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#1320 by aero on 10 Mar, 2015 23:17
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....
See http://forum.nasaspaceflight.com/index.php?topic=36313.msg1339803#msg1339803QuoteI did calculate the Eagleworks cavity without the HD-PE dielectric section.
And what number did you get?
The frequency for the TM221 mode shape (without the dielectric) is 2.00709 GHz.
Is there another particular mode you are interested to know the frequency for?
I'll need to think on that. It seems, from the images you posted, that the mode is the same for you and Eagleworks. So what (if anything) is close to freq = 1.937115E+009 Hz? And was the Eagleworks photos taken with that drive frequency? -
#1321 by Rodal on 10 Mar, 2015 23:52
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....
See http://forum.nasaspaceflight.com/index.php?topic=36313.msg1339803#msg1339803QuoteI did calculate the Eagleworks cavity without the HD-PE dielectric section.
And what number did you get?
The frequency for the TM221 mode shape (without the dielectric) is 2.00709 GHz.
Is there another particular mode you are interested to know the frequency for?
I'll need to think on that. It seems, from the images you posted, that the mode is the same for you and Eagleworks. So what (if anything) is close to freq = 1.937115E+009 Hz? And was the Eagleworks photos taken with that drive frequency?
Take a look at the enclosed report from Paul March for a mode which NASA's COMSOL analyst identified as TM112 "like TM110 at top, and TM111 at bottom" with a frequency of 1.9355 GHz.
I only calculated a few modes.
Regarding your question "And was the Eagleworks photos taken with that drive frequency?" I presume that the photo was taken for the EM Drive with a dielectric (which would give a slightly lower frequency) while my computation was without the dielectric.
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#1322 by Notsosureofit on 11 Mar, 2015 00:18
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@ RODAL
Just got a minute but from your p expression;
If L1/c1 = L2/c2
del f = (1/2*f)*((c1*c2)/(L1*L2))*b^2*((1/dD1^2)-(1/dD2^2))
might be a solution ??
Got to check the thinking later.
Night !
I find your previous expression
del f = ( f/(2*c^2)) * (c1^2-c2^2)
more physically appealing, since it goes to zero for equal dielectric constants, regardless or their dielectric length,
while on the other hand
del f = (1/2*f)*((c1*c2)/(L1*L2))*b^2*((1/dD1^2)-(1/dD2^2))
goes to zero for equal dielectric lengths, regardless of their dielectric constants.
The previous expression is only valid approximation for a "uniformly varying dielectric". There is no L1 and L2 in that case.
What do you think might maximize the second expression ? (valid only for L1/c1 = L2/c2 )
Mmmm, so for L1/c1 = L2/c2 we can rewrite as:
del f = (b^2/(2*f*D^2))*(c1^2-c2^2) ==> 0 as c1 => c2 so max c1 vs c2 ??
But we still need a general solution instead of a case by case by inspection.
Still, they both vary as (c1^2-c2^2) and are almost opposite cases.
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#1323 by Rodal on 11 Mar, 2015 00:32
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....
See http://forum.nasaspaceflight.com/index.php?topic=36313.msg1339803#msg1339803QuoteI did calculate the Eagleworks cavity without the HD-PE dielectric section.
And what number did you get?
The frequency for the TM221 mode shape (without the dielectric) is 2.00709 GHz.
Is there another particular mode you are interested to know the frequency for?
I'll need to think on that. It seems, from the images you posted, that the mode is the same for you and Eagleworks. So what (if anything) is close to freq = 1.937115E+009 Hz? And was the Eagleworks photos taken with that drive frequency?
Take a look at the enclosed report from Paul March for a mode which NASA's COMSOL analyst identified as TM112 "like TM110 at top, and TM111 at bottom" with a frequency of 1.9355 GHz.
I only calculated a few modes.
Regarding your question "And was the Eagleworks photos taken with that drive frequency?" I presume that the photo was taken for the EM Drive with a dielectric (which would give a slightly lower frequency) while my computation was without the dielectric.
