EM Drive - User contributions [en]

@notsosureofit Hypothesis

2015-07-16T15:29:39Z

Notsosureofit:

The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)

== Basic Expression ==
Starting with the expressions for the frequency of a cylindrical RF cavity [https://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity]:


<math>f = \cfrac{c}{2π}\sqrt{(\cfrac{X}{R})^2+(\cfrac{pπ}{L})^2}</math>

where "c" is the speed of light in the medium (the speed of light in vacuum divided by the square root of the product of the relative magnetic permeability times the relative electric permittivity of the medium).

For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function.
[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.

and for TE modes, X = X'[subm,n] = the n-th zero of the derivative of the m-th Bessel function.
[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.

* Here is a table [http://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlx] to 15 digits precision for the roots of the cylindrical Bessel functions X[sub m,n] and for the roots of its derivative X'[subm,n] from m=0 to m=10, and from n=1 to n=5

Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.


<math>\Delta f = \cfrac{1}{2f}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

''This is a cylindrical approximation and could be replaced with a tapered dielectric index of refraction in a cylindrical cavity.''

and from there the expression for the acceleration g from:


<math>g = \cfrac{c^2}{L}\cfrac{\Delta f}{f}</math>

such that:


<math>g = \cfrac{c^2}{2Lf^2}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

''This is the acceleration at which the dispersion of the tapered cavity is balanced out by the dispersion due to its acceleration.''

Using the "weight" of the photon in the accelerated frame from:


<math>W = \cfrac{hf}{c^2}g</math>

where we make the connection via the Equivalence Principle that the acceleration of a photon seen in the rest frame is that which is balanced out in the accelerated frame. That is, the dispersion of the tapered cavity reduces to zero (along the axis) in that accelerated frame of reference.

Such that:

<math>W = T = \cfrac{h}{L}\Delta f</math>

We identify that as the thrust per photon:


<math>T = \cfrac{h}{2Lf}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

Notice that this is the static thrust per photon in a rest (un-accelerated) frame traveling with the cavity. That is to say, thrust is dependent on the acceleration that the physical cavity experiences and goes to zero at the acceleration g. This is an example of a negative feedback system where the steady state acceleration in the cavity frame of a free cavity will always be less than that calculated from the static force. It has no dependence on the linear velocity. (The case of circular motion is different in that the centrifugal "force" is dependent on angular velocity and will further negatively affect the thrust.)

If the number of photons is 

<math>\cfrac{P}{hf}(\cfrac{Q}{2πf})</math>

then the total thrust is


<math>NT = \cfrac{PQ}{4πLf^3}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

or

<math>NT = \cfrac{2PQ}{L(2πf)^3}(c X)^2 (\cfrac{1}{Ds^2}-\cfrac{1}{Db^2})</math>

or

<math>NT=\cfrac{2PQ}{L ω^3}(c X)^2 (\cfrac{1}{Ds^2}-\cfrac{1}{Db^2})</math>

where Ds = diameter at small end, Db = diameter at big end and ω = angular frequency.

== Example ==
Here is an example of the force of each mode vs frequency for m = 0 to 10, n = 1 to 5, p = 1 to 3 from the table referenced above.

[[File:00 chart21.jpg]]

In this case Rs = 0.0794 m, Rb = 0.1397 m, L = 0.2286 m (the dimensions of the truncated cone cavity tested at NASA Eagleworks as reported by Brady et.al.) and PQ = 2*10^6 watts.

The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

For constant geometrical dimensions, and constant quality factor and input power, the asymptotic behavior of thrust is inversely proportional to the cube of the frequency and proportional to the square of X.

___________________________________________________________

== Appendix 1. ==
Appendix 1.

Proof that scaling dimensions inversely proportional to frequency keeps the thrust invariant:

Suppose that the thrust at frequency <math>f_1</math>, and dimensions <math>L_1</math>, <math>Ds_1</math>, and <math>Db_1</math> is

<math>NT_1 = \cfrac{2PQ}{L_1(2πf_1)^3}(c X)^2 (\cfrac{1}{Ds_1^2}-\cfrac{1}{Db_1^2})</math>

then, at frequency <math>f_2</math> a multiple of frequency <math>f_1</math>

<math>f_2 = n f_1 </math>

where the frequency ratio

<math>n=\cfrac{f_2}{f_1} </math>

can be any irrational number (not equal to zero). Scaling dimensions to be inversely proportional to the frequency ration n:

<math>L_2=\cfrac{L_1}{n} </math>

<math>Ds_2=\cfrac{Ds_1}{n} </math>

<math>Db_2=\cfrac{Db_1}{n} </math>

and substituting, we get the thrust for frequency <math>f_2</math> and dimensions <math>L_2</math>, <math>Ds_2</math>, and <math>Db_2</math> to be:

<math>NT_2 = \cfrac{2PQ}{L_1(2πf_1 n)^3}(c X)^2 (\cfrac{1}{(\cfrac{Ds_1}{n})^2}-\cfrac{1}{(\cfrac{Db_1}{n})^2})</math>

and since the factor of <math>n^3</math> occurs both in the numerator and the denominator, it cancels out, leaving

<math>NT_2 = NT_1</math>

If the mode shape is kept invariant, for constant quality factor and input power, the thrust force is invariant, independent of frequency when the diameter and the length of the cavity are both scaled to change inversely proportional to the frequency ratio n.

___________________________________________________________

== Appendix 2. ==
Appendix 2.

An interesting expression to examine is <math>\cfrac{fc}{g} </math>

It represents the number of cycles for the photons in the cavity to reach velocity c if they were free to do so at the acceleration g.

In that respect <math>\cfrac{g}{fc} </math> represents a degree of coupling between the standing waves in the cavity and a traveling wave.

