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#2320 by Notsosureofit on 28 Jan, 2016 11:40
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Just passing through again...
The wavefunction of a rotating (bound) emdrive system cannot be a free energy generator. It acts like any other 2D oscillator and its energy increases with P, not PQ. Only the linear free space wavefunction is free of this "phase braking", if you will and does not have linear eigenvalues. I think this has been mentioned numerous times by various people. -
#2321 by Rodal on 28 Jan, 2016 12:33
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Just passing through again...
The wavefunction of a rotating (bound) emdrive system cannot be a free energy generator. It acts like any other 2D oscillator and its energy increases with P, not PQ. Only the linear free space wavefunction is free of this "phase braking", if you will and does not have linear eigenvalues. I think this has been mentioned numerous times by various people.
Meeting you in the corridor while you are quickly passing through...
1) There is an angular velocity below which the wavefunctions of a rotating resonant cavity do not drastically change, and therefore they remain standing waves as in a non-rotating cavity. After all, resonating cavities tested in Labs, are on the Earth that is rotating around its axis once a day (7.27 × 10^-5 rad/s) and around the Sun once a year ( 2.0x10^-7 rad/s), and around the center of our Galaxy...
This limit angular velocity is proportional to c/R for an optical cavity, which appears like a significant number. Have you calculated that this is an actual practical limit to render the rotating EMDrive free-energy generator impossible for the EM Drive force/power being claimed by EM Drive experimenters?
2) TheTraveller is planning a rotary experiment with the EM Drive. Is the geometry and angular velocity that TheTraveller planning to test below or above the limit angular velocity at which the wavefunctions of a linear resonator drastically change ? In other words, is TheTraveller's experiment going to be subject to this "phase braking"?
attachment: frequency difference as a function of angular speed for optical cavity
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#2322 by SeeShells on 28 Jan, 2016 12:46
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I think most of us are trying to look at the emdrive from the perspective of fundamental physics. Everything in this realm is pretty well buttoned up
...
a couple of key fundamentals have eluded us. Having no theory yet, I can only believe these are the the areas where the emdrive effect might reside. I cannot see fundamental physics working to explain it.
I used known physics when I posit that the lower-sideband EM momentum is exhausted as heat, resulting in a momentum imbalance and thrust. It seems appropriate to first investigate what tested and established physics may be in play before resorting to the extraordinary.
Why no comments or cites of my NEPSOP/Nibiruian Conjecture? I find it discouraging and troubling. I refrain from idle chatter here, preferring research instead. Why am I the only one interested in dispersion and dynamics of acceleration and Doppler effects? It pertains to CoE/CoM and thrust, tuning at/near cutoff and the dynamics of the frustrum itself.
See here!
http://forum.nasaspaceflight.com/index.php?topic=39004.msg1472941#msg1472941
Why isn't there more reverse-engineering of more of Shawyer's work, rather than discussing Cones, Q, and return loss ad-nausem? I think it is remiss of us not to consider most if not all of what he's written, and then understand the salient properties and phenomena. We find him discussing and employing a high-Q cone tuned at cutoff. So some of us set off to do likewise, while pretty much ignoring what he's said about motor/generator effects and CoE through a Doppler mechanism. His central point, even if bogus, is the difference in forward and reverse group velocity which is a property of the frustrum anisotropic dispersion. Anisotropic dispersion, anisotropic Doppler spreading, and asymmetrical spectral dissipation seem connected....Herein lies the basis for much of the emotion about the emdrive. Does one believe new physics is even possible? IMO you would almost have to considering what we observe and cannot yet explain...gravity and the expanding universe.
Moreover I believe its about attitude, and having a certain sort of existential faith. Does one believe, have faith, that the existence is knowable, understandable, reasonable, and that one's efforts to create our meaning through purpose are worthwhile? Does one have enough faith to invest time and treasure, suffering "the pidgeons from h*ll" (as some refer), messing all over their efforts? Ah, to 'start again at your beginnings, and never breath a word about your loss'.
At Reddit an indictment of delusion and counsel of despair was posted about perhaps one of the most faithful (consequently ironically, least credible) who was among us. Perhaps correctly, perhaps not. Yet if there wasn't the faith of those willing to pay the price, would there be any great achievements or progress, save for dumb luck? Whose to know till after the hand's played?
Nice post good questions.