I compute a frequency of 1.97396 GHz for mode TM112 without the dielectric. -
#1324 by Star-Drive on 11 Mar, 2015 02:46
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Dr. Rodal:
"From the few reports where I saw the dielectric materials tested by R. Shawyer, what I recall is Shawyer using inorganic dielectric materials. This is important to understand the reports that Shawyer has abandoned the use of dielectric materials. Without knowing specifically what dielectric materials did Shawyer abandon, the fact that he abandoned them is not that useful."
Shawyer used a commercial ceramic dielectric resonator with an e-r = ~38 and a Q of greater than 10,000. We tried a similar commercial grade ceramic dielectric resonator material like the ones from Temex-ceramics and generated zip with same. Hard ceramics with low electrostrictive coefficients and no piezoelectric response apparently are dead-ends for this EM-Drive application.
http://www.temex-ceramics.com/site/en/dielectric-resonators-cermatmenu-28.html
http://www.temex-ceramics.com/site/fichiers/dielectric.pdf
Acknowledge that "neoprene" rubber covers a multitude of formulations, but it turns out that most if not all of them have low Q-factors at microwave frequencies that disqualify them from this application even if they have a large electrostrictive coefficient. What counts in this low power EM-drive dielectric "amplifier" appears to be a dielectric with the largest electrostrictive/piezoelectric coefficient combined with a high Q-factor at microwave frequencies.
Best, Paul M.
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#1325 by aero on 11 Mar, 2015 04:43
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@Rodal
Can there be a resonance in the empty cavity at the low frequency of 1.6859 GHz?
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#1326 by Rodal on 11 Mar, 2015 10:50
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@Rodal
Can there be a resonance in the empty cavity at the low frequency of 1.6859 GHz?
Take a gander at page 3 of the attachment (from a previous post by Paul March) to http://forum.nasaspaceflight.com/index.php?topic=36313.msg1344168#msg1344168 -
#1327 by Rodal on 11 Mar, 2015 23:31
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Continuing from message, http://forum.nasaspaceflight.com/index.php?topic=36313.msg1339803#msg1339803, using the exact solution information, I plotted the information as a Vector Density Plot to better understand the magnetic field in modes TM22p, where p can be 1, 2, 3 etc. On this cross-section, TM221, TM222 and TM223, etc, look practically identical, except for different intensity magnitude for the higher frequency modes with TM22p where p>1.
The vector plot shows the direction and magnitude of the magnetic vector field on the base for the mode presently being tested by NASA Eagleworks. It helps understand the reason for the hot and cold intensities.
Below I show:
1) The NASA Finite Element prediction and NASA's thermal IR imaging measurement
2) Vector Intensity Plot of mode TM222 using the exact solution (click the image to magnify it)
3) An Intensity Plot of mode TM221 using the exact solution (with another color scheme)
4) Another Intensity Plot of mode TM221 using the exact solution (with another color scheme)
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#1328 by Rodal on 12 Mar, 2015 13:30
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....
Dr. Rodal:
....
Acknowledge that "neoprene" rubber covers a multitude of formulations, but it turns out that most if not all of them have low Q-factors at microwave frequencies that disqualify them from this application even if they have a large electrostrictive coefficient. What counts in this low power EM-drive dielectric "amplifier" appears to be a dielectric with the largest electrostrictive/piezoelectric coefficient combined with a high Q-factor at microwave frequencies.
Best, Paul M.
Paul,
(*) Neoprene® is Dupont's trade name for Chloroprene rubber (CR), so in the rest of this post I will refer to it by its technical name Chloroprene rubber (CR).
The fact that NASA Eagleworks tested a dielectric made of Chloroprene rubber (CR) and found out that this rubber material is "disqualified for this (EM Drive) application" because the measured thrust using this rubber material as a dielectric is insignificant compared to using PTFE or HD-PE has important consequences that should be pointed out.
