Prof. Laithwaite's Gyroscope Experiments Part V

Is there a reduction in constant centrifugal force?

One point repeatedly made by Professor Laithwaite was that his experiments were showing a reduction in the centrifugal force that a precessing gyroscope should exert at its central pivot. This effect was the basis for his patent application for gyroscopic propulsion (WIPO International Application No PCT/GB95/01027, filed 05-05-95). See here. (It's a PDF).

Also see "A System for the Transfer of Mass Derived from the Principle of Conservation of Momentum," by Prof. E. R. Laithwaite and W. R. C. Dawson, at  http://www.gyroscopes.org/masstran.asp

Another UM model

A 30kg precessing gyroscope. The graph shows forces on the joint between the shaft and the central axle.
Colour key for forces:—   x-direction: red;   y-direction: green;   z-direction: blue.
(Note re signs: The forces measured are joint reaction forces jRFx, jRFy, jRFz.  So centripetal force
is being measured horizontally — equal in magnitude; opposite in sign to centrifugal force).

The above figure shows a UM model that was adapted slightly from an earlier one, specifically to check centrifugal force at the joint between the shaft and the central axle.

Data: gyro wheel mass: 30kg, rotational inertia 0.4426 kg-m², spinning at 200 rad/s, at radius 0.6m from the central axle, in gravity 9.81 m/s². For simplicity, the shaft carrying the wheel has negligible mass (1 gram).

As always, when the spinning gyro is simply released from its horizontal starting position, it initially drops, and then nutates while it is precessing. I tried damping the joint between the shaft and the central axle to reduce this, but that interfered too much with the precessional speed and hence the centrifugal force. So instead I left the system completely undamped, but started it with an initial precessional speed between the central axle and the tower of 1.995 rad/sec, which is the steady-state precessional speed for this case. This eliminates the nutation.

Results

The gyroscope completes one precessional revolution in 3.15 sec. So its precessional speed is 2π/3.15 = 1.995 rad/sec, and the centrifugal force exerted at the central joint should be:—
mω²r = 30 × 1.995² × 0.6 = 71.616 N.

From text files of the graphed results, I got the following values for the joint forces:— 
x-direction peak 71.64 N; y-direction peak 71.64 N. Since these forces are sinusoidal, with a 90º phase shift between them, no more analysis is required: the measured centrifugal force is a constant 71.64 N. 

As a check, the vertical z-direction force was also measured, at 294.3 N, comparing well with the expected value of 30 × 9.81 = 294.3 N.

So, computer modelling gives an orthodox result for a smoothly precessing gyroscope.

Postscript — video

I have added a video of this model, above.

The purple trace is the locus of the center of the gyro wheel. Note that, because images were taken only at 0.02 second intervals for this video, the small irregular wheel markings may be hard to see, or may appear to show the wheel turning the wrong way ("spoked-wheel effect"). But it really turns correctly, i.e. clockwise as viewed from the central pivot outwards.

Prof. Laithwaite's Gyroscope Experiments Part IV

Video

Video of Part 4 ("The Jabberwock") from Professor Laithwaite's original 1974 Christmas lecture is at http://richannel.org/christmas-lectures/1974/1974-eric-laithwaite#/christmas-lectures-1974-eric-laithwaite--the-jabberwock

The "double-joint" experiment begins at about 33:30, and the system is shown briefly, twice, in its initial balanced state, at 33:50 and 34:06. The gyro does indeed rise as shown in the second image below.

Double-joint experiment — static balance

Double-joint experiment — finish

The "double-joint" experiment — computer modelling

A 30kg gyroscope and balance-weight on a jointed shaft, as in Professor Laithwaite's "double-joint" experiment.
The graphs show the height above ground level of the gyro wheel (red) and the balance-weight (dark blue).

The above image shows a gyroscope with an extra [single d.o.f. rotational] joint in its shaft, as in Professor Laithwaite's "double-joint" experiment shown above.

