Professor Laithwaite's Gyroscope Experiments Part I

Before leaving the topic of gyroscopes, I want to comment on a forty-year-old experimental result that I must admit I still don't understand well. With modern technology it could probably be resolved easily enough, but I won't be holding my breath waiting for that to happen!

Videos

The experiment is shown in these videos:—

The first video shows Eric R. Laithwaite, Emeritus Professor of Heavy Electrical Engineering at Imperial College, London, force-precessing, then easily lifting a heavy, spinning gyroscope weighing 40 pounds. The second video shows an Australian replication of this experiment, again with a gyroscope weighing 40 pounds.

1975 — A space odyssey

Professor Laithwaite's experiment in the video above is a repeat (with a heavier gyro) of the experiment he did and wrote up in his article "1975 — A space odyssey" in Electrical Review, 28 March/4 April 1975, p398.

In the image above from that article, Professor Laithwaite is resisting forces that should be 24 pounds vertically plus 17 pounds horizontally with only the little finger of his right hand. He says:—

"Fig. 5 shows me supporting an 18 lb wheel revolving at 2,000 rev/min on a 6 lb shaft, 22 in long on my little finger with my arm fully extended towards the camera. It is not posed; it is an action shot and I am rotating at about 1 revolution in 2 seconds about a vertical axis, dragging the gyro around faster than its natural precession speed under gravity. The wheel is rising quite rapidly (about 3 ft vertically in half a revolution of me). What is most dramatic is my ability under this forced precession to lift the other end of the rod also. Had the gyro merely transferred its mass to its first point, i.e. my finger, I could not have supported 24 lb at arm's length, let alone accelerated it upwards. Had there been the usual centrifugal force it would have been Mrω²/g, which with M = 18 lb, r = 3 ft and ω = π rad/s, works out at about 17 lb, the shaft would certainly have been snatched from my finger. Photographs, of course, can be faked, but anyone can repeat the experiment for themselves." 

The important part

I have added the emphasis on what is the most important and difficult-to-explain part of this experiment. There would seem to be only two possible explanations, both very unlikely: either Prof. Laithwaite was much stronger than anyone realised, including himself, or else the gyroscope was exerting much less downwards force than its natural weight (and also less than expected centrifugal force) at the point where its axle was being held.

I'll look at some experiments and modelling of this, next time.

The Polar Gyroscope, Part II

Efficient extraction of energy

Last time, I suggested that the only way to extract energy efficiently using a polar gyroscope would be to permit full gyroscopic action to occur. So, as well as the energy gained as the Earth rotates beneath the initially non-rotating axle and outer gimbal, more energy will then also be obtained from rotation between the inner and outer gimbals, as the latter does start to rotate, and full gyroscopic action occurs. As before, another torsion spring can be installed at the rotational joint between the gimbals, to absorb this energy for delivery later.

Full gyroscopic action, with the inner gimbal permitted to turn

Resetting

A problem occurring now is that the inner gimbal can only turn through a limited angle, e.g. as shown above. After that, it must be reset. If not, the gyroscope will soon go into "gimbal lock", rendering it useless for any further energy extraction.

In theory, resetting could be done by decelerating the gyro rotor to rest, turning the inner gimbal and rotor back to its starting angle, with no net energy penalty, then accelerating the rotor back up to its original speed. But in practice this would be a very crude, "brute-force" method. Even a very small percentage loss in transferring the huge amount of rotational energy away from, and then back to the spinning rotor would be likely to cancel any other energy gain.

Energy and power gain

Ignoring resetting difficulties for now, let's see what energy could be gained from the 100 tonne gyroscope shown above, with details as given last time.

In my second version of the model, the fixed joint between the gimbals was replaced with a rotational joint. Both this joint and the other rotational joint between the axle and the hub were provided with torsion springs, which could be given user-assigned values as desired.

Graphs of joint angles between the axle and the hub, and between the gimbals, vs time, as the Earth turns
beneath the large polar gyroscope. Here, both joints have torsion springs of  κ = 1e6 N-m/rad

Results

I found that for a wide range of torsion spring constants, from κ = 1e4 to 1e8 N-m/rad, and in a fairly wide range of experiments, there was essentially the same power output, i.e. 0.14 watts. Tabulated values are given below for the experiment graphed above, where the axle/hub joint undergoes a complete half-sinewave of oscillation, back to zero angle, in which time the gimbal joint reaches a maximum angle, with maximum stored energy in its spring. Each time the experiment is run, both joints have torsion springs of the same κ value. (Note that below about κ = 1e4 N-m/rad, the gyroscope risks going into gimbal lock in this experiment).

