"Perpetual Torque" Air Molecule Motor

An earlier air molecule motor

Several years before working on the "perpetual force" air molecule motor discussed in my last few posts, I worked on an earlier idea, which I now call a "perpetual torque" air molecule motor. (I had originally called it a "Semi-Maxwell's Demon"). Here is the report I wrote on it, from the late 1980s:—

                                                        [quote begins]

A SEMI-MAXWELL'S DEMON

— A report containing the elements of a specification

1. INTRODUCTION

   Since the publication of "Theory of Heat" by James Clerk Maxwell in 1871 it has been recognised that if a device could be constructed which would sort air molecules in an appropriate way, then energy could be extracted from them (Ref 1). It would therefore provide an inexhaustible, non-polluting and portable energy source, having no fuel cost, and able to operate continuously anywhere within the earth's atmosphere.

   The sorting device has been termed a "Maxwell's Demon." A "complete" Maxwell's Demon would not only sort molecules, but would also extract energy from them, and in doing so would return them to their original conditions of temperature and pressure. A complete Maxwell's Demon would clearly break the second law of thermodynamics. It is generally accepted that it would be impossible to construct such a device.

   Most of the investigation of this subject has followed Maxwell's original idea of sorting air molecules by velocity (i.e. speed and direction), to achieve a temperature difference. Sorting by direction only, to achieve a pressure difference, has been mentioned (Ref 5), but little investigation of other possible methods of operation seems to have been made.

   The main theoretical objections to a Maxwell's Demon follow from its requirement for a kind of intelligence (e.g. Ref 2), or at least a kind of memory (Ref 3) or information gathering ability (Ref 4). This is also usually associated with a requirement for animation at the molecular level.

   If all the air in the earth's atmosphere is potentially available as the working fluid, then the requirement for a complete Maxwell's Demon to return the air molecules that interact with it to their original conditions is of no practical significance. If this requirement is abandoned, then various devices can be envisaged which would extract energy from air molecules by using some kind of sorting process, but would not break the second law of thermodynamics, and would not require any of the attributes listed in the previous paragraph. One such "semi-Maxwell's Demon" is discussed further in the remainder of this report.

2. PURPOSE

   It is the purpose of this report to describe a device which will extract energy in a useful form from the thermal motion of air molecules. It has the following features:—

   1.  It has no requirement for intelligence, memory, information gathering or animation at the molecular level.

   2.  It sorts air molecules by direction only to achieve an energy output in the form of rotational mechanical energy.

   3.  It takes in air at ambient temperature. Its working fluid is, in theory, the whole of the earth's atmosphere.

   4.  It exhausts air at a temperature below ambient.

   5.  It has only one moving part: a rotor made up of a very large number of identical "blades".

   6.  It requires the distance between adjacent parallel blades to be less than the mean free path of the surrounding air molecules. (At normal atmospheric pressure the mean free path of air molecules is about 0.1 micrometre).

3. DESCRIPTION OF THE DEVICE

   The device is a single structure, i.e. a rotor made up of many "blades" of the correct shape and size, which will experience a torque as a result of the impacts of air molecules when it is immersed in the atmosphere. Molecules arrive at these impacts from completely random directions, with no direction more prevalent than any other. However the design of the device ensures that the net effect of the molecular impacts from certain directions is to produce a couple on each blade, which in turn gives rise to a net torque about a central axle. This torque is not cancelled by the effects of molecular impacts from all other directions. Thus the device is designed to achieve, automatically, and by its structure alone, a sorting process sufficient for its purpose.

Figure 1

   Figure 1c shows a portion of the device. With the notation shown, this portion consists of a series of blades of width Δr in the x direction, and spacing d. The blades are all inclined at an angle Φ to the z axis. Both Δr and d are smaller than the mean free path of the surrounding air molecules, λ. As a starting point, possible values are:—

   Δr = 0.2 × λ ;   d = 0.05 × λ ;   Φ = 45 degrees.

   The blades are fixed together at suitable intervals with spacers S, to ensure rigidity.

   The blade thicknesses are made small compared to their widths.

   The series of blades may be extended indefinitely in the positive and negative y and z directions, to form a "sheet" of blades. In other words, the blades may be any length, and there may be any number of blades.

   Figure 1b shows portions of some sheets of blades.

