Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 1805609 times)

Offline Rodal

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The Huffington Post gives the EM drive a spin around the photon drive block.

http://m.huffpost.com/us/entry/7489064

Update from hackaday about their EM drive.

https://hackaday.io/project/5596-em-drive/log/18994-cavity-finished
They test the Baby EM Drive next week !

Oh  baby, baby !   :)
« Last Edit: 06/04/2015 06:50 PM by Rodal »

Offline wallofwolfstreet

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What is the rationale for the "Spring Force" artifact?

I thought @frobnicat had disposed of that issue.

Please provide what spring materials you know of that have a substantially different modulus of elasticity E in compression than in tension (this would be useful to experimenters, I guess, to avoid), what is the difference in value for E between compression and tension, and why you think that the spring used by Berca would display a substantial difference in E between tension and compression.

The overwhelming number of materials commonly used as springs have practically the same modulus of Elasticity in tension than in compression.

With deformations large enough, the issue that comes up is not one of bilinearity between tension and compression, but it is one of nonlinearity.  For large deformations spring materials behave with a cubic nonlinearity, but they are still elastic and have same properties in tension and compression.

You would have to reach plasticity (permanent deformation) of a metal to exhibit significant differences between tension and compression.

I think you are overthinking the issue quite a bit here. 

In Iulian's setup, the spring looked to be in tension.  When the deflection of the cantilevered torque arm is downwards, the deflection of the spring increases and the tension would increase.  When deflection is up, tension decreases.  The force provided by the spring is not a constant in both instances, and is therefore a source of error. 

"the chamber walls in the Brady et al. tests a"  an issue ?

have we forgotten about the tests that Paul March reported with the EM Drive outside the chamber walls?

I don't claim that all of those confounding factors are an issue in all emdrive tests ever performed.  I suppose we can rule out Electrostatic induction with chamber walls for that specific test run.  We can't rule it out in general though, and so it's on the list.         

Offline Rodal

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What is the rationale for the "Spring Force" artifact?

I thought @frobnicat had disposed of that issue.

Please provide what spring materials you know of that have a substantially different modulus of elasticity E in compression than in tension (this would be useful to experimenters, I guess, to avoid), what is the difference in value for E between compression and tension, and why you think that the spring used by Berca would display a substantial difference in E between tension and compression.

The overwhelming number of materials commonly used as springs have practically the same modulus of Elasticity in tension than in compression.

With deformations large enough, the issue that comes up is not one of bilinearity between tension and compression, but it is one of nonlinearity.  For large deformations spring materials behave with a cubic nonlinearity, but they are still elastic and have same properties in tension and compression.

You would have to reach plasticity (permanent deformation) of a metal to exhibit significant differences between tension and compression.

I think you are overthinking the issue quite a bit here. 

In Iulian's setup, the spring looked to be in tension.  When the deflection of the cantilevered torque arm is downwards, the deflection of the spring increases and the tension would increase.  When deflection is up, tension decreases.  The force provided by the spring is not a constant in both instances, and is therefore a source of error. 
...

Overthinking, me ?  Nahh  ;)




DERIVATION OF SPRING STIFFNESS IN TERMS OF FORCE AND DISPLACEMENT

Formula from strength of materials

stress = Force /Area                              (uniform normal stress distribution on the cross-sectional area)
strain =displacement/(original length)     (definition of strain)

stress = E strain     (constitutive relationship = linear modulus of elasticity E)

Then it trivially follows that:

Force =( E * Area/ originalLength ) * displacement

Force = SpringStiffness * displacement   (a linear stiffness relationship between force and displacement)

where

springStiffness =  E Area/ originalLength

It doesn't matter whether it is tension or compression if the material has a unique E (which most materials do)

It doesn't matter the amount of tension if the material has a linear stress-strain relationship giving a linear E

In essence, if you are worrying about the "amount of tension" affecting the force, then you are positing a material with a nonlinear stress-strain relationship.

