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#100 by Rodal on 08 Jun, 2016 18:08
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CONSERVATION of MOMENTUM and calculation of forces
The following conservation of momentum equation can be easily shown to be automatically satisfied by Maxwell's equations, (without any extra conditions). The conservation of momentum equation for an electromagnetic continuous closed system is
where J is the electric current density and ρ the electric charge density.
The electromagnetic momentum density is
In the above expressions, S is the Poynting vector field discussed here: https://forum.nasaspaceflight.com/index.php?topic=39214.msg1529920#msg1529920
and σ is the stress tensor discussed here: https://forum.nasaspaceflight.com/index.php?topic=39214.msg1526577#msg1526577 , and ∇·σ denotes the divergence of the stress tensor field.
The continuous form of the Lorentz force per unit volume, f, is defined as follows:
So, we can express the conservation of momentum equation in terms of the Lorentz force per unit volume, the derivative with respect to time of the Poynting vector, and the divergence of the stress tensor as follows:
Incorrect definitions of body force for unsteady behavior of the EM Drive in published papers
Several authors of papers attempting to calculate the EM Drive force incorrectly define the force as being due only to one term in the equations of motion, for example, as due only to the derivative with respect to time of the electromagnetic momentum density, or as being due only to the divergence of the stress tensor. This is incorrect. For general unsteady behavior, the body force is due to all these terms in the equation of motion and not just to one of these terms. By defining the force on the EM Drive as being due to only one term in the equations of motion, these authors arrive at a completely incorrect result: that a solution of Maxwell's equations or a solution of Yang-Mills equations (which imply conservation of momentum) can lead to self-acceleration of the center of mass, which is in complete contradiction with conservation of momentum.
1) Alexander Trunev, for example in his paper
"General Relativity and Dynamical Model of Electromagnetic Drive"
Alexander Trunev
Научный журнал КубГАУ, №116(02), 2016 года
http://ej.kubagro.ru/get.asp?id=5781&t=1
in his Equations (8), (13), (14), and (21) and (22), Trunev defines and proceeds to calculate forces for the EM Drive only defined taking into account the derivative with respect to time of the Poynting vector and hence disregarding the balancing effect (in the equation of conservation of momentum) of the term corresponding to the divergence of the stress tensor.
2) Juan Yang. Similarly in several of Juan Yang's papers, for example this one:
"Prediction and experimental measurement of the electromagnetic thrust generated by a microwave thruster system"
Yang Juan(杨涓), Wang Yu-Quan(王与权), Ma Yan-Jie(马艳杰), Li Peng-Fei(李鹏飞), Yang Le(杨乐), Wang Yang(王阳), and He Guo-Qiang(何国强)
Chin. Phys. B Vol. 22, No. 5 (2013)
cpb.iphy.ac.cn/EN/article/downloadArticleFile.do?attachType=PDF&id=53411
Yang similarly defines the force as being due to the time derivative of the Poynting vector (or, equivalently, in absence of body forces, (using the divergence theorem), as only due to the divergence of the stress tensor):Quote from: Yang et.al.Obviously the right hand of Eq. (8) is the EM force exerted on the EM field boundary of the limited closed volume
In Yang et.al., she correctly sets up the conservation of momentum equation:
which for f=0 (no charges and no electric currents inside the cavity of the EM Drive), simply states that the divergence of the stress tensor should equal the derivative with respect to time of the electromagnetic momentum, (hence no force on the center of mass-energy of the EM Drive). Yet, Yang et.al. incorrectly define the force as only being due to either term separately (which are of equal magnitude) instead of being due to the difference of both terms (a difference which, under no external forces, is exactly zero).
3) Guido Fetta, in his paper
Guido P. Fetta. "Numerical and Experimental Results for a Novel Propulsion Technology Requiring no On-Board Propellant", 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Propulsion and Energy Forum,
http://dx.doi.org/10.2514/6.2014-3853
calculates the force, in Equations (4) and (5) of the above mentioned paper as being due to the time-averaged integral of the (negative of the) stress tensor component
- σ3 = u - p
= u - εo E2
= ((1/μo) B2 - εo E2)/2
= (μo H2 - εo E2)/2
(See https://forum.nasaspaceflight.com/index.php?topic=39214.msg1526577#msg1526577: this is the so-called "Lagrangian Density", which is an invariant under Lorentz transformations as well as an invariant under rotations).
This is wrong for general unsteady behavior, as in radio-frequency excitation of the EM Drive, the force should have been defined also taking into account the derivative with respect to time of the Poynting vector.
EXAMPLE 1. Two lumped masses connected with a spring, oscillating in space
This error is similar to making the following error in a harmonic oscillator.