At last count from Wiki http://emdrive.wiki/Theory
Roger Shawyer's EMDrive basic theory [1]
Roger Shawyer's EMDrive full theory paper [2]
Prof. Juan Yang's theory [3]
Dr. Harold Sonny White's Quantum vacuum plasma thruster model (QVP thruster)
Evanescent waves[4]
@notsosureofit Hypothesis
Mike McCulloch's MiHsC Theory
Todd Desiato (@WarpTech)'s Evanescent Wave Theory
Curving Rf beams[5] - The magnitude of the bending needed, was not shown by the thermal camera images taken at Eagleworks.
Declan Traill's suggested Classical Physics explanation [6]
If we go back into time (I have a hot tub
) and read the thousands of posts on here through the years you'll run across the musings of the physics of this drive and the theories are almost countless. Even the wonderful Foobie Dust theory.
Right now I like the Foobie Dust theory because their simply isn't enough raw data that's been tested for and released to draw conclusions or even a glimmer of one.
A couple that strike me are that I'm hoping to bring to the table are.
Is there a difference in potential between the ends of a resonating cavity that would provide a DC component to the drive operation? This is a biggie.
Is there a difference in measured thrusts tuning across a resonate point, effectively through cutoffs? Another biggie.
Is there a difference in sweeping through the cutoffs and the mode generated?
Is there a difference in observed static pressure measurements and acceleration, does the drive provide a steady state of acceleration? A huge biggie.
Have the modes of a drive been thoroughly investigated and confirmed with thermal imaging? EagleWorks, so we have one.
Are there differences in thrusts due to drive orientation? Not really done but some effects were seen in Tajmar's test.
What are the measurements using a Michelson-type interference experiment, using a Quartz rod through the center of the cavity negating issues with heated air. A little test done by EagleWorks showed something just out of the noise.
Does the the effect scale in a linear fashion or does it follow another non-linear line? Does mode effect it? Not done.
Do Diamagnetic materials truly increase the thrusts? Maybe.
Is there a difference in a noisy AM splattered broad band RF source vs a narrow one using the same drive?
These are just a few of the questions that I'm looking at and before we paper physics this thing to death we need answers to these simple questions.
Shell
Ahhh, one more. Has anyone placed simple hanging strips of cassette tape around the drive away from the thermal plume? One of my first questions on joining here. I have the old cassette ready to gut for this test.
One more! Do we truly have thrust?
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#2323 by Flyby on 28 Jan, 2016 13:19
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One of the things I'd like to see addressed in the real world tests is whether or not the E/H fields "move" inside a frustum (as seen in some MEEP solutions). That way we could establish whether or not the software simulations correlate with reality.
I think it will become essential to have high fidelity software simulations, because of the large amount of real world parameters that makes it very hard to build and investigate every possible iteration, in search of optimal performance...
Ideally, there should interval spaces detection grids along the length axis, that give live feedback. Something like that thermopaper test, but then with the possibility to register in a dynamical way. But I guess that's way out of the DIY budgets and possibilities...
At this stage, it is so damn hard to see in what direction an explanation could be found. Theories go all over the place in search for answers...
But before jumping the gun , it would be nice to have some solid confirmation of thrust, no?
At this moment we can't even agree on that (believers<>non believers) because irrefutable data (be it positive or negative) is lacking.
IF this thing is real, I suspect we do not need "new physics", but just a better understanding of the processes involved. And with a better understanding, the insight on how CoM is preserved, will come. -
#2324 by Notsosureofit on 28 Jan, 2016 13:56
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Just passing through again...
The wavefunction of a rotating (bound) emdrive system cannot be a free energy generator. It acts like any other 2D oscillator and its energy increases with P, not PQ. Only the linear free space wavefunction is free of this "phase braking", if you will and does not have linear eigenvalues. I think this has been mentioned numerous times by various people.
Meeting you in the corridor while you are quickly passing through...
1) There is an angular velocity below which the wavefunctions of a rotating resonant cavity do not drastically change, and therefore they remain standing waves as in a non-rotating cavity. After all, resonating cavities tested in Labs, are on the Earth that is rotating around its axis once a day (7.27 × 10^-5 rad/s) and around the Sun once a year ( 2.0x10^-7 rad/s), and around the center of our Galaxy...
This limit angular velocity is proportional to c/R for an optical cavity, which appears like a significant number. Have you calculated that this is an actual practical limit to render the rotating EMDrive free-energy generator impossible for the EM Drive force/power being claimed by EM Drive experimenters?