If we agree that the spring material has a constant modulus of elasticity E, then the SpringStiffness  is constant as well:

Force = SpringStiffness * displacement  (this is known as Hooke's law)

then

delta (Force) = SpringStiffness  * delta (displacement)



EXAMPLE: SAME ABSOLUTE VALUE OF DISPLACEMENT IN UPWARDS AND DOWNWARDS DIRECTION

So let's say that the neutral position is for z (vertical coordinate)  = 0

F = SpringStiffness  z

(so z=0 means F=0)

for z = + positiveDisplacement

positive Force =  SpringStiffness  * positiveDisplacement

for z = - positiveDisplacement

negative Force =  - SpringStiffness  * positiveDisplacement

so

positive Force = - negative Force

Same displacements up or down translate into same absolute value of force up or down



EXAMPLE: DIFFERENT ABSOLUTE VALUE OF DISPLACEMENT IN UPWARDS THAN DOWNWARDS DIRECTION

for z = + positiveDisplacement

positive Force =  SpringStiffness  * positiveDisplacement

for z = - (1/7) * positiveDisplacement

negative Force = - (1/7) SpringStiffness  * positiveDisplacement

so

positive Force = - 7 negative Force

or, equivalently,

negative  Force = - (1/7) positive Force

That spring force is balanced by the force on the cantilever, which is being measured.

In essence, the spring is linear .
What is the source of error ? ???
« Last Edit: 06/04/2015 07:53 PM by Rodal »

Offline Star One

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The Huffington Post gives the EM drive a spin around the photon drive block.

http://m.huffpost.com/us/entry/7489064

Update from hackaday about their EM drive.

https://hackaday.io/project/5596-em-drive/log/18994-cavity-finished
They test the Baby EM Drive next week !

Oh  baby, baby !   :)

Is such a dinky drive a good idea for testing?

Offline phaseshift

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Would it be helpful to subjectively assign a "possible impact on thrust" to each of the possible experimental artifacts as they go onto the wiki.  Something like Thermal: high, Bouyancy: high, My Shoe Size: low (extremely). Three levels would be more than enough: High, Medium, Low. Seems this might help experimenters in prioritizing their efforts. 

Then group the list by the potential impact on thrust.
"It doesn't have to be a brain storm, a drizzle will often do" - phaseshift

Offline SeeShells

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...

So, while I would like to hear updates from Iulian on his progress I would rather not add his 'data' to the table until he says "I think I'm seeing thrust", but not just due to the excitement of the moment.

It doesn't matter to me, data in any form is so rare right now. As as long as I realize where it came from, it's fine. Beggars can't be choosers. A couple of months or a year from now I will be picky.

Offline Rodal

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Beggars can't be choosers.

Love that  ;)

We are beggars with a Tar Baby.
« Last Edit: 06/04/2015 07:56 PM by Rodal »

Offline kencolangelo

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As an onlooker I do often wonder about the possible magnitude of the artifacts.
Is it reasonable to think that any configuration of the system could interact with Earth's magnetic field enough to explain the resulting thrust?
Could even a dedicated electrostatic "air pusher" taking this basic frustrum form generate these sorts of figures with this kind of power input?
Basically, in the worst case scenarios, where the system is explicitly designed to generate the artifacts, what magnitude of artifacts would we see?

Offline X_RaY

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Wouldn't the tunnelling effect also be constrained by conservation of momentum and therefore apply at both ends of the frustrum?
You have to look at the energy density regarding radiation pressure, and don't ignore the lateral conical walls.
Then perform a quantum tunneling analysis.  Momentum will be favored to one side if there is a gradient of emission.

correct and
The tunneling effect acts instantaneous. At the moment a photon is tunneling it impulse acts, that's like its reflected in a wall <z (lower qua the real length of the cavity). There has to be a blue shift of the signal means higher frequency like calculated r and z dependent.

Are you sure that's a net blue shift?  The frustum has to gain momentum which means the photon loses energy and red shifts.  Is the blue shift something that photon's do when they tunnel?
Yes, if there is a potential barrier (cutoff frequency, diameter )most of the photons would be reflected (may be at the sidewall may be at the energy barrier) but some photons able to tunneling that barrier in just zero time, i think than the cavity acts like shorter than it is.
The small end looks like it is narrow to the small end. Its more a intuitiv thing, i have the luck to work with conical cavities for special applications. Got network analyser, Spectrum Analyzer, circulator, load, tapered cavities all available and i am able to build conical cavities like a want but in K-Band area
 8)

I'm just wondering.. if tunneling happens instantaneously (in the literal sense), then there is no time to measure anything - it happens without any dt . Hence, I don't think it can be said that photons increase or decrease frequency during the transition through the barrier.. if there is null time passing, then logically no measurements can take place, from which we can derive a claim about how frequencies of photons might change during a null time transition.
;)

OK, i got a little bit tired yesterday. first i dont think about a redshift in the sense of lower energie. Of course the energie per cycle have to be constant if the cavity is superconducting, in the case of copper there is loss caused by eddy currents and therefore thermal heating, this leads to bigger bandwidth.
Inside a waveguide the wavenumber is different to free space. It's geometrically frustrated..
And i don't think about increase or decrease frequency during the transition through the cutoff barrier.
The frequency shift and phase shift at tunneling is of course equal to zero.


