Roll control force free body diagram

[Hot Wings]

I'm pretty clear on the physics and math behind the offset gimbal and control forces in the pitch axis. I'm not having much luck figuring out the same in the roll axis. There seem to be 2 options and I don't know which one applies to the real world physics. First is from this view of a rotor head in roll with the blades span wise to the direction of flight.
In this case the rotor thrust vector always passes directly through the roll pivot. The resulting FBD would then have the CG of the complete aircraft offset by the sin of the roll angle, essentially the same as any weight shift control system. If this is the proper way to look at this then the roll control force would have to be calculated from the desired change in rotor orientation in radians/sec?
The question in this case then becomes one of - What range of angular velocity is normal for gyro roll control? Pi radians/sec is normal for a sedate fixed wing and 3 Pi in the aerobatic realm.

The other option is that there is that there is some rotor 'blow back' due to the roll input. This doesn't seem likely, other than the different lift of the forward and aft blade due to spanwise flow.

If this is the way the physics work then the roll control force gets figured essentially the same way as the pitch control force?


Can anyone here guide me down the correct path?

 

[C. Beaty]

Cyclic pitch control: tilting the rotor head applies cyclic pitch variation to the rotor in the same way as tilting the swash-plate of a helicopter.

Here’s the rotor head of a Bell-47: the swash-plate rocks the rotor about the cyclic pitch pivots. Not much different from a Bensen type rotor.

 

[C. Beaty]

Tilt head cyclic: Tilting the rotorhead can only rotate the blade in pitch.

 

[Hot Wings]

Tilt head cyclic: Tilting the rotorhead can only rotate the blade in pitch.

Agreed - but still a bit confused.

Assuming no rudder input at the start of the roll the standard Bensen style would act like a spindle hub with respect to roll? If so only after the relative wind vector has changed would the teter axis become active/needed due to the roll input?

 

[XXavier]

This animation helps to understand how tilting the rotorhead produces a pitch cyclic variation of the blades. The larger the tilt, the more important the pitch variation. The rotorhead of (most of) our gyros works like a universal (cardan) joint...

Universal joint - Wikipedia

en.wikipedia.org

 

[C. Beaty]

The rotor develops a line of thrust along its tip plane axis. The passage of this thrust line relative to the CG develops a roll/pitch moment.

The momentum of the rotor is far too great to be controlled directly by human muscle power; it must be flown to its desired orientation via cyclic pitch control.

 

[Jean Claude]

Thanks to the cyclic control, the plane of rotation is controlled without effort to the plane of the hub.
It just requires a little delay.
If the rotor has the usual characteristics, the delay is about 0.1* delta:
For example with a continues roll rate of 30 degrees per second, the tip path plane is delayed of hub has to be tilted by about 3 degrees.

 

[Hot Wings]

It just requires a little delay.

I was considering reformulating my question but this makes that unnecessary. Sometimes crafting the question well makes the asking redundant because the answer becomes obvious.

I can now go to the math stage.

@JC and off topic:
I presume that you are the same JC that is responsible for the Pelican? There are quite a few people that would like to know more about the history of and any future plans for that project. I am one and the Pelican is what inspired me to take on the responsibility for the Fauvel AV-36.

 

[Jean Claude]

Many designers think that flying with low power requires a high aspect ratio, like gliders without any power.
But since a glider never needs to climb in the atmosphere, its weight is not a handicap.

A plane with low power is not at all like a glider because its weight is very harmful to take off. A low aspect ratio being lighter becomes better.
This is what I wanted to show with the 12 Hp Pelican.
The resemblance with the Fauvel AV36 is only the airfoil (very positive Cm)

 

[Hot Wings]

The resemblance with the Fauvel AV36 is only the airfoil (very positive Cm)

Off topic - but I started this thread. *

I disagree!
I was about to start designing my own version of the Pelican when the rights to the AV became available. In my opinion the Pelican is visually a low aspect ratio AV-36.

One of my personal design parameters was/is being able to put the plane on a trailer for transport to home storage. As strange as it seems the AV-36, with folding wings, takes up less floor space than the Pelican.

If you would consider offering plans I think there is actually a larger market for the Pelican than there is for the AV-36/361. Given the history of the Pelican/Vampyre I can understand why you may want to stay away from that market.

* I'm new here so I don't know how strict the "on topic" rules are enforced or expected to be followed?

 

[Jean Claude]

My goal was not to reduce the floor space, but the best aspect ratio to reduce the power required.
AV36 can not flight with a 12 hp engine
I have no plans to sell. I just wanted to prove the idea

 

[Hot Wings]

I have no plans to sell.

That will make some people disappointed - but I understand the many reasons not to sell plans.

The AV-36 won't climb well on 12 Hp as the best L/D requires around 8 Hp but it's demonstrated L/D at higher speeds is surprisingly low for a flying wing of that time period.