#### D_Dom

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##### Re: EM Drive Developments
« Reply #2140 on: 10/16/2014 05:23 AM »
Theoretically not much difference between theory and practice, practically the differences are significant.
Space is not merely a matter of life or death, it is considerably more important than that!

#### Rodal

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##### Re: EM Drive Developments
« Reply #2141 on: 10/16/2014 12:35 PM »
While stumbling through Shawyer's papers, I reached the conclusion that his thrust equation, after substituting the parameter names that Prof. M used, is:

T = 2*So * P*Q/c *(RF wavelength/w_big - RF wavelength/w_small) or

T = 2*So  *P*Q/f  *(1/w_big  - 1/w_small)

where So = (1 - (RF wavelength^2)/(w_big*w_small))^-1

In other words, Shawyer's thrust model differs from Prof. M's thrust model by a multiplicative factor of 2*So .

That of course assumes that I interpreted Shawyer's definition of terms correctly.

Shawyer's equation looks, superficially, very similar to McCulloch's equation (upon substituting in McCulloch's equation the frequency in the denominator by  f= c / Lambda0), except for the factor of 2/(1 -( (Lambda0^2)^2)/(Lambda1*Lambda2)). However, in McCulloch's equation, f is the frequency in the waveguide, so for McCulloch's equation, f is not equal to c / Lambda0 because Lambda0 is the wavelength in 3-D free space, not the wavelength inside the microwave guide.

Shawyer defines Lambda0 as the "free-space propagation wavelength" and makes a difference between the wavelength inside the microwave cavity (which he calls Lambdag) and the wavelength propagation in free space Lambda0.

A one-dimensional waveguide restricts the three dimensional "free space" propagation of the electromagnetic wave to a single dimension.  Therefore, the 3-D free-space wavelength is shorter than the wavelength in the microwave guide.

I would expect that, the wavelength in the guide, Lambdag=  Lambda0/cos(phi), where phi is  the angle between the crest lines and the waveguide longitudinal axis.  Since cosine is always less than unity, Lambdag is always greater than Lambda0.  In other words, "RF wavelength" is greater than Lambda0.

An interpretation of Shawyer's Lambda0 as RF wavelength would lead to a factor of 2 / (1 - (RF wavelength^2)/(w_big*w_small)) ~ 6 for NASA's truncated cone, multiplying the present equation, leading to predicted forces that would be 6 times larger than the experimentally measured ones.

Using Lambda0, as intended by Shawyer, would lead to a predicted force closer to the experimentally measured one.  So basically, I don't agree with replacing Lambda0 by RF wavelength without taking into account the fact that RF wavelength must be longer than Lamda0.

Also notice that Shawyer gives an equation for the thrust taking into account the dielectric (see:  http://www.newscientist.com/data/images/ns/av/shawyertheory.pdf  equation 11)
« Last Edit: 10/16/2014 01:44 PM by Rodal »

#### JohnFornaro

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##### Re: EM Drive Developments
« Reply #2142 on: 10/16/2014 12:49 PM »
Quote from: some random guy on an intertube thread...
As a veteran member of the American Statistical Association...

Oh right.  Everybody knows that the chances of a coin landing on its edge are fifty-fifty.  You gotta have better credentials than that!
Sometimes I just flat out don't get it.

#### aceshigh

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##### Re: EM Drive Developments
« Reply #2143 on: 10/16/2014 01:32 PM »
Quote from: some random guy on an intertube thread...
As a veteran member of the American Statistical Association...

Oh right.  Everybody knows that the chances of a coin landing on its edge are fifty-fifty.  You gotta have better credentials than that!

I thought those were the chances of a coin landing head or tails?

#### JohnFornaro

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##### Re: EM Drive Developments
« Reply #2144 on: 10/16/2014 02:27 PM »
does this pertain?

arxiv.org/pdf/1312.3267
Sometimes I just flat out don't get it.

#### JohnFornaro

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##### Re: EM Drive Developments
« Reply #2145 on: 10/16/2014 02:36 PM »
Quote from: some random guy on an intertube thread...
As a veteran member of the American Statistical Association...

Oh right.  Everybody knows that the chances of a coin landing on its edge are fifty-fifty.  You gotta have better credentials than that!

I thought those were the chances of a coin landing head or tails?

See video.  Happens all the time.  Sheesh.