   Figure 1a shows the complete device, which consists of many sheets of blades, each formed into a cylinder. These cylinders are arranged concentrically, with some small separation (greater than λ) between each cylinder and its neighbours. However each cylinder is fastened to its neighbours at intervals, so that they form a rigid rotor which can turn as a single unit about the axle A.

   The complete device can be made any convenient size.

   It will probably be desirable to design the fastenings between cylinders, and between the innermost cylinder and the axle, in the form of blades of a radial flow fan, to promote gross air movement through the cylinders.

4. ANALYSIS

   A complete analysis would aim to determine the exact result of immersing the device in the atmosphere. That is, it would determine the net effect of all the molecular impacts occurring on the device, or a representative portion of it, over a given period.

   For an initial analysis, some simplifying assumptions were made. The three most significant were:—

   - It was assumed, for simplicity, that all molecules have equal mass and speed.

   - It was assumed that molecules entering between the blades of the device undergo only specular impacts with blades (i.e. impacts with incidence and reflection angles equal), until they exit. In this case, each impact force is proportional to the cosine of the angle of incidence between the molecule's track and the normal to the blade hit.

   - It was also assumed that the blade widths and spacings are sufficiently small that the number of inter-molecular collisions inside the blades is generally negligible.

   Consider molecules entering any pair of adjacent blades on the outermost cylinder. If the product

   Fz.r = (impact force resolved in z direction) × (perpendicular distance from impact point to an imaginary plane at x = r1 + Δr/2)

is calculated and summed for every impact, a graph of the form shown in Figure 2 is obtained.

Figure 2

   NOTE: The dashed portion of the graph requires further comment. Referring to Figure 1c and setting Φ = 45 degrees, if molecules enter the blades with a velocity component in the xz plane at an angle just less than 45 or 225 degrees, then a few such molecules will undergo very many rebounds, giving a net high negative Fz.r product. It is assumed, as shown in the dashed portion of the graph, that these few molecules will, as a result of their increasingly long track length, eventually end this behaviour. This could be from either an inter-molecular collision, or a non-specular molecule/blade collision.

   The form of Figure 2 shows that forces resolved in the z direction from impacts of molecules arriving onto the blades from angles in the xz plane between 45 to 90 degrees, and between 225 to 270 degrees, produce a couple centred on, and parallel to, the plane P. This couple is not cancelled by impacts of molecules arriving from other directions. As shown in Figure 3, the couples from each blade in the outermost cylinder add circumferentially.

 

Figure 3

   Similarly, considering all other cylinders, the couples from every blade in the complete device add together to produce a net torque about the axle A in Figure 1. (Forces resolved in the x direction produce no net effect. Forces resolved in the y direction are always zero).

5. CONCLUSIONS

   This report describes a device which will experience a torque from molecular impacts when immersed in the atmosphere. Therefore, if permitted to rotate, it will convert some of the kinetic energy of air molecules impacting on it into rotational mechanical energy.

   In giving up some of its kinetic energy, the air exhausted from the device will be cooled below ambient temperature. This difference between the final and initial states of the air (i.e. the working fluid) is the reason why the device does not break the second law of thermodynamics. To regain its original temperature the exhaust air must acquire energy from an outside source, e.g. the sun. The device is therefore an energy converter, drawing free energy from the sun via the environment, as does, for example, a hydro-electric power station.

   The device will have all the benefits listed in the first paragraph of this report. In addition, the cooling of the exhaust air will be beneficial in most applications.

   Detailed modelling on a large computer seems necessary to determine precisely how far inter-molecular collisions are tolerable inside the device, and how specular/diffuse individual molecule/blade collisions should be. The modelling should consider the effects of many molecules interacting with a representative portion of the device. The results should be compared with what may become achievable in practice, and what would be required to optimise the design. The requirement for a fairly low rate of internal inter-molecular collisions seems essential, but the requirement for specular collisions could probably be relaxed considerably — perhaps to an already achievable value (Ref 6).

   The effects caused by molecules that could potentially undergo very many rebounds, e.g. those discussed in the NOTE of section 4, should be thoroughly investigated. Perhaps, for some particular combinations of design parameters, the effects of these molecules could largely cancel the effects of all other molecules. However it does not seem possible that this could occur generally.

   Other matters requiring further investigation include the optimum separation between adjacent cylinders, the optimum design of fastenings between cylinders, filtration of incoming air, and how much of the energy output should be used to achieve forced air circulation. A full analysis should also take proper account of the velocity distribution of air molecules.