In this case Rs = 0.0794 m, Rb = 0.1397 m, L = 0.2286 m (the dimensions of the truncated cone cavity tested at NASA Eagleworks as reported by Brady et.al.) and PQ = 2*10^6 watts.

The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). For a cylindrical cavity <math>\Delta f</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case), which means that the acceleration <math>g</math> is zero. Hence the number of cycles <math>\cfrac{fc}{g}</math> approaches infinity for a cylindrical cavity.

[[File:00 chart21-2.jpg]]

@notsosureofit Hypothesis

2015-07-14T01:43:58Z

Notsosureofit:

The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)

Starting with the expressions for the frequency of a cylindrical RF cavity [https://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity]:


<math>f = \cfrac{c}{2π}\sqrt{(\cfrac{X}{R})^2+(\cfrac{pπ}{L})^2}</math>

where "c" is the speed of light in the medium (the speed of light in vacuum divided by the square root of the product of the relative magnetic permeability times the relative electric permittivity of the medium).

For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function.
[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.

and for TE modes, X = X'[subm,n] = the n-th zero of the derivative of the m-th Bessel function.
[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.

* Here is a table [http://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlx] to 15 digits precision for the roots of the cylindrical Bessel functions X[sub m,n] and for the roots of its derivative X'[subm,n] from m=0 to m=10, and from n=1 to n=5

Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.


<math>\Delta f = \cfrac{1}{2f}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

''This is a cylindrical approximation and could be replaced with a tapered dielectric index of refraction in a cylindrical cavity.''

and from there the expression for the acceleration g from:


<math>g = \cfrac{c^2}{L}\cfrac{\Delta f}{f}</math>

such that:


<math>g = \cfrac{c^2}{2Lf^2}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

''This is the acceleration at which the dispersion of the tapered cavity is balanced out by the dispersion due to its acceleration.''

Using the "weight" of the photon in the accelerated frame from:


<math>W = \cfrac{hf}{c^2}g</math>

where we make the connection via the Equivalence Principle that the acceleration of a photon seen in the rest frame is that which is balanced out in the accelerated frame. That is, the dispersion of the tapered cavity reduces to zero (along the axis) in that accelerated frame of reference.

Such that:

<math>W = T = \cfrac{h}{L}\Delta f</math>

We identify that as the thrust per photon:


<math>T = \cfrac{h}{2Lf}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

Notice that this is the static thrust per photon in a rest (un-accelerated) frame traveling with the cavity. That is to say, thrust is dependent on the acceleration that the physical cavity experiences and goes to zero at the acceleration g. This is an example of a negative feedback system where the steady state acceleration in the cavity frame of a free cavity will always be less than that calculated from the static force. It has no dependence on the linear velocity. (The case of circular motion is different in that the centrifugal "force" is dependent on angular velocity and will further negatively affect the thrust.)

If the number of photons is 

<math>\cfrac{P}{hf}(\cfrac{Q}{2πf})</math>

then the total thrust is


<math>NT = \cfrac{PQ}{4πLf^3}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

or

<math>NT = \cfrac{2PQ}{L(2πf)^3}(c X)^2 (\cfrac{1}{Ds^2}-\cfrac{1}{Db^2})</math>

or

<math>NT=\cfrac{2PQ}{L ω^3}(c X)^2 (\cfrac{1}{Ds^2}-\cfrac{1}{Db^2})</math>

where Ds = diameter at small end, Db = diameter at big end and ω = angular frequency.

Here is an example of the force of each mode vs frequency for m = 0 to 10, n = 1 to 5, p = 1 to 3 from the table referenced above.

[[File:00 chart21.jpg]]

In this case Rs = 0.0794 m, Rb = 0.1397 m, L = 0.2286 m (the dimensions of the truncated cone cavity tested at NASA Eagleworks as reported by Brady et.al.) and PQ = 2*10^6 watts.

The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

For constant geometrical dimensions, and constant quality factor and input power, the asymptotic behavior of thrust is inversely proportional to the cube of the frequency and proportional to the square of X.

___________________________________________________________

Appendix 1.

Proof that scaling dimensions inversely proportional to frequency keeps the thrust invariant:

Suppose that the thrust at frequency <math>f_1</math>, and dimensions <math>L_1</math>, <math>Ds_1</math>, and <math>Db_1</math> is

<math>NT_1 = \cfrac{2PQ}{L_1(2πf_1)^3}(c X)^2 (\cfrac{1}{Ds_1^2}-\cfrac{1}{Db_1^2})</math>

then, at frequency <math>f_2</math> a multiple of frequency <math>f_1</math>

<math>f_2 = n f_1 </math>

where the frequency ratio

<math>n=\cfrac{f_2}{f_1} </math>

can be any irrational number (not equal to zero). Scaling dimensions to be inversely proportional to the frequency ration n:

<math>L_2=\cfrac{L_1}{n} </math>

<math>Ds_2=\cfrac{Ds_1}{n} </math>

<math>Db_2=\cfrac{Db_1}{n} </math>

and substituting, we get the thrust for frequency <math>f_2</math> and dimensions <math>L_2</math>, <math>Ds_2</math>, and <math>Db_2</math> to be:

<math>NT_2 = \cfrac{2PQ}{L_1(2πf_1 n)^3}(c X)^2 (\cfrac{1}{(\cfrac{Ds_1}{n})^2}-\cfrac{1}{(\cfrac{Db_1}{n})^2})</math>

and since the factor of <math>n^3</math> occurs both in the numerator and the denominator, it cancels out, leaving

<math>NT_2 = NT_1</math>

If the mode shape is kept invariant, for constant quality factor and input power, the thrust force is invariant, independent of frequency when the diameter and the length of the cavity are both scaled to change inversely proportional to the frequency ratio n.

___________________________________________________________

Appendix 2.

An interesting expression to examine is <math>\cfrac{fc}{g} </math>

It represents the number of cycles for the photons in the cavity to reach velocity c if they were free to do so at the acceleration g.