*note to myself, it's difficult for me to translate my mind into an english text. :-\
But bad english is one of the most spoken language of the world. ;D

Offline SeeShells

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As an onlooker I do often wonder about the possible magnitude of the artifacts.
Is it reasonable to think that any configuration of the system could interact with Earth's magnetic field enough to explain the resulting thrust?
Could even a dedicated electrostatic "air pusher" taking this basic frustrum form generate these sorts of figures with this kind of power input?
Basically, in the worst case scenarios, where the system is explicitly designed to generate the artifacts, what magnitude of artifacts would we see?
So many things to consider when testing a EM Frustum and many have criticized EagleWorks for testing at such a low power level. Think of this, by designing the testing to be lower power they can look for effects that a higher power might mask out. I've said before you can't hear the music if you bang the drums loudly. Now they have a low power baseline they can ramp it up a little and compare the two and flag the differences. It's quite smart if you ask me. 

Offline wallofwolfstreet

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What is the rationale for the "Spring Force" artifact?

I thought @frobnicat had disposed of that issue.

Please provide what spring materials you know of that have a substantially different modulus of elasticity E in compression than in tension (this would be useful to experimenters, I guess, to avoid), what is the difference in value for E between compression and tension, and why you think that the spring used by Berca would display a substantial difference in E between tension and compression.

The overwhelming number of materials commonly used as springs have practically the same modulus of Elasticity in tension than in compression.

With deformations large enough, the issue that comes up is not one of bilinearity between tension and compression, but it is one of nonlinearity.  For large deformations spring materials behave with a cubic nonlinearity, but they are still elastic and have same properties in tension and compression.

You would have to reach plasticity (permanent deformation) of a metal to exhibit significant differences between tension and compression.

I think you are overthinking the issue quite a bit here. 

In Iulian's setup, the spring looked to be in tension.  When the deflection of the cantilevered torque arm is downwards, the deflection of the spring increases and the tension would increase.  When deflection is up, tension decreases.  The force provided by the spring is not a constant in both instances, and is therefore a source of error. 
...

Overthinking, me ?  Nahh  ;)




DERIVATION OF SPRING STIFFNESS IN TERMS OF FORCE AND DISPLACEMENT

Formula from strength of materials

stress = Force /Area                              (uniform normal stress distribution on the cross-sectional area)
strain =displacement/(original length)     (definition of strain)

stress = E strain     (constitutive relationship = linear modulus of elasticity E)

Then it trivially follows that:

Force =( E * Area/ originalLength ) * displacement

Force = SpringStiffness * displacement   (a linear stiffness relationship between force and displacement)

where

springStiffness =  E Area/ originalLength

It doesn't matter whether it is tension or compression if the material has a unique E (which most materials do)

It doesn't matter the amount of tension if the material has a linear stress-strain relationship giving a linear E

In essence, if you are worrying about the "amount of tension" affecting the force, then you are positing a material with a nonlinear stress-strain relationship.

If we agree that the spring material has a constant modulus of elasticity E, then the SpringStiffness  is constant as well:

Force = SpringStiffness * displacement  (this is known as Hooke's law)

then

delta (Force) = SpringStiffness  * delta (displacement)



EXAMPLE: SAME ABSOLUTE VALUE OF DISPLACEMENT IN UPWARDS AND DOWNWARDS DIRECTION

So let's say that the neutral position is for z (vertical coordinate)  = 0

F = SpringStiffness  z

(so z=0 means F=0)

for z = + positiveDisplacement

positive Force =  SpringStiffness  * positiveDisplacement

for z = - positiveDisplacement

negative Force =  - SpringStiffness  * positiveDisplacement

so

positive Force = - negative Force

Same displacements up or down translate into same absolute value of force up or down



EXAMPLE: DIFFERENT ABSOLUTE VALUE OF DISPLACEMENT IN UPWARDS THAN DOWNWARDS DIRECTION

for z = + positiveDisplacement

positive Force =  SpringStiffness  * positiveDisplacement

for z = - (1/7) * positiveDisplacement

negative Force = - (1/7) SpringStiffness  * positiveDisplacement

so

positive Force = - 7 negative Force

or, equivalently,

negative  Force = - (1/7) positive Force

That spring force is balanced by the force on the cantilever, which is being measured.