   A problem exists at present in constructing a device to the design described in this report, in that the manufacture of blades with the extremely small dimensions required seems to be beyond the present state of the art. However, as progress in nanotechnology continues, it is to be expected that the manufacturing problems would eventually be solved.

   It might be possible using available methods to build a low-power prototype device to operate at reduced air pressure, where the longer mean free path would allow larger blade sizes.

6. REFERENCES

Ref 1: Theory of Heat. J. Clerk Maxwell, Longmans, Green and Co, (1871).

Ref 2: Mathematische Vorlesungen am der Universitat Gottingen VI, Leipzig und Berlin. M. U. Smoluchowski (1914) — quoted in Ref 5.

Ref 3: "On the Reduction of Entropy of a Thermodynamic System Caused by Intelligent Beings," L. Szilard in Z. Physik 53 840-856 (1929).

Ref 4: "Maxwell's Demon Cannot Operate: Information and Entropy I," L. Brillouin in J. Applied Physics, 22/3, 334-337 (March 1951).

Ref 5: "Maxwell's Demon," W. Ehrenberg in Scientific American, 217/5, 103-110 (November 1967).

Ref 6: "On Stresses in Rarefied Gases Arising from Inequalities of Temperature," J. Clerk Maxwell in Proceedings of the Royal Society, 27, 304 (1878); Appendix dated May 1879. [About 50% of air molecules striking a glass surface were specularly reflected]. 

                                                    [quote ends]

Remarks

1.  I did do some 3D computer analysis of this idea, to obtain the graph shown in Figure 2. Because no more advanced methods were available to me at the time, I wrote and used a BASIC program. This modelled air molecules arriving with equal probability from any direction (actually any equal-area portion of two hemispheres; one on each side of an array of blades). Those molecules that were able to strike a defined, fixed-area region of the blades were tracked, with the torque generated from each impact aggregated, until they exited. Every impact was fully specular.

2.  At the present time, I don't think that this "perpetual torque" approach holds as much promise for real-world applications as the "perpetual force" motor discussed previously. But I decided to include this report anyway, as it completes the record of my investigations into air motors of these kinds, and shows some of the history and background of what I now think is the better "perpetual force" version.


Back in 2015

I leave for my Christmas/New Year holidays tomorrow, so this longer than usual post will be my last for 2014. I'll be back in a fortnight or so.

"Perpetual Force" Air Molecule Motor Part IV

Statistical analysis

In order to determine the significance of the silux modelling results discussed in my last couple of posts, I'll have to get into statistical decision theory. It's a long time since I've done anything in that area, so I'll use a worked textbook example as a basis, adapting it to suit. For the record, I'll use solved problem no. 5, p173 of Theory and Problems of Statistics, by Murray R. Spiegel, Schaum Publishing Co., 1961.

Adapting this, we have:—

A. Combined cases

    For the combined set of 22 cases modelled, the foil moved fully upwards in 20 cases. Determine whether the results are significant at the (a) 0.05 and (b) 0.01 level of significance.

Solution:
    If p is the probability of the foil moving fully upwards, then we have to decide between the following two hypotheses:

    Ho: p = 0.5, and the foil is only moving randomly, i.e. the results are due to chance.

    Hi: p > 0.5, and the effect is genuine, i.e. there really is an overall imbalance in air molecule impacts which causes the foil to move upwards.

    We choose a one-tailed test, since we are not interested in the foil moving predominantly against the predicted direction of motion.

    If the hypothesis Ho is true, the mean (μ) and standard deviation (σ) of the results are given by

    μ = Np = 22 × 0.5 = 11   and

    σ = √(Npq) = √(22 × 0.5 × 0.5) = 2.3452

(a) For a one-tailed test at the 0.05 significance level, we must choose the ordinate z1 for the standard normal curve (i.e. the bell curve) so that the area of the curve to the right of the ordinate is 0.05. Then the area between 0 (at the center of the curve) and z1 is 0.4500, and so z1 = 1.645.

(b) For a one-tailed test at the 0.01 significance level, we must choose the ordinate z1 so that the area of the curve to the right of the ordinate is 0.01. Then the area between 0 and z1 is 0.4900, and so z1 = 2.330.

    The 20 upwards-movement cases in standard units = (20 - 11)/2.3452 = 3.8376, which is greater than both 1.645 and 2.330. This means that the results obtained are significant at both the 0.05 and the 0.01 levels, i.e. they are "highly significant" and we can conclude that the effect is genuine.