[Edit:  Ooo.  Ooo.  From the snappy comeback department:  That's what fifty-fifty means!  Lands on its edge fifty times out of fifty!]
« Last Edit: 10/16/2014 04:12 PM by JohnFornaro »
Sometimes I just flat out don't get it.

#### Rodal

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##### Re: EM Drive Developments
« Reply #2146 on: 10/16/2014 02:39 PM »
does this pertain?

arxiv.org/pdf/1312.3267

Pertain ? We're sorry all attendants are still busy Please continue to hold and your call will be answered by the next available attendant Thank you for your patience -

Yes, in the restricted, narrowly specific sense of showing the conservation of momentum and the conservation of energy of photons hitting a perfect mirror and being reflected from the surface (page 2 of that reference).   As previously discussed in another post in this thread, most of the microwave photons get reflected from the copper surfaces.

The reflected photon will be red-shifted for a mirror moving away from the source in the case of a mirror moving at a significant speed with respect to the speed of light in a vacuum.  However, in our case this effect is zero, therefore the reflected photon has exactly the same frequency (and hence the same energy),  the momentum ( a vector quantity) of the reflected photon has the same magnitude (same frequency) but it is oriented in the opposite direction upon reflection.  Since the magnitude is exactly the same, the change in momentum (of the photons hitting the wall and getting reflected) is purely due to change in direction and not due to frequency shifting.

No regarding the negative index materials  because they are artificial man-made structures where the refractive index has a negative value over some frequency range and no known natural materials exhibits this property, definitely not the copper walls in the microwave cavities of the EM Drives.  In my opinion discussion of "dynamic Casimir effects" (mirror walls moving at speeds near the speed of light) and "metamaterials" (materials with negative index of refraction) with respect to the EM  Drives is a distraction, since none of that can take place in the EM Drives.

Thanks for bringing it to our attention.

Here is the refractive index for copper.  In our case the wavelengths are about ~ 150 000 micrometers long, or about 10^5, which is way to the right in the picture below (way off the horizontal scale), hence the refractive index is positive and very large in magnitude (the very few photons making into the copper will have a phase velocity orders of magnitude lower than the speed of light in vacuum).
« Last Edit: 10/16/2014 03:34 PM by Rodal »

#### Rodal

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##### Re: EM Drive Developments
« Reply #2147 on: 10/16/2014 03:41 PM »
...

I get.

Shawyer   Experimental   Demonstrator
Dimension -   meters   meters
w_big, in.    0.1600     0.2800
w_small, in    0.1050     0.0778
height, in    0.1700     0.3811
w_small, external view.       0.1711

The Demonstrator has a constant external small end diameter for about half the length. I speculate that the taper continues internally with the constant diameter section there for whatever reason. That constant diameter section is about 0.1711 meter. Did the Chinese do both sizes?

Edit: I don't think you should use demonstrator numbers. W_big is OK, it's from the text but w_small is probably to small and height to large. I expect the taper stops in the cylindrical section at a height of about 300 mm based on the Experimental and Eagleworks device ratios.. Point is, I can't tell the dimensions of the demonstration device cavity because of the construction. Garbage in, garbage out so just don't use the above Demonstrator numbers I guess.

One could make the same argument regarding NASA Eagleworks internal dimensions (only the internal dimensions matter regarding mode shapes !!) see picture below.  We have discussed this before.  Yes garbage in/garbage out, but experimental information (even when not perfect)  in the eyes of a discerning scientist/engineer is not garbage.  If one throws all information out that is not perfect one ends up with practically nothing to analyze.  What applies here is the following (I first heard this from the Dutch scientist W.Koiter):

"Extreme rigor in analysis leads to rigor mortis"

In this case the scientific/engineering judgement comes in knowing what is the difference in mode shapes between the geometry below and the geometry of a perfect truncated cone.  I made that assessment, so I included the NASA Eagleworks truncated cones and both  Shawyer truncated cones in the data.  What matters mostly are the flat base surfaces of the truncated cone.  This is supported by the data I have previously shown.
Regarding frequency and mode shapes the statistical analysis I have shown demonstrates that there is too much uncertainty anyway to conclude anything.  As brought up by Ludwick this problem is not due to the geometry but it is instead due to the researchers trying but failing to keep the frequency the same when at resonance and high Q due to the extremely narrow bandwith expected at high Q.