In essence, the spring is linear .
What is the source of error ? ???


I thought “overthinking” was the wrong phrase to use, but now I'm not so sure ;).  You did a great job of accounting for linearities in the above post.  You accounted for linearity of the spring force (no complaints here).  The deflection of a cantilevered beam is also linear with respect to force applied (so good so far on the linearity front)http://en.wikipedia.org/wiki/Deflection_%28engineering%29

However, there is a non-linearity in the analysis that you didn’t account for, and it ends up justifying my initial remarks.  Sin(theta) is not a linear function. 

The linearity of beam deflection implies that for a given Thrust magnitude, applied in the up and then the down direction, the deflections deltaup and deltadown must also be equal in magnitude and opposite in direction (See the terrible paint drawing).  We then have that Ldown, the total length of the spring when thrust is applied in the down direction, is greater than Lup, total length of the spring when thrust is applied in the up direction.  As you have so rigorously proven springs are linear.  For linearity of the spring to matter though, we must have that the change in length going from Lnot to Lup is the same as Lnot to Ldown.

Let’s assume that to be true (In isn’t in my picture because I don’t account for deflection that occurs in the x direction, which may or may not be linear with respect to force applied.  If it isn't true. then I could stop my comment here, because we would have failed to meet the condition above.)

Now is where we have the issue.  Calculate the change in force in the y direction due to the change in length of the spring.  It is after all the spring force in the y direction that matters for the balance reading (trivial to prove with just an FBD).  You will immediately see that the change in y direction spring force is not a linear function of Thrust.  This is the source of error.     

Offline Rodal

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I thought “overthinking” was the wrong phrase to use, but now I'm not so sure ;).  You did a great job of accounting for linearities in the above post.  You accounted for linearity of the spring force (no complaints here).  The deflection of a cantilevered beam is also linear with respect to force applied (so good so far on the linearity front)http://en.wikipedia.org/wiki/Deflection_%28engineering%29

However, there is a non-linearity in the analysis that you didn’t account for, and it ends up justifying my initial remarks.  Sin(theta) is not a linear function. 
Well, the conversation now has shifted from "Spring Error" to you claiming that there is a geometric nonlinearity in Berca's tests.

Whatever it is you are trying to represent by the angle theta, let's say that for Power OFF, you have an angle

theta= thetaInitial

and that for Power ON, pointing UP you have an angle

thetaOnUP = thetaInitial + deltaThetaUP

and that for Power ON, pointing DOWN you have an angle

thetaOnDOWN = thetaInitial + deltaThetaDOWN

(where deltaThetaDOWN is a negative number)

then the change going up is

changeUP = Sin[thetaInitial + deltaThetaUP] - Sin[thetaInitial ]

               = Sin[thetaInitial]Cos[deltaThetaUP] + Cos[thetaInitial]Sin[deltaThetaUP] - Sin[thetaInitial ]

for small change in angle

deltaThetaUP  ~ 0

the expansion of the Sin and Cos series give: (see http://en.wikipedia.org/wiki/Trigonometric_functions#Series_definitions )

Cos[deltaThetaUP] ~ 1
Sin[deltaThetaUP]  ~ deltaThetaUP

changeUP = Sin[thetaInitial] + Cos[thetaInitial] deltaThetaUP - Sin[thetaInitial ]
               =  Cos[thetaInitial] deltaThetaUP



the change going down is

changeDOWN = Sin[thetaInitial + deltaThetaDOWN] - Sin[thetaInitial ]

                     = Sin[thetaInitial]Cos[deltaThetaDOWN] + Cos[thetaInitial]Sin[deltaThetaDOWN] - Sin[thetaInitial ]

for small change in angle

deltaThetaDOWN  ~ 0

the expansion of the Sin and Cos series give:   (see http://en.wikipedia.org/wiki/Trigonometric_functions#Series_definitions )


Cos[deltaThetaDOWN] ~  1
Sin[deltaThetaDOWN]  ~ deltaThetaDOWN

changeDOWN =  Sin[thetaInitial] + Cos[thetaInitial] deltaThetaDOWN - Sin[thetaInitial ]
                     =  Cos[thetaInitial] deltaThetaDOWN



So for small deflections of the EM Drive, the effect is also linear:

changeUP       =  Cos[thetaInitial] deltaThetaUP
changeDOWN =  Cos[thetaInitial] deltaThetaDOWN

(where deltaThetaDOWN is a negative number)

In general we can write that the change in the Sin of theta is equal to a constant times the change in the angle


changeInSin[theta] = Constant * changeInAngle

where Constant = Cos[thetaInitial]

There is no geometric nonlinearity for small forces of the EM Drive, because the force produced by the EM Drive is tiny (fractions of a gram), which also involve tiny changes in displacement, and tiny changes in rotation

Again: we are talking here about very  small forces produced by the EM Drive, and hence very small displacements, and very small rotations produced by the EM Drive.