Since Chloroprene rubber (CR) has a coefficient of thermal expansion up to 158% greater than the coefficient of thermal expansion of HD PE:
THERMAL EXPANSION COEFFICIENT
Chloroprene rubber (CR) 125*10^(-6) to 190*10^(-6) 1/(deg K) http://techcenter.lanxess.com/docs/pdft/e5-14.pdf
High Density Polyethylene (HD PE) 120*10^(-6) 1/(deg K)
http://www.engineeringtoolbox.com/pipes-temperature-expansion-coefficients-d_48.html
This experimental finding further nullifies the conjecture that the experimental measurements are an artifact due to movement of the center-of-mass by thermal expansion of the dielectric.
(This conjecture has been recently explored by @frobnicat. According to @frobnicat's conjecture, based on thermal expansion, under no condition should the thrust force measurement have been smaller for Chloroprene rubber (CR) than for HD PE)
(*)
LIST of MANUFACTURER TRADENAMES for Chloroprene rubber (CR)
Lanxess (Bayer AG) BAYPRENE
Denka Kagaku Kogyo CHLOROPRENE
Showa Denko SHOPRENE
TOSOH Corporation SKYPRENE
DuPont NEOPRENE
http://en.wikipedia.org/wiki/Chloroprene -
#1329 by Rodal on 12 Mar, 2015 14:59
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....
Dr. Rodal:
....
Acknowledge that "neoprene" rubber covers a multitude of formulations, but it turns out that most if not all of them have low Q-factors at microwave frequencies that disqualify them from this application even if they have a large electrostrictive coefficient. What counts in this low power EM-drive dielectric "amplifier" appears to be a dielectric with the largest electrostrictive/piezoelectric coefficient combined with a high Q-factor at microwave frequencies.
Best, Paul M.
Paul,
(*) Neoprene® is Dupont's trade name for Chloroprene rubber (CR), so in the rest of this post I will refer to it by its technical name Chloroprene rubber (CR).
The fact that NASA Eagleworks tested a dielectric made of Chloroprene rubber (CR) and found out that this rubber material is "disqualified for this (EM Drive) application" because the measured thrust using this rubber material as a dielectric is insignificant compared to using PTFE or HD-PE has important consequences that should be pointed out.
Since Chloroprene rubber (CR) has a coefficient of thermal expansion up to 158% greater than the coefficient of thermal expansion of HD PE:
THERMAL EXPANSION
Chloroprene rubber (CR) 125*10^(-6) to 190*10^(-6) 1/(deg K) http://techcenter.lanxess.com/docs/pdft/e5-14.pdf
High Density Polyethylene (HD PE) 120*10^(-6) 1/(deg K)
http://www.engineeringtoolbox.com/pipes-temperature-expansion-coefficients-d_48.html
This experimental finding further nullifies @frobnicat's conjecture that the experimental measurements are an artifact due to thermal expansion of the dielectric.
(According to @frobnicat's conjecture, based on thermal expansion, under no condition should the thrust force measurement have been smaller for Chloroprene rubber (CR) than for HD PE)
(*)
LIST of MANUFACTURER TRADENAMES for Chloroprene rubber (CR)
Lanxess (Bayer AG) BAYPRENE
Denka Kagaku Kogyo CHLOROPRENE
Showa Denko SHOPRENE
TOSOH Corporation SKYPRENE
DuPont NEOPRENE
http://en.wikipedia.org/wiki/Chloroprene
@Frobnicat's conjecture is based on the shifting of the center of mass due to thermal expansion.
Not only Chloroprene-Rubber (CR) has a higher coefficient of thermal expansion than High-Density-Polyethylene-HDPE, but Chloroprene-Rubber (CR) also has a higher density than High-Density-Polyethylene-HDPE.
So this further nullifies the center-of-mass movement by thermal expansion conjecture.
According to @frobnicat's conjecture, the denser, higher-thermal-expansion material ("Neoprene®") should have produced a higher measured "thrust", but NASA Eagleworks results show the opposite: the denser, higher-thermal expansion material ("Neoprene®") resulted in insignificant thrust.
