...Wasn't Shawyer's equation some how based on cylinders also? ...

...Could it be that the best force is some how slightly off resonance? ...

... Do we have plots of force as frequency is changed from peak resonance to slightly off? ...

... Could throwing in the dielectric slightly throw it off resonance?

Shawyer uses several approximate equations as well, for the same reason (because there is no closed-form solution for a truncated cone). Unlike Notsosureofit, Shawyer does not clearly state what are his approximations. I find Shawyer's papers, regarding his equations and his free-body-diagrams to be very unorthodox.According to TheTraveller's post in the last few pages, Shawyer is using the cut-off equation for a cylinder.

these two thrusters aren't the same flight thruster. What I'm getting from TheTraveller is that the flight thruster that Shawyer is standing next to in the pic above is copper (kinda does look coppery when you zoom in), and that the one on the table is copper inside/and coated outside. I'm not sure. @TheTraveller, did I get that right?

The high density polyethylene discs dielectric's relative permittivity is 2.27 at 2.0 GHz with a dissipation factor of ~0.0005.

Ok, so I'm being told by PM that IRT this post above,http://forum.nasaspaceflight.com/index.php?topic=37642.msg1382564#msg1382564these two thrusters aren't the same flight thruster. What I'm getting from TheTraveller is that the flight thruster that Shawyer is standing next to in the pic above is copper (kinda does look coppery when you zoom in), and that the one on the table is copper inside/and coated outside. I'm not sure. @TheTraveller, did I get that right?

@TheTraveller,Just a thought, but if you use Google Sheets, instead of Excel, you can write your own functions in javascript instead of using 1000s of cells to perform calculations and do vlookups.I haven't done it in years but its pretty easy. Conceptually it might be easier in some cases.Cheers

Quote from: phaseshift on 06/01/2015 12:46 AM@TheTraveller,Just a thought, but if you use Google Sheets, instead of Excel, you can write your own functions in javascript instead of using 1000s of cells to perform calculations and do vlookups.I haven't done it in years but its pretty easy. Conceptually it might be easier in some cases.CheersI did it the way I did so I could graph the guide wavelength change from end to end and be able to see if and where it hit cutoff.

I think it is important for all to remember that the EM drive is a physical system, not a mathematical one. In the physical system, cutoff is not a line in the sand that you shall not cross, rather it is (probably) the center of a range where propagation drops below some relative value of db. The EM drive will do as it does over a range of frequencies, plus or minus, just some will do better than others.Add: Its also important that the magnatron drive is a noisy source so the cavity will select its own operating frequency. It would be nice to have the maximum power transfer from source to cavity but very often "Perfect" is the enemy of "Good enough."

Quote from: aero on 05/31/2015 04:43 PMI think it is important for all to remember that the EM drive is a physical system, not a mathematical one. In the physical system, cutoff is not a line in the sand that you shall not cross, rather it is (probably) the center of a range where propagation drops below some relative value of db. The EM drive will do as it does over a range of frequencies, plus or minus, just some will do better than others.Add: Its also important that the magnatron drive is a noisy source so the cavity will select its own operating frequency. It would be nice to have the maximum power transfer from source to cavity but very often "Perfect" is the enemy of "Good enough."Classic definition of cutoff is 3db. A single cavity will not have a steep shape factor in stopbands, no brickwall is correct. Return loss will be much more transitional in the passband... IOW i'd design and tune for best S11 performance at center frequency simply to keep the signal source protected as a matter of safety and efficiency. Also the bessel function has a shallower shape factor. Its best known characteristic is flat group time delay in passband for radar/pulse applications. Really, the frustum is a poor bandpass, being so assymetrical around a center frequency....but maybe that's part of the mystery

Just for fun I took the TheTraveler's equations for determining the end plate spacing, but instead of slicing the frustum into 1000 cylinders I sliced it into 5,000,000. His result: 139.22907 millimetersMy result: 139.3682 millimetersdifference of 0.139 millimetersFrom what TheTraveler has written, and as I have understood it, Shawyer used a similar technique to perform approximate calculations, and as others have said "good enough to get the job done". I'll have to go with this for now until something better comes along. Thank You TheTraveler.In order to figure out why the EM drive works we can't use this technique (probably), but to build one this seems good enough.

Quote from: phaseshift on 05/31/2015 11:55 PMJust for fun I took the TheTraveler's equations for determining the end plate spacing, but instead of slicing the frustum into 1000 cylinders I sliced it into 5,000,000. His result: 139.22907 millimetersMy result: 139.3682 millimetersdifference of 0.139 millimetersFrom what TheTraveler has written, and as I have understood it, Shawyer used a similar technique to perform approximate calculations, and as others have said "good enough to get the job done". I'll have to go with this for now until something better comes along. Thank You TheTraveler.In order to figure out why the EM drive works we can't use this technique (probably), but to build one this seems good enough.A simplistic way to see if this makes the nut for construction is to multiply the discrepancy by Q and see if the result remains substantially less than a quarter of a wavelength. So for 2.5 GHz (lambda/4=30mm),60,000*0.139 = 8340 mm. Well, sorry about that, but that's the price for high Q.

