My Gyroscope Experiments Part II

Torque output for rate input

This is a very speculative post, concerning the ability of a gyroscope to produce a torque output when given a rate input.

Fig 1.  Steady state conditions for a single axis gyroscope.
Ref: Analysis and Design of the Gyroscope for Inertial Guidance, Ira Cochin.

I've posted the above image before, when discussing the non-gyroscopic case (d). I now draw attention to the first case (a), which notes that a gyroscope produces a torque output when given a rate input (i.e. a change of angle over time). Obviously if the torque output is allowed to turn through some finite angle, then an output of energy must be delivered. The question is: could it be possible to separate this effect out from the "converse" effect noted in the second case, i.e. that a torque input gives a rate output?

Fig 2. A gyroscope with a connection between its gimbals

This question is shown in the 3D drawing above, which has a connection, shown in very schematic form, between the inner and outer gimbals of the gyroscope. Arms are joined to these gimbals, which are connected together via components in a "black box" (or a "black sphere" in this case). So, is it possible that this connection could be made using only passive components, such as links, springs, dampers, energy storing/delivering flywheels etc, in such a way that a net energy output could be delivered with only a rate input — i.e. without much torque input?

I haven't got much further with this idea beyond confirming that there is no net energy production for simple mechanical links between the gimbals.

Review

I'll now review, with some brief final comments, some of the discrepancies already discussed between actual versus predicted gyroscopic performance.

1. Torque applied to the output axis of a gyroscope
     (post of 17 January 2015).

Textbooks (e.g. case (d) in Fig 1 above) and finite-element computer analysis agree that the result should be non-gyroscopic, i.e. that it should make no difference whether the gyro wheel is spinning or not. This does not agree with experiment. (I suspect, but cannot confirm that finite-differences analysis, in which joints and bearings generally have some "flexibility", would give a more realistic result).

2. Prof. Laithwaite's "double-joint" experiment
     (posts of 14 and 21 February 2015).

The result obtained by computer analysis is different from either the result predicted by Prof. Laithwaite, or the result he obtained in his experiment.

3. Force-precessing, then lifting a heavy gyroscope
     (post of 31 January 2015).

It would be easy enough to show, from a strict energy-conservation point of view, that a strong enough experimenter could initially expend sufficient energy to force-precess a gyroscope significantly faster than its natural precessional speed, in which case the subsequent easy lift would be explained. But I'm far from convinced that either Prof. Laithwaite, or the experimenter in the Australian replication video was really doing that. A well-instrumented physical experiment would be needed to make progress in this area.

I have the building and testing of a heavy gyroscope on my "to-do" list, but unfortunately that will be well into the future.

4. Reduced centrifugal force for a precessing gyroscope
     (posts of 7 and 14 March 2015).

I have shown that Prof. Laithwaite's claims of reduced centrifugal force were quite correct, provided that his gyroscopes were nutating as well as precessing, as they surely would have been. However I don't agree that this effect could be developed into a net imbalanced-force propulsion system.

This concludes my series of posts on gyroscopes.