In that respect <math>\cfrac{g}{fc} </math> represents a degree of coupling between the standing waves in the cavity and a traveling wave.

In this case Rs = 0.0794 m, Rb = 0.1397 m, L = 0.2286 m (the dimensions of the truncated cone cavity tested at NASA Eagleworks as reported by Brady et.al.) and PQ = 2*10^6 watts.

The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). For a cylindrical cavity <math>\Delta f</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case), which means that the acceleration <math>g</math> is zero. Hence the number of cycles <math>\cfrac{fc}{g}</math> approaches infinity for a cylindrical cavity.

[[File:00 chart21-2.jpg]]

@notsosureofit Hypothesis

2015-07-14T01:25:26Z

Notsosureofit:

The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)

Starting with the expressions for the frequency of a cylindrical RF cavity [https://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity]:


<math>f = \cfrac{c}{2π}\sqrt{(\cfrac{X}{R})^2+(\cfrac{pπ}{L})^2}</math>

where "c" is the speed of light in the medium (the speed of light in vacuum divided by the square root of the product of the relative magnetic permeability times the relative electric permittivity of the medium).

For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function.
[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.

and for TE modes, X = X'[subm,n] = the n-th zero of the derivative of the m-th Bessel function.
[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.

* Here is a table [http://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlx] to 15 digits precision for the roots of the cylindrical Bessel functions X[sub m,n] and for the roots of its derivative X'[subm,n] from m=0 to m=10, and from n=1 to n=5

Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.


<math>\Delta f = \cfrac{1}{2f}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

''This is a cylindrical approximation and could be replaced with a tapered dielectric index of refraction in a cylindrical cavity.''

and from there the expression for the acceleration g from:


<math>g = \cfrac{c^2}{L}\cfrac{\Delta f}{f}</math>

such that:


<math>g = \cfrac{c^2}{2Lf^2}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

''This is the acceleration at which the dispersion of the tapered cavity is balanced out by the dispersion due to its acceleration.''

Using the "weight" of the photon in the accelerated frame from:


<math>W = \cfrac{hf}{c^2}g</math>

where we make the connection via the Equivalence Principle that the acceleration of a photon seen in the rest frame is that which is balanced out in the accelerated frame. That is, the dispersion of the tapered cavity reduces to zero (along the axis) in that accelerated frame of reference.

Such that:

<math>W = T = \cfrac{h}{L}\Delta f</math>

We identify that as the thrust per photon:


<math>T = \cfrac{h}{2Lf}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

Notice that this is the static thrust per photon in a rest (un-accelerated) frame traveling with the cavity. That is to say, thrust is dependent on the acceleration that the physical cavity experiences and goes to zero at the acceleration g. It is not dependent on the linear velocity. (The case of circular motion is different in that the centrifugal "force" is dependent on angular velocity and will negatively affect the thrust.)

If the number of photons is 

<math>\cfrac{P}{hf}(\cfrac{Q}{2πf})</math>

then the total thrust is


<math>NT = \cfrac{PQ}{4πLf^3}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

or

<math>NT = \cfrac{2PQ}{L(2πf)^3}(c X)^2 (\cfrac{1}{Ds^2}-\cfrac{1}{Db^2})</math>

or

<math>NT=\cfrac{2PQ}{L ω^3}(c X)^2 (\cfrac{1}{Ds^2}-\cfrac{1}{Db^2})</math>

where Ds = diameter at small end, Db = diameter at big end and ω = angular frequency.

Here is an example of the force of each mode vs frequency for m = 0 to 10, n = 1 to 5, p = 1 to 3 from the table referenced above.

[[File:00 chart21.jpg]]

In this case Rs = 0.0794 m, Rb = 0.1397 m, L = 0.2286 m (the dimensions of the truncated cone cavity tested at NASA Eagleworks as reported by Brady et.al.) and PQ = 2*10^6 watts.

The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

For constant geometrical dimensions, and constant quality factor and input power, the asymptotic behavior of thrust is inversely proportional to the cube of the frequency and proportional to the square of X.

___________________________________________________________

Appendix 1.

Proof that scaling dimensions inversely proportional to frequency keeps the thrust invariant:

Suppose that the thrust at frequency <math>f_1</math>, and dimensions <math>L_1</math>, <math>Ds_1</math>, and <math>Db_1</math> is

<math>NT_1 = \cfrac{2PQ}{L_1(2πf_1)^3}(c X)^2 (\cfrac{1}{Ds_1^2}-\cfrac{1}{Db_1^2})</math>

then, at frequency <math>f_2</math> a multiple of frequency <math>f_1</math>

<math>f_2 = n f_1 </math>

where the frequency ratio

<math>n=\cfrac{f_2}{f_1} </math>

can be any irrational number (not equal to zero). Scaling dimensions to be inversely proportional to the frequency ration n:

<math>L_2=\cfrac{L_1}{n} </math>

<math>Ds_2=\cfrac{Ds_1}{n} </math>

<math>Db_2=\cfrac{Db_1}{n} </math>

and substituting, we get the thrust for frequency <math>f_2</math> and dimensions <math>L_2</math>, <math>Ds_2</math>, and <math>Db_2</math> to be:

<math>NT_2 = \cfrac{2PQ}{L_1(2πf_1 n)^3}(c X)^2 (\cfrac{1}{(\cfrac{Ds_1}{n})^2}-\cfrac{1}{(\cfrac{Db_1}{n})^2})</math>

and since the factor of <math>n^3</math> occurs both in the numerator and the denominator, it cancels out, leaving

<math>NT_2 = NT_1</math>

If the mode shape is kept invariant, for constant quality factor and input power, the thrust force is invariant, independent of frequency when the diameter and the length of the cavity are both scaled to change inversely proportional to the frequency ratio n.