Note1, what is involved here is called a perturbation analysis, which is quite common in Physics.  Such perturbation is also involved in the analysis for beam bending or shell structures used by engineers when the design a rocket spaceship. 


Note2, if you are interested in a nonlinearity, involving a thermal instability affecting the EM Drive, then this is an excellent paper that is highly recommended:  ;)

https://www.researchgate.net/publication/268804028_NASA%27S_MICROWAVE_PROPELLANT-LESS_THRUSTER_ANOMALOUS_RESULTS_CONSIDERATION_OF_A_THERMO-MECHANICAL_EFFECT
« Last Edit: 06/04/2015 10:22 PM by Rodal »

Offline frobnicat

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I think you are overthinking the issue quite a bit here. 

In Iulian's setup, the spring looked to be in tension.  When the deflection of the cantilevered torque arm is downwards, the deflection of the spring increases and the tension would increase.  When deflection is up, tension decreases.  The force provided by the spring is not a constant in both instances, and is therefore a source of error. 
...
...
EXAMPLE: SAME ABSOLUTE VALUE OF DISPLACEMENT IN UPWARDS AND DOWNWARDS DIRECTION

So let's say that the neutral position is for z (vertical coordinate)  = 0

F = SpringStiffness  z

(so z=0 means F=0)

for z = + positiveDisplacement

positive Force =  SpringStiffness  * positiveDisplacement

for z = - positiveDisplacement

negative Force =  - SpringStiffness  * positiveDisplacement

so

positive Force = - negative Force

Same displacements up or down translate into same absolute value of force up or down
...

Agree.  Maybe the misconception stems from the fact that the spring is "pre-tensioned" and variations occur around this tensioned equilibrium point. I don't see how to illustrate this specific situation more clearly than going with algebraic values (rather than absolute ones) to disambiguate signs.

With all axis going upward (force and position) and origin z=0 at natural rest length of spring (with no force on it at all) Hookes law goes as Fspring/frustum=-k*z, k being spring stiffness, lets say 1000N/m. Running around a pre-tensioned equilibrium means that we have a Weight (of the test article) pulling downward, W=-100N for instance, plus the Thrust T. At any equilibrium (no acceleration) Fspring/frustum opposes other forces (or pseudo-forces) acting on the frustum :  Fspring/frustum=-(W+T). For T=0 the spring is resting at z=z0 such that W-k*z0=0. With the given values, z0=-10cm (that is, below origin, sorry for the inconvenience).

Now in general when T is not necessarily 0, noting displacement d (again positive upward) deviation from z0 : z=z0+d then we have
(W+T)=k*(z0+d) => W-k*z0+T=k*d => T=k*d

d=+.01mm => T=10mN
d=-.01mm => T=-10mN

Now this is a dismembered dead horse...  ::)

Overthinking that a little more, in Iulian set-up this is likely not the stiffness of the "weight offset" pulling spring that dictates the displacement, but the likely higher stiffness (not "strength" as it is not kg rated) of the electronic scale that supports the residual weight left over from the pull-up spring. Divided by the lever ratio. And ignoring the compliance in flexion of the arm... oh well, isn't saying "all linear" sufficient, at least to discard up/down asymmetries in measurements ?

Ahem, too slow an answer...
« Last Edit: 06/04/2015 10:16 PM by frobnicat »

Offline wallofwolfstreet

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I thought “overthinking” was the wrong phrase to use, but now I'm not so sure ;).  You did a great job of accounting for linearities in the above post.  You accounted for linearity of the spring force (no complaints here).  The deflection of a cantilevered beam is also linear with respect to force applied (so good so far on the linearity front)http://en.wikipedia.org/wiki/Deflection_%28engineering%29

However, there is a non-linearity in the analysis that you didn’t account for, and it ends up justifying my initial remarks.  Sin(theta) is not a linear function. 
Well, the conversation now has shifted from "Spring Error" to you claiming that there is a geometric nonlinearity in Berca's tests.

I don't understand your picture and how it may relate to Iulian's test.

