....

Do you have a reference giving frequency, Q, power and thrust measurements for the Flight Thruster?This is the only reference I have for data for the Flight Thruster: http://emdrive.com/flightprogramme.html, I can't find a Q reported.

The Flight thruster programme covers the design and development of a 300 Watt C Band flight thruster. This has a specified thrust of 85 mN, and a mass of 2.92Kg. Overall dimensions are 265mm diameter at the baseplate and a height of 164mm.

Development testing of the unit, up to a power of 600 W, is under way, and to date, has given a mean specific thrust of 330 mN/kW.[…]This is needed to ensure the input frequency matches the resonant frequency of the high Q (60,000) cavity, over the full input power range and the qualification temperature specification.

The Dynamic performance of the non superconducting Flight Test model, manufactured and tested by SPR Ltd, and described in REF 3 [N.B.: 2010 Toulouse TECHNO DIS paper] was modeled with a cavity Q_{u} = 50,000 and F_{res}=3.85 GHz.

@ RODALStill have question about the Shawyer "Demo" cavity w/ 174mN. What are the current estimates of the cone dimensions, frequency (3.85GHz?), and Q (6000 est?). When I put in TM02 and 450W, I get 174.8microN, rather than the 174milliN reported. I would like to recheck those numbers. Even w/ Q=45000, I need to get X up around (65 Very high mode) to get those numbers. Is that possible w/ 3.85GHz ??Thanks

Quote from: frobnicat on 02/25/2015 11:37 PM... When thermal expansion displaces a part of a system relative to the rest of a system, the rest of the system will recoil. Whatever displaces a part of a system relative to the rest of the system, this displacement implies a force F_system_part. The rest of the system will recoil. Recoil is the acceleration due to the opposite force (F_part_system). An unrestrained, homogeneous, isotropic, free to expand but in one direction material, will produce a force when expanding against the wall against which it rests.Why is it so hard to reach consensus now ?With respect to the HD PE dielectric, now I see your thinking. I think you think of it as a dynamic problem, for example, if instead of the HD PE we would have an explosive inside the cavity glued to the left wall, the effect of the explosive would be to force the wall towards the left.However, thermal expansion does not work like that. There are no dynamic forces caused by a material experiencing thermal expansion such that it is free to expand. Thermal expansion is a very slow process that does not involve second order derivatives with respect to time. If a uniaxial isotropic material is glued to a wall, it will just expand without producing any force whatsoever on the wall it is glued to. If free, it will just expand, strain = alpha *deltaT. No stress if it is free to expand.Can't use thermal expansion as a form of propellant-less propulsion.

... When thermal expansion displaces a part of a system relative to the rest of a system, the rest of the system will recoil. Whatever displaces a part of a system relative to the rest of the system, this displacement implies a force F_system_part. The rest of the system will recoil. Recoil is the acceleration due to the opposite force (F_part_system). An unrestrained, homogeneous, isotropic, free to expand but in one direction material, will produce a force when expanding against the wall against which it rests.Why is it so hard to reach consensus now ?

For what it's worth, I don't think the given numbers (265mm base diameter and 164mm axial height) can possibly be right for the inner cavity of the thruster in the photo- not unless whatever plates that are inserted within the ends are several centimeters thick. The only way that the height is only .6188 or 62% of the base diameter is if the 265mm base diameter is measured from the widest part of the exterior of the base plate, and the height is measured from where the slope of the exterior walls flattens out on top and bottom as roughly indicated by the yellow arrows in the attached photo. If that happened to be the case, then 189mm would be the exterior diameter of the top plate.But there's almost no way, in my humble opinion, that 265mm, 164mm and 189mm are correct for the inner cavity. Unless, again, the plates (diaelectric?) inserted inside the end plates in the inner cavity are several centimeters thick. I'm pretty confident in saying that. The distortion in the photo isn't nearly enough to account the discrepancy.I only point this out to maybe prevent some confusion, and now retreat to my recliner and leave the real work to minds more learned than mine.

In summary, what do you think are the most likely inner dimensions?