___________________________________________________________

Appendix 2.

An interesting expression to examine is <math>\cfrac{fc}{g} </math>

It represents the number of cycles for the photons in the cavity to reach velocity c if they were free to do so at the acceleration g.

In that respect <math>\cfrac{g}{fc} </math> represents a degree of coupling between the standing waves in the cavity and a traveling wave.

In this case Rs = 0.0794 m, Rb = 0.1397 m, L = 0.2286 m (the dimensions of the truncated cone cavity tested at NASA Eagleworks as reported by Brady et.al.) and PQ = 2*10^6 watts.

The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes <math>TM_{mnp}</math> and <math>TE_{mnp}</math>.

Notice that for a cylindrical cavity, it takes an infinite number of cycles for the photons in the cavity to reach velocity c (if they were free to do so at the acceleration <math>g</math>). For a cylindrical cavity <math>\Delta f</math> is zero (since the the diameters at both ends are the same, and therefore there is no gradient in that case), which means that the acceleration <math>g</math> is zero. Hence the number of cycles <math>\cfrac{fc}{g}</math> approaches infinity for a cylindrical cavity.

[[File:00 chart21-2.jpg]]

File:00 chart21-2.jpg

2015-06-02T02:11:47Z

Notsosureofit:

@notsosureofit Hypothesis

2015-06-02T02:11:04Z

Notsosureofit:

The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)

Starting with the expressions for the frequency of a cylindrical RF cavity [https://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity]:


<math>f = \cfrac{c}{2π}\sqrt{(\cfrac{X}{R})^2+(\cfrac{pπ}{L})^2}</math>

where "c" is the speed of light in the medium (the speed of light in vacuum divided by the square root of the product of the relative magnetic permeability times the relative electric permittivity of the medium).

For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function.
[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.

and for TE modes, X = X'[subm,n] = the n-th zero of the derivative of the m-th Bessel function.
[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.

* Here is a table [http://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlx] to 15 digits precision for the roots of the cylindrical Bessel functions X[sub m,n] and for the roots of its derivative X'[subm,n] from m=0 to m=10, and from n=1 to n=5

Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.


<math>\Delta f = \cfrac{1}{2f}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

''This is a cylindrical approximation and could be replaced with a tapered dielectric index of refraction in a cylindrical cavity.''

and from there the expression for the acceleration g from:


<math>g = \cfrac{c^2}{L}\cfrac{\Delta f}{f}</math>

such that:


<math>g = \cfrac{c^2}{2Lf^2}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

''This is the acceleration at which the dispersion of the tapered cavity is balanced out by the dispersion due to its acceleration.''

Using the "weight" of the photon in the accelerated frame from:


<math>W = \cfrac{hf}{c^2}g</math>

where we make the connection via the Equivalence Principle that the acceleration of a photon seen in the rest frame is that which is balanced out in the accelerated frame. That is, the dispersion of the tapered cavity reduces to zero (along the axis) in that accelerated frame of reference.

Such that:

<math>W = T = \cfrac{h}{L}\Delta f</math>

We identify that as the thrust per photon:


<math>T = \cfrac{h}{2Lf}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

If the number of photons is 

<math>\cfrac{P}{hf}(\cfrac{Q}{2πf})</math>

then the total thrust is


<math>NT = \cfrac{PQ}{4πLf^3}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

or

<math>NT = \cfrac{2PQ}{L(2πf)^3}(c X)^2 (\cfrac{1}{Ds^2}-\cfrac{1}{Db^2})</math>

or

<math>NT=\cfrac{2PQ}{L ω^3}(c X)^2 (\cfrac{1}{Ds^2}-\cfrac{1}{Db^2})</math>

where Ds = diameter at small end, Db = diameter at big end and ω = angular frequency.

Here is an example of the force of each mode vs frequency for m = 0 to 10, n = 1 to 5, p = 1 to 3 from the table referenced above.

[[File:00 chart21.jpg]]

In this case Rs = 0.0794m, Rb = 0.1397m, L = 0.2286m.

For constant geometrical dimensions, and constant quality factor and input power, the asymptotic behavior of thrust is inversely proportional to the cube of the frequency and proportional to the square of X.

___________________________________________________________

Appendix 1.

Proof that scaling dimensions inversely proportional to frequency keeps the thrust invariant:

Suppose that the thrust at frequency <math>f_1</math>, and dimensions <math>L_1</math>, <math>Ds_1</math>, and <math>Db_1</math> is

<math>NT_1 = \cfrac{2PQ}{L_1(2πf_1)^3}(c X)^2 (\cfrac{1}{Ds_1^2}-\cfrac{1}{Db_1^2})</math>

then, at frequency <math>f_2</math> a multiple of frequency <math>f_1</math>

<math>f_2 = n f_1 </math>

where the frequency ratio

<math>n=\cfrac{f_2}{f_1} </math>

can be any irrational number (not equal to zero). Scaling dimensions to be inversely proportional to the frequency ration n:

<math>L_2=\cfrac{L_1}{n} </math>

<math>Ds_2=\cfrac{Ds_1}{n} </math>

<math>Db_2=\cfrac{Db_1}{n} </math>

and substituting, we get the thrust for frequency <math>f_2</math> and dimensions <math>L_2</math>, <math>Ds_2</math>, and <math>Db_2</math> to be:

<math>NT_2 = \cfrac{2PQ}{L_1(2πf_1 n)^3}(c X)^2 (\cfrac{1}{(\cfrac{Ds_1}{n})^2}-\cfrac{1}{(\cfrac{Db_1}{n})^2})</math>

and since the factor of <math>n^3</math> occurs both in the numerator and the denominator, it cancels out, leaving

<math>NT_2 = NT_1</math>

If the mode shape is kept invariant, for constant quality factor and input power, the thrust force is invariant, independent of frequency when the diameter and the length of the cavity are both scaled to change inversely proportional to the frequency ratio n.