2) TheTraveller is planning a rotary experiment with the EM Drive. Is the geometry and angular velocity that TheTraveller planning to test below or above the limit angular velocity at which the wavefunctions of a linear resonator drastically change ? In other words, is TheTraveller's experiment going to be subject to this "phase braking"?
attachment: frequency difference as a function of angular speed for optical cavity
No, I'm not talking about the relativistic rotational limit. If one of the 2D axies is time, then the eigenfunctions are only linear in a Rindler transform (ie, an accelerating frame of reference.)
More if I get time, really loaded w/ vacuum work right now.
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#2325 by Tellmeagain on 28 Jan, 2016 14:27
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#2326 by SeeShells on 28 Jan, 2016 14:49
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One of the things I'd like to see addressed in the real world tests is whether or not the E/H fields "move" inside a frustum (as seen in some MEEP solutions). That way we could establish whether or not the software simulations correlate with reality.
I can see why the physicists are chomping at the bit to get their hands on read solid data (I am too as an engineer), because if this truly works and whether it's new or old physics it will be a game changer in our understanding of nature.
I think it will become essential to have high fidelity software simulations, because of the large amount of real world parameters that makes it very hard to build and investigate every possible iteration, in search of optimal performance...
Ideally, there should interval spaces detection grids along the length axis, that give live feedback. Something like that thermopaper test, but then with the possibility to register in a dynamical way. But I guess that's way out of the DIY budgets and possibilities...
At this stage, it is so damn hard to see in what direction an explanation could be found. Theories go all over the place in search for answers...
But before jumping the gun , it would be nice to have some solid confirmation of thrust, no?
At this moment we can't even agree on that (believers<>non believers) because irrefutable data (be it positive or negative) is lacking.
IF this thing is real, I suspect we do not need "new physics", but just a better understanding of the processes involved. And with a better understanding, the insight on how CoM is preserved, will come.
Four things could possibly happen.
It doesn't work, we collect our marbles and go home discovering the why of the anomalous thrust. A few still try.
It works but isn't usable. We kick the frustum can around for a bit to see if we can't make it work better, a majority collect their marbles and go home.
It works with limits. Build and refine it and study it, make it as good as we can.
It works beyond our wildest dreams and either by using GR or a whole new branch of understanding of physics our world changes. A whole new industry opens up. NASA will get its wings again. Our children will inherit the stars.
My dreams give me the aspiration to build it my hopes give me the drive to build the best I can simply because of a article in Forbes where it was said "Inventing a time machine would be more dramatic than EmDrive but not a lot more. A force engine would be like inventing fire."
http://www.forbes.com/sites/investor/2015/05/29/investor-alert-emdrive-could-make-uber-seem-about-as-disruptive-as-a-sweat-smear/
We need to do this right, we need to test it and evaluate it with the best tools we can get, opportunities like this don't come along often where we get a payoff no matter what happens and the jackpot if it does. I'd like to see the jackpot but I'll be happy with any of the results and accept whatever happens.
Shell -
#2327 by rfmwguy on 28 Jan, 2016 14:49
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Ok, step by step, with the little that is known.
(snip)
If I remember right, most of a year ago, Doctor Rodal concluded the ideal angle for the sides would be on the order of 30-33 degrees. Shawyer's hands on engineering efforts support this.
(snip)
A 33 degree interior angle is very shallow for a frustum using Db of 10 inches and Ds of 6.25 inches. Quick calc shows the height would only be a couple of inches. An exterior angle, or 57 degrees would be about 3 inches in height. My latest design has about 78 degrees interior. OK, where am I going wrong? -
#2328 by Rodal on 28 Jan, 2016 15:03
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Ok, step by step, with the little that is known.
(snip)
If I remember right, most of a year ago, Doctor Rodal concluded the ideal angle for the sides would be on the order of 30-33 degrees. Shawyer's hands on engineering efforts support this.
(snip)
A 33 degree interior angle is very shallow for a frustum using Db of 10 inches and Ds of 6.25 inches. Quick calc shows the height would only be a couple of inches. An exterior angle, or 57 degrees would be about 3 inches in height. My latest design has about 78 degrees interior. OK, where am I going wrong?
Before going too far on this discussion, you have to remember that "a picture is worth a thousand words", particularly when talking about angles.