« Last Edit: 10/16/2014 04:06 PM by Rodal »

#### aero

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##### Re: EM Drive Developments
« Reply #2148 on: 10/16/2014 04:12 PM »
@Rodal

Quote
An interpretation of Shawyer's Lambda0 as RF wavelength would lead to a factor of 2 / (1 - (RF wavelength^2)/(w_big*w_small)) ~ 6 for NASA's truncated cone, multiplying the present equation, leading to predicted forces that would be 6 times larger than the experimentally measured ones.

Thanks! I ran some numbers and discovered the problem - Now I know what caused it.
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#### JohnFornaro

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##### Re: EM Drive Developments
« Reply #2149 on: 10/16/2014 04:17 PM »
does this pertain?

arxiv.org/pdf/1312.3267

Pertain? We're sorry all attendants are still busy...

Even tho 99% of the time, you want to place an order, please listen carefully to all of our arbitrarily and always recently changed menu options, knowing full well that "place an order" is at the end of the list.  Oh.  And did we say that we're experiencing "unusually heavy phone traffic", like we do all the time, regardless of time of day or season?   And good luck in getting a human being who speaks English sufficiently well to actually take an order...
« Last Edit: 10/16/2014 07:46 PM by JohnFornaro »
Sometimes I just flat out don't get it.

#### aero

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##### Re: EM Drive Developments
« Reply #2150 on: 10/16/2014 05:11 PM »
@Rodal
Quote
In this case the scientific/engineering judgement comes in knowing what is the difference in mode shapes between the geometry below and the geometry of a perfect truncated cone.  I made that assessment, so I included the NASA Eagleworks truncated cones and both  Shawyer truncated cones in the data.  What matters mostly are the flat base surfaces of the truncated cone.  This is supported by the data I have previously shown.

Ok. If I assume the cavity shape of the Demonstrator is the same shape as the Experimental model, then using the published text numbers for the overall diameters, 280 mm and 160 mm, by ratio I calculate the Demonstrator dimensions as:

w_big = 0.28 meters
w_small = 0.18375 meters
height = 0.2975 meters

These are most likely usable numbers but feel free to use the best data you have available.

My problem with this is, "How does he justify larger dimensions on the resonate cavity while using the same or higher frequency drive?"
It must be buried in his theory somewhere.
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#### Rodal

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##### Re: EM Drive Developments
« Reply #2151 on: 10/16/2014 05:52 PM »
@Rodal
Quote
In this case the scientific/engineering judgement comes in knowing what is the difference in mode shapes between the geometry below and the geometry of a perfect truncated cone.  I made that assessment, so I included the NASA Eagleworks truncated cones and both  Shawyer truncated cones in the data.  What matters mostly are the flat base surfaces of the truncated cone.  This is supported by the data I have previously shown.

Ok. If I assume the cavity shape of the Demonstrator is the same shape as the Experimental model, then using the published text numbers for the overall diameters, 280 mm and 160 mm, by ratio I calculate the Demonstrator dimensions as:

w_big = 0.28 meters
w_small = 0.18375 meters
height = 0.2975 meters

These are most likely usable numbers but feel free to use the best data you have available.

My problem with this is, "How does he justify larger dimensions on the resonate cavity while using the same or higher frequency drive?"
It must be buried in his theory somewhere.

Excellent question.

I think the answer is simple:  Shawyer may not have the capability to calculate the mode shapes and the amplitude vs. frequency inside the cavity.

Even NASA Eagleworks, using COMSOL Finite Element failed to use a Finite Element mesh discrete enough to closely match the frequency amplitude curve.  Please see attached figure comparing COMSOL FE analysis of NASA Eagleworks compared with actual S22 plot and it is evident that the COMSOL analysis is way off (particularly taking into account the extremely small narrow bandwidths at high Q resonance as pointed out by Ludwick)

There is a huge difference between: A) frequency between NASA's COMSOL analysis and the S22 plot and B) Amplitude between NASA's COMSOL analysis and the S22 plot; particularly at the critical frequencies of 1933 and 1937 GHz that were used by NASA Eagleworks.  It is even a mystery why NASA Eagleworks chose to test at those particular frequencies, as remarked by Ludwick.