Quote from: deltaMass on 06/01/2015 02:14 AMQuote from: phaseshift on 05/31/2015 11:55 PMJust for fun I took the TheTraveler's equations for determining the end plate spacing, but instead of slicing the frustum into 1000 cylinders I sliced it into 5,000,000. His result: 139.22907 millimetersMy result: 139.3682 millimetersdifference of 0.139 millimetersFrom what TheTraveler has written, and as I have understood it, Shawyer used a similar technique to perform approximate calculations, and as others have said "good enough to get the job done". I'll have to go with this for now until something better comes along. Thank You TheTraveler.In order to figure out why the EM drive works we can't use this technique (probably), but to build one this seems good enough.A simplistic way to see if this makes the nut for construction is to multiply the discrepancy by Q and see if the result remains substantially less than a quarter of a wavelength. So for 2.5 GHz (lambda/4=30mm),60,000*0.139 = 8340 mm. Well, sorry about that, but that's the price for high Q.Speaks loudly for a tuning cylinder or RF tuner. At 1000 slices there were 4 significant digits, 50,000 slices there were 5 significant digits, 5,000,000 slices raised it to 6 significant digits - but as it's just an approximation anyway 1000 slices seems adequate considering it needs to be tuned anyway.

Quote from: deltaMass on 06/01/2015 02:14 AMQuote from: phaseshift on 05/31/2015 11:55 PMJust for fun I took the TheTraveler's equations for determining the end plate spacing, but instead of slicing the frustum into 1000 cylinders I sliced it into 5,000,000. His result: 139.22907 millimetersMy result: 139.3682 millimetersdifference of 0.139 millimetersFrom what TheTraveler has written, and as I have understood it, Shawyer used a similar technique to perform approximate calculations, and as others have said "good enough to get the job done". I'll have to go with this for now until something better comes along. Thank You TheTraveler.In order to figure out why the EM drive works we can't use this technique (probably), but to build one this seems good enough.A simplistic way to see if this makes the nut for construction is to multiply the discrepancy by Q and see if the result remains substantially less than a quarter of a wavelength. So for 2.5 GHz (lambda/4=30mm),60,000*0.139 = 8340 mm. Well, sorry about that, but that's the price for high Q.Cost of the high Q is your narrow band Rf generator needs to be able to track frustum resonance changes via some feedback mechanism. The Rf generator I'll be using can move in 1kHz increments, so should be OK to keep the frequency in the middle of the thrust bandwidth.BTW I plan to work in pulsed mode. Do a pulse, measure thrust, switch the coax feed to the spectrum analyser, measure the max Q frequency, switch back the excitation antenna to the Rf amp, adjust the freq if necessary and give it another pulse. Around the loop it goes. Should be able to do this many times a second.That way I get 2 feedback channels to help to initially keep the excitation frequency in the middle of the Q bandwidth and/or inthe centre of the thrust bandwidth once it start to develop.

Quote from: phaseshift on 06/01/2015 02:24 AMQuote from: deltaMass on 06/01/2015 02:14 AMQuote from: phaseshift on 05/31/2015 11:55 PMJust for fun I took the TheTraveler's equations for determining the end plate spacing, but instead of slicing the frustum into 1000 cylinders I sliced it into 5,000,000. His result: 139.22907 millimetersMy result: 139.3682 millimetersdifference of 0.139 millimetersFrom what TheTraveler has written, and as I have understood it, Shawyer used a similar technique to perform approximate calculations, and as others have said "good enough to get the job done". I'll have to go with this for now until something better comes along. Thank You TheTraveler.In order to figure out why the EM drive works we can't use this technique (probably), but to build one this seems good enough.A simplistic way to see if this makes the nut for construction is to multiply the discrepancy by Q and see if the result remains substantially less than a quarter of a wavelength. So for 2.5 GHz (lambda/4=30mm),60,000*0.139 = 8340 mm. Well, sorry about that, but that's the price for high Q.Speaks loudly for a tuning cylinder or RF tuner. At 1000 slices there were 4 significant digits, 50,000 slices there were 5 significant digits, 5,000,000 slices raised it to 6 significant digits - but as it's just an approximation anyway 1000 slices seems adequate considering it needs to be tuned anyway.It needs to be continually tuned is what Shawyer said to me.

Quote from: TheTraveller on 06/01/2015 02:28 AMQuote from: phaseshift on 06/01/2015 02:24 AMQuote from: deltaMass on 06/01/2015 02:14 AMQuote from: phaseshift on 05/31/2015 11:55 PMJust for fun I took the TheTraveler's equations for determining the end plate spacing, but instead of slicing the frustum into 1000 cylinders I sliced it into 5,000,000. His result: 139.22907 millimetersMy result: 139.3682 millimetersdifference of 0.139 millimetersFrom what TheTraveler has written, and as I have understood it, Shawyer used a similar technique to perform approximate calculations, and as others have said "good enough to get the job done". I'll have to go with this for now until something better comes along. Thank You TheTraveler.In order to figure out why the EM drive works we can't use this technique (probably), but to build one this seems good enough.A simplistic way to see if this makes the nut for construction is to multiply the discrepancy by Q and see if the result remains substantially less than a quarter of a wavelength. So for 2.5 GHz (lambda/4=30mm),60,000*0.139 = 8340 mm. Well, sorry about that, but that's the price for high Q.Speaks loudly for a tuning cylinder or RF tuner. At 1000 slices there were 4 significant digits, 50,000 slices there were 5 significant digits, 5,000,000 slices raised it to 6 significant digits - but as it's just an approximation anyway 1000 slices seems adequate considering it needs to be tuned anyway.It needs to be continually tuned is what Shawyer said to me. Exactly! So an approximate solution is adequate IMO.Can you sample and feed at the same location? I thought the sample needed to be at center and the feed toward one end or the other?

Not that this all matters, because 1: Shawyer's formula for computing thrust has been definitely falsified by EagleWorks down to 1..2%