DENSITY (g/cm^3)
Chloroprene-Rubber-CR ("Neoprene®")
1.25 to 1.37 http://www.westernrubber.com/wp-content/uploads/OVERSEAS-COMPOUNDS-Publication-558-Rev-A.pdf
1.4 to 1.6 http://www.makeitfrom.com/compare/Chloroprene-Rubber-CR-Neoprene/High-Density-Polyethylene-HDPE/
High-Density-Polyethylene-HDPE
0.93 to 0.97 http://en.wikipedia.org/wiki/High-density_polyethylene
0.947 to 0.965 http://www.dow.com/polyethylene/na/en/prod/hdpe.htm
0.95 to 1.27 http://www.makeitfrom.com/compare/Chloroprene-Rubber-CR-Neoprene/High-Density-Polyethylene-HDPE/ -
#1330 by Polonius on 12 Mar, 2015 18:38
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Hey fellas, long time lurker, first time poster here.
I'm not even going to pretend to understand half the maths that have been tossed around in this thread. I'm in complete awe of the work you guys have been doing to solve this mystery. I do have a question though, and forgive me for my ignorance.
Does anyone know if this effect scales with the size of the frustum? Could the frequency of the microwaves be adjusted to allow the same level of force in a microscopic frustum that is shown Nasa's macroscopic frustum? If this is the case, would a sequence of many millions of tiny frustums not provide a great deal more force than one large frustum?
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#1331 by Notsosureofit on 12 Mar, 2015 18:43
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Hey fellas, long time lurker, first time poster here.
I'm not even going to pretend to understand half the maths that have been tossed around in this thread. I'm in complete awe of the work you guys have been doing to solve this mystery. I do have a question though, and forgive me for my ignorance.
Does anyone know if this effect scales with the size of the frustum? Could the frequency of the microwaves be adjusted to allow the same level of force in a microscopic frustum that is shown Nasa's macroscopic frustum? If this is the case, would a sequence of many millions of tiny frustums not provide a great deal more force than one large frustum?
Hopefully, that's one of the things we want to try and find out. -
#1332 by Rodal on 12 Mar, 2015 19:05
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Hey fellas, long time lurker, first time poster here.
One thing one knows for sure is that the smaller the frustum, the higher the natural frequency, so in order to excite a given mode shape, one would have to use higher excitation frequencies for smaller frustrums.
I'm not even going to pretend to understand half the maths that have been tossed around in this thread. I'm in complete awe of the work you guys have been doing to solve this mystery. I do have a question though, and forgive me for my ignorance.
Does anyone know if this effect scales with the size of the frustum? Could the frequency of the microwaves be adjusted to allow the same level of force in a microscopic frustum that is shown Nasa's macroscopic frustum? If this is the case, would a sequence of many millions of tiny frustums not provide a great deal more force than one large frustum?
@Notsosureofit has disclosed in this forum's thread his plans to test a smaller cavity with a higher excitation frequency, and his plan to use a Gunn diode (http://en.wikipedia.org/wiki/Gunn_diode) to generate the microwaves inside the cavity.
Concerning the use of literally "millions" of these devices (as in an Integrated Circuit), this could no longer involve microwaves (if possible at all) but it would mean much higher frequencies, because the wavelengths get cut-off due to the size of the cavity hence a much smaller cavity implies that the lowest natural frequency must be much higher.
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#1333 by frobnicat on 12 Mar, 2015 19:08
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....
....
...
@Frobnicat's conjecture is based on the shifting of the center of mass due to thermal expansion.
Yep.
here, there in answer to zen-in's concerns around X axis that it would be actually worse around Z, and there
This last one being important because it shows 3 things :
- The rest angular deviation of the arm from its initial position because of CoM's shifts in test article is worse than the angle of said CoM's shift as seen from the axis Z. 1µm deviation of CoM will cause more than one µm LDS deviation.
- Such LDS deviation will be interpreted as a sustained force when there is just a mass standing at some new place.