κ [N-m/rad]                            1e4           1e5              1e6               1e7                 1e8
Gimbal joint angle [rad]      0.5721  0.06028  0.006039  0.0006036  0.0000601
Stored spring energy [J]      1636.5   181.68      18.234         1.8217           0.1806
Elapsed time [s]                     11753     1300.6     130.15          13.07             1.30
Power output [W]                 0.1392    0.1397      0.1401         0.1394          0.1389

The above results are of only moderate accuracy, using a mouse-positioned cursor on the graphs, rather than the more accurate but tedious method of saving simulation data for later examination.

Conclusion

From these experiments I conclude that although a large polar gyroscope can extract some energy from the rotating Earth, it is far too little to be of any practical use. So it is not worth spending more time on the resetting difficulties.

The Polar Gyroscope, Part I

Extracting energy with a polar gyroscope

Other than exploiting the Earth's tides, the simplest, most often suggested method for extracting energy from the Earth's rotation is to exploit the torque that occurs when it turns on its axis against some other device which is not turning. The device usually suggested is a large gyroscope. For simplicity, the gyroscope would be installed at either the north or the south pole, as in the UM model shown below (although that would not be essential, provided it was oriented so that its outer gimbal axis remained parallel with Earth's polar axis):—

Universal Mechanism model of a very large gyroscope with input/output axis
aligned with the Earth's polar axis = the z-ordinate (blue)

The basic idea of using a gyroscope to extract energy from the rotating Earth is common enough on various websites and has been patented, e.g. in German patents DE 102006057073 and 102006053069, and US patent 5313850. However, I have never seen anyone do any computer modelling of it, to give estimates of expected energy output for realistic cases. One reason for that, I suspect, is because there is a serious problem with this idea as it is usually presented. I'll explain that shortly.

Note: Planetary energy extraction can be taken much further theoretically than I do here. For example, see "A Mechanical Principle for Acquisition of Useful Power on a Celestial Body Through Utilisation of its Planetary Precession" by Kyril Vulkov, Journal of the British Interplanetary Society, 55, pp394-397, 2002; abstract at http://www.jbis.org.uk/paper.php?p=2002.55.394

Gyroscope details

The gyroscope that I used in my model is as shown above. It is of "traditional" design with a metallic rotor, rather than a more modern carbon-fibre, polyester-fibre or fused-silica type, which would all have higher energy densities. Its rotor has the following details:—

Material:                 Maraging steel
Diameter:               4.5 meters
Width:                     1.5 meters
Mass:                       100 tonnes = 100000 kg
Inertia tensor:        Ixx (red): 331230 kg-m²
                                   Iyy (green) and Izz (blue): 179270 kg-m²
Rotational speed:   125 rad/sec, ≈ 1200 rpm

In this model, the hub (dark green) is forced to rotate constantly at the Earth's rotational speed of 0.00007292115 rad/sec. The axle (yellow) is rigidly joined to the outer gimbal. A torsion spring is installed between the hub and the axle. The spring absorbs energy as it is twisted, for delivery later, as the Earth rotates the hub with respect to the (initially) non-rotating axle and gimbals.

In my first version of this model, following the usual way in which this idea is presented, the axle and outer gimbal were also rigidly joined to the inner gimbal, to form a single component. (In UM, rigid joints like these are achieved with a 6 d.o.f. joint with all degrees of freedom switched off).

A non-gyroscopic result

However, as I had already suspected, there was no gyroscopic effect at all in this model. Whatever rotational speed was given to the rotor made zero difference to the result. The rotor might just as well have been a dead (non-rotating) mass rigidly joined to the gimbals. 

As Prof. Gray says in his book A Treatise on Gyrostatics and Rotational Motion (p10), "...gyrostatic resistance to change of direction of the axis of rotation is bound up with freedom of the gyroscope to turn as a whole with precessional motion." With the gimbals and the axle all rigidly joined there can be no such freedom for precessional turning. Note that all joints in the model are the mathematically "perfect" joints of finite-element computer analysis.

This situation is shown as the fourth case (d) in the above figure, from Analysis and Design of the Gyroscope for Inertial Guidance, by Ira Cochin (p36). As seen in this case, the gyroscope's angular momentum H plays no part in the result, which is non-gyroscopic.

A gyroscope with a single gimbal able to turn only about a vertical axis

But doesn't it work in practice?

When I set up my small gyroscope as shown, and try to turn the rotor plus gimbal with respect to the base, there is significantly more resistance to turning when the gyro rotor is spinning, than when it is at rest. This resistance to turning was the property exploited by the French experimentalist Léon Foucault, as one of his methods of determining the rotation of the Earth. (Reference Comptes Rendus no 35, 1852).