And notice that the remark made in the report about removing the dielectric resulted in no thrust refers to a completely different frequency which is off to the right of the right vertical margin of both the COMSOL and the S22 plots.  So why did NASA Eagleworks conduct their dielectric test at a different frequency which is off the plots and different from the other tests?  My reading of this: NASA conducted the dielectric "test" early on (as remarked in the report) at a frequency in which the amplitude is much lower and that's why they measured no thrust: they got no thrust due to the amplitude resonance curve and not due to the dielectric.
« Last Edit: 10/16/2014 06:13 PM by Rodal »

#### aero

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##### Re: EM Drive Developments
« Reply #2152 on: 10/16/2014 06:11 PM »
Ok.

Now, didn't you show that thrust was not strongly dependent on frequency? But photon momentum is strongly dependent on frequency (as is energy) so does this imply that thrust is not strongly dependent on photon momentum? Or can your approach separate momentum and energy?
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#### Rodal

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##### Re: EM Drive Developments
« Reply #2153 on: 10/16/2014 06:16 PM »
Ok.

Now, didn't you show that thrust was not strongly dependent on frequency? But photon momentum is strongly dependent on frequency (as is energy) so does this imply that thrust is not strongly dependent on photon momentum? Or can your approach separate momentum and energy?
No, what I showed was that the variation with frequency overwhelmed the ability to regress the data because of the nonlinearity of the amplitude vs frequency curve and the paucity of frequency data.

On the contrary, the measured thrust is most dependent on amplitude of the resonance curve and the amplitude is very nonlinearly dependent on frequency.

#### aero

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##### Re: EM Drive Developments
« Reply #2154 on: 10/16/2014 06:25 PM »
Ok.

Now, didn't you show that thrust was not strongly dependent on frequency? But photon momentum is strongly dependent on frequency (as is energy) so does this imply that thrust is not strongly dependent on photon momentum? Or can your approach separate momentum and energy?
No, what I showed was that the variation with frequency overwhelmed the ability to regress the data because of the nonlinearity of the amplitude vs frequency curve and the paucity of frequency data.

On the contrary, the measured thrust is most dependent on amplitude of the resonance curve and the amplitude is very nonlinearly dependent on frequency.

Ok that makes sense.
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#### Rodal

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##### Re: EM Drive Developments
« Reply #2155 on: 10/16/2014 06:33 PM »
Ok.

Now, didn't you show that thrust was not strongly dependent on frequency? But photon momentum is strongly dependent on frequency (as is energy) so does this imply that thrust is not strongly dependent on photon momentum? Or can your approach separate momentum and energy?
No, what I showed was that the variation with frequency overwhelmed the ability to regress the data because of the nonlinearity of the amplitude vs frequency curve and the paucity of frequency data.

On the contrary, the measured thrust is most dependent on amplitude of the resonance curve and the amplitude is very nonlinearly dependent on frequency.

Ok that makes sense.

What the experimental data shows is that the experimental force depends on high Q and resonance.  The researchers don't really know ahead of time exactly at what frequency the highest amplitude will take place.  To make matters worse they don't appear to have the means to keep the frequency within the very narrow bandwidth that accompanies a high Q.  So completing an experiment is a tall order (I think this is the reason why Eagleworks did so few experiments: each one was a challenge).
« Last Edit: 10/16/2014 06:33 PM by Rodal »

#### Rodal

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##### Re: EM Drive Developments
« Reply #2156 on: 10/16/2014 06:39 PM »
It is like somebody trying to tune to a radio transmission without knowing at what frequencies the transmissions are being broadcast.   The payoff is getting the highest amplitude, but you are lucky just to receive a transmission, finding out at what frequency the highest amplitudes take place was beyond the capabilities of any of these researchers: they only looked at two frequency ranges: 1.9 GHz (NASA) and 2.5 GHz (UK and China).
To make matters worse your receiver is difficult to keep tuned at the right frequency, once you receive the broadcast, the frequency may wonder off and your amplitude may wonder on and off as well, and certainly will vary in amplitude during the receiving time (which for Eagleworks was only ~30 to 40 seconds).
And to make matters much worse, the transmissions having the highest amplitude are the ones that have the narrowest bandwidth, so those frequencies are the hardest to find, they are the hardest to tune to, and once you find them they are the hardest to stay tuned to.