B. Second set of cases only

    If we now look only at the second set of 11 cases modelled, the foil moved fully upwards in 9 cases.

    With a similar analysis, we get μ = 5.5 and σ = 1.6583

    The 9 upwards-movement cases in standard units = 2.1106, which is greater than 1.645, but less than 2.330. So these cases alone would be considered "probably significant" implying that further investigation is warranted.

Further investigation, and final comments

The results obtained so far do look promising, and certainly support the basic idea of a force imbalance, arising from the impacts of air molecules on a device that has "structure" at an appropriate microscopic scale.

One of several questions yet to be resolved is:— Do some more subtle boundary effects play a part in the complete success of the original small-container model? If so, what exactly are they, and could they also be exploited in a real physical model?

I have already mentioned some reasons against placing too much faith yet in these results, i.e. the unrealistic modelling of the air molecules, boundary effects, and the 2D rather than 3D analysis.

The silux analysis done so far has to be 2D. A 3D analysis would be greatly preferable. (But I have to admit I don't yet know enough about 3D finite elements analysis programs to be confident in doing such an analysis for cases like these, where large numbers of individual molecules are involved. For example: how are molecule joints to be dealt with?)

I know of only one good 3D finite differences program, "sonar-code," which unfortunately is not for sale to the public [but see Update below]. The animation shown at http://www.realphysics.ch/sonar.htm indicates that this program would most probably be well-adapted to modelling large numbers of individual air molecules.

There is another problem that I think will apply to any realistic computer modelling of air molecule impacts: on a normal "laboratory" scale, the molecules are extremely small, and there will be a huge number of them, nearly all travelling at very high speeds. This will place very high demands on the computer, to achieve correct elastic impacts in the extremely small time durations for each impact. Probably supercomputers would be required for such modelling.

[Update April 2018: There is another website for sonar simulation, at https://sonarsimulation.com/. From there (under "Products > download"), it is now possible to download and install sonar-3D-LAB for free, and to build models with it. However sonar-3D-SIM will also be needed to run simulations on these, and there is currently no information on when that will be available for download, or its pricing.]

"Perpetual Force" Air Molecule Motor Part III

Still on the topic of the very significant force imbalance obtained in the eleven silux-model cases previously discussed, I decided to further investigate possible mundane explanations for this imbalance.

Pressure difference?

Could there have been a systematic starting pressure imbalance? Let's investigate that:— 

The center of gravity of the foil shown in Fig 2 is represented by the blue line, at the start of the simulation. The area above the line is 5.33333 × 20 cm² and the area below is 4.66667 × 20 cm². So if air pressure is exactly balanced above and below the foil, we should have a theoretical ratio of 5.33333/4.66667 = 1.142855, for the number of molecules above the line divided by the number of molecules below the line.

Fig 5. Checks for any systematic starting pressure imbalance

After counting the molecules for the starting configurations of all the cases analysed in Fig 4, I got the results tabulated in Fig 5 above. This shows that in only four of the eleven cases was there an above average starting pressure on the lower side of the foil. There was a deficit in the other seven cases. So a systematic pressure difference can be ruled out as an explanation for these results.

Boundary Effects?

In order to further investigate boundary effects I re-made the model with a larger container (was 20 × 10 cm², now 25 × 15 cm²). The foil was the same except for its ends, which were truncated vertically. This is a fairer representation of a small portion of what in reality would be a far longer foil than is being modelled here.

Fig 6. First run for re-made silux model, with larger container

Fig 7. Results for further cases run with re-made model

Results

Results of the first case run are shown in Fig 6 above. As before, I ran another ten cases, summarised in Fig 7 above. Ultimate upwards movement still occurs in 9 out of 11 cases. In only one other case did the foil move to within one foil thickness of the lower boundary. In that case a boundary effect was occasionally visible, i.e. molecules were sometimes seen to impact directly more than once between the lower boundary and the foil. Even though the foil did not move fully down (whereas it did in two other cases), and it eventually moved fully up, I decided to discard that case as inconclusive, replacing it with another case.

How significant are these results? I'll look at that next.

"Perpetual Force" Air Molecule Motor Part II

Modelling of further cases

I modelled ten more cases of the foil in a container with air molecules, as discussed previously. The foil was held stationary for a further 1s, 2s, etc up to 10s, before being released, in order to obtain a different random starting distribution of molecules for each case. 