- The LDS deviation is counter-intuitive for orientation. A mass travelling to the right (like an expanding dielectric disc on the small end) will not increase the LDS distance but will decrease it. So the idea that the dielectric expansion could drive the rise actually observed is very well nullified already. It is further nullified by the weak relative power dissipated at the small end, and by the high thermal resistivity of the dielectric that makes only an extremely thin layer to heat in contact to copper, and from some initial heat conduction simulation of mine gets initially less than .01µm per second of CoM shift (for the whole dielectric block) that is clearly too weak to get the LDS readings anywhere.Quote
Not only Chloroprene-Rubber (CR) has a higher coefficient of thermal expansion than High-Density-Polyethylene-HDPE, but Chloroprene-Rubber (CR) also has a higher density than High-Density-Polyethylene-HDPE.
So this further nullifies @Frobnicat's conjecture.
According to @frobnicat's conjecture, the denser, higher-thermal-expansion material ("Neoprene®") should have produced a higher measured "thrust", but NASA Eagleworks results show the opposite: the denser, higher-thermal expansion material ("Neoprene®") resulted in insignificant thrust.
...
Nope. (and I dare say, we are yet to see the charts recording those "insignificant thrusts" with or without such or such dielectric thereof, but this is an aside)
My conjecture is not about dielectric disc's CoM shift playing an important role in the thrust (did I say that ? Where ?) My conjecture is about some test article part's CoM shifting to the left (toward the small end) relative to fixation on the arm. Now what is susceptible to move to the left ? You know that better than anyone, you "invented" the inward buckling of the big end cap. The part that is the most heavily heated (granted this is not by a blowtorch !) and that has a boundary constraint such that, in first approximation, there is a square root between the delta expansion in plane and the resulting displacement perpendicular to plane : buckling is a very efficient amplifier. Under such buckling or near buckling conditions, the mass*displacement of the big end cap would play the major part of test article CoM's shift. Quantitative estimates ongoing...
The problem with thermal explanations is that, in particular in vacuum, given the low temperature deltas (a few °C) the evacuated heat rates are quite low relative to the received powers. The time constants to thermal equilibrium appear way beyond the 45s of a whole run. Therefore the fact that on some "thrusts" rises we see what looks like a thermal first order constant rate heat charge against a proportional loss don't hold water. At 45s the various parts are still swallowing heat at constant rate and evacuating near to none, we would have a near linear rise in temperature wrt time all way through. So if LDS delta is proportional to Com shift (as per the tilted pendulum component), Com shift proportional to expansion, expansion proportional to temperature, and temperature proportional to time, we should see a linear rise, and not a "step". Yes but the buckling could make Com shift proportional to square root of expansion. Now look at the chart below and see the step not as a cst-cst*exp(-cst*t) as per a naive thermal explanation but as a cst*sqrt(cst*t).
So the "attack" and the "sustain" can both be very well explained by progressive thermal expansion near buckling conditions and by a slightly tilted Z axis. Now for the fall (decay) : for those still believing that thermal explanations are irrelevant, how is it possible that the decay is lingering at high LDS values for so long after power off ? But, with so low thermal radiation for cooling, there is no reason (from my conjectures so far) that there would be any significant decay at all : from my hypothesis the signal should stay constantly high at power off, only starting falling at a very small rate (much smaller that the rise rate).
This is why I said in previous post to Star-Drive that I don't believe in thermal effect as being the only cause of observed signal, from the shapes. Not because of rise and sustain (square root buckling amplification + tilted Z allowing for sustained "thrusts" by sustained relative Com's displacements) but because of decay. I do have an idea to explain that : Rodal have you considered that the supporting copper ring around the FR4 big end cap would also expand thermally ? What would happen if there was a (thermal conduction driven) temperature "delay" between the cap and the ring so that when the power stops the difference between cap temperature and ring temperature falls fast enough to be compatible with the time constant of the observed decay ? This is my leading conjecture. I now do believe again in the possibility of a purely thermal explanation wholly consistent with both magnitude and shape of signal.
Edit : also not clear how the drifting baseline would fit in this framework of moving CoMs, would need a test article CoM rightward overall before power on and well after power off, looks like a contradiction of some of the hypothesis above...