I think what is happening here is that although the gyroscope is theoretically unable to turn as a whole with precessional motion, in practice even a very small amount of play or deformation in the bearing between the gimbal assembly and the base does allow a very small amount of such precessional turning to occur. This is sufficient to cause the added resistance to turning about the vertical axis. However, I think there would be problems, or at least serious inefficiencies in trying to extract energy without permitting full gyroscopic action to occur. I'll look at that next time.

Energy from the Rotating Earth

It's now time to start discussing the third of the possibilities for a mechanical perpetual motion that I mentioned back on 14 April 2014, i.e. extracting energy from the rotating Earth.

An interesting webpage

About a year ago, I found and bookmarked an interesting Chinese webpage on this topic, part of the pat365.com website titled "Laboratory for Expression and Retrieval of Patents." It displays as 世界专利信息试验检索平台 , and the URL for the page of interest is http://pat365.com/search/refineSearchAction.dotypeURL='getM'&refineSearch=pc/DE102008011487

75 German patents

I found a total of 75 patents, all German, at the URL given above. (I couldn't use it very well, because its navigation is in Chinese, and some of the patents are in German only, without English translations). Although the page of interest is titled 重力或惯性发动机 Gravity or Inertia Motors, several of the patents have at least some association with extracting energy from the rotating Earth, such as DE 102009034866, 102008036795, 102007062672, 102008003693, 102006057073, 102006053069, and 102006015324.

Patents on espacenet

The most comprehensive patent collection that I know of is the European Patent Office's at http://www.epo.org/searching/free/espacenet.html. If I know a patent number, I can always find it there. However, I have never had great success searching for particular topics there. No doubt that's partly my fault; however espacenet have done some annoying things in the past (like changing the prefix for Japanese patents to "JPS" without making their search engine tolerant for the older "JP" prefix which they had been using).

Patents versus the real world

From even a fairly cursory look at patents, it's obvious that there is quite a lot of interest in extracting energy from the rotating Earth. I had hoped to examine in detail some of the German patents mentioned above, but haven't done so; partly because the pat365.com webpage went offline for several months, and has only recently re-appeared.

Of course, anyone can apply for, and can usually get a patent; but the key question is — does the patented device really work? Next time I'll look at the most common idea for extracting energy from the rotating Earth, which is to use a gyroscope.

Recapitulation

"Structure" at the microscopic level

The basic idea behind my last few posts is that a permanent force generator could be built to exploit either the zero-point fluctuations responsible for Casimir Effect, or the thermal motion of air molecules at normal temperature and pressure.

Even though there is no preferred direction for either the zero-point fluctuations or the air molecule movements (i.e. they are both isotropic), the idea is that energy can still be extracted from them provided that the devices designed to do that have correctly designed and manufactured structures at the microscopic level.

Are there any precedents?

I know of one already existing technology whose performance depends on having the correct structure at the microscopic level. The modern term for these items is "gauge blocks," which we older engineers used to call "Johansson slip gauges."

A metric set of gauge blocks

Gauge blocks "wrung" together into a stack

The above two open-source images (from Wikipedia) show gauge blocks, which have been "wrung" together to create a single stack, in the second image. Obviously, some force keeps the gauges together.

The discussion at http://en.wikipedia.org/wiki/Talk%3AGauge_block shows I'm not the only person to suggest gauge blocks stick together at least partly from Casimir Effect, although the suggestion wasn't well received.

Whether they stick together because of Casimir Effect, or air pressure (or, as I believe, a combination of both), gauge blocks have "structure" sufficient for their purpose at the microscopic level, i.e. in their case they have microscopically flat adjoining surfaces. This enables them to perform in a way that is not seen with metal blocks finished to a "normal" standard of flatness.

An "Air plus Casimir Force" motor

Note that Alt 2 in the specification drawing I've posted previously could be made conducting, i.e. from metal. Then it could work from both air molecule interactions and Casimir effect. (Experimentally, assuming it does become possible to make foils according to that drawing, it would be worth contrasting the performance of two Alt 2 prototypes with the same physical dimensions; but with one made of conducting material, and the other of insulating material.)

Further computer analysis

Whether or not foils as specified in the drawing could be made now, or in the near future, realistic computer modelling of such foils could almost certainly be done now — but not by me. These days, I don't have access to the necessary hardware or software. As already mentioned, modelling that would give really credible results will very likely require supercomputers.

See http://www.isgtw.org/feature/glueing-together-multi-scale-world

In my personal opinion, realistic modelling of such foils would be very worthwhile.


This concludes my series of posts on devices with structure at the microscopic level.