Appendix 2.

An interesting expression to examine is <math>\cfrac{fc}{g} </math>

It represents the number of cycles for the photons in the cavity to reach velocity c if they were free to do so at the acceleration g.
In that respect it represents a degree of coupling between the standing waves in the cavity and a traveling wave.

[[File:00 chart21-2.jpg]]

@notsosureofit Hypothesis

2015-06-01T23:17:03Z

Notsosureofit:

The proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)

Starting with the expressions for the frequency of a cylindrical RF cavity [https://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity]:


<math>f = \cfrac{c}{2π}\sqrt{(\cfrac{X}{R})^2+(\cfrac{pπ}{L})^2}</math>

where "c" is the speed of light in the medium (the speed of light in vacuum divided by the square root of the product of the relative magnetic permeability times the relative electric permittivity of the medium).

For TM modes, X = X[sub m,n] = the n-th zero of the m-th Bessel function.
[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.

and for TE modes, X = X'[subm,n] = the n-th zero of the derivative of the m-th Bessel function.
[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.

* Here is a table [http://wwwal.kuicr.kyoto-u.ac.jp/www/accelerator/a4/besselroot.htmlx] to 15 digits precision for the roots of the cylindrical Bessel functions X[sub m,n] and for the roots of its derivative X'[subm,n] from m=0 to m=10, and from n=1 to n=5

Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.


<math>\Delta f = \cfrac{1}{2f}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

''This is a cylindrical approximation and could be replaced with a tapered dielectric index of refraction in a cylindrical cavity.''

and from there the expression for the acceleration g from:


<math>g = \cfrac{c^2}{L}\cfrac{\Delta f}{f}</math>

such that:


<math>g = \cfrac{c^2}{2Lf^2}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

''This is the acceleration at which the dispersion of the tapered cavity is balanced out by the dispersion due to its acceleration.''

Using the "weight" of the photon in the accelerated frame from:


<math>W = \cfrac{hf}{c^2}g</math>

where we make the connection via the Equivalence Principle that the acceleration of a photon seen in the rest frame is that which is balanced out in the accelerated frame. That is, the dispersion of the tapered cavity reduces to zero (along the axis) in that accelerated frame of reference.

Such that:

<math>W = T = \cfrac{h}{L}\Delta f</math>

We identify that as the thrust per photon:


<math>T = \cfrac{h}{2Lf}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

If the number of photons is 

<math>\cfrac{P}{hf}(\cfrac{Q}{2πf})</math>

then the total thrust is


<math>NT = \cfrac{PQ}{4πLf^3}(\cfrac{c}{2π})^2X^2(\cfrac{1}{Rs^2}-\cfrac{1}{Rb^2})</math>

or

<math>NT = \cfrac{2PQ}{L(2πf)^3}(c X)^2 (\cfrac{1}{Ds^2}-\cfrac{1}{Db^2})</math>

or

<math>NT=\cfrac{2PQ}{L ω^3}(c X)^2 (\cfrac{1}{Ds^2}-\cfrac{1}{Db^2})</math>

where Ds = diameter at small end, Db = diameter at big end and ω = angular frequency.

Here is an example of the force of each mode vs frequency for m = 0 to 10, n = 1 to 5, p = 1 to 3 from the table referenced above.

[[File:00 chart21.jpg]]

In this case Rs = 0.0794m, Rb = 0.1397m, L = 0.2286m.

For constant geometrical dimensions, and constant quality factor and input power, the asymptotic behavior of thrust is inversely proportional to the cube of the frequency and proportional to the square of X.

___________________________________________________________

Appendix 1.

Proof that scaling dimensions inversely proportional to frequency keeps the thrust invariant:

Suppose that the thrust at frequency <math>f_1</math>, and dimensions <math>L_1</math>, <math>Ds_1</math>, and <math>Db_1</math> is

<math>NT_1 = \cfrac{2PQ}{L_1(2πf_1)^3}(c X)^2 (\cfrac{1}{Ds_1^2}-\cfrac{1}{Db_1^2})</math>

then, at frequency <math>f_2</math> a multiple of frequency <math>f_1</math>

<math>f_2 = n f_1 </math>

where the frequency ratio

<math>n=\cfrac{f_2}{f_1} </math>

can be any irrational number (not equal to zero). Scaling dimensions to be inversely proportional to the frequency ration n:

<math>L_2=\cfrac{L_1}{n} </math>

<math>Ds_2=\cfrac{Ds_1}{n} </math>

<math>Db_2=\cfrac{Db_1}{n} </math>

and substituting, we get the thrust for frequency <math>f_2</math> and dimensions <math>L_2</math>, <math>Ds_2</math>, and <math>Db_2</math> to be:

<math>NT_2 = \cfrac{2PQ}{L_1(2πf_1 n)^3}(c X)^2 (\cfrac{1}{(\cfrac{Ds_1}{n})^2}-\cfrac{1}{(\cfrac{Db_1}{n})^2})</math>

and since the factor of <math>n^3</math> occurs both in the numerator and the denominator, it cancels out, leaving

<math>NT_2 = NT_1</math>

If the mode shape is kept invariant, for constant quality factor and input power, the thrust force is invariant, independent of frequency when the diameter and the length of the cavity are both scaled to change inversely proportional to the frequency ratio n.

@notsosureofit Hypothesis

2015-06-01T02:09:35Z

Notsosureofit:

File:00 chart21.jpg

2015-06-01T01:56:18Z

Notsosureofit:

@notsosureofit Hypothesis

2015-05-29T14:58:51Z

Notsosureofit:

@notsosureofit Hypothesis

2015-05-29T14:45:39Z

Notsosureofit:

@notsosureofit Hypothesis

2015-05-29T14:26:09Z

Notsosureofit:

List of Suggested Experiments

2015-05-29T01:41:44Z

Notsosureofit:

This page compiles suggestions for as-yet untested variations in experiment designs for EmDrive testing. When possible, links to the original suggestion and a brief description of the justification for this test are provided.

