Prof. Laithwaite's Gyroscope Experiments Part VII

Is there a reduction in time-varying centrifugal force?

So far, my computer modelling of smoothly precessing gyroscopes has given orthodox results. Nevertheless, I believe that Professor Laithwaite was quite correct in claiming a reduction in centrifugal force exerted by a precessing gyroscope, and I'll now explain why.

Nutation

Those physicists and others who were quick to denigrate Prof. Laithwaite and his gyroscope experiments apparently failed to notice that, according to strictly orthodox physics, he must have been correct in claiming a reduction in centrifugal force for a precessing gyroscope. That is because in the experiments where he made this claim, his gyroscopes would have been nutating as well as precessing. This can make a large change to the centrifugal force.

It's also possible that this effect was not fully appreciated by Prof. Laithwaite himself. In my opinion, it explains the significant reductions he reported in the centrifugal force exerted by a precessing gyroscope. As we'll see, this force can not only be reduced: hard though it may be to imagine, under the right conditions it can drop to zero, and even beyond, to a net negative value!

A high speed air-driven gyroscope on a stand which can tip over.
Nutation is not clearly visible in this experiment, but it must be occurring,
as long as there was hardly any added precessional motion at the start.
A gyro spinning at high speed will undergo many nutations per revolution of precession,
which may be so small (low-amplitude) that they are difficult or impossible to see.

(In the following discussion, I assume that over no more than a single revolution of precession, friction tending to damp out nutations is negligibly small).

Nutation can cause zero net centrifugal force in a given direction

The experiment shown above starts at about 28:00 in the video at http://richannel.org/christmas-lectures/1974/1974-eric-laithwaite#/christmas-lectures-1974-eric-laithwaite--the-jabberwock

We can quibble about how clearly it is demonstrating a lack of centrifugal force, versus the ability of the gyro to shift its weight back to its central pivot. Nevertheless, if a gyroscope is undergoing cuspidal nutation, as Prof. Laithwaite's must have been (at least at the start of his experiments when he simply released them, without any added precessional motion) then if there is an integral number of cusps over 0º to 180º of precession, the net force resolved along a 90º line is not merely reduced; it must be reduced to zero. In more detail:—

A gyroscope undergoing four cycles of cuspidal nutation in 180º of precession.
The graphs show joint forces in x-direction (red) and y-direction (green).

The image above shows the gyroscope already modelled before, with a 30kg wheel at 0.6m radius from the central axle. Its wheel's rotational speed is now 271.9 rad/sec, and it starts aligned with the x-axis, at zero precessional speed. This causes it to undergo four cuspidal nutations in 180º of precession, as shown by the locus of the wheel center (purple). Only the centrifugal force resolved in the 90º direction on this arc of precession, i.e. in the y-direction, is of interest now (green trace on graph). When the mean value of this graph is found, [using "Mean" from UM's Processor of Variables] it is only -0.00589 N. When the graph is integrated, [using "Integral"] it is only -0.00067 N-s. So there is essentially zero net force in the y-direction, as should be expected (I'll explain that further next time).

Video

See the video of this experiment below.