This is the standard definition of the angle θ, it is measured from the longitudinal axis of axisymmetry to the lateral conical wall, so that the frustum goes from an angle -θw at the left wall on this picture to an angle +θw at the right wall on this picture:
in other words, the angle θ is half the interior angle between both lateral conical walls, that is why I usually refer to it as the "half cone angle"
What definition are you using, rfmwguy? -
#2329 by rfmwguy on 28 Jan, 2016 15:05
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#2330 by rfmwguy on 28 Jan, 2016 15:07
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ConeCalc software: http://www.i-logic.com/conecalc.htmOk, step by step, with the little that is known.
(snip)
If I remember right, most of a year ago, Doctor Rodal concluded the ideal angle for the sides would be on the order of 30-33 degrees. Shawyer's hands on engineering efforts support this.
(snip)
A 33 degree interior angle is very shallow for a frustum using Db of 10 inches and Ds of 6.25 inches. Quick calc shows the height would only be a couple of inches. An exterior angle, or 57 degrees would be about 3 inches in height. My latest design has about 78 degrees interior. OK, where am I going wrong?
Before going too far on this discussion, you have to remember that "a picture is worth a thousand words", particularly when talking about angles.
This is the standard definition of the angle θ, it is measured from the longitudinal axis of axisymmetry to the lateral conical wall, so that the frustum goes from an angle -θw at the left wall on this picture to an angle +θw at the right wall on this picture:
What definition are you using, rfmwguy? -
#2331 by Rodal on 28 Jan, 2016 15:11
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...
No wonder. You are using a completely different definition of cone angle
ConeCalc software: http://www.i-logic.com/conecalc.htm
You are talking in an inverse language to ThinkerX and me:
rfmwguyAngle = 90 degrees - θ
where the angle θ is the half cone angleQuote from: rfmwguyMy latest design has about 78 degrees interior.
Translation from "rfmwguy angle" to conventional definition : θ = 90 degrees - 78 degrees = 12 degrees
When using that software, you should calculate
θ = 90 degrees - rfmwguyAngle
and discuss cone angle as θ, so that we all speak the same language
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#2332 by rfmwguy on 28 Jan, 2016 15:20
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Well, not my angle but sheetmetal helper I-Logic. Plug your ideal frustum without dielectric into ConeCalc online, let us know what their sheet says....
No wonder. You are using a completely different definition of cone angle
ConeCalc software: http://www.i-logic.com/conecalc.htm
You are talking in an inverse language to ThinkerX and me:
rfmwguyAngle = 90 degrees - θ
where the angle θ is the half cone angleQuote from: rfmwguyMy latest design has about 78 degrees interior.
Translation from "rfmwguy angle" to conventional definition : θ = 90 degrees - 78 degrees = 12 degrees
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#2333 by Rodal on 28 Jan, 2016 15:24
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It is your angle when you are not using the same definition as other people:
Well, not my angle but sheetmetal helper I-Logic. Plug your ideal frustum without dielectric into ConeCalc online, let us know what their sheet says....
No wonder. You are using a completely different definition of cone angle
ConeCalc software: http://www.i-logic.com/conecalc.htm
You are talking in an inverse language to ThinkerX and me:
rfmwguyAngle = 90 degrees - θ
where the angle θ is the half cone angleQuote from: rfmwguyMy latest design has about 78 degrees interior.
Translation from "rfmwguy angle" to conventional definition : θ = 90 degrees - 78 degrees = 12 degrees
1) You are using a different definition than the people you quote (ThinkerX and me)
2) You are using a different definition than Greg Egan used for his discussion of the EM Drive
3) You are using a different definition than used by WarpTech and others used in these EM Drive threads
4) You are using a different definition than used in the wiki EM Drive experimental section http://emdrive.wiki/Experimental_Results
5) You are using a different definition than used in discussions of geometry of the EM Drive with aero, FluxCapacitor and Flyby in previous thread discussions.
...
. Sheetmetal helper I-Logic just calls it an angle, it doesn't call it the "cone half angle".
Anyway, when discussing geometry people should use drawings, because there are multiple interior angles, so unless you use a standard definition, or better you show a drawing, there is bound to be confusion
And when discussing parameters (angles, lengths, etc.) people should adopt common definitions, otherwise we have a tower of Babel
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#2334 by rfmwguy on 28 Jan, 2016 15:33
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OK, I'll put your dimension in the formula:
It is your angle when you are not using the same definition as other people. Sheetmetal helper I-Logic just calls it an angle, it doesn't call it the "cone half angle".