Note: For purposes of this list, the baseline for experimentation is considered to be a copper fustrum with either a magnetron or coaxial RF feed operated at approximately 2.45Ghz, similar to Shawyer's Feasability Study

== Design/Shape Modifications ==
# Replace solid endplates with a circular grid design similar to the endplates used by Cullen in his 1950's waveguide experiments,<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1370479#msg1370479 Forum post by Rodal]</ref> or a mesh as the one used for the glass windows in home-microwave-ovens, having a spacing between mesh or grids small enough such that only wavelengths smaller than that can get through.<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1376108#msg1376108 Forum post by demofsky]</ref> Purpose: to allow convection through the fustrum, eliminate buoyancy, thermal jet effects, natural thermal convection currents, and other gas effects.
# Place [http://en.wikipedia.org/wiki/Ferrite_(magnet) ferrite beads] in the fustrum, either one large one next to an endplate or a pattern of them along a line in the longitudinal direction. Purpose: to increase attenuation gradient in TE modes, having an axial magnetic field.<ref>[http://forum.nasaspaceflight.com/index.php?topic=37642.msg1380265#msg1380265 Forum post by Rodal] summarizing several prior posts.</ref>
# Build Large end plate out of [http://en.wikipedia.org/wiki/Permeability_%28electromagnetism%29#Values_for_some_common_materials Metglas] or a similar material with high magnetic permeability like cast iron or any ferrite.<ref>[http://forum.nasaspaceflight.com/index.php?topic=37642.msg1381091#msg1381091 Forum post by Flyby] referencing earlier posts.</ref> Purpose: to test de Aquino's conjecture regarding the effect of power dissipation at the end faces of the truncated cone.
# Place a ruby inside near one of the ends to emit at 2.4 GHz as used in solid state Masers.
# Fill the fustrum with ammonia gas to emit at 24GHz. Purpose: To produce maser-like amplification inside the fustrum.<ref>[http://forum.nasaspaceflight.com/index.php?topic=37642.msg1379801#msg1379801 Forum post by aero], in response to [http://forum.nasaspaceflight.com/index.php?topic=37642.msg1379763#msg1379763 Rodal's explanation of the history of maser development].</ref>
# Place a dielectric next to the Small end, as done by NASA Eagleworks, who found extruded HDPE to be slightly better than extruded PTFE. Do not use molded (instead of extruded) polymers. NASA Eagleworks found that Neoprene rubber performed poorly as a dielectric in the EM Drive, as it resulted in considerably less thrust.
# Separate resonance and attenuation chambers (proposed by WarpTech)
# Apply a silver or gold coating to the inside of a copper fustrum. Purpose: The increase microwave reflectivity, and therefore increase Q factor.

== Experimental Measurement Setups ==
# Use smokesticks to test for out-gassing and hot air jets from the fustrum<ref>Credit to @Seeshells</ref>
# Test on a zero-g simulator flight.
# Cavendish Pendulum<ref>http://web.archive.org/web/20080508011932/http://www.sas.org/tcs/weeklyIssues_2005/2005-07-01/feature1/index.html</ref>

== References ==
<references/>

List of Suggested Experiments

2015-05-29T01:34:51Z

Notsosureofit: /* Experimental Measurement Setups */

@Notsosureofit is planning testing with a Gunn diode

2015-05-29T01:31:14Z

Notsosureofit:

@Notsosureofit is planning testing with a Gunn diode

[[File:Gunn Diode.jpg]]

in a vacuum chamber, possibly this one

[[File:Chamber 1.jpg]]

File:Chamber 1.jpg

2015-05-29T01:29:49Z

Notsosureofit:

@Notsosureofit is planning testing with a Gunn diode

2015-05-29T01:25:30Z

Notsosureofit:

@Notsosureofit is planning testing with a Gunn diode

[[File:Gunn Diode.jpg]]

in a vacuum chamber, possibly this one

@Notsosureofit is planning testing with a Gunn diode

2015-05-29T01:23:49Z

Notsosureofit:

@Notsosureofit is planning testing with a Gunn diode

[[File:Gunn Diode.jpg]]

File:Gunn Diode.jpg

2015-05-29T01:22:17Z

Notsosureofit:

@Notsosureofit is planning testing with a Gunn diode

2015-05-29T01:16:39Z

Notsosureofit:

@Notsosureofit is planning testing with a Gunn diode

2015-05-29T01:12:48Z

Notsosureofit:

@Notsosureofit is planning testing with a Gunn diode

[[File:https://www.dropbox.com/s/vdueo9mi6l3s4kb/2015-02-27%2011.18.24.jpg?dl=0]]

@Notsosureofit is planning testing with a Gunn diode

2015-05-28T19:01:50Z

Notsosureofit: Created page with "@Notsosureofit is planning testing with a Gunn diode"

@Notsosureofit is planning testing with a Gunn diode

Building

2015-05-28T18:55:19Z

Notsosureofit:

This page will collect any photos, plans, and instructions for do-it-yourselfers. Efforts with enough documentation will be provided their own pages.