« Last Edit: 10/16/2014 06:59 PM by Rodal »

#### frobnicat

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##### Re: EM Drive Developments
« Reply #2157 on: 10/16/2014 06:54 PM »
Ok, this is preliminary :
I wrote a small program to generate some exhaustive search on formulas upon the relevant factors then sieving those formulas that fit the available data. This is completely theoretically agnostic but it does check for dimensional consistency (as far as kg m s units are concerned). The search goes on for any product of the terms a  b  L  Q  P  F  c  (respectively w_big   w_small   wavelength=c/Freq   Power   Thrust    Speed_of_light) with all possible whole exponents from -2 to +2 (going through 0) and tries to equal 1 (with the experimental data). It also tries an "extended" term (exterm) that is a combination of 2 homogeneous terms ( that is  a  b  or L ) at any power -2 to +2 through any of the operators  sum  difference  geometrical_average, and then to any power -2 to +2.
This does cover the formula by McCulloch but not Shawyer's.

Example of understanding the following dumps : McCulloch's formula reads
a^0  b^0  L^1  Q^1  P^1  F^-1 c^-1   |a^-1 - b^-1|^1  =  1
or said otherwise  F = P Q L/c (1/b - 1/a)
Note that the difference operator for the extended term is enclosed in absolute value (manual permutation needed to remove it).

The sieve goes like that : use the formula on each of the seven data points to generate a value hopefully close to 1. If it is not close to 1 but close to a given value (say 2) for all the data points then we have a constant fudge factor, but if the standard deviation around it is small this is still interesting : a strong relation still holds between the terms in such formula. The mean and deviation are calculated in log space, that is a mean of 0 is a best result (formula gives values around 1) while a mean of -1 or +1 says the formula gives values e (=2.72) times too low or too big.

Data input :

/// With maxes for ranges
t_data data_in[Nrec] =
{
//                                 w_big  w_small  lambda      Q     power   force
{"Shawyer (2008) a",        1.0 ,  16    ,  8    , C/2.45  ,  5900 ,  850   , 16       },
{"Shawyer (2008) b",        1.0 ,  28    ,  4    , C/2.45  , 45000 , 1000   , 214      },
{"Juan (2012) TE011",       1.0 ,  28    ,  4    , C/2.5   , 32000 , 1000   , 214      },
{"Juan (2012) TE012",       1.0 ,  28    ,  4    , C/2.45  , 50000 , 1000   , 315      },
{"Brady et al. (2014) a",   1.0 ,  24.75 , 16.5  , C/1.933 ,  7320 ,   16.9 ,   0.0912 },
{"Brady et al. (2014) b",   1.0 ,  24.75 , 16.5  , C/1.937 , 18100 ,   16.7 ,   0.0501 },
{"Brady et al. (2014) c",   1.0 ,  24.75 , 16.5  , C/1.88  , 22000 ,    2.6 ,   0.0554 },
};

Here we go :

Thresholds : mean=3.00   stddev=0.62

a    b    L    Q    P    F    c                        mean   stddev
---------------------------------------------------------------------
a^0  b^-2 L^2  Q^1  P^1  F^-1 c^-1                      1.62   0.59