Results

In all of these cases also, (summarised in the spreadsheet below) the foil moved generally upwards in the container, reaching velocities between 0.02138 and 0.09513m/s just before hitting the upper boundary. On only one occasion did it move to (just) within one foil thickness of the lower boundary, and even then I didn't notice any molecules impacting directly between that boundary and the foil. Boundary effects do play a part in accelerating the foil near the end of the simulation, but only because it has already moved to within about half a foil thickness from the upper boundary.

Fig 4. Spreadsheet of results for foil in container with air molecules

Discussion

Is this a credible result, i.e. would such a device really work? Could it really deliver a perpetual net force, and energy, from nothing more than "thin air"? 

The probability of the foil moving to the upper boundary 11 times in a row by chance is the same as tossing a coin to get 11 heads in a row, i.e. 1 in 2^11 = 1 in 2048 = 0.0004883. Still, these eleven "spot-check" results are not fully conclusive. The three main reasons for that are the unrealistic modelling of the air molecules, boundary effects, and the 2D rather than 3D analysis.

The physical data for the air molecules used in the model are:—

radius 2mm, mass 0.261 gram, initial velocity 1.414 m/s. 

These data are vastly different from the (approximate) data for real air molecules (mostly N2 with some O2):—

radius 0.00000025mm, mass 4.8 × 10^-23 gram, rms velocity 500m/s.

Also the foil mass, modelled at 1kg, is far heavier than would be the case for a foil of the correct scale interacting with real air molecules.

Nevertheless, I find these results so far to be interesting. They do suggest that further work on this idea would be worthwhile.

"Perpetual Force" Air Molecule Motor Part I

Can the movement of air molecules be exploited?

Fig 1. Specification drawing for foil with tapered holes
Alt 2 has foil thickness 0.05 micron, and hole dia 0.01 micron at upper surface; 0.002 micron at lower surface.
Alt 3 has foil thickness 0.5mm, and hole dia 0.1mm at upper surface; 0.02mm at lower surface.

I'll now say something about the foil shown and specified as Alt 2 in the above specification drawing, which I first posted on 17 September. I wanted to see whether a foil like this would experience a net force just from being immersed in air at normal temperature and pressure.

Operating principle

The proposed operating principle was similar to the Casimir-force foil, except that instead of zero-point energy fluctuations, it would be air molecule impacts delivering energy/momentum to the foil — but again to a higher degree on the lower surface. Air molecules arriving at the upper surface would generally enter the holes, and would be reflected from the sides of the holes, exerting only small forces resolved vertically, before (probably) exiting at the lower surface. Air molecules arriving at the lower surface would be more likely to hit that surface, because of its decreased hole diameter, exerting large forces resolved vertically.

No supplier

As already stated, no-one was able to supply any of the foils described in the specification drawing; not even Alt 3, which was a much larger version of Alt 2, and hence would have been much easier to make. Alt 3 was also intended for air molecule impacts, but in a fairly high vacuum, where the mean free path length of the molecules would be a lot higher.

Silux model

Since I was unable to test this idea in any physical experiment, I decided, later on, to see what could be done with a silux model. (For anyone unfamiliar with silux, see my posts of 7 April and 13 April 2014 on this blog).

The file folder named "models" that comes with the silux program includes a model named "Model and Simulation of an Almost Ideal Gas", which is also described further in the free PDF document named "Samples 2D" (page 49). This model demonstrates how the impacts of individual gas molecules, when aggregated together, produce an upward force that balances a weighted piston within a cylinder. (It also demonstrates visually how molecule velocities vary naturally over time — presumably a correct Maxwellian velocity distribution is eventually achieved, although it would take a lot of work to verify that).

I adapted this model to check the effect of air molecule impacts on a small, non-optimised portion of a foil, as shown in Fig 2 below. 

Fig 2. Silux model of a small portion of a foil with tapered holes,
in a container with 200 air molecules

Model details

I started with the 100 molecules in the original model, duplicating them again for a total of 200. Each molecule has a radius of 2mm, a mass of 0.261 gram, and is originally started at a velocity of 1.414m/s, as originally created by silux. The seven triangles are made into a single foil of mass 1kg, constrained by a macro against sideways or rotational movement. Movement up or down is permitted. All molecular impacts, to other molecules, or the foil, or the fixed container, are always 100% elastic. Gravity is inactive. The container "volume" in this 2D model is 20cm × 10cm = 200cm².