Whatever it is you are trying to represent by the angle theta, let's say that for Power OFF, you have an angle

theta= thetaInitial

and that for Power ON, pointing UP you have an angle

thetaOnUP = thetaInitial + deltaThetaUP

and that for Power ON, pointing DOWN you have an angle

thetaOnDOWN = thetaInitial + deltaThetaDOWN

(where deltaThetaDOWN is a negative number)

then the change going up is

changeUP = Sin[thetaInitial + deltaThetaUP] - Sin[thetaInitial ]

               =Sin[thetaInitial]Cos[deltaThetaUP] + Cos[thetaInitial]Sin[deltaThetaUP] - Sin[thetaInitial ]

for small change in angle

deltaThetaUP  ~ 0

the expansion of the Sin and Cos series give: (see http://en.wikipedia.org/wiki/Trigonometric_functions#Series_definitions )

Cos[deltaThetaUP] ~0
Sin[deltaThetaUP]  ~ deltaThetaUP

changeUP =Sin[thetaInitial] + Cos[thetaInitial] deltaThetaUP - Sin[thetaInitial ]
               =  Cos[thetaInitial] deltaThetaUP



the change going down is

changeDOWN = Sin[thetaInitial + deltaThetaDOWN] - Sin[thetaInitial ]

               =Sin[thetaInitial]Cos[deltaThetaDOWN] + Cos[thetaInitial]Sin[deltaThetaDOWN] - Sin[thetaInitial ]

for small change in angle

deltaThetaDOWN  ~ 0

the expansion of the Sin and Cos series give:   (see http://en.wikipedia.org/wiki/Trigonometric_functions#Series_definitions )


Cos[deltaThetaDOWN] ~0
Sin[deltaThetaDOWN]  ~ deltaThetaDOWN

changeDOWN =Sin[thetaInitial] + Cos[thetaInitial] deltaThetaDOWN - Sin[thetaInitial ]
                     =  Cos[thetaInitial] deltaThetaDOWN



So for small deflections of the EM Drive, the effect is also linear:

changeUP =   Cos[thetaInitial] deltaThetaUP
changeDOWN =  Cos[thetaInitial] deltaThetaDOWN

(where deltaThetaDOWN is a negative number)


changeInSin[theta] = Constant * changeInAngle

where Constant = Cos[thetaInitial]

There is no geometric nonlinearity for small forces of the EM Drive, because the force produced by the EM Drive is tiny (fractions of a gram), which also involve tiny changes in displacement, and tiny changes in rotation

We are talking here about very  small forces produced by the EM Drive, and hence very small displacements, and very small roatations produced by the EM Drive.



Note1, what is involved here is called a perturbation analysis, which is quite common in Physics.  Such perturbation is also involved in the analysis for beam bending or shell structures used by engineers when the design a rocket spaceship. 


Note2, if you are interested in a nonlinearity, involving a thermal instability affecting the EM Drive, then this is an excellent paper that is highly recommended:  ;)

https://www.researchgate.net/publication/268804028_NASA%27S_MICROWAVE_PROPELLANT-LESS_THRUSTER_ANOMALOUS_RESULTS_CONSIDERATION_OF_A_THERMO-MECHANICAL_EFFECT

The "Spring Error" and the geometric non-linearity are one in the same. My initial wording of this issue was simply: Spring Force (Iulian).  You are the one who brought up the linearly of the spring constant as though that was the issue, not me.  I never claimed springs aren't linear, or anything to the sort (although I see how you could have come to that conclusion from my initial response, which is my fault for not being clear and fleshing it out right then and there).

The picture is of Iulian's cantilevered arm, where the right side half-circle indicates the fixed connection of one end of the spring, and the other half-circle represents the connection of the spring to the arm.  The arm has been omitted.  I colour coded three cases, black for the initial case (no thrust), red for the case were thrust is upwards (hence the upwards deflection) and green for the case where thrust is downwards.  By "Theta", I mean the angle made between the horizontal and the spring, as I tried to denote with the three colored semi-circles in the top right (which I failed to label). 

Now that we have that out of the way, we can actually address this issue.  There is, unequivocally, a geometrical non-linearity with the spring arranged as such.  If you don't believe me, and think the above statement is false, I urge you to get out the old pencil and paper and do the FBD yourself with the spring arranged as drawn, no small angle approximations.  Sure, an angle arbitrarily close to zero brings this error arbitrarily close to zero.  But deflection exists, and this error exists with it.  You can argue that it is negligible for the case of experimentation because of the small thrust of the emdrive, and I would probably agree if I could be bothered to solve the equations and find out exactly how negligible.  Negligible or not though, it does exist.   