a    b    L    Q    P    F    c      exterm            mean   stddev
---------------------------------------------------------------------
a^1  b^-2 L^2  Q^1  P^1  F^-1 c^-1   (a^ 1 + b^ 1)^-1   1.28   0.61
a^2  b^-2 L^2  Q^1  P^1  F^-1 c^-1   (a^ 2 + b^ 2)^-1   1.42   0.60
a^-1 b^-2 L^-1 Q^1  P^1  F^-1 c^-1   (a^-2 + L^-2)^-2   0.46   0.60 *
a^-2 b^-2 L^0  Q^1  P^1  F^-1 c^-1   (a^-2 + L^-2)^-2  -0.14   0.60 *
a^-1 b^-2 L^1  Q^1  P^1  F^-1 c^-1   (a^-2 + L^-2)^-1   0.74   0.58
a^-2 b^-2 L^2  Q^1  P^1  F^-1 c^-1   (a^-2 + L^-2)^-1   0.15   0.61 *
a^-1 b^-2 L^1  Q^1  P^1  F^-1 c^-1   (a^-1 + L^-1)^-2   0.13   0.58 *
a^-2 b^-2 L^2  Q^1  P^1  F^-1 c^-1   (a^-1 + L^-1)^-2  -0.46   0.60 *
a^0  b^-2 L^1  Q^1  P^1  F^-1 c^-1   (a^-1 + L^-1)^-1   1.17   0.61
a^-1 b^-2 L^2  Q^1  P^1  F^-1 c^-1   (a^-1 + L^-1)^-1   0.58   0.58
a^-1 b^-2 L^2  Q^1  P^1  F^-1 c^-1   (a^ 1 + L^ 1)^1    2.06   0.58
a^-2 b^-2 L^2  Q^1  P^1  F^-1 c^-1   (a^ 1 + L^ 1)^2    2.51   0.57
a^-2 b^-2 L^2  Q^1  P^1  F^-1 c^-1   (a^ 2 + L^ 2)^1    1.90   0.57
a^0  b^0  L^2  Q^1  P^1  F^-1 c^-1   |a^-2 - b^-2|^1    1.31   0.61
a^0  b^0  L^1  Q^1  P^1  F^-1 c^-1   |a^-1 - b^-1|^1    0.46   0.61 <-
a^-1 b^1  L^2  Q^1  P^1  F^-1 c^-1   |a^-1 - b^-1|^2   -0.76   0.54 *
a^0  b^-2 L^-2 Q^1  P^1  F^-1 c^-1   |a^-2 - L^-2|^-2   2.48   0.61
a^1  b^-2 L^-1 Q^1  P^1  F^-1 c^-1   |a^-2 - L^-2|^-1   2.64   0.56
a^0  b^-2 L^0  Q^1  P^1  F^-1 c^-1   |a^-2 - L^-2|^-1   2.05   0.55
a^0  b^-2 L^1  Q^1  P^1  F^-1 c^-1   |a^-1 - L^-1|^-1   2.50   0.57
a^-2 b^-2 L^2  Q^1  P^1  F^-1 c^-1 sqrt(a^-2 L^-2)^-1   1.02   0.58
a^-1 b^-2 L^2  Q^1  P^1  F^-1 c^-1 sqrt(a^-1 L^-1)^-1   1.32   0.58

Checked : 94140625
Validated : 21769

McCulloch's formula is indicated with the arrow, stars show decent candidates.
We note that all selected solutions with both a decent absolute magnitude (mean near 0) and low deviation all share the same factors  F = Q P/c times something in meters^-1. This geometric factor, (1/b - 1/a) for McCulloch, allows for a lot of variations while still giving correct predictions. This is not surprising since L and a and b all are in a comparable range, this is hard to confirm a clear relation. While (1/b - 1/a) has a good look compared to others, I wouldn't say we have to explain why we should have this particular formula. More data required. On the other hand the QP/c term (and probably QPL/c) seems a clear winner to be accounted for.

Being a little more selective on standard deviation but allowing for huge fudge factors

Thresholds : mean=12.00  stddev=0.56

a    b    L    Q    P    F    c                        mean   stddev
---------------------------------------------------------------------

a    b    L    Q    P    F    c      exterm            mean   stddev
---------------------------------------------------------------------
a^1  b^-1 L^2  Q^0  P^1  F^-1 c^-1   (a^-2 + b^-2)^1   -6.98   0.53
a^2  b^1  L^1  Q^0  P^1  F^-1 c^-1   (a^-2 + b^-2)^2   -6.19   0.55
a^1  b^-2 L^2  Q^0  P^1  F^-1 c^-1   (a^-1 + b^-1)^1   -6.84   0.54
a^2  b^-1 L^1  Q^0  P^1  F^-1 c^-1   (a^-1 + b^-1)^2   -5.92   0.54
a^1  b^-2 L^2  Q^0  P^1  F^-1 c^-1   (b^-1 + L^-1)^1   -6.67   0.54
a^2  b^-2 L^1  Q^0  P^1  F^-1 c^-1   (b^ 1 + L^ 1)^-1  -7.60   0.55
a^2  b^-2 L^2  Q^0  P^1  F^-1 c^-1   (b^ 2 + L^ 2)^-1  -7.51   0.55
a^2  b^0  L^0  Q^0  P^1  F^-1 c^-1   |a^-2 - b^-2|^1   -7.40   0.56
a^1  b^-1 L^1  Q^0  P^1  F^-1 c^-1   |a^-1 - b^-1|^1   -8.33   0.55
a^1  b^1  L^0  Q^0  P^1  F^-1 c^-1   |a^-1 - b^-1|^2   -9.48   0.56 *
a^-1 b^1  L^2  Q^1  P^1  F^-1 c^-1   |a^-1 - b^-1|^2   -0.76   0.54
a^0  b^-2 L^0  Q^1  P^1  F^-1 c^-1   |a^-2 - L^-2|^-1   2.05   0.55
a^2  b^-2 L^-2 Q^1  P^1  F^-1 c^-1   |a^-1 - L^-1|^-2   4.56   0.52
a^1  b^-2 L^0  Q^1  P^1  F^-1 c^-1   |a^-1 - L^-1|^-1   3.09   0.55
a^2  b^-2 L^2  Q^0  P^1  F^-1 c^-1 sqrt(a^-2 b^-2)^1   -7.18   0.55
a^2  b^-2 L^1  Q^0  P^1  F^-1 c^-1 sqrt(a^-1 b^-1)^1   -7.14   0.54
a^2  b^-2 L^1  Q^0  P^1  F^-1 c^-1 sqrt(b^-1 L^-1)^1   -6.84   0.55
a^1  b^-2 L^2  Q^0  P^1  F^-1 c^-1 sqrt(b^-1 L^-1)^1   -7.43   0.55

