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.