To be honest, the fact that you employed a linear approximation to sin for small angles ought to be enough to convince you that there is a geometrical non-linearity.       

Offline Rodal

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To be honest, the fact that you employed a linear approximation to sin for small angles ought to be enough to convince you that there is a geometrical non-linearity.       

I'm sorry, you are simply wrong, there is no geometric nonlinearity involved in Berca's measurements because the forces of the EM Drive are extremely small. Higher order terms are negligible.  Physicists and engineers are familiar with examples like this throughout nature.  It is called perturbation analysis.  For example, the small angle approximation is also involved in the formula for beam bending or for shell deformations that aerospace engineers routinely use. Good luck and goodbye
« Last Edit: 06/04/2015 10:56 PM by Rodal »

Offline wallofwolfstreet

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To be honest, the fact that you employed a linear approximation to sin for small angles ought to be enough to convince you that there is a geometrical non-linearity.       

You are simply wrong, there is no geometric nonlinearity involved in Berca's measurements because the forces of the EM Drive are extremely small.  Good luck and goodbye

Well I guess there is no convincing you, and I'm sorry to hear that.  Nature doesn't make approximations.    For no non-zero value of theta, does sin(theta)=theta exactly .  Ergo, there is a non-linearity in Iulian's setup with his spring arranged as is.  Maybe you don't think it is big enough to warrant a mention on the sources of error page, and that's fine by me.  Rest assured though, it is there.       

Offline frobnicat

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To be honest, the fact that you employed a linear approximation to sin for small angles ought to be enough to convince you that there is a geometrical non-linearity.       

You are simply wrong, there is no geometric nonlinearity involved in Berca's measurements because the forces of the EM Drive are extremely small.  Good luck and goodbye

Well I guess there is no convincing you, and I'm sorry to hear that.  Nature doesn't make approximations.    For no non-zero value of theta, does sin(theta)=theta exactly .  Ergo, there is a non-linearity in Iulian's setup with his spring arranged as is.  Maybe you don't think it is big enough to warrant a mention on the sources of error page, and that's fine by me.  Rest assured though, it is there.     

Remember discussing a similar "relevance" issue with dr Rodal (inertial recoils from thermal expansions, yes it's 0, no it's not...). Do you think it is big enough to play a significant role in the apparent up/downward disparity ? What size roughly would have to be the arc span to make such non linearity relevant at, say, even only 1% ? Do you see the arm actually move to such extent ? Personally I had to run numbers before I was convinced that a "not 0" was close enough to 0 to be negligible in practice (and hence null, kind of, at least for the discussion).

Offline rfmwguy

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Short snippet of Ruby code that computes the Shawyer Design Factor the way TheTraveller has in his spreadsheet.

def compute_design_factor( small_diameter_meters, large_diameter_meters, frequency_hz, jC)
   
    cM = 299705000.0
    cf = cM / frequency_hz
    jCFPI = jC * cf / Math::PI
 
    b = Math.sqrt( 1 - ( jCFPI / large_diameter_meters ) ** 2 )   
    s = Math.sqrt( 1 - ( jCFPI / small_diameter_meters ) ** 2 )
   
    df = (b - s) / ( 1 - b * s )
   
    return df
   
end

jC = BesselJ Cutoff

Before doing Df or resonance calc you need to know excitation mode TMm,n,p or TEm,n,p and the appropriate BesselJ value as per that mode. BesselJ value is driven by mode TE or TM and the associated m & n values.  p refers to the number of 1/2 waves between the end plates.

There are 2 tables provided. One for TE mode and one for TM mode. Each is indexed by the selected m & n values.

As example to use TE013 mode, use the TE table and the value at the intersection of the m=0 & n=1. = 3.8318  Then adjust end plate spacing or frequency or Df, via altering either/both end plate diameters to fit the desired number of p 1/2 waves between the end plates.

Tables attached.

And what? The above method coming directly out of your spreadsheet and produces the same values - I had to bounce all over to pull all the cells together and then simplify all the duplicate references :) - not sure what you're trying to point out - other than for people to use the above tables to pick a value for jC?

Yes use the tables, for now, to select the appropriate BesselJ value for the excitation mode.

Next version will directly calc the BesselJ value for the selected mode.

Ay the heart of the Df equation is the cutoff wavelength, which is driven by the BesselJ value for the selected excitation mode.

TE11 has a different Df than TE01 and different again for TM01. There is no one value for BesselJ.