For the part in blue : I don't see the qualitative difference you make between an explosive detonating on a left wall and a plastic block glued to a left wall and thermally expanding, in both cases it is thermal expansion. A material that expands is never completely free to expands, it must at least overcome its own inertia, even if slow quasi-static expansion occurs... Take for instance a slice of the material at the right of the slab, when the whole slab is heating, its distance from the left wall increase (meaning non 0 velocity), it has a mass, it was initially at velocity 0, so going from velocity 0 to some non null velocity implies an acceleration at some time, and this slice has a mass, so the rest of the slab had to push it, hence stress. The slower the process the weaker the forces, but weak is not 0. So maybe there is no leftward force of the plastic block expanding rightward during the phase of heating at constant rate if that means constant velocity of block's CoM, but at some time between start of heating and constant rate there has been a leftward force (on the wall). Likewise at some time between this phase of constant rate heating (constant expansion velocity) and stabilisation at constant position (end of movement to the right, 0 velocity again) there must be a deceleration, that is a leftward acceleration that corresponds to the block pulling the wall toward the right : if it wasn't glued it couldn't decelerate and would leave the left wall.The integrated forces between initial static position (at 0 relative velocity) and final static position (at 0 relative velocity) will be 0, since by definition the force (kg m/s²) when integrated is the exchanged momentum (kg m/s). So yes "Can't use thermal expansion as a form of propellant-less propulsion" in the sense that it can't give long lasting momentum (deltaV) to a spacecraft. But it can lend small temporary momentum to be paid back a little later, since it can give momentary speed, it can give long lasting displacement : by integrating the momentary "bump" in momentum(t) the craft of mass M will have shifted its position by X while the moving part of mass m has moved x, with MX=-mx (in kg m units). And from this point of view, this displacement is the same whether the mass m moved distance x fast or ultra-slowly. Equalling force terms to 0 because movement is slow would fail to predict that : weak forces for long time do the same "displacement job" as strong forces for short time.So a spacecraft A that is already at exact same velocity than spacecraft B but a few inches apart could dock to it just by shifting an inner part's mass. Obviously the mass shift can't be recycled to "inchworm" spacecraft's position again and again : to put the part at it's original position means losing the whole system's gained displacement. But the point is : that don't depend on the specifics of what makes the part move.So what's the point ? Regardless of what exactly would make a part move relative to another in the frustum, we know that 50µN for 45s, interpreted as a slowly occurring recoil effect (ever-accelerating part), amounts for an integrated "mass displacement" of .5*50e-6*45²=0.05 kg m that is either 50 grams moving 1m, or 1kg moving 5cm, or 10kg moving 5mm. Sorry, this is a repeat.

If the 265mm base diameter that Shawyer gave does in fact refer the the exterior diameter of the base plate and if the height is measured from the yellow arrows indicated in the aforementioned photo, which is the only way I can reconcile his figures with the photo, then my best guess for the inner resonance cavity is:224mm base diameter145mm top diameter164mm height (given by Shawyer).Here's the chart if anyone is interested, cluttered though it has admittedly become.

Quote from: lasoi on 03/01/2015 12:58 AMIf the 265mm base diameter that Shawyer gave does in fact refer the the exterior diameter of the base plate and if the height is measured from the yellow arrows indicated in the aforementioned photo, which is the only way I can reconcile his figures with the photo, then my best guess for the inner resonance cavity is:224mm base diameter145mm top diameter164mm height (given by Shawyer).Here's the chart if anyone is interested, cluttered though it has admittedly become.Thanks! That brings that X number down to ~55. Still a very high mode, but 3.85GHz !