Well, not my angle but sheetmetal helper I-Logic. Plug your ideal frustum without dielectric into ConeCalc online, let us know what their sheet says....
No wonder. You are using a completely different definition of cone angle
ConeCalc software: http://www.i-logic.com/conecalc.htm
You are talking in an inverse language to ThinkerX and me:
rfmwguyAngle = 90 degrees - θ
where the angle θ is the half cone angleQuote from: rfmwguyMy latest design has about 78 degrees interior.
Translation from "rfmwguy angle" to conventional definition : θ = 90 degrees - 78 degrees = 12 degrees
Anyway, when discussing geometry people should use drawings, because there are multiple interior angles, so unless you use a standard definition, or better you show a drawing, there is bound to be confusion
And when discussing parameters (angles, lengths, etc.) people should adopt common definitions, otherwise we have a tower of Babel
Result of Cone Calculation
Cone Dimensions
Dia A 10.5000
Dia B 6.2500
Height 1.3800
Cone Angle 33.0000
Flat Pattern Dimensions
Large Radius 6.2599
Small Radius 3.7261
Angle A 150.9607
Width X 12.1200
Height Y 5.3257
Cord 12.1200
Full or Half Cone: Half
So, your 33 degree cone angle, half cone gives us a height of 1.38 inches.
Is there an on-line worksheet or program that translates your 33 degrees into a proper cutting template?
Edit - BTW, thanks to @Mulletron for the heads-up on this template software
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#2335 by Rodal on 28 Jan, 2016 15:42
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...
OK, I'll put your dimension in the formula:
Result of Cone Calculation
Cone Dimensions
Dia A 10.5000
Dia B 6.2500
Height 1.3800
Cone Angle 33.0000
Flat Pattern Dimensions
Large Radius 6.2599
Small Radius 3.7261
Angle A 150.9607
Width X 12.1200
Height Y 5.3257
Cord 12.1200
Full or Half Cone: Half
So, your 33 degree cone angle, half cone gives us a height of 1.38 inches.
Is there an on-line worksheet or program that translates your 33 degrees into a proper cutting template?
Edit - BTW, thanks to @Mulletron for the heads-up on this template software
1) That angle of 33 degrees (approximately, from memory I recall writing that it look like 30 degrees) should be referred to as "Shawyer's superconducting EM Drive" angle and not as my angle. I'm certainly not known in these threads for following Shawyer's prescriptions for the EM Drive. 
2) <<Is there an on-line worksheet or program that translates ...33 degrees into a proper cutting template?>> I don't use on-line software to calculate angles of right-angle triangles like in a cone, I just use my several-decades old Hewlett-Packard calculator
3) For an angle of 30 degrees we can do the calculation in our head (no software or calculator or table), since Sin[30 degrees] = 0.5 (exactly)
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#2336 by rfmwguy on 28 Jan, 2016 15:48
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OK, I couldn't find anywhere where 33 degrees would do anything for people fabricating frustums. Also, you said:...
OK, I'll put your dimension in the formula:
Result of Cone Calculation
Cone Dimensions
Dia A 10.5000
Dia B 6.2500
Height 1.3800
Cone Angle 33.0000
Flat Pattern Dimensions
Large Radius 6.2599
Small Radius 3.7261
Angle A 150.9607
Width X 12.1200
Height Y 5.3257
Cord 12.1200
Full or Half Cone: Half
So, your 33 degree cone angle, half cone gives us a height of 1.38 inches.
Is there an on-line worksheet or program that translates your 33 degrees into a proper cutting template?
Edit - BTW, thanks to @Mulletron for the heads-up on this template software
1) That angle of 33 degrees (approximately, from memory I recall writing that it look like 30 degrees) should be referred to as "Shawyer's superconducting EM Drive" angle and not as my angle. I'm certainly not known in these threads for following Shawyer's prescriptions for the EM Drive.
2) I don't use on-line software to calculate angles of right-angle triangles like in a cone, I just use my old Hewlett-Packard calculator
"because there are multiple interior angles"
Just so I have my head screwed on straight my interpretation of a geometric cone is that there are only two internal angles, the angle of the cone measured from either the top or bottom plate.