Define an (undamped) harmonic oscillator consisting of two masses connected by a spring, floating freely in space:
It is trivial to show that the equation of motion for this system is:
m d2x/dt2 + k x = 0
where:
x = x2 - x1 = distance between the two masses
m = m1*m2/(m1+m2) is the "reduced mass": ½ of the harmonic mean of the masses
k = spring stiffness
t = time
and that the solution is a simple harmonic motion of period 2 π √(m/k), the frequency is the reciprocal of this: f = (1/(2 π))√(k/m), and the “angular frequency” ω, is ω = √(k/m)
The center of mass, never accelerates under this vibration, only the positions of the two masses oscillate with respect to the fixed center of mass:
One can readily see from the reduced mass expression that if one mass is much lighter than the other mass, that the lighter mass will exhibit larger motion. In the limit, if one mass is much greater, the much larger mass is practically immobile and the center of mass is located nearer to the center of mass of the larger mass.
In this equation of motion, the term m d2x/dt2 is due to the derivative with respect to time of the momentum, and hence it is analogous to the term due to the derivative with respect to time of the Poynting vector. Similarly, the spring term kx is analogous to the term due to the divergence of the stress tensor (using the stress-strain equation).
Defining the force as being due only to the derivative with respect to time of the Poynting vector (as done by Trunev, or as effectively done by Yang) is analogous to as defining the force in the harmonic oscillator as the force on the mass due to inertia: m d2x/dt2, or since m d2x/dt2 =- k x , equivalently as defining the force as being due to the negative of the spring stiffness force.
This is an incorrect treatment of the problem. As in the harmonic oscillator example described above the center of mass never accelerates. An external force F is required to accelerate the center of mass, in which case the force is equal to
m d2x/dt2 + k x = F
The external force is equal to the addition of both terms: m d2x/dt2 and k x, and not just equal to one of them.
EXAMPLE 2. Conservation of momentum for continuous non-relativistic media in unsteady motion
Another example is the Cauchy momentum equation that describes the non-relativistic momentum transport in any continuum media. This equation of motion can be written in convective (or Lagrangian) embedded coordinates that follow the material points:
where ρ is the density (mass/volume) at the point considered in the continuum (for which the continuity equation holds), σ is the stress tensor, and g contains all of the body forces per unit mass (often simply gravitational acceleration). u is the flow velocity vector field, which depends on time and space. The symbol D/Dt corresponds to the substantial or material derivative https://en.wikipedia.org/wiki/Material_derivative), such that Dy/Dt, for a tensor field y is:
In the above equation describing conservation of momentum in non-relativistic continuum media, the term due to the divergence of the stress tensor ∇·σ is analogous to the divergence of the stress tensor ∇·σ term in the conservation of momentum equation for electromagnetic media. The term ρ Du/Dt due to the derivative with respect to time of the momentum is analogous to the term (1/c2)∂S/∂t in the equation for conservation of electromagnetic momentum.
Note that it would be completely incorrect to define, for general unsteady behavior, the body force acting on the center of mass as being due only to the derivative with respect to time of the momentum ρ Du/Dt or being due only to the divergence of the stress tensor ∇·σ. No, in general, for unsteady behavior, the body force must take into account both terms: the change of momentum with respect to time, as well as to take into account the divergence of the stress tensor.
Only for steady-state problems (for which the momentum does not change with time) can one define the body force to be equal in magnitude to the divergence of the stress tensor. And for unsteady behavior, only for problems in which the divergence of stress is zero, would be correct to define the body force magnitude to be equal to the derivative with respect to time of the momentum.
Correct definition of body force for unsteady excitation of the EM Drive
Similarly, for a cavity with no electric charges and no electric currents inside the cavity, the proper force definition that would move the center of mass of the EM Drive would be:
where f is a force per unit volume acting on the center of mass.
The force being defined by Trunev and by Yang as just the derivative with respect to time of the Poynting vector is non-zero for a resonant cavity, for the same reason that the inertial force and the spring force are non-zero in a harmonic oscillator: it is due to the fact that energy goes from the electric field (that changes harmonically with time) to the magnetic field (that also changes harmonically with time but is out of phase) and vice-versa. In a harmonic oscillator, one has kinetic energy going into potential energy and vice-versa (with no movement of the center of mass). For steady-state oscillations, as shown by Greg Egan, Maxwell's equation's solution shows that the cyclic time average of the derivative with respect to time of the Poynting vector and the cyclic time average of the divergence of the stress tensor are both zero.
However, for the transient problem of the EM Drive (not discussed by Greg Egan in his article), both the Poynting vector field and the stress tensor fields exhibit oscillations around an exponentially decaying growth with respect to time. Thus, under transient radio-frequency excitation of a resonant cavity, the cyclic time-average of the Poynting vector field will not be zero. This does not mean that there is a net force on the center of mass that can be explained by Maxwell's equations (or by Yang-Mills equations, which also satisfy conservation of momentum). Rather, this force due to the time derivative of the Poynting vector changing exponentially with time is perfectly balanced by the force due to the divergence of the stress tensor, and vice-versa.