Quote from: Notsosureofit on 03/01/2015 01:20 AMQuote from: lasoi on 03/01/2015 12:58 AMIf the 265mm base diameter that Shawyer gave does in fact refer the the exterior diameter of the base plate and if the height is measured from the yellow arrows indicated in the aforementioned photo, which is the only way I can reconcile his figures with the photo, then my best guess for the inner resonance cavity is:224mm base diameter145mm top diameter164mm height (given by Shawyer).Here's the chart if anyone is interested, cluttered though it has admittedly become.Thanks! That brings that X number down to ~55. Still a very high mode, but 3.85GHz !McCulloch's equation gives 148 milliNewtons for Shawyer's demo, comparing pretty well with Shawyer's reported measurements of 80 to 214 millinNewtons, see:http://physicsfromtheedge.blogspot.com/2015/02/mihsc-vs-emdrive-data-3d.htmlI understand that you need to use X=26 in your equation for Shawyer's Demo, also a high mode.On the other's hand McCulloch's equation is off by a factor >10 for NASA Eagleworks test results.

Quote from: frobnicat on 02/28/2015 11:20 PM

Quote from: Rodal on 03/01/2015 12:00 AMQuote from: frobnicat on 02/28/2015 11:20 PMPlease, I'm not accustomed to such tools as those used for thermoacoustics. There is not enough of a life to learn all... Just applying more rudimentary reasoning : my slab of PTFE, volumetrically heated, free floating alone, would expand as much leftward than rightward. If glued to a left wall inside an heavy hull, it will expand more rightward than leftward (in the same inertial reference frame) : necessarily it means that at some time there have been a force of the wall on the slab, otherwise a solid object as a wall wouldn't have been needed to prevent the slab to expand leftward. If such wall exerted no force at all, the slab would have expanded through the wall as if it didn't existed. Ahem.So if by "speed of thermal expansion is constant" you mean a phase when in all place there is a constant rate dT/dt, and therefore all positions are also changing at constant rate (dx/dt constant), well yes, in such phase there is no acceleration and no force. But what is going on between dT/dt = 0 and dT/dt =cst, that is between an instant where dx/dt=0 and an instant where dx/dt=cst ? Surely at some time there is a force involved. Now, maybe it's usually neglected because it is negligible for all practical purpose, but if we are to integrate µN ...So if there is no "thermal expansion acceleration" how do you go from a state of no thermal expansion to a state of ongoing thermal expansion ? Step like ? But this step would still represent some momentum impulse...Please define the "speed of thermal expansion" that is supposed to be constant, I don't get it.For instance if one is heating volumetrically a mass of material at linearly growing power at constant rate P(t)=cst t, then we have a heat energy Q that goes as t², and so does temperature T, and if we assume a slow (quasi-static) rate, the material will be at length l(t)=cst + cst*t² hence ldot=velocity=cst*t hence acceleration=cst hence constant inertial force to overcome...

Quote from: Rodal on 02/28/2015 07:57 PMQuote from: flux_capacitor on 02/28/2015 07:30 PM....Interesting thing to note: Shawyer claims the engine starts to accelerate only when the magnetron frequency locks to the resonant frequency of the thruster, following an initial warm up period where it does not move; thus according to him eliminating possible spurious forces.....That's very interesting stuff. Thank you for bringing it up.Do you have a reference as to where Shawyer made that interesting claim?Yes, it is in the same 2008 paper you have just cited in the message above this one, entitled "MICROWAVE PROPULSION – PROGRESS IN THE EMDRIVE PROGRAMME":http://www.emdrive.com/IAC-08-C4-4-7.pdfWhere Shawyer noted:QuoteThe frequency offset curve shows that initial magnetron thermal drift ends with frequency lock. At this point, 130 secs into the test run, the velocity data shows the start of acceleration under power. The prior thermal drift period, with no acceleration, shows that the thrust is not a result of spurious thermal effects. When the power is turned off, at 210 secs, there is a coast period as the slosh effects of 5kg of coolant maintain a reduced acceleration. This is followed by the deceleration due to the friction torque. A maximum velocity of 2cm/s was achieved and a total distance of 185cm was "flown".

Quote from: flux_capacitor on 02/28/2015 07:30 PM....Interesting thing to note: Shawyer claims the engine starts to accelerate only when the magnetron frequency locks to the resonant frequency of the thruster, following an initial warm up period where it does not move; thus according to him eliminating possible spurious forces.....That's very interesting stuff. Thank you for bringing it up.Do you have a reference as to where Shawyer made that interesting claim?