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#2337 by Rodal on 28 Jan, 2016 15:56
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...
No, you should not make such assumptions. It is always better to use drawings to communicate, and to make sure one is using the same geometrical definitions as other people. Otherwise there will be confusion
OK, I couldn't find anywhere where 33 degrees would do anything for people fabricating frustums. Also, you said:
"because there are multiple interior angles"
Just so I have my head screwed on straight my interpretation of a geometric cone is that there areonly two internal angles, the angle of the cone measured from either the top or bottom plate.
Case in point:
1) For a cone, most references use the half cone angle and refer to it as the cone angle. Why do they use this half-cone angle instead of the complete interior angle? Because of symmetry.
2) For a cone, there are references that use twice the half cone angle and refer to it as the cone angle (in other words they use the complete interior angle at the apex of the cone)
3) You instead use the angle between the conical wall and the base of the frustum
That's three angles right there.
4) You could invent another rfmwguy angle as the half angle between the conical wall and the base and you would have 4 angles, and so on and on. There is also the 90 degree angle between the longitudinal axis and the base. -
#2338 by rfmwguy on 28 Jan, 2016 16:04
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Uhhhh, OK. Seems a bit overcomplicated for a metal fabricator, but I do recall this was Greg Egan's calculation of preference. BTW, ConeCalc generates a nice cad file....
No, you should not make such assumptions. It is always better to use drawings to communicate, and to make sure one is using the same geometrical definitions as other people. Otherwise there will be confusion
OK, I couldn't find anywhere where 33 degrees would do anything for people fabricating frustums. Also, you said:
"because there are multiple interior angles"
Just so I have my head screwed on straight my interpretation of a geometric cone is that there areonly two internal angles, the angle of the cone measured from either the top or bottom plate.
Case in point:
1) For a cone, most references use the half cone angle and refer to it as the cone angle. Why do they use this half-cone angle instead of the complete interior angle? Because of symmetry.
2) For a cone, there are references that use twice the half cone angle and refer to it as the cone angle (in other words they use the complete interior angle at the apex of the cone)
3) You instead use the angle between the conical wall and the base of the frustum
That's three angles right there.
4) You could invent another rfmwguy angle as the half angle between the conical wall and the base and you would have 4 angles, and so on and on. There is also the 90 degree angle between the longitudinal axis and the base.
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#2339 by Rodal on 28 Jan, 2016 16:06
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..
OK, this will be the last post I will have on geometry.
OK, I'll put your dimension in the formula:
Result of Cone Calculation
Cone Dimensions
Dia A 10.5000
Dia B 6.2500
Height 1.3800
Cone Angle 33.0000
...
Your calculation is incorrect, if by diameters, you are referring to what we, at this thread, have been calling the diameters of the flat bases of a frustum of a cone EM Drive.
Since (10.5-6.25)/2 = 4.25/2=2.125
that gives a base for the right angle triangle of 2.125 (the difference between the big base radius and the small base radius).
Defining the cone half angle as per this geometry, that has been the convention in the EM Drive thread, and the EM Drive wiki:
The tangent of the cone half-angle is equal to the base of the right-triangle divided by the frustum of a cone's height.
Hence a cone half angle of 33 degrees would give a height for the frustum of a cone (with big diameter=10.5 and small diameter=6.25) of
2.125/Tan[33 degrees] = 3.27 instead of 1.38
Big Diameter of the flat base of the frustum of a cone = 10.5
Small Diameter of the flat base of the frustum of a cone = 6.25
Height (measured perpendicular to the flat bases) of the frustum of a cone = 3.27
Cone half angle of the frustum of a cone = 33 degrees
_____________________
Again, the error in your calculation is due to you using the incorrect angle in your calculation:
if you incorrectly use
rfmwguyAngle = 90 degrees - 33 degrees = 57 degrees
as the cone half-angle, then you incorrectly derive the following height:
2.125/Tan[57 degrees] = 1.38
_________
EDIT: my initial height calculation of 6.54 instead of 3.27 (using a calculator and my head ) corrected for a factor of 2 because I initially subtracted the diameters instead of subtracting the radii to calculate the base of the right triangle defining the height of the frustum in terms of the tangent of the half angle of the cone.
) and read the thousands of posts on here through the years you'll run across the musings of the physics of this drive and the theories are almost countless. Even the wonderful Foobie Dust theory.
