Precession of teetered autogyro rotor

[llwindy]

I came across discussions on the precession of the rotor disc for a teetered gyrocopter here. However, I think the discussion was not settled hence I will open it here again.

Let's start with a unhinged two bladed gyrocopter rotor connected to a shaft. Suppose we keep the aircraft on the ground, and start up the rotor. Then, when direct tilt is applied to the rotor axis i.e. the rotational axis is tilted (not cyclic, don't bother about the engine weight either) for sure gyroscopic precession occurs as this system is a gyroscope. Much like a propeller aircraft which starts a looping and has to account for the precession due to the rotation of the propeller and its axis.

Now, following De la Cierva and many others, let's add a teeter hinge such that the blades can flap. This changes a lot in terms of analysis. The rotor is not longer a gyroscope, and the 90 degrees phase lag is due to resonance! I would like to tilt the rotor as before but I am stuck in understanding conceptually. For that matter, I have added a picture as it says more than a 1000 words.

To me it seems that it matters when I apply the tilt. In situation A, the rotor will initially remain in the same plane as I can not transfer any moment due to the hinge. However, in situation B the tilt is perpendicular to the hinge and therefore, it is as if I am tilting a fixed rotor.

This seems contradictory. Moreover, what happens when the rotor is in an intermediate position between A and B?

 

[Vance]

I came across discussions on the precession of the rotor disc for a teetered gyrocopter here. However, I think the discussion was not settled hence I will open it here again.

Let's start with a unhinged two bladed gyrocopter rotor connected to a shaft. Suppose we keep the aircraft on the ground, and start up the rotor. Then, when direct tilt is applied to the rotor axis i.e. the rotational axis is tilted (not cyclic, don't bother about the engine weight either) for sure gyroscopic precession occurs as this system is a gyroscope. Much like a propeller aircraft which starts a looping and has to account for the precession due to the rotation of the propeller and its axis.

Now, following De la Cierva and many others, let's add a teeter hinge such that the blades can flap. This changes a lot in terms of analysis. The rotor is not longer a gyroscope, and the 90 degrees phase lag is due to resonance! I would like to tilt the rotor as before but I am stuck in understanding conceptually. For that matter, I have added a picture as it says more than a 1000 words.

To me it seems that it matters when I apply the tilt. In situation A, the rotor will initially remain in the same plane as I can not transfer any moment due to the hinge. However, in situation B the tilt is perpendicular to the hinge and therefore, it is as if I am tilting a fixed rotor.

This seems contradictory. Moreover, what happens when the rotor is in an intermediate position between A and B?

View attachment 1157590

Welcome to the rotary wing forum IIwindy.

I find the way rotor control works on a two blade semi-rigid rotor particular interesting.

I teach it by demonstrating how it works on the aircraft with the aircraft on the ground and the rotor stopped. There is a lot going on to control a gyroplane rotor.

In my opinion a rotor with no flapping hinges would take a great deal of force to tilt.

I don’t know where I would get that force as a pilot.

The flapping hinge is what allows cyclic control allowing the rotor disk to achieve its new commanded position aerodynamically.

You may find value in reading chapter 16 of the gyroplane flying handbook.

https://www.ronsgyros.com/Gyroplane_Flying_Handbook.pdf

As far as I know Juan De la Cierva did not use a two blade rotor with a teeter hinge. He used multi-blade rotors with flapping hinges and lead-lag hinges.

The two blade semi rigid rotor that is so popular today for gyroplanes came along many years later.

 

[Doug Riley]

Windy: You and many, many others who are trying to figure out how we make our rotors change orbit, may make the mistake of thinking that our arm muscles PUSH the rotor disk to its new orbit. As Vance says, that would take one heck of a lot of force, and anyway the rotor would not tilt in the direction we pushed.

Flapping or teeter hinges, combined with a tilt-able rotor spindle, create the exact mechanical equivalent of the swashplate cyclic pitch system commonly used in helicopters. Look at a helo swashplate -- it's easier to visualize how it works, but the gyro's tilt-spindle-teeter-hinge setup works exactly the same way. Both work by creating cyclic pitch changes.