The simulation is started with the model configured as above. This is after a few seconds of prior running with the foil also held fixed, to ensure that the air molecule velocities are "randomised" before the foil is released.

Fig 3. Silux model at end of simulation

Results:

After 3.981 seconds of simulation time the foil is about to hit the upper boundary of the container, as shown. By then it has moved 0.03883m upwards, and has an upwards velocity of 0.02612m/s.

This looked reasonably promising, so I decided to look at some more cases, which I'll discuss next time.

I'm Back!

The first hiatus is over: I'm now back.

Here is a brief update on the three issues that caused the hiatus. Without going into too much detail:—

First issue: Should have been completely resolved by now, but isn't. That's no real surprise, in this modern world of ever-decreasing standards of performance. I still have some reason to expect a resolution by the end of the year.

Second issue: A health issue which now seems to have disappeared. Hopefully it won't return.

Third issue: Another initially hard to diagnose health issue. It was eventually diagnosed, and after minor surgery it's now resolved.

So all in all, things are not as bad as they could have been, and I intend to resume posting to this blog on about a weekly basis.

Hiatus

First hiatus

When I wrote on 28 August that other things had a way of intervening, one such "thing" had already done so. Now two more have; to the extent that I must now assign a higher priority to resolving these issues than posting to this blog.

I hope to be back by early November, but it may not be until some time in December.

I have quite a bit more to say here, and fully intend to say it. Until then, I guess it's "au revoir", and certainly not "adieu".

Casimir Effect Space Propulsion Part IV

Could it really work?

As I've said previously, for the last 24 years or so, I have thought that a net Casimir force would probably be exerted on a thin metal plate covered with extremely small tapered holes on one side only. Is this idea "forever impossible", or might it be possible, and just "ahead of its time"? 

As always, the only way to be certain about whether any new idea will work is to build a physical prototype, and test it.

Back in 1994, I tried to do exactly that.

Specification drawing for foil with tapered holes.
The drawing was originally A3 size, so some notes may not be clear.
Alt 1 (on the left) is most relevant for a Casimir Effect force generator. It is for a metal foil 1 micron thick, with hole diameter 0.1 micron at the top surface.

Request for Quote

The above image shows a specification drawing that I commissioned in October 1994 (with a few names edited out; otherwise original). I sent it, with a request to quote for any of the foils shown, to a few specialist materials suppliers. I received only one reply, from Goodfellow Cambridge Limited. It's short enough to quote in full:—

    Thank you for your enquiry.

    We regret that we are unable to manufacture any of the foils shown in your drawing 9410-3-01.

So, twenty years ago no-one could supply the requested foils, or at least no-one was prepared to say to a member of the public that they could supply them. So I was unable to make any further progress with this idea.

Whether these foils could be supplied now (2014) I do not know. My guess is that if they really do act as Casimir force generators, it would be very unlikely now that anyone who could make them would be willing (or even permitted?) to sell them openly.

Casimir Effect Space Propulsion Part III

Fig 3. Data for a 3m³ thruster consisting of many Casimir force generating plates assembled together.
Typical configurations for six thrusters in a small spacecraft are also shown.

A Thruster exploiting Casimir Effect

As described in Fig 2 of my previous post, I expect that a net Casimir force would be exerted on a thin metal plate covered with extremely small tapered holes on one side only. So, to create a thruster of moderate volume that could exert a usefully large force, we would just combine many such plates together, separated by spacers of very low-density, non-conducting material, as shown above. The spacers would permit a reasonable range of zero-point energy fluctuations to exist in the gaps between the plates.

Fig 4. Spacecraft — horizontal and vertical sections

As Figs 3 and 4 show, I went as far as doing a schematic design for a small "UFO" - shaped spacecraft incorporating Casimir-force thrusters. (I re-drew Figs 3 and 4 as CAD drawings for this blog, because my original pencil drawings would not scan well).

Casimir Effect Space Propulsion Part II

My own look at Casimir Effect

Nearly a quarter-century ago, after reading Hal Puthoff's article (Ref 5 below) I decided to look further into the possibility of adapting Casimir Effect into a perpetual force generator for spacecraft propulsion. At that time I wrote the following:—

                                        [quote begins]

Casimir Effect as a possible method of spacecraft propulsion.