When the simulation is run on this model, the result is unlike either Prof. Laithwaite's Fig. 4.15, or the result achieved in his experiment. After some initial settling-down, [a force opposing the combined weight of all moving components is applied to the central axle, and there is a damper between that axle and the tower] the heights of both the gyro wheel and the balance-weight oscillate over time. The wheel is always lower than the balance-weight, as was expected from orthodox theory, but the angle of the joint is opposite from Fig 4.15.

The "double-joint" experiment — conclusion

Computer modelling of the double-joint experiment shows only orthodox behaviour, and fails to replicate the result demonstrated by Prof. Laithwaite. After having been exactly balanced initially, the modelled gyro wheel does not show any sign of transferring its weight any further back than the added shaft joint. The portion of the shaft carrying the wheel now has its center of mass at a greater radius, and presumably does not transfer its weight, which would explain why the wheel drops down below the balance-weight.

Of course, if there is even a very slight overall excess of weight on the balance-weight side when in operation with the wheel's weight transferred, the wheel does rise. In doing this, the system behaves essentially in the same way that a sensitive precision balance would behave. But in that case, at least in the computer model, the imbalance is obvious at the initial (static balance) part of the experiment.

My modelling so far cannot explain either the double-joint experiment, or more importantly, the apparent lack of weight that an experimenter feels when he first force-precesses, then lifts a heavy spinning gyroscope.

I have the building and testing of a heavy physical gyroscope on my "to-do" list. 

Prof. Laithwaite's Gyroscope Experiments Part III

A subjective loss of weight

I have been discussing the strange phenomenon of the apparent lack of weight that an experimenter feels when he first force-precesses, then lifts a heavy spinning gyroscope. When Professor Laithwaite did this, he described the gyroscope as "light as a feather." In the Australian replication, the comment was "it feels incredibly light as I do that."

Although as I have pointed out, these experiments could have been better instrumented to gain much better data, let's assume for now that the orthodox conclusion of no weight loss of the experimenter plus gyroscope, throughout the lifting experiment, is correct. Can that possibly be reconciled with the loss of weight felt subjectively at the experimenter's hand?

Unorthodox explanations

The "falling-away" laboratory frame will have some influence, but I doubt that it could fully explain this phenomenon. I think we are forced to look for unorthodox explanations. One possibility is that the gyroscope is somehow transferring its weight back not just as far as the experimenter's hand, but instead to his elbow joint, or even his shoulder joint — which does not rise as the gyroscope rises.

I would be quite skeptical about that idea, except that there seems to be some support for it in one of Professor Laithwaite's experiments.

The "double-joint" experiment — background

On two separate occasions, Professor Laithwaite was invited by the Royal Institution to give the "Christmas Lecture" a.k.a. the "Faraday Lecture", traditionally a very prestigious event. His first lecture in 1966, on electromagnetic devices, was well-received. His second lecture in 1974, on gyroscopes, was so controversial that for the first and only time ever the Royal Institution refused to publish it. It was subsequently published independently as Engineer Through The Looking-Glass.

[Reference: Engineer Through The Looking-Glass, E. R. Laithwaite, ISBN-10: 0563129794]

One of the experiments performed in this lecture (the "double-joint" experiment) is shown, with the gyro non-spinning at first, in the sketch below from page 51 of this book:—

Fig. 4.14 The double-joint experiment — initial state

Prof. Laithwaite says:—

"...First the system is balanced by means of the adjustable weight about the tower pivot, as shown in Fig. 4.14, with the stationary gyro and bearing ring hanging freely from the second pivot. The wheel is then spun and raised until the whole gyro axle is horizontal and from this position it is released. If the spinning wheel succeeds in transferring its weight to the second pivot by precession, the bearing ring and piece of spindle up to the second point are 'dead-weight', and must surely cause the gyro to precess about the vertical tower pivot whilst adopting an attitude as shown in Fig. 4.15.

