=(dF/dx)/F.
But if one has a function F=exp(k(x).x) then (dF/dx)/F=k(x) + xdk(x)/dx
If F has no exponential format is worse.
The wave solutions in spherical coodinates are the form exp(+ik.r)/r and exp(-ik.r)/r only when r goes to infinity.
E = A e - γ r
γ = - (1/E) dE/dr = α + j β
because this is only true for γ = constant
So, really
- (1/E) dE/dr = γ + r dγ/dr
So Zeng and Fan's expression is exact when dγ/dr = 0, that is when γ is constant.
and approximate for dγ/dr ~ 0 (γ nearly constant)
so in the images shown in http://forum.nasaspaceflight.com/index.php?topic=38203.msg1414705#msg1414705 above and in Zeng and Fan's figures, the γ expression is more accurate as a measure of attenuation where γ is flat (where the gradient dγ/dr ~ 0 ) and nearly constant, which is more nearly the case for values such that:
γ = 0 (NO ATTENUATION)
Gamma = alfa (attenuation) + jbeta (propagation)
No attenuation = zero alfa
Be careful. The expression for gamma does not make sense for stationary waves ( a superposition of two counter propagating waves and, of course, with diferent gammas) -
#174 by Rodal on 10 Aug, 2015 02:55
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Yes I realize that. There is no harm in showing it simply as -(1/E)dE/dr without the meaning attached by Zeng and Fan, to understand what -(1/E)dE/dr looks like.
Gamma = alfa (attenuation) + jbeta (propagation)
No attenuation = zero alfa
Becareful. The expression for gamma do not make sense for stationary waves ( two counter propagating waves and, of course, with diferent gammas)
-(1/E)dE/dr is only dependent on r since E is separated into multiplicative components of the three spherical coordinates
(1/E)dE/dr just means the gradient of the logarithmic of the electric field, since
-(1/E)dE/dr = - d(Log[E]/dr (no approximation here, this is a correct expression for the logarithmic gradient) -
#175 by deltaMass on 10 Aug, 2015 02:59
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Pedantically it's the gradient of the log of the field, rather than the log of the gradient
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#176 by rfmwguy on 10 Aug, 2015 03:16
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Interesting reddit link... https://neolegesmotus.wordpress.com
Seems like a similar senario to spr, tho design is different. Italian non newtonian propulsion company. Hmmmmm
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#177 by Rodal on 10 Aug, 2015 03:18
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Pedantically it's the gradient of the log of the field, rather than the log of the gradient
The term "logarithmic gradient" (not log of a gradient) has been employed in the Mathematics, Continuum Mechanics, Fluid Mechanics and Heat Transfer literature short for "the gradient of the log of the field"
http://bit.ly/1IDbv4a
because "logarithmic gradient" is less awkward and its precise meaning is given by the equation
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#178 by Rodal on 10 Aug, 2015 03:20
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Interesting reddit link... https://neolegesmotus.wordpress.com
Seems like a similar senario to spr, tho design is different. Italian non newtonian propulsion company. Hmmmmm
What's up with the Iron Cross on it ?
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#179 by rfmwguy on 10 Aug, 2015 03:23
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You've got me doc...not a company logo...decoration apparently.Interesting reddit link... https://neolegesmotus.wordpress.com
Seems like a similar senario to spr, tho design is different. Italian non newtonian propulsion company. Hmmmmm
What's up with the Iron Cross on it ?