1. Casimir — brief biography.

    Hendrik B. G. Casimir, one of the foremost theoretical physicists of the 1930's and 1940's, later became Technical Head of the Philips Research Laboratories. He first wrote in 1948 on the effect that now bears his name (Ref 1 & Fig 1). Briefly, this states that if you take two flat parallel metal plates and place them very close together, a force of attraction will occur between them. The origin of the force is of interest — it arises as predicted by quantum theory from fluctuations in the very fabric of space-time itself, which permeate the whole universe.

Fig 1.  Brief explanation of Casimir Effect, and force calculation for plates separated by 100 nm

2. "Reality" of Casimir Effect.

    In experiments starting in 1957, Casimir Effect has been verified beyond doubt (Ref 2 p235) yet it is still dealt with poorly, if at all, in physics courses. Also for a long time after Ref 1 was published, even specialists seemed unaware of it. Thus Bryce DeWitt wrote in 1989 (Ref 2 P247):—

"This made me sit up and take notice. I knew nothing of Casimir's original work (1948,1949) and had not heard of Sparnaay's experiments (1957).... I had always been taught that the zero - point energy of a quantized field was unphysical, and Casimir was saying that this view was wrong.... Just how deep the Casimir effect goes has become apparent in the years since 1960. I can think of hardly anything today more pertinent to quantum gravity."

3. Using Casimir Effect to generate a permanent net force.

    The "classical" Casimir Effect occurs because conducting plates placed close together exclude certain zero - point fluctuations from the region between the plates. Note the
important difference between this and, for example, the attraction between two magnets. The fluctuations are truly ubiquitous throughout the universe and are external to the plates, whereas the magnets attract because of localised currents (electron movements) within the magnets.

    The crucial question now is, can Casimir Effect cause a net force on just a single metal plate? I say yes, if one side of the plate is covered with tapered, blind holes. See Fig 2. (Note the extremely small hole size).

Fig 2.  A thin metal plate (shown in cross-section) covered with tapered holes on one side only,
as a possible Casimir force generator

4. Why a net force should be generated.

4.1 Equivalence Principle

    The device of Fig 2 is a microscopic analogue of the acoustic or radar energy absorbing surface used in anechoic chambers etc, so possibly the equivalence principle can be cited in its support. (But note that the details of energy absorption are not quite equivalent).

4.2 Analogy with "classical" Casimir Effect.

    Provided the sides of the tapered holes are sufficiently smooth, most fluctuations will reflect in a specular rather than a diffuse manner, and the notes on Fig 2 will apply.

4.3 Support from the theoretical literature.

    Equation 1.8 of Ref 3 shows that the energy density near a plane conductor deformed by curvature differs from that near a flat one, and the sharper the curvature, the greater the difference. So the device of Fig 2 which has one side flat and the other with many sharp curves should experience different energy densities at the two sides, and hence a net force.

5. Practical details.

    See Fig 3.

6. References.

Ref 1. H.B.G. Casimir, 1948, Proc. Kon. Ned. Akad. Wetenschap 51 p793

Ref 2. A. Sarlemijn & M.J. Sparnaay eds 1989 Physics in the Making, Elsevier Science Pub. Co.

Ref 3. P. Candelas, 1982, Annals of Physics (N.Y.) 143, p241

Ref 4. H.B.G. Casimir, 1983 Haphazard Reality: Half a Century of Science, Harper & Row

Ref 5. H. Puthoff, 1990, "Everything for Nothing", New Scientist 28 July 1990 p36

                                        [quote ends]


I'll give Fig 3 mentioned above, and discuss it in detail, next time.


UPDATE, end of 2016:—

I have found two other references predicting that a single plate should experience a strong permanent net Casimir force as I have suggested above, provided one side is left flat, and the other is covered with extremely small indentations. The shape of the indentations is probably less critical than their size. One option suggests a cylindrical shape; and the other trapezoidal, see the Russian (English-language) references http://vixra.org/pdf/1512.0276v1.pdf and http://vixra.org/pdf/1404.0097v1.pdf.

Casimir Effect Space Propulsion Part I

Perpetual Force Generator

I may be accused of drifting a bit off-topic with these posts on inertial propulsion etc, but I still have in mind the idea of driving a perpetual motion wheel by means of perpetual force generators arrayed around its rim.

Wheel with perpetual force generators

One example of a perpetual force generator would be an inertial propulsion device, for as long as it could be kept running, but there are other possibilities.

The next few posts will examine the concept of a perpetual force generator exploiting Casimir Effect.

The Quantum Vacuum Plasma Thruster

I see that the "Quantum Vacuum Plasma Thruster", an example of (hopefully) practical exploitation of Casimir Effect has appeared on the internet; see the NASA pdf: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492.pdf
for more.