Once the mode is selected and resonance is obtained, the physical antenna placement, length & design must be correct to excite the frustum in the mode that the frustum has been designed for.

Further to obtain the highest Q possible, the frustum impedance must match that of the Rf generator. To do that will require the physical ability to adjust the antennas local enviroment by some physically adjustable means.

I'm working to bring those placement & length calculations and impedance tuning methods to the calculator.

As it exists now, there are several more stages to be added.

There are several ways to match to 50 ohms. My plans are to use a simple monopole antenna rather than a loop. Loops will affect the coupling energy directed along the axis of the frustum. In the pic below (bandpass filter) 2 coupling loops are adjusted (rotated) that effectively changes the 3dB BW of the cavity (more coupling, more BW).

So to avoid unknowns, it might be good to go with a simple 1/4 wave monopole. Eagleworks had a coupling loop on the small end (not the side) which polarized the RF perpendicular to the frustum axis. Again, not enough data released to determine if this is significant. FWIW...

http://www.qsl.net/sm7ovk/cavity.gif

Offline Rodal

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I don't particularly agree with the focus and wording (I see the word "amateur" is present in the wiki) for Iulian Berca's experiment, when the same degree of stringent rigor is not dedicated to the tests reported by very small private companies in the UK and the USA and a University in China for their tests in ambient conditions.

Iulian Berca's real name  (and not a monicker) is being used in the EM Drive wiki article and in discussions in this thread to refer to his experiments.  I looked up Iulian Berca in the Internet, and I found out that Iulian has an Electrical Engineering degree from Politehnica University of Bucharest, and has won a Prize at the International robotic contest "Eurobot" August 2006 .   Therefore I think it is wrong (in many ways) to characterize his experiments as those of an "amateur" (particularly when they are compared in the spreadsheet to the experiments by other engineers at really tiny companies in the UK and US).  I have therefore taken the liberty to change the entry in the EM Drive wiki to the following:

Quote
After the invention of the EM Drive by Roger Shawyer, Iulan Berca was the first independent electrical engineer to fabricate a working EmDrive and successfully record force from the device.

Which is a more equanimous description.

Quote from: Iain D. Smith
Do not underestimate the determination of a quiet man.
« Last Edit: 06/05/2015 01:10 AM by Rodal »

Offline wallofwolfstreet

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To be honest, the fact that you employed a linear approximation to sin for small angles ought to be enough to convince you that there is a geometrical non-linearity.       

You are simply wrong, there is no geometric nonlinearity involved in Berca's measurements because the forces of the EM Drive are extremely small.  Good luck and goodbye

Well I guess there is no convincing you, and I'm sorry to hear that.  Nature doesn't make approximations.    For no non-zero value of theta, does sin(theta)=theta exactly .  Ergo, there is a non-linearity in Iulian's setup with his spring arranged as is.  Maybe you don't think it is big enough to warrant a mention on the sources of error page, and that's fine by me.  Rest assured though, it is there.     

Remember discussing a similar "relevance" issue with dr Rodal (inertial recoils from thermal expansions, yes it's 0, no it's not...). Do you think it is big enough to play a significant role in the apparent up/downward disparity ? What size roughly would have to be the arc span to make such non linearity relevant at, say, even only 1% ? Do you see the arm actually move to such extent ? Personally I had to run numbers before I was convinced that a "not 0" was close enough to 0 to be negligible in practice (and hence null, kind of, at least for the discussion).

I see where Rodal is coming from.  Believe it or not, I am also an engineer.  Have an undergrad degree in mechanical engineering and math.  It's not that I don't understand the small angle approximation, or how to derive it from cancelling higher order terms in the taylor expansion, or that I somehow don't believe it's used in engineering practice (I use it too!).

For me though, never in a million years would I feel comfortable saying that because you can approximate an error source to zero, it must in fact be zero, especially when I haven't done a single calculation to see just how approximate my approximation ends up being.

To answer your question, I would have do the maths.  I might in the next few days, but it's hardly worth it. 

This is basically a clash with theory and practice.  In practice, maybe sin(theta)=theta is accurate to within the 10^(-50) decimal place, and I'm just being a pedant (but I wouldn't feel comfortable making that claim without having done the math).  In the most accurate theoretical model, no approximations (ie. the real world), the spring will always constitute a source of error.  Until the math conclusively indicates it is too small to matter, how can we justify ignoring it?

Anyways, this argument is largely off-topic for the EMdrive.  Want to kiss and make up Rodal :) :-*?   
« Last Edit: 06/05/2015 12:17 AM by wallofwolfstreet »

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