# [[Mulletron's Build]]
# Kurt Zeller (@zellerium) and Brian Kraft from Cal Poly are starting a build as well, using a constant cross-section cavity containing a polymer dielectric.<ref>[https://forum.nasaspaceflight.com/index.php?topic=36313.msg1368153#msg1368153 Forum post by @zellerium]</ref>
# @DIYFan - TBD
# [[@Notsosureofit is planning testing with a Gunn diode]].<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1370647#msg1370647 Later forum post by @Rodal, can't find original post]</ref>
# @TheTraveller<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1370597#msg1370597 Forum post by @TheTraveller]</ref>
# @Iulian Berca<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1371164#msg1371164 Forum post by @Iulian Berca]</ref> - Fabricated a drive in May 2015 and was posting videos at [http://www.masinaelectrica.com/emdrive-independent-test/ his website]. In [https://www.youtube.com/watch?v=Rbf7735o3hQ Test 3.1] he reported a force measurement toward "the small end" and later a smaller measurement in the [https://www.youtube.com/watch?v=KAMttfMC8PI reverse orientation]. As of 5/21/15 the magnitude and significance of these measurements were being debated on the [http://forum.nasaspaceflight.com/index.php?topic=36313.msg1377695#msg1377695 NSF forum].
# @SeeShells<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1371206#msg1371206 Forum post by @SeeShells]</ref>
# @R. W. Keyes / Andromeda Research - high power, 1-20KW magnetron, superconductor Magnesium diboride on silicon carbide, to start summer 2015
# @movax (Paul Kocyla) and Jo Hinchliffe<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1372073#msg1372073 Forum post by Hackaday.io]</ref> - Building the original 2.45 GHz thruster according to the Chinese paper and their own 25 GHz design simultaneously, with estimated completion date of July 2015. See [https://hackaday.io/project/5596-em-drive Hackaday project] for more details, as well as [http://n-o-d-e.net/post/119343131451/building-a-diy-emdrive an interview with Paul].
# Others?

== Modelling ==
@phaseshift has built a SketchUp model<ref>[http://forum.nasaspaceflight.com/index.php?topic=37642.msg1380107#msg1380107 post by @phaseshift]</ref> ([[File:EM_Thruster.skp]]) of a frustrum based on the estimated Shawyer Flight Thruster dimensions.

== References ==
<references />

@notsosureofit Hypothesis

2015-05-28T00:48:11Z

Notsosureofit:

Theory

2015-05-28T00:26:54Z

Notsosureofit:

This page will outline some candidate theories of operation (or non-operation).

== Debunking Theories ==
*These theories should be explained, then debunked with the simplest explanation, with a link to a dedicated page to show the work or work in progress that backs up that explanation.

=== Experimental error ===
* It's all a hoax/conspiracy
* Simple measuring error
* Thermal effects
* Mechanical vibration
* Magnetic effects with environment

These are discussed in more detail at [[Possible Error Sources]].

=== Proponent Theories ===
* Guido Fetta's, Cannae Drive creator's Theory
* Roger Shawyer's, EM Drive creator's theory
* Quantum foam MHD
* Harold White's Quantum vacuum plasma thruster (QVP thruster)
* Harold White's Warp effects
* [[Evanescent waves]]<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1330521#msg1330521 2/2/15 post by @aero modeled evanescent waves] using [http://ab-initio.mit.edu/wiki/index.php/Meep MEEP]. Conclusion was that, due to rapid dropoff at the frustum surface, these were of insufficient magnitude to explain the thrust.</ref>
* Transfer of linear momentum from the Quantum Vacuum to magnetoelectric and chiral molecules <ref>http://forum.nasaspaceflight.com/index.php?topic=36313.msg1330846#msg1330846 and http://forum.nasaspaceflight.com/index.php?topic=36313.msg1333392#msg1333392 </ref>
* [[@notsosureofit Hypothesis]]
* [[Mike McCulloch's MiHsC Theory]]
* Curving Rf beams<ref>[http://forum.nasaspaceflight.com/index.php?topic=37642.msg1379281#msg1379281 Post by @aero]</ref> - The magnitude of the bending needed, was not shown by the thermal camera images taken at Eagleworks.

8/5/14 - Greg Egan [http://www.gregegan.net/SCIENCE/Cavity/Cavity.html obtained an exact solution] for the resonant modes (having azimuthal quantum number m=0, constant electromagnetic field variation in the azimuthal direction) of a cavity in the shape of a truncated cone with spherical ends. Greg Egan calculated the forces and showed a proof that the net force is zero and therefore that there is no thrust force in a resonant electromagnetic cavity of any arbitrary shape, and for any arbitrary mode shape, when the cavity is analyzed according to the standing wave solution of Maxwell's equations.

== References ==
<references />

@notsosureofit Hypothesis

2015-05-27T20:45:24Z

Notsosureofit:

@notsosureofit Hypothesis

2015-05-27T20:32:58Z

Notsosureofit:

@notsosureofit Hypothesis

2015-05-27T19:51:43Z

Notsosureofit:

@notsosureofit Hypothesis

2015-05-27T19:49:28Z

Notsosureofit:

Theory

2015-05-27T19:25:50Z

Notsosureofit:

This page will outline some candidate theories of operation (or non-operation).

== Debunking Theories ==
*These theories should be explained, then debunked with the simplest explanation, with a link to a dedicated page to show the work or work in progress that backs up that explanation.

=== Experimental error ===
* It's all a hoax/conspiracy
* Simple measuring error
* Thermal effects
* Mechanical vibration
* Magnetic effects with environment

These are discussed in more detail at [[Possible Error Sources]].

=== Proponent Theories ===
* Guido Fetta's, Cannae Drive creator's Theory
* Roger Shawyer's, EM Drive creator's theory
* Quantum foam MHD
* Harold White's Quantum vacuum plasma thruster (QVP thruster)
* Harold White's Warp effects
* [[Evanescent waves]]<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1330521#msg1330521 2/2/15 post by @aero modeled evanescent waves] using [http://ab-initio.mit.edu/wiki/index.php/Meep MEEP]. Conclusion was that, due to rapid dropoff at the frustum surface, these were of insufficient magnitude to explain the thrust.</ref>
* Transfer of linear momentum from the Quantum Vacuum to magnetoelectric and chiral molecules <ref>http://forum.nasaspaceflight.com/index.php?topic=36313.msg1330846#msg1330846 and http://forum.nasaspaceflight.com/index.php?topic=36313.msg1333392#msg1333392 </ref>
* [[Notsosureofit's theory based on Equivalence Principle]]<ref>[http://emdrive.echothis.com/@notsosureofit_Hypothesis]</ref>
* [[Mike McCulloch's MiHsC Theory]]
* Curving Rf beams<ref>[http://forum.nasaspaceflight.com/index.php?topic=37642.msg1379281#msg1379281 Post by @aero]</ref> - The magnitude of the bending needed, was not shown by the thermal camera images taken at Eagleworks.