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#1334 by aero on 12 Mar, 2015 19:49
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Hey fellas, long time lurker, first time poster here.
One thing one knows for sure is that the smaller the frustum, the higher the natural frequency, so in order to excite a given mode shape, one would have to use higher excitation frequencies for smaller frustrums.
I'm not even going to pretend to understand half the maths that have been tossed around in this thread. I'm in complete awe of the work you guys have been doing to solve this mystery. I do have a question though, and forgive me for my ignorance.
Does anyone know if this effect scales with the size of the frustum? Could the frequency of the microwaves be adjusted to allow the same level of force in a microscopic frustum that is shown Nasa's macroscopic frustum? If this is the case, would a sequence of many millions of tiny frustums not provide a great deal more force than one large frustum?
@Notsosureofit has disclosed in this forum's thread his plans to test a smaller cavity with a higher excitation frequency, and his plan to use a Gunn diode (http://en.wikipedia.org/wiki/Gunn_diode) to generate the microwaves inside the cavity.
Concerning the use of literally "millions" of these devices (as in an Integrated Circuit), this could no longer involve microwaves (if possible at all) but it would mean much higher frequencies, because the wavelengths get cut-off due to the size of the cavity hence a much smaller cavity implies that the lowest natural frequency must be much higher.
There is also the materials issue. The behavior of copper, for example, and the dielectric is much changed at much higher frequencies. By much, I mean "a lot" not "a little bit." By the time you got 4000 of them in the space of the current frustum, none of your materials would behave as they do in the current frustum. -
#1335 by Rodal on 12 Mar, 2015 21:16
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....
We had a discussion with reference to a drawing presented by Paul March showing thermal expansion of the dielectric.
My conjecture is not about dielectric disc's CoM shift playing an important role in the thrust (did I say that ? Where ?) ...
I recall you arguing that thermal expansion of the dielectric would produce a force in the same direction as the measured force. I argued against it, on the basis that the dielectric has a free surface and it is free to expand unrestrained. A homogenous isotropic material free to expand uniaxially produces no thermal stresses. Only restrained materials produce thermal stresses. Furthermore I argued that the maximum speed of thermal expansion is governed by the speed of sound and that there is no second order derivative with respect to time due to thermal expansion. There is no "acceleration of thermal expansion". And that Fourier's equation contains only a first order derivative with respect to time, no second order derivative.
What's important is that the experiments by Paul March showing insignificant thrust force measurements when using the Chloroprene-Rubber-CR ("Neoprene®") as compared to when using High Density Polyethylene, invalidate the conjecture of the measurements being an artifact due to thermal expansion (as for example advanced by the Oak Ridge group (section 7 of http://web.ornl.gov/~webworks/cppr/y2001/pres/111404.pdf)).
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1344997#msg1344997
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1344942#msg1344942 -
#1336 by Notsosureofit on 12 Mar, 2015 21:52
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http://web.ornl.gov/~webworks/cppr/y2001/pres/111404.pdf)).
The subject of thermal "pumping" is one that will have to be carefully considered in any Cavandish experiment. What procedures are best for it's elimination ? Making sure the CG of the heated object doesn't move ?
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#1337 by frobnicat on 12 Mar, 2015 22:32
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@Rodal,
Yes, that was about recoil forces, my arguments are still valid, a block of material starting to expand thermally will push a wall against which it is resting, whether the expanding material is the hot gas of an explosion or a block of PTFE heating from the left against copper at 0.1°C/s, it's only a (huge) difference of magnitude, not of nature (as far as recoil is concerned). Done some number, such recoil is not significant given inertia of pendulum. Like 0.1µN on the 1st second of heating. Kind of, order of magnitude. Please call it 0 if you feel so inclined. But I will continue to stand on my position on italic statement (separate post later to avoid mixing).
About dielectric role : Paul March is not really showing insignificant thrust force measurements, he is stating that there is insignificant thrust, we are yet to see the corresponding charts of those situations of insignificant thrust. If it's a flat line as flat as for the 50Ohm null test, very well, that will put all speculation about thermal expansions at rest (provided the exciting frequencies are adapted to the absence of dielectric to get similar modes and therefore similar heating patterns). We really lack a catalog of hundred of "events".