The starred one seems the more symmetric. It reads
F = 13100 P/c ab(1/b-1/a)^2

Interestingly it requires no Q value nor wavelength. The constant factor compensates for the absence of Q in absolute magnitude. It is dimensionless. I don't know how it could be interpreted, otherwise than a coincidence in looking at 21769 formulas.
« Last Edit: 10/16/2014 09:03 PM by frobnicat »

#### aero

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##### Re: EM Drive Developments
« Reply #2158 on: 10/16/2014 06:57 PM »
And because there are only 2 cavity shapes and 3 cavity sizes you are going to have the same problem trying to sus out a dependency on cavity height, aren't you.

It seems to me that the greater the height of the cavity, the more difficult it will be to tune. That is, if the cavity is one wavelength high then a small error in frequency will give one delta error in wavelength and one delta off of the resonance peak, but if the cavity is 12 wavelengths high, that same small error in frequency will give 12 deltas error off of resonance peak.

I think that current technology can deal with this if it is brought to bear on the problem.
Retired, working interesting problems

#### Rodal

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##### Re: EM Drive Developments
« Reply #2159 on: 10/16/2014 07:10 PM »

...
McCulloc's formula is indicated with the arrow, stars show decent candidates.
We note that all selected solutions with both a decent absolute magnitude (mean near 0) and low deviation all share the same factors  F = Q P/c times something in meters^-1. This geometric factor, (1/b - 1/a) for McCulloch, allows for a lot of variations while still giving correct predictions. This is not surprising since L and a and b all are in a comparable range, this is hard to confirm a clear relation. While (1/b - 1/a) has a good look compared to others, I wouldn't say we have to explain why we should have this particular formula. More data required. On the other hand the QP/c term (and probably QPL/c) seems a clear winner to be accounted for.

OK.  First applause to you for great effort, using the computational-brute-force approach.  Great frobnicating

1) It looks like there is no formula found using the brute-force computational approach (examining  21769 formulas) that does appreciable better than McCulloch's regarding appreciably minimizing Standard Deviation

2) I don't like allowing any fudge factors whatsoever.  So it looks like the alternatives (which only improve the mean, but not the StdDev) are:

a^-2 b^-2 L^2  Q^1  P^1  F^-1 c^-1   (a^-2 + L^-2)^-1   0.15   0.61 *
a^-1 b^-2 L^1  Q^1  P^1  F^-1 c^-1   (a^-1 + L^-1)^-2   0.13   0.58 *

compared to McCulloch's

a^0  b^0  L^1  Q^1  P^1  F^-1 c^-1   |a^-1 - b^-1|^1    0.46   0.61 <-

The first formula (in blue) is interesting since it involves the surface areas
But please notice that the formula involves the addition of surface a to surface L,
Strange formula.  Can't immediately make sense of it...
Why pick (a^-2 + L^-2)^-1  ?

These formulas are telling us that the big diameter surface (a) is more important

NOTE: For McCulloch's formula to be interpreted as F = P Q L/c (1/b - 1/a).  We must satisfy the following requirement:  MeasuredFrequency = c/L; therefore L = c / MeasuredFrequency; as prescribed by frobnicat
« Last Edit: 10/16/2014 08:34 PM by Rodal »

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