Hence to correctly calculate the total force on the EM Drive's center of mass one has to calculate all the forces involved,
If one is to also consider electric charges and currents, one has to also take these forces into account (ρE and JxB), when calculating the total force on the center of mass. The total force on the center of mass is composed of the time derivative of the Poynting vector, the divergence of the stress tensor, and the Lorentz force. Just as in a harmonic oscillator where one has inertial forces and spring forces, and the center of mass will only move due to an external total force on the center of mass, similarly for the EM Drive one has to take into account all the forces, and thus it is incorrect for Trunev and Yang to define the force acting on the center of mass as being due to only one of these terms. Also, just as in the harmonic oscillator one has to also consider a damping force (if there is damping present) in the EM Drive one also has to consider power loss terms if one is going to take into account the power loss which leads to a finite value of the quality of resonance Q (due to finite conductivity in the metal walls, for example).
For more information on how to correctly calculate forces for electromagnetic continua, see the classic text by Professor Melcher at MIT (sorry he is no longer with us):
Melcher, James R., Continuum Electromechanics. Cambridge, MA: MIT Press, 1981. ISBN: 9780262131650
and particularly, the excellent monograph:
Paul Penfield Jr., H.A. Haus, Electrodynamics of Moving Media. 1967, Cambridge,Mass.: MIT Press. ISBN-13: 978-0262160193 -
#101 by X_RaY on 13 Jun, 2016 20:17
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@FattyLumpkin
This is the best Cannae like design I could get out of FEKO LITE till now. Would need a full version to come closer to
Monomorphic´s sims.
https://forum.nasaspaceflight.com/index.php?topic=39772.msg1530441#msg1530441
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#102 by Rodal on 13 Jun, 2016 20:43
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@FattyLumpkin
Great work!
This is the best Cannae like design I could get out of FEKO LITE till now. Would need a full version to come close to
Monomorphic´s sims.
https://forum.nasaspaceflight.com/index.php?topic=39772.msg1530441#msg1530441
1) Have you also tried to model the Cannae device with EM Pro, for which you do not have the limitations of FEKO Light?
2) When you used EM Pro in the previous pages for other calculations, did you use the Finite Element module of EM Pro or the finite difference module of EM Pro? -
#103 by X_RaY on 13 Jun, 2016 21:08
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1)I did not test this using EMPro.@FattyLumpkin
Great work!
This is the best Cannae like design I could get out of FEKO LITE till now. Would need a full version to come close to
Monomorphic´s sims.
https://forum.nasaspaceflight.com/index.php?topic=39772.msg1530441#msg1530441
1) Have you also tried to model the Cannae device with EM Pro, for which you do not have the limitations of FEKO Light?
2) When you used EM Pro in the previous pages for other calculations, did you use the Finite Element module of EM Pro or the finite difference module of EM Pro?
This FEKO run was the first try to use this kind of design.
2) The few sims I showed here were based on the FEM-Eigenresonance solver.
For the frustum design I did pure FEM calculations also(amplitude&phase over frequency) with antenna and antenna feed but for the argumentation the Eigenresonances are close enough compared to the much more time consuming frequency sweep FEM´s.
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#104 by Rodal on 15 Jun, 2016 18:21
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Further to this issue about Boundary Conditions, Jackson has an excellent discussion in his masterpiece Classical Electrodynamics, 3rd Edition, pages 352 to 356 (ISBN-10: 047130932X; ISBN-13: 978-0471309321). Pay special attention to the graph on page 355, Fig. 8.2 "Fields near the surface of a good, but not perfect conductor". For a good but not perfect conductor, for example copper as used in the EM Drive, and as modeled in Meep with the Drude equation model, a very tiny magnitude electric field parallel to the surface will be present, as well as a very tiny magnetic field perpendicular to the surface. The electric field parallel to the surface is inversely proportional to the square root of the conductivity:
This solution exhibits the expected rapid exponential decay (skin depth), and Pi/4 phase difference. For a good conductor, the fields inside the metal conductor are parallel to the surface and propagate normal to it, with magnitudes that depend only on the tangential magnetic field parallel to the surface, that exists just outside the surface of the metal conductor.
As shown in the graphs in Jackson's book, and as one can readily calculate these fields are practically zero, insignificant for copper, due to its very high conductivity. Therefore it is not a surprise that Meep does not show a significant difference in the fields calculated using the perfect conductor model vs. the Drude model. The main influence of the finite conductivity Drude model is to allow the calculation of a finite Q (instead of an infinite Q). But again, the boundary condition is such that the electric field parallel to the surface and the magnetic field perpendicular to the surface must be practically zero at the surface, due to the very high conductivity of copper. This is particularly so for the experiments of EM Drive where experimenters seek a high Q, which is tantamount to practically zero fields for these variables. It is completely inconsistent for EM Drive experimenters to advocate a high Q (Shawyer even claiming to research superconducting EM Drives) and not realize that these boundary conditions are such that these fields must be practically zero at the surface of the good conductor.
