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I am trying to simplify gyroscopic precession for PPL Helicopter students and in the process confused myself. Many texts define it as processing a force 90 degrees when the force is applied 'parallel to the axis of rotation' while others say 'perpendicular to the axis of rotation'. I even read text where they brought in a force applied 'perpendicular to the plane of rotation' (which I understand is the same as 'parallel to the axis of rotation').

Example 1: Gyroscopic precession. -- A characteristic of all rotating bodies. When a force is applied to a rotating body parallel to its axis of rotation, the rotating body will tilt in the direction of the applied force 90 degrees later in the plane of rotation. or When force is applied perpendicular (at 90 degrees) against any rotating object like our spinning bicycle wheel. (which I understand as being the same as parallel to the axis of rotation)

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Example 2 When a torque is applied perpendicular to the axis of rotation... enter image description here

Or is the effective force always 90 degrees against the spinning wheel regardless of whether the force applied is 90 degrees to the axis or parallel to the axis?

Assistance would be greatly appreciated. Thank you!

Maryke
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You first have to express thing in terms of torque, otherwise there is no clear answer.

Precession occurs if a torque is applied perpendicular to the axis of rotation. Such a torque can be applied with a force, or a set of forces (often a pair of opposite forces is used). Those forces then should have at least a component perpendicular to the torque you want to create, the concept of torque requires that.

But together, this just means that the force you need must have a component that is perpendicular to a torque that is perpendicular to the rotation axis. That can be solved with forces parallel to this axis, but also with forces perpendicular to the axis. Using torque is the only way to see what is going on!

Jos Bergervoet
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So this is for a presentation for Helicopter students. And yeah, many texts are written by authors who only have partial understanding, so you end up with different authors contradicting each other to some extent.

My approach is: understanding of the underlying dynamics such that I don't need any memorization. Anytime I need it I reconstruct the reasoning. (With every repetition that reconstructing-the-reasoning goes faster.)


(It may be that you have an expectation that the phenomenon is very complicated, and that for helicopter students rote learning is the only option. I assert: transparent understanding is accessible for everyone.)



As pointed out in the answer by Jos Bergervoet, it is necessary to specify applied force in terms of torque.


About onset of gyroscopic precession:

I need to establish some basics first:
When a torque is applied to a spinning wheel the initial/momentary response is to yield to that torque (a little). It is the motion of yielding to the initial torque (a little) that induces the subsequent precessing motion.

Discussion of onset of gyroscopic precession, illustrated with diagrams, is in a 2012 answer by me to a question titled 'What determines the direction of precession of a gyroscope?'

In that discussion I capitalize on symmetry. The reasoning is simplified by a division in quadrants.


In that 2012 answer I use the case of a gimbal mounted gyro wheel with the spin axis parallel to the local horizontal.

So, in order to visualize the response of the rotating helicopter blades you remap the orientations of the explanation to that case.

If you have any follow-up questions: contact information for me is available on my stackexchange profile page.




About the assertion at the start of this answer, that the rotating object yields (a little):

This property of onset of gyroscopic precession is for example pointed out in the Feynman lectures (Vol 1, chapter 20, section 3, The gyroscope . In addition, it has been experimentally verified with an tabletop experiment. Svilen Kostov and Daniel Hammer, 2010, 'It has to go down a litte, in order to go around'

Cleonis
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  • It does get slightly easier with every reconstruction (I think). I wanted to contact you to clarify something but the link to your contact page is not working. I agree that in an effort for some authors to simplify the concepts, they create more confusion. If looking at your explanation from 2012, a torque force was applied directly to the spinning wheel instead of using a brown weight attached to the roll axis, then the reaction would be the same? Assuming that the force would be coming from the same side as the brown weight? – Maryke Mar 02 '24 at 08:27
  • @Maryke Here is a direct link to the page with contact information on my website. (That page gives an email address to contact me. The letters are displayed as an image, so copy/paste does not work for it. To enter the email address in the address bar of an email program: type the letters.) In the 2012 explanation: yeah, the brown weight in the image is there to represent application of a torque. The explanation I posted on stackexchange (in 2012) is an abbreviated version of the one on my own website. – Cleonis Mar 02 '24 at 08:58
  • @Maryke Incidentally, I came up with that 4 quadrants scheme in the course of explaining the operating principle of a particular type of flow metering device. Link: Coriolis flow meter Mass that is moving away from an axis of rotation will tend to lag behind, and mass that is moving towards the axis of rotation will tend to pull ahead. Also: a youtube video (channel name: gyroscopes), that vividly shows response to change of orientation. The gyro wheel is swiveled, and in response the wheel pitches. (Pitching motion will give swivel response.) – Cleonis Mar 02 '24 at 09:37