8/5/14 - Greg Egan [http://www.gregegan.net/SCIENCE/Cavity/Cavity.html obtained an exact solution] for the resonant modes (having azimuthal quantum number m=0, constant electromagnetic field variation in the azimuthal direction) of a cavity in the shape of a truncated cone with spherical ends. Greg Egan calculated the forces and showed a proof that the net force is zero and therefore that there is no thrust force in a resonant electromagnetic cavity of any arbitrary shape, and for any arbitrary mode shape, when the cavity is analyzed according to the standing wave solution of Maxwell's equations.

== References ==
<references />

@notsosureofit Hypothesis

2015-05-27T19:21:36Z

Notsosureofit: Force derivation for tapered cylindrical EM cavity.

@notsosureofit Hypothesis

2015-05-27T19:11:09Z

Notsosureofit: Notsosureofit's hypothesis based on the Equivalence Principle[3]

@notsosureofit

Theory

2015-05-20T17:15:20Z

Notsosureofit:

This page will outline some candidate theories of operation (or non-operation).

== Debunking Theories ==
*These theories should be explained, then debunked with the simplest explanation, with a link to a dedicated page to show the work or work in progress that backs up that explanation.

=== Experimental error ===
* It's all a hoax/conspiracy
* Simple measuring error
* Thermal effects
* Mechanical vibration
* Magnetic effects with environment

These are discussed in more detail at [[Possible Error Sources]].

=== Proponent Theories ===
* Guido Fetta's, Cannae Drive creator's Theory
* Roger Shawyer's, EM Drive creator's theory
* Quantum foam MHD
* Harold White's Quantum vacuum plasma thruster (QVP thruster)
* Conservation of momentum breaking theories
** Mike McCulloch's MiHsC<ref>[http://physicsfromtheedge.blogspot.co.uk/2015/05/mihsc-vs-29-anomalies.html 3/5/15 post by Mike McCulloch, MiHsC vs 29 anomalies]</ref> - this deserves an entire subsection - see http://physicsfromtheedge.blogspot.co.uk/
* Harold White's Warp effects
* [[Evanescent waves]]<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1330521#msg1330521 2/2/15 post by @aero modeled evanescent waves] using [http://ab-initio.mit.edu/wiki/index.php/Meep MEEP]. Conclusion was that, due to rapid dropoff at the frustum surface, these were of insufficient magnitude to explain the thrust.</ref>
* Transfer of linear momentum from the Quantum Vacuum to magnetoelectric and chiral molecules <ref>http://forum.nasaspaceflight.com/index.php?topic=36313.msg1330846#msg1330846 and http://forum.nasaspaceflight.com/index.php?topic=36313.msg1333392#msg1333392 </ref>
* Notsosureofit's Equivalence Principle hypothesis <ref>http://forum.nasaspaceflight.com/index.php?topic=36313.msg1375157#msg1375157</ref>

8/5/14 - Greg Egan [http://www.gregegan.net/SCIENCE/Cavity/Cavity.html modeled the resonant modes of a conical cavity].

== References ==
<references />

Theory

2015-05-20T16:13:46Z

Notsosureofit: /* Proponent Theories */

This page will outline some candidate theories of operation (or non-operation).

== Debunking Theories ==
*These theories should be explained, then debunked with the simplest explanation, with a link to a dedicated page to show the work or work in progress that backs up that explanation.

=== Experimental error ===
* It's all a hoax/conspiracy
* Simple measuring error
* Thermal effects
* Mechanical vibration
* Magnetic effects with environment

These are discussed in more detail at [[Possible Error Sources]].

=== Proponent Theories ===
* Guido Fetta's, Cannae Drive creator's Theory
* Roger Shawyer's, EM Drive creator's theory
* Quantum foam MHD
* Harold White's Quantum vacuum plasma thruster (QVP thruster)
* Conservation of momentum breaking theories
** Mike McCulloch's MiHsC<ref>[http://physicsfromtheedge.blogspot.co.uk/2015/05/mihsc-vs-29-anomalies.html 3/5/15 post by Mike McCulloch, MiHsC vs 29 anomalies]</ref> - this deserves an entire subsection - see http://physicsfromtheedge.blogspot.co.uk/
* Harold White's Warp effects
* [[Evanescent waves]]<ref>[http://forum.nasaspaceflight.com/index.php?topic=36313.msg1330521#msg1330521 2/2/15 post by @aero modeled evanescent waves] using [http://ab-initio.mit.edu/wiki/index.php/Meep MEEP]. Conclusion was that, due to rapid dropoff at the frustum surface, these were of insufficient magnitude to explain the thrust.</ref>
* Transfer of linear momentum from the Quantum Vacuum to magnetoelectric and chiral molecules <ref>http://forum.nasaspaceflight.com/index.php?topic=36313.msg1330846#msg1330846 and http://forum.nasaspaceflight.com/index.php?topic=36313.msg1333392#msg1333392 </ref>
* Notsosureofit's Equivalence Principle hypothesis

8/5/14 - Greg Egan [http://www.gregegan.net/SCIENCE/Cavity/Cavity.html modeled the resonant modes of a conical cavity].

== References ==
<references />