NOTE: for those not having ready access to Jackson's monograph, the following discussion by a professor at Duke University is also good: https://www.phy.duke.edu/~rgb/Class/phy319/phy319/node59.html
Further to this issue about Boundary Conditions, Wolfgang Panofsky and Melba Phillips give a very useful rule of thumb, in their book:
Classical Electricity and Magnetism
Wolfgang Panofsky and Melba Phillips
Second Edition
Addison-Wesley , 1962
in page 214, section 13-1:
the ratio of the tangential component of E to its normal component
and
the ratio of the normal component of H to its tangential component
for an interface between a dielectric and a conductive metal is given by the ratio of the skin depth to the wavelengh
For the EM Drive problem with a copper cavity at ~2 GHz, we know that the skin depth is in the order of a micrometer, while the wavelength is in the order of several tenths of a meter, therefore this ratio should be smaller than 10-5, therefore when seen in a graph, the magnetic vector field H should appear tangential to the metallic surface and the electric vector field E should appear normal to the metallic surface, since the perpendicular components of these fields are hundreds of thousands of times smaller at the metal interface.
If a numerical calculation shows otherwise, this indicates that there is something very wrong with the calculation ("Garbage in = Garbage out") and the source of this error should be explored -
#105 by X_RaY on 24 Aug, 2016 19:02
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Q difference for spherical and flat endplates
As example for the sperical case I will use the numbers of Greg Egan that can be find on the following website:
http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html
Greg Egan, sperical end plates(These values assume an idealised smooth copper surface):
r1=25mm, r2=100mm, θ=20°
TE012, f=9.359GHz, Q=37,864
To get an idea of the difference we can make a simple relation as follows by using a similar cavity with flat endplates (diameters and length of the sidewall is the same as in the sperical case)
with recalculated dimensions in cylindrical coordinates:
SD=17.101mm, BD=68.404mm, L=70.477mm
a recalculation of θ with the rounded numbers gives a cone half angle of 19,99998° which is close enough for this approximation...
Using the formula for frequency and Q as discussed earlier in this thread:
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1476704#msg1476704
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1473268#msg1473268
we get:
TE012, f=10.953GHz, Q=30,963
The ratio of Q (sperical/flat)in this case is roughly 1.223.
This number may be different for other modes and cavity dimensions because it depends on the exact geometry, frequency, mode, surface resistance, volume to surface ratio and so on.
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#106 by Rodal on 06 Sep, 2016 21:50
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This is re-posted here, to enable more direct finding of these calculations to use in the future for other orbits and spacecraft
I hope there is no confusion re the various projects going on at Cannae...as folks know I've been conducting a study of them
So they are using miles instead of kilometers to specify an orbit?
1) for the cubesat, they say they are orbiting it at less than 150 miles...not kilometers. Mr. Feta told me there would be no super-cooling of this device. I'm left to conclude that the cooling of their thruster will be passive and that the thruster will be kept in shadow at all times
...
150*1.60934=241
So their orbit is really 241 km ?
That makes a difference ! Thanks
I calculated with 150 km. (I recall pointing this out weeks ago, when they first announced, that instead of using customary SI units, Cannae is using Miles, oh well
)
Just like the probe that crashed on Mars years ago (different units !)
Will recalculate with 150 miles tomorrow (Is it US Miles
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US Survey mile = International mile =1.60934 km
Nautical mile = 1.852 km
Roman mile = 1.481 km
Chinese mile = 0.5 km
Let's work through the numbers for Cannae's proposed Cubesat mission, using 240 km instead of 150 km:
http://cannae.com/cubesat/
http://cannae.com/cannae-is-developing-a-cubesat-thruster/
http://www.popularmechanics.com/science/energy/a22678/em-drive-cannae-cubesat-reactionless/
The publicity picture appears to show a larger than 1x3U Cubesat, the second link talks about a 6U Cubesat
Orbit (assume circular orbit at published distance, interpreted as US Miles)
ro=150 USmile *1.60934 km/USmile ~ 240 km
Orbital velocity (Assuming circular orbit at 240 km)
G=6.67408 * 10^-11 m^3 kg^-1 s^-2
M=5.972 * 10^24 kg (mass of the Earth)
R=6.371*10^6 m (mean radius of the Earth)
r = R + ro
= 6.371*10^6 m+ 240*10^3 m
v=7765 m/sec
Drag Surface area: assume a minimum cross-sectional area, for a 1x3U Cubesat with cross-sectional drag surface of 0.10m x 0.30 m, perpendicular to the orbital plane(this assumes that the solar panels are always parallel to the orbital velocity vector)
Assume minimum configuration:
1x3U Cubesat (Notice that picture shows a larger Cubesat and link discusses a 6U Cubesat. The thrust necessary for larger Cubesats can be obtained by simple scaling of the appropriate cross-sectional area. For example, a 2x3U Cubesat will have twice the minimum cross-sectional area of a 1x3U Cubesat)
A=0.10m *0.30m
= 0.03 m^2
Drag coefficient
CD=2 (*)
Reynerson, "Aerodynamic Disturbance Force and Torque Estimation for Spacecraft and Simple Shapes Using Finite Plate Elements Part I: Drag Coefficient"
https://www.researchgate.net/publication/221910818_Aerodynamic_Disturbance_Force_
and_Torque_Estimation_for_Spacecraft_and_Simple_Shapes_Using_Finite_Plate_Elements_
Part_I_Drag_Coefficient/figures?lo=1
de Vries, "Cubesat Drag Calculations "https://e-reports-ext.llnl.gov/pdf/433600.pdf
Olttroge et.al.,"An evaluation of Cubesat Orbital Decay",
http://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1144&context=smallsat
Atmospheric Density
MSISE90 std atmosphere (for 240 km)
(References:
This link enables the computation and plotting of any subset of MSIS parameters:
http://omniweb.gsfc.nasa.gov/vitmo/msis_vitmo.html
http://ccmc.gsfc.nasa.gov/models/modelinfo.php?model=MSISE ) (*)
@Mean solar activity rhoMean= 9.91 x 10^-11 kg m^-3
@Maximum solar activity rhoMax= = 4.08 x 10^-10 kg m^-3
rhoMax/rhoMean=4.117
The solar cycle is very important,
since air density, and hence drag, is very much dependent on solar activity. It is what brought Skylab down ( https://en.wikipedia.org/wiki/Skylab#Solar_activity ):QuoteBritish mathematician Desmond King-Hele of the Royal Aircraft Establishment predicted in 1973 that Skylab would de-orbit and crash to earth in 1979, sooner than NASA's forecast, because of increased solar activity. Greater-than-expected solar activity heated the outer layers of Earth's atmosphere and increased drag on Skylab.