Fig. 4.15

What did happen was that the gyro end raised itself to the position shown in Plate 4.11, whilst precessing about the vertical tower axis in the expected direction. There appeared to be no ordinary explanation for this but it reaffirmed my belief, which I first expressed in a Friday evening Discourse at the Royal Institution on 8 November 1974, that a gyro exhibited phenomena that were not to be found in any other mechanical object, and could well be worthy of a study at a level not hitherto attempted..."

Plate 4.11 The double-joint experiment — final state

I'll do some further study of the "double-joint" experiment myself, next time.

Prof. Laithwaite's Gyroscope Experiments Part II

Experiments and modelling

I don't have a large gyroscope, but I did try one very simple experiment: I tried to lift a weight of 31 pounds (an old U-shaped modified transformer core) with one hand at arm's length. I was simply unable to lift it like that, or even at somewhat less than arm's length.

I have done some modelling of this gyro-lifting problem in UM (Universal Mechanism).

UM model of a precessing gyroscope whose base is attached to the rotating Earth.
This modelling is still "work in progress"

The above image shows a gyroscope with a 30kg wheel which can be force-precessed if desired, and whose base is attached to the rotating Earth. Generally speaking, we know that a spinning gyroscope likes to orient itself with respect to an absolute inertial frame, rather than to an Earth-based laboratory frame. So, the idea is to see whether the locus of the gyroscope's base, which is "falling away" from a straight-line inertial frame as the Earth rotates, causes any change in expected behaviour (such as an apparent weight reduction, or an energy imbalance — e.g. less than the expected amount of energy required to raise the gyroscope through a vertical distance as seen in the laboratory frame). So far I haven't found anything really significant; but I could, and probably should do more investigation.

I'll have more to say about other non-gyroscopic rotating-Earth experiments in the future.

Better physical experiments

Regardless of theoretical modelling, it would be very desirable to repeat Prof. Laithwaite's physical gyro-lifting experiment with modern torque, force and position measuring equipment. Instead of just standing on the ground, the experimenter would stand on equipment capable of measuring and recording the instantaneous torque and force he was exerting throughout the lift (including starting and stopping the precession of the gyro). Some method of recording the instantaneous torque and force, both vertical and horizontal, being exerted at the all-important point of contact between the experimenter's hand and the axle would also be essential. Finally, the instantaneous position in all three dimensions of both the gyro wheel and the experimenter's hand should be recorded.

Depending on the results obtained, it might be necessary to go on to a second experiment, partly to deal with the extremely unlikely "explanation" seen occasionally, that energy is somehow being taken from the spinning gyroscope wheel, and somehow assisting its rise. (Examination of the gyroscope's construction shows that the wheel's bearings should isolate it from delivering energy like this — the wheel can only lose energy gradually from air and bearing friction). Measurements of the wheel's rotational velocity, and hence its energy could be made, but then spurious losses from bearing friction, e.g. during the initial precession, could be a problem. Probably a gyroscope with a better wheel suspension, such as magnetic or even superconductive (Meissner effect) suspension would be necessary in that case. Also, a sensitive strain-gauge on the shaft could be worthwhile.

The recorded data from properly instrumented experiments could be analysed to give results such as the energy being input and delivered over time; whether there is really any weight reduction being measured at the gyro axle; and assuming the lifting force is roughly constant, whether there is any tendency for the gyro to accelerate upwards (as could be expected in a "falling-away" laboratory frame), etc.

Yes, I'm aware that a video comes up at the end of the Australian replication video I posted last time (by clicking on one of the option buttons) that shows the experimenter standing on a domestic scale, from which it is concluded there is no weight loss. But to me, this is an inadequately-instrumented and far from decisive experiment.

Sussex University experiments

An ordinary domestic scale is not even as good as the instrumentation that Prof. Laithwaite used in his Sussex University experiments more than two decades ago, from which his understanding of "mass transfer" evolved; see the video below at about 21:08—  

At least it's good to see Prof. Laithwaite unrepentant at the end of this video, totally convinced that he had discovered something new and useful.