Now if you can leave recoil effects aside for a moment (I know we had quite a discussion on that), isn't it speaking to you that there is now a situation where LDS_reading(t)=cst1*Thrust(t)+cst2*CoMPosition(t) where cst1 and cst2 are in the same ballpark ? That we are (well I am) no longer speaking of Force(t)=M*d˛CoMPosition(t)/dt˛ (recoil) where CoMs displacement can't sustain a force for a significant amount of time but we are now in "direct drive" from displacement of CoM to LDS reading ?
The Oak ridge group analysis is irrelevant (recoil effects, not considering a tilted pendulum), the dielectric material density, expansion coefficient, thermal conductivity are probably not relevant directly as this is on the cold end. They are relevant for microwave modes and heating patterns.
Now, please please please, comment on that : LDS_reading(t)=cst1*Thrust(t)+cst2*CoMPosition(t) where cst1 and cst2 are in the same ballpark
Do you agree or not ? If not why. If yes, do you think it is important or not, if not why. And I'm speaking of the hot end. We have a really rich thermal phenomenology here. Please try to understand what I'm saying, if you are still interested in possible conventional explanations and not just to quickly dismiss such possibilities. Such possibility would require careful understanding of the pendulum system and test article, not confusion of CoMPosition(t) with d˛CoMPosition(t)/dt˛.
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#1338 by Rodal on 12 Mar, 2015 23:05
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http://web.ornl.gov/~webworks/cppr/y2001/pres/111404.pdf)).
The subject of thermal "pumping" is one that will have to be carefully considered in any Cavandish experiment. What procedures are best for it's elimination ? Making sure the CG of the heated object doesn't move ?
Concerning movement of the Center of Mass of the object by thermal expansion, such movement should very slow unless you use very thin shells (for which, the issue of thermal buckling should be considered). Unless you use very thin shells and shapes that can change shape suddenly due to thermal instability, such movement should be negligible when considering the response of a few seconds. By all means avoid thin flat plates that are constrained at the edges. Curved thin shells are much better in this respect than thin flat plates.
Equations 14, 15 and 16 of the above Oak Ridge reference are incorrect. Such equations cannot be found in any classic work on thermoelasticity (for example on Boley and Wiener's monograph), and for good reason.
The authors begin by converting the expression for the coefficient of thermal expansion:
LengthFinal - LengthInitial= alpha*(Tfinal - Tinitial)
to a differential form
dL /L= alpha *dT
This is equivalent to stating that the differential of the logarithmic strain equals alpha*dT
Then, the authors use Newton's second law:
F = m * a = m * d^2 x / dt^2 to obtain a force for the unrestrained thermal expansion using the acceleration, as follows
dL/dt = L * alpha * dT/dt
d^2L/dt^2 = L * alpha * d^2T/dt^2
This is wrong, because thermal expansion proceeds at a constant speed: the speed of sound in the material.
The derivative of a constant is zero. Hence its derivative is zero, and not L * alpha * d^2T/dt^2. The equations that follow from the authors with terms involving mass* alpha * d^2T/dt^2 are therefore non-existent.
That's why such "thermal expansion recoil force" equations do not appear in any classic reference on thermoelasticity. -
#1339 by Rodal on 12 Mar, 2015 23:11
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@Rodal,
Yes, that was about recoil forces, my arguments are still valid, a block of material starting to expand thermally will push a wall against which it is resting, whether the expanding material is the hot gas of an explosion or a block of PTFE heating from the left against copper at 0.1°C/s, it's only a (huge) difference of magnitude, not of nature (as far as recoil is concerned). Done some number, such recoil is not significant given inertia of pendulum. Like 0.1µN on the 1st second of heating. Kind of, order of magnitude. Please call it 0 if you feel so inclined. But I will continue to stand on my position on italic statement (separate post later to avoid mixing).
....