....Interesting thing to note: Shawyer claims the engine starts to accelerate only when the magnetron frequency locks to the resonant frequency of the thruster, following an initial warm up period where it does not move; thus according to him eliminating possible spurious forces.....

The frequency offset curve shows that initial magnetron thermal drift ends with frequency lock. At this point, 130 secs into the test run, the velocity data shows the start of acceleration under power. The prior thermal drift period, with no acceleration, shows that the thrust is not a result of spurious thermal effects. When the power is turned off, at 210 secs, there is a coast period as the slosh effects of 5kg of coolant maintain a reduced acceleration. This is followed by the deceleration due to the friction torque. A maximum velocity of 2cm/s was achieved and a total distance of 185cm was "flown".

Quote from: frobnicat on 03/01/2015 01:37 AMQuote from: Rodal on 03/01/2015 12:00 AMQuote from: frobnicat on 02/28/2015 11:20 PMPlease, I'm not accustomed to such tools as those used for thermoacoustics. There is not enough of a life to learn all... Just applying more rudimentary reasoning : my slab of PTFE, volumetrically heated, free floating alone, would expand as much leftward than rightward. If glued to a left wall inside an heavy hull, it will expand more rightward than leftward (in the same inertial reference frame) : necessarily it means that at some time there have been a force of the wall on the slab, otherwise a solid object as a wall wouldn't have been needed to prevent the slab to expand leftward. If such wall exerted no force at all, the slab would have expanded through the wall as if it didn't existed. Ahem.So if by "speed of thermal expansion is constant" you mean a phase when in all place there is a constant rate dT/dt, and therefore all positions are also changing at constant rate (dx/dt constant), well yes, in such phase there is no acceleration and no force. But what is going on between dT/dt = 0 and dT/dt =cst, that is between an instant where dx/dt=0 and an instant where dx/dt=cst ? Surely at some time there is a force involved. Now, maybe it's usually neglected because it is negligible for all practical purpose, but if we are to integrate µN ...So if there is no "thermal expansion acceleration" how do you go from a state of no thermal expansion to a state of ongoing thermal expansion ? Step like ? But this step would still represent some momentum impulse...Please define the "speed of thermal expansion" that is supposed to be constant, I don't get it.For instance if one is heating volumetrically a mass of material at linearly growing power at constant rate P(t)=cst t, then we have a heat energy Q that goes as t², and so does temperature T, and if we assume a slow (quasi-static) rate, the material will be at length l(t)=cst + cst*t² hence ldot=velocity=cst*t hence acceleration=cst hence constant inertial force to overcome...What changes with time (very slowly, due to the low thermal diffusivity of HD PE) is the temperature.So, one has to solve Fourier's equation (temperature vs time). And the thermal expansion and thermal stresses follow from that. There is no second order derivative with respect to time in Fourier's equation. There is only a first order derivative with respect to time, and other terms containing a second order derivative with respect to space.There is no "acceleration of temperature term in Fourier's equation". Hence no intrinsic "thermal wave Fourier equation". No "inertia of temperature" term and no "inertia of thermal expansion" term.You may compute a thermal strain changing with time due to the temperature changing with time: T(t) hence epsilon(t)=alpha*T(t), and a strain rate also changing with time (due to the change with time of the temperature).The coefficient of thermal expansion is very small, by several orders of magnitude. There is nothing there to produce a large acceleration of thermal deformation term. The "acceleration of thermal deformation" in HD PE should be negligible, and when you multiply it by the mass it should give a negligible force. Such dynamic terms are neglected in thermal problems. Even in the Pioneer anomaly problem, involving extremely small accelerations, what is discussed is the thermal radiation producing recoil forces, but nobody has brought up "thermal expansion forces due to the thermal expansion changing with time", one reason for this being that such thermal expansion cannot accelerate the center of mass for an object free in space, of course. But no issues of "acceleration of thermal expansion" bringing dynamic forces on the antenna either.