That is not how physics works. The C of G is only relevant as the point through which the weight (gravity) can be considered to act - hence the name. Otherwise there are just the equal and opposite couples and there is nothing whatever to say about forces acting around any point.
I am amazed by the the amount of discussion this has generated. When I was teaching this to student pilots in the 70s it was a five minute item at the end of the lesson on the design and function of tail rotors/fenestrons. The summary is a two-sentence paragraph with a diagram very like Ascend Charlie's.

Not sure you are right about that - you need a point for a force to work around or opposing forces to create a couple - a pivot point essentially, and that is the C of G.

Force x arm = moment

I've taught the same as AC to student pilots since the 80s but it is a simplistic and easily explainable version of the truth - as Lofty Marshall used to say- P of F is just a simple explanation of things we know happen, it isn't scientific or mathematical proof.

No, you do not. There is no pivot with a helicopter in the hover. A couple is a couple is a couple.
And every couple has its moment, it does not have a pivot.

This is a matter of static equilibrium and pretty straightforward. If things begin to move then it starts to get complicated and inertia brings the CoG into consideration. Then:

SAS: “Did anyone bring up Transmission mounting that differs from a true vertical to the Airframe?”

The S-64 with 3 degrees left. If SA still owned the design,I’d not be surprised to learn that the ensuing discussions were still ongoing.

I think the pivot point is the rotor hub. That's why the weight (considered at the CG) can provide an offsetting force.

Rotor thrust is acting from the hub, not the CG. When the T/R thrust tilts the fuselage left, the CG is no longer under the hub, and a restoring moment is created. The 2 moments are continually playing games with each other.

You clearly understand what is going on, but what you have written above could still be confusing. An accurate explanation must use the terminology correctly.
When introducing levers in elementary science, a physics teacher as I was, will only use moments about a fixed pivot/fulcrum. That is as far as Galileo went.
This makes the calculations easy to understand and completely hides the existence of the couples in equilibrium. If someone's education goes no further they will continue to think in those terms when faced with rotational effects and be forever looking for a pivot. That is not your situation, but it is that of many that have posted on this topic, including Nick Lappos.
A couple is a rotational effect, a vector, and its size is a moment. They are not the same thing once you advance from the simplifications of elementary science.
If you replace 'moment' with 'couple' above all is well, except that 'are continually playing games with each other' is not a decent substitute for 'are in equilibrium' or 'are in balance'.
I'm sorry to be picky, but these things matter to me. :8

Well, I also have a science degree with a major in physics, but when dealing with helicopter pilots, I reduce things to the minimum to help understanding. They are simple folk, as you might be aware...

However, the degree was 50 years ago, and I had forgotten the subtle differences between moments and couples.

So, to put things right, we have a couple of couples coupling in the back of the helicopter. Better?

Maybe, but some simplifications are possibly counter-productive.

Much the same as mine, but I have been back to school for a second career since. :)

Every couple has its moment, as I said above.

I think Nick's education did progress a little further...…..:eek:

I am certain that it did.

Mighty Gem and Arm out the window provided simple and accurate explanations at #2 ad #9, only for Nick Lappos to confuse things with incorrect statements at #10 and #26. Q max attempted to put things right at #17, #29 and #38, but the seeds of doubt were already sewn.

Some wind up being a climatic event too which is not always a good thing.

Ah,”simple folk”. Hard to place Mr. Lappos in that group. Second in his class at Georgia Tech,but more to the point, over three decades or so at Sikorsky,I’ve been at any number of meetings with Nick and our resident PhD’s and in those discussions dear friends, Mr Lappos won/loss record remains unbeaten. His main problem was that he was often more than a tad ahead of everyone on the subject at hand,so there was some misunderstanding as a result. Count me in that crowd on occasion.

I am sitting here isolating myself, so I am up for the challenge, in a friendly way.:)

While I have been lurking here, I have read back over a number of threads to which NL has contributed and I have assured myself of his very high credentials. I, too, have been impressed by his lucid explanations and I understand how he came to earn guru status. But gurus can be mistaken. This is just plain wrong:

and your experience of testing and designing helicopters is????

Don't get me wrong, I'm not equipped for an academic argument with you on physics but I have flown helicopters for 38 years and the height of the TR from the MR really makes no difference to the hover attitude.

Nil, of course, but I did once read a lot of information from Westland, Boscombe Down and what I think is now the US DCIT. I also had some access to the Sikorsky manual mentioned in the parallel thread.
Just to clarify that you are thinking of the design position of the tail rotor relative to the main rotor? NL himself says this about that: :)
The attitude of a helicopter in the hover is tail low. In level forward flight it is more or less horizontal. The vertical distance from the line of the tail rotor thrust to the rotor head changes. It is that separation that is most relevant to tail rotor roll, although it is not the sole contribution, as a rehearsal of this thread will point out.

When I said that we helicopter drivers are "simple folk" I wasn't casting nasturtiums at Nick or John. I was referring to the way that things need to be simplified for students to understand them, but the simplification makes the student believe the wrong thing.

Many years ago, Nick put out a list of Helicopter Urban Myths, and among the myths were the misconceptions such as:

"The rotor system IS a gyroscope", rather than "it sometimes behaves LIKE a gyroscope."
"There is an area of high pressure air under the hovering disc, and this makes a cushion of high pressure air that the aircraft sits on". Bong! Wrong!
"Flapping to equality is happening all the time, so the advancing blade is flapping UP to equalise the lift."
O. M. G.......

Are your observations limited to a teetering rotor head like the R-22 or generalized to include the articulated/hingeless head with significant hinge offset? It seems an H-60/S-92/EC-145 arraignment doesn't put the T/R thrust line very far below the MRH in hover.

OK Syd, a genuine question for my education:

We have been discussing couples that create rotation of a body - how do you identify the axis of that rotation? Is it along the line between (in this case as in ACs diagram) MR head and TR and, if so, where along that line?

My point about height of TR having little effect is that I have flown helicopters with both high and low TR (of both clockwise and anti-clockwise rotation and differing head designs) yet the roll angle in the hover is always between 2 and 4 degrees with that upper limit being on a semi rigid MRH with a large effective hinge offset.

Interesting question, Herr Krebs.

The left-rotation couple has the rotor hub at one end, and the tail rotor at the other - well above the CG. No idea where the axis would be.
The right-rotation couple has the rotor hub at one end, and the CG at the other end. I don't think the axis could be at the extremity, at the CG.

But does it really matter, other than giving you something to think about, and divert your mind from the lack of Lou Rawls and the closure of Dan Murphy's?