For example, imagine that you push your gyro's stick forward. As you have observed, because of the teeter hinge, this action does not "muscle" the spinning rotor forward. Instead, it causes the rotor to experience a cyclic pitch change as it swings through the 9 o'clock - 3 o'clock position in its rotational cycle. If the rotor spins counterclockwise viewed from above, then the blade passing through the 3 o'clock position pitches down (relative to the plane of the rotor disk), while the blade passing through 9 o'clock experiences an increase in pitch. Because of precession lag, the 3 o'clock blade begins to descend as soon as it "feels" the decreased pitch, but its descent maxes out at the 12 o'clock position. The 9 o'clock blade behaves in the same lagged fashion, reaching its maximum upward excursion as it reaches 6 o'clock. IOW, both blades experience a 90-degree precession lag.

Thus, the rotor disk precesses (tilts) to a more disk-forward axis in response to the forward stick movement.

The energy needed to accomplish the tilt doesn't come from the pilot's muscles after all. Instead, it's extracted from the rotor's own store of kinetic energy. In effect, the rotor is its own servo motor. Power steering!

There's no free lunch when it comes to energy, though. The energy that the rotor expends to tilt itself causes a temporary slight reduction in rotor RPM. With normal cyclic pitch changes of a fraction of one degree, this RPM loss isn't enough to matter.

 

[Aerofoam]

This concept of: "Is it weight shift, or is it cyclic" eluded me until I posed the question and someone gave a description similar to the one above.
To distill it to it's simplest form using the example of initiating a left turn:

When you apply left stick to the rotating blades, the stick force is doing almost nothing when the blades are 90deg. to the direction of flight.
(Like a weight shift wing)
But when they are oriented fore and aft, your small stick force is tilting the rotor blades 5 cycles per second at 300RPM.
That new cyclical tilt is causing the front blade to pitch down and the aft blade to tilt up. The apex of this new path is 90 deg. after the control input, so the rotor is now tilting left. So it really is cyclic input in it's simplest form.
It takes very little movement of the blade path to effect this change, so the control inputs are small and don't require much force.

I am guessing that if you built a fat chord, 60 RPM rotor, you could feel the resistance through the stick as a 1 second pulse, or stick shake opposing your control input, but at 300rpms with the centrifugal force and gyroscopic stability on a typical rotor, it 's dampened enough to not notice.

 

[XXavier]

Welcome to the rotary wing forum IIwindy.

I find the way rotor control works on a two blade semi-rigid rotor particular interesting.

I teach it by demonstrating how it works on the aircraft with the aircraft on the ground and the rotor stopped. There is a lot going on to control a gyroplane rotor.

In my opinion a rotor with no flapping hinges would take a great deal of force to tilt.

I don’t know where I would get that force as a pilot.

The flapping hinge is what allows cyclic control allowing the rotor disk to achieve its new commanded position aerodynamically.

You may find value in reading chapter 16 of the gyroplane flying handbook.

https://www.ronsgyros.com/Gyroplane_Flying_Handbook.pdf

As far as I know Juan De la Cierva did not use a two blade rotor with a teeter hinge. He used multi-blade rotors with flapping hinges and lead-lag hinges.

The two blade semi rigid rotor that is so popular today for gyroplanes came along many years later.

Cierva experimented with 2-blade rotors, for example in this demonstration of a 'jump takeoff'.

In this case, the blades appear to be individually hinged.

However, it's also true that Cierva patented –in 1926– the semi-rigid rotor:

 

[Aerofoam]

That is a great diagram, I didn't realize he came up with the delta hinge angle in fig. 4.

 

[Vance]

Cierva experimented with 2-blade rotors, for example in this demonstration of a 'jump takeoff'.

In this case, the blades appear to be individually hinged.

However, it's also true that Cierva patented –in 1926– the semi-rigid rotor:

View attachment 1157591

I stand corrected. Thank you.

 

[WaspAir]

To repeat a bit of a rant that I have posted elsewhere, as an instructor, I have assiduously avoided using gyroscopic and precession terms with my students because they easily lead to misconceptions.

Gyroscope implies stability that doesn't exist (ask any R22 student how stable her teetering rotor is, and you'll see what I mean). Likewise, precession is wholly unnecessary to explain phase lag. It is easier