Quoting from the above:—

How does a Q-thruster work? A Q-thruster uses the same principles and equations of motion that a conventional plasma thruster would use, namely Magnetohydrodynamics (MHD), to predict propellant behavior. The virtual plasma is exposed to a crossed E and B-field which induces a plasma drift of the entire plasma in the E×B direction which is orthogonal to the applied fields. The difference arises in the fact that a Q-thruster uses quantum vacuum fluctuations as the fuel source eliminating the need to carry propellant. This suggests much higher specific impulses are available for QVPT systems limited only by their power supply's energy storage densities. Historical test results have yielded thrust levels of between 1000-4000 micro-Newtons, specific force performance of 0.1N/kW, and an equivalent specific impulse of ~ 1×10^12 seconds.

While it's good to see NASA actively investigating Casimir force thrusters (at last!) the performance cited seems very poor, when set against the high energy required to produce the electric and magnetic fields.

Can we not do better than this, ideally with a thruster that produces a net Casimir force simply from its own structure/geometry, without the need for any high energy consuming E or B fields? I'll look at that next time.

Coriolis Force and Inertial Propulsion Part II

The centrifugal gun and Newton's third law

Previously I have pointed out that the only force exerted on the mass-projectile in a centrifugal gun, Fc, and the reaction force exerted on its rotor, Fr, are always both perpendicular to the mass's direction of motion. However, any force bringing the mass to rest must of course be exerted along its direction of motion. This raises the question:— if the rotor is otherwise unconstrained while it rotates, is Newton's third law still obeyed overall between the mass and the rotor?

Back in the early 1980s, I decided to look into this in some detail.

Coriolis force vectors exerted on a rotor expelling a mass

The image above shows the Coriolis force reaction vectors (blue) being exerted on an anti-clockwise turning rotor, when a mass enters it, and is accelerated through a radial tube in the rotor. The first question of interest is: when added, do the Coriolis force vectors give a resultant that has a direction exactly opposite to that followed by the expelled mass? 

To put this another way: when the mass has been expelled, is it travelling in a direction exactly opposite to that of the rotor? Furthermore, is there an exact balance between i) the force through distance required to slow the mass down and reverse its direction for the next operating cycle, and ii) the force through distance required to bring the rotor to rest? Unless both of these conditions are met, an inertial propulsion machine must be possible. (Recall that Newton's third law requires an equal and opposite reaction force).

Was I first?

Before attempting any answers, I should mention that although I once thought I was first to see this possibility, I don't think so now.

The Death of Rocketry

In 2000 I obtained the book The Death of Rocketry (1980) from author/inventor Robert Cook (see http://www.forceborne.com). This book is mainly concerned with Cook's two inertial propulsion inventions, see US Patents 3,683,707 and 4,238,968.

However, I found these inventions less interesting than another idea discussed and illustrated in the book, as shown, which is essentially the same as mine, and was probably thought of earlier:—

The Death of Rocketry, Fig. 6-14, p85

The comment on this idea (by co-author Joel Dickinson) ends:—

"The principle looked sound, but to construct a model would be nightmarish. To Cook, destroying all this energy by collision seemed a crime, so we abandoned these ideas."

I am not at all convinced that the kinetic energy imparted to the masses must necessarily be "destroyed". I think it would only require a bit of engineering (not especially difficult) to recover this energy.

Silux models, and further work

When I had become proficient with silux, I made a few models of this "inertial propulsion by Coriolis force" idea. As far as the questions I posed above are concerned, I can only say at present:—

- None of my models have shown any deviation from an exact 180º angle between the direction travelled by the mass and that travelled by the rotor, after the mass has been expelled from the rotor. So my modelling so far does not indicate any possibility of inertial propulsion.

- However, I have done nothing more than a few spot-checks, only on rotors with radial tubes, turning at constant speed. So I have not checked any rotors with the following adaptations:—

- Curved tubes or varying speeds (including various methods of imparting and varying rotor speed).

- Obtaining a high initial impulse-force when the mass is first picked up by the rotor, as suggested in Cook's Fig. 6-14 above.

- Making the mass as a gear, whose teeth mesh with a rack in the rotor's tube, and also possibly varying the rotational inertia of the gear-mass during the operating cycle.

All of these things are worth checking, and are on my priority-list, but other things have a way of intervening!