Observe the chart below for where we are now, and the predicted activity in the future:
Drag Force
DMax =(1/2) CD rhoMax A v^2
=(1/2) 2 (4.08 x 10^-10 kg m^-3) (0.03 m^2) (7765)^2
=7.38*10^(-4) N
DMean = DMax/4.117
=1.79*10^(-4) N
Solar radiation pressure is negligible: 4.5 (absorption) to 9 (reflection) μN /m2, so radiation force will be less than 0.27 μN. (For LEO, the radiation pressure from the Earth is hard to model as it depends on cloud albedo, but it is smaller than solar and thus also negligible).
Mass = 1.33 kg/U
3U =4 kg
6U =8 kg
Acceleration due to Atmospheric Drag
For 3U, mass=4 kg
aMax= DMax/Mass
=7.38*10^(-4) N/4 kg
=1.85*10^(-4) m/s^2
aMean=DMean/Mass
=1.79*10^(-4) N /4 kg
=4.40*10^(-5) m/s^2
Maximum Power available from sunlight = 10 watts
From Cannae's announcement: http://cannae.com/cubesat/QuoteOur thruster configuration for the cubesat mission with Theseus is anticipated to require less than 1.5 U volume and will use less than 10 watts of power to perform station keeping thrusting.
Effective power available , assuming a common-low-to-moderate-inclination circular orbit at 240 km altitude, as shown in this picture by Cannae:
and hence taking into account that solar panels will be experiencing eclipse ~ 50% of the time, and considering that solar panels must be kept always parallel to the orbital velocity vector, at all times)
P=(1/2) 10 watts (*)
=5 watts
Assume no safety margin: SafetyMargin=1
Necessary thrust
TMax= SafetyMargin* DMax
= 7.38*10^(-4) N
TMean= TMax /(rhoMax/rhoMean)
= 1.79*10^(-4) N
Necessary Thrust/PowerInput
TMax /PowerInput= 7.38*10^(-4) /5 W
= 148 μN/W
TMean /PowerInput= 1.79*10^(-4) N /5 W
= 36 μN/W
Conclusion:
The orbit makes a big difference, concerning the requirements for such a mission. While a 150 km would require ~1 milliNewton/Watt to ensure no deorbiting, an orbit of 240 km requires substantially less thrust/PowerInput. Note that most Cubesat launches are at 300 - 400 km - The ISS maintains an orbit with an altitude of between 330 and 435 km by means of reboost manoeuvres using the engines of the Zvezda module or visiting spacecraft.
Cannae's mission for keeping in orbit for 6 months a Cubesat, assuming:
* minimum configuration 1x3U Cubesat, with cross sectional area of only 0.03 m2
* no safety margin
* mean Solar activity
* that the solar panels are kept always parallel to the orbital velocity vector (otherwise drag will be much greater)
requires a Thrust/PowerInput= 36 microNewton/Watt which is consistent with NASA's previously reported results for copper resonant cavities excited at ~2 GHz :
http://www.libertariannews.org/wp-content/uploads/2014/07/AnomalousThrustProductionFromanRFTestDevice-BradyEtAl.pdf
http://emdrive.wiki/Experimental_Results
However, maximum Solar activity would require about 150 microNewton/watt.
If the solar panels are not kept parallel to the orbital velocity vector at all times, drag will be much greater, and hence much greater thrust would be required.
Furthermore, this assumes no safety margin.
Also this is based on a minimum configuration 1x3U Cubesat, with minimum cross sectional area of only 0.03 m2
The Cannae publicity picture appears to show a larger than 1x3U Cubesat configuration instead, and if so, a larger cross-sectional area which would require a proportionally larger thrust force to overcome atmospheric drag.
The link http://cannae.com/cannae-is-developing-a-cubesat-thruster/ describes a 6U Cubesat. If it is a 2x3U Cubesat, then the minimum cross-sectional area is twice what is calculated above and therefore the atmospheric drag will require twice the thrust calculated above for a 1x3U Cubesat.
Also, worthy of note when planning a 6 month mission in Low Earth Orbit:I know I sound like a broken record, but I would really like to know how they plan to separate out thrust effects from the high variability of atmospheric density at those altitudes.
_________________________________________
(*) Thanks to Marshall Eubanks for providing these estimates. I am responsible for any errors in using them.
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#107 by Willem Staal on 07 Sep, 2016 09:28
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mr Rodal,
I am hugely interested in the theory of these EM Drives and i wonder:
Could the overall effect be a result of a phase transition of a standing wave? A Dutch scientist called Christiaan Huygens observed synchronization of pendulum clocks, and he discovered that at some times they run in phase or in anti-phase due to vibations trought walls or on a table.
Could it be that a a similar behavour occur also in a EM drive frustrum where the amplitude of the waves are truncated by the shape of the frustrum while the waves forced into sychronization phase? So the energy of the amplitude escapes somewhere trought the copper of the frustrum and then produce thrust? not as a detectable force but as a phase or anti phase synchronization event? -
#108 by Rodal on 08 Sep, 2016 18:50
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Atmospheric drag on the sat is measurable, but it cannot be ameliorated by always keeping the sat solar array parallel to the orbital velocity vector
Incorrect statement. On the contrary, it is well known that atmospheric drag is minimized by minimizing the cross-sectional area perpendicular to the drag force.
Thus, the minimum drag orientation is indeed flying with solar array paralell to the orbital velocity vector. This is known in Aerospace Engineering as flying "edge on" or flying in the low-drag feathered position. Flying edge on significantly reduces drag (as it is easy to verify by calculation, since the drag is proportional to the cross-sectional area perpendicular to the drag force).
If flying a spacecraft with solar arrays on gimbals, in the edge-on position the alpha gimbal is fixed. If desired, the alpha gimbal could be removed to lower weight.
This is what was assumed in my calculations: edge-on flying, with no gimbal, the solar array being fixed to the Cubesat, as in Cannae's picture.The satellite must rotate about its own axis about once every 90 minutes to keep the array pointed at the sun. This rotation will continue in Earth's shadow....
No. There is no law that imposes such a solar-array orientation as the only option.
When designing a solar array orientation for a Low Earth Orbit (LEO) there are several options for orientation of the solar array:
1) Sun pointing
The spacecraft may maintain (if so desired) a fixed orientation with respect to Earth, and a gimbal (alpha gimbal) can be used to track the Sun as the spacecraft rotates in orbit. A beta gimbal (rotation around the longitudinal axis of the solar arrays) can compensate for variations in the angle of the Sun to the orbital plane.
This is not the only alternative.
You propose a more extreme version of the sun-pointing configuration where the solar-array is fixed to the Cubesat and hence the whole Cubesat has to rotate continuously in order to keep Sun-pointing all the time.
This is a flying configuration that produces a much greater drag force.
In addition, since you are using no gimbals, you have to rotate the whole spacecraft to accomplish your proposed Sun-pointing at all times. Thus, you propose, as the only choice available, a flying configuration that produces greater drag, and that in addition requires rotating the spacecraft.
If one calculates this, one arrives at the conclusion that flying with sun-pointing configuration at all times will require a thrust that exceeds the published claims for copper EM Drive. (The kind of EM Drive that Cannae is reporting will fly in this mission). (*)
2) Hybrid. For example Sun pointing during iluminated position of orbit, and edge on during eclipse (to minimize drag). During eclipse the solar array can be gimbaled edge on to the orbital velocity vector, which will require a rotation of ~70 to 75 degrees twice per orbital period.
For example, the ISS adopts a hybrid solar array orientation: it points the solar array at the Sun (and takes the drag penalty) when in light, goes into a perpendicular mode in the dark. The ISS "furls" its solar panels when in darkness.
3) Edge on during the entire orbit. This is the option that what was assumed to minimize drag in my calculations, since EM Drive's (assuming that they would work somehow) are very limited in the thrust/PowerInput available. This was made very clear in the calculations.
This is what was assumed: edge-on flying during the entire orbit, with no gimbal, the solar array being fixed to the Cubesat, as in Cannae's picture:
Flying with the solar-arrays "edge-on" means that the amount of power available from the solar arrays will be decreased. This reduction was explicitly taken into account in my analysis !
Flying edge-on during the entire orbit, besides minimizing drag, has the advantage that it keeps the spacecraft facing the Earth at all times, which may be beneficial for missions to monitor the Earth.
This is not an option that is impossible, or that I invented "out of thin air". It is a well-known configuration option.
See articles by G. Landis and C. Lu, (AIAA) and by Anigstein and Sanchez Pena (IEEE) on analysis of solar panel orientation in low altitude satellites.
You state that flying with the solar-arrays Sun-pointing all the time is the only option. This is not so. It is simple to run the numbers and show that the option you appear to consider as the only possible option (Sun-pointing) will require significantly greater thrust, and that according to published claims for a copper EM Drive (if it were to work as claimed) would not be able to overcome.
____
(*) As a minor detail, being picky, the sketch and absolutist demand for such a complete rotation once per orbit needs further consideration. As we all know, the Earth rotates around the Sun once per _year_ (the Earth's orbit). Hence, the sun rotates once per _year_ in an inertial reference frame tied to the Earth's orbit Not once per spacecraft_orbit_.
The ISS itself rotates once per orbit to keep one side always looking at the Earth (it has an "up" and a "down" side - the cupola, for example, is on the down side and always points at the Earth) and that means that its solar panels _counterrotate_ when the Sun is up.
Hence the Sun-pointing option, besides involving greater drag, involves a level of complexity that is undesirable for a smallsat mission like the one proposed by Cannae.
By contrast, the flying "edge on" or flying in the low-drag feathered position is much simpler, involving minimum drag, and complexity. -
#109 by X_RaY on 06 Nov, 2016 16:44
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Low order TE0np modes in a "flying saucer" like cavity.
https://www.scientificsonline.com/product/large-parabolic-reflectors-12?gclid=Cj0KEQjwhvbABRDOp4rahNjh-tMBEiQA0QgTGge0SE4e6mkfaHf2PHMvrl0O0WC9sYiQ8hwtbo306-0aAgiR8P8HAQ
This design tends to change the mode-integer "n" rather than "p" (or "m")over frequency.
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#110 by X_RaY on 08 Nov, 2016 18:01
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Added for conservation, Copy of the original post of the main EM-Drive thread
1. FEKOIs there anyone who has study a half-sphere shaped resonator regarding the emdrive?
In contrast to a parabolic one (where the focal depth for rays much shorter than the size of the structure itself was equal to the point where the baseplate was present).
http://forum.nasaspaceflight.com/index.php?topic=39214.msg1607020#msg1607020
Now I did an FEA with the half-sphere shape. What I found is a massive fieldstrength, much higher than I ever have observed in the sims before. The Q should be very high.
1) What is the numerical analysis package you are using ? (FEKO, etc.)
2) What numerical technique are you using to solve the equations? (Finite Element Method?, Boundary Element Method?, Finite Difference Method Space Domain?)?
3) What is the type of solution method?
A) Is it an eigensolution to the eigenvalue problem where there is no antenna in the model?
B) Or a steady state solution using an antenna and a spectral method to obtain a solution?
C) Or a transient solution using an antenna and a Finite Difference Time Domain to obtain a solution?
D) If you used an antenna, with a spectral steady-state solution or a transient Finite-Difference-Time-Domain solution, what was the type of antenna and where was it located?
4) What are the boundary conditions that you use in the model? Are you assuming a perfect conductor?
If not, how are you modeling an imperfect conductor like copper?
5) How is the quality factor (Q) calculated?
6) How are eddy currents calculated in the model?
Thanks
2. MOM & FEM
3. ?
A. No, no eigenvalue calculation, magnetic Dipole (30mm above the flat plate at the central axis)
B. FEM
C. No FDTD
4.First time the boundary was defined to be PEC. Couldn't believe this numbers, therefore I used Copper, thickness 1mm for the second run (see diagrams).
Field pics are from the PEC-run.
5.No till now the Q is not calculated. My statement was due to the fieldstrength.
6. Good question, It's a internal calculation of FEKO, don't know their code
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#111 by Peter Lauwer on 09 Nov, 2016 17:30
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The White et al. 2016 paper (the leaked, non-peer reviewed version, which still can be downloaded from http://www.nextbigfuture.com/2016/11/new-nasa-emdrive-paper-shows-force-of.html):
I haven't read a lot of discussion of the paper yet. Some remarks can be made, though, and questions asked. It looks like a solid piece of work, greatly admirable engineering work and clear discussion. We don't know from when this version is (the pdf I downloaded doesn't give a creation date, only 26 Aug 2016 as modification date). It doesn't look like two years of work to me (but probably they could not work full-time on it). I am a bit disappointed that they don't show results of other dielectric inserts (what they probably did).
A few issues and questions:
- I wonder whether switching direction in their way, with the whole RF stuff (amplifier etc) attached to the large endplate, is the best to do. As they write, they had retuning problems when using a 'split configuration mode'. But if you use a flexible cable, it should be possible to turn only the cavity by 180 degrees and leave the RF stuff at the same position and orientation.
- Do I see a saturation effect around 60 W? See Figs. 13, 15 and 19. It does not seem to be so much work to perform, say, 100 measurements. Then they could have shown with statistics that there is a difference in force between the 60 W and the 80 W input, or not. Now that is not clear (their premise is probably that there SHOULD be a linear dependence on power: dangerous).
- I am still a bit worried about the liquid metal contacts they use to supply the DC power to the torsion balance (many amps!). It is not likely that these will give rise to the signals they observe, but I haven't seen a test of their influence on the measurement.
Maybe more later,
Peter.
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#112 by X_RaY on 11 Nov, 2016 08:11
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Regarding PM from Rodal, 11/11/2016 12:44 AM
http://www.altairuniversity.com/wp-content/uploads/2015/03/UserManual.pdf
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#113 by X_RaY on 12 Nov, 2016 13:06
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Due to the request of Jean-Philippe Montillet and Jose' Rodal I did simulations using FEKO (students edition) to plot the fields along the surfaces ot the Brady cone without dielectric insert for the TM010 mode.
I found the TM010 at 1020 MHz using an electrical dipole as source. Frustum material is copper.
Source power was defined to be 1Watt (30dBm).
For the final run I increased the coverge accuracy to the maximal level and have set the Mesh density to "Fine" (best when using automatic frequency dependend mesh).
Pleace note that the diagrams units are in dB, this is due to one of each E H curves is almost at the zero level when it is displayed linear.
EDIT
v2.png shows the same model with increased mesh and more points along the lines where the measurements is taken
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#114 by X_RaY on 13 Nov, 2016 16:44
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Results for Brady cone with HDPE-disc at the small end plate. Source power was defined to be 1Watt (30dBm).
εR=2.27
tanδ=0.00031
DIA*=158.75mm
Height=54mm
* to simplify the model I used a diameter equal to the end plate diameter instead of the 156.7mm reported by EW
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#115 by Peter Lauwer on 15 Nov, 2016 10:07
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"According to Woodward, who saw a copy of the paper shortly after it had been accepted for peer review, the main difference between the accepted copy and the leaked early release is that the latter has way more theory trying to explain the results. Supposedly the AIAA would only accept the paper if White and his colleagues ditched the quantum vacuum theory and just published the results of their research without trying to explain it."
http://motherboard.vice.com/read/the-fact-and-fiction-of-the-nasa-emdrive-paper-leak -
#116 by Peter Lauwer on 15 Nov, 2016 10:36
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The White et al. 2016 paper (the leaked, non-peer reviewed version, which still can be downloaded from http://www.nextbigfuture.com/2016/11/new-nasa-emdrive-paper-shows-force-of.html):
I haven't read a lot of discussion of the paper yet. Some remarks can be made, though, and questions asked. It looks like a solid piece of work, greatly admirable engineering work and clear discussion. We don't know from when this version is (the pdf I downloaded doesn't give a creation date, only 26 Aug 2016 as modification date). It doesn't look like two years of work to me (but probably they could not work full-time on it). I am a bit disappointed that they don't show results of other dielectric inserts (what they probably did).
A few issues and questions:
- I wonder whether switching direction in their way, with the whole RF stuff (amplifier etc) attached to the large endplate, is the best to do. As they write, they had retuning problems when using a 'split configuration mode'. But if you use a flexible cable, it should be possible to turn only the cavity by 180 degrees and leave the RF stuff at the same position and orientation.
- Do I see a saturation effect around 60 W? See Figs. 13, 15 and 19. It does not seem to be so much work to perform, say, 100 measurements. Then they could have shown with statistics that there is a difference in force between the 60 W and the 80 W input, or not. Now that is not clear (their premise is probably that there SHOULD be a linear dependence on power: dangerous).
- I am still a bit worried about the liquid metal contacts they use to supply the DC power to the torsion balance (many amps!). It is not likely that these will give rise to the signals they observe, but I haven't seen a test of their influence on the measurement.
Maybe more later,
Peter.
What is also missing in the paper, is quantitative data about their measurement device (torsion pendulum). Especially what the response is (you can estimate it a bit from the response to the electric calibration pulse, but some more detail would be justified in a study like this) and the resolution. And something about its drift. -
#117 by WarpTech on 15 Nov, 2016 18:00
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Warp Tech's Updated Theory
Note: The thrust equation at the end, depends on the Neper frequency. This is [resistance x capacitance]-1.
If we assume this time period to be proportional to the diameter of the frustum, then the time-independent part of this equation reduces to @Notsosureofit's thrust formula. Where, the gradient derivative is expressed as the difference between two potentials.
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#118 by X_RaY on 17 Nov, 2016 16:20
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Jean-Philippe,
this is the result for the alternative situation you was looking for. Source power was defined to be 1Watt (30dBm) as before.
Regards
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#119 by Peter Lauwer on 18 Nov, 2016 10:30
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"According to Woodward, who saw a copy of the paper shortly after it had been accepted for peer review, the main difference between the accepted copy and the leaked early release is that the latter has way more theory trying to explain the results. Supposedly the AIAA would only accept the paper if White and his colleagues ditched the quantum vacuum theory and just published the results of their research without trying to explain it."
http://motherboard.vice.com/read/the-fact-and-fiction-of-the-nasa-emdrive-paper-leak
So this is not true. Their pilot wave theory is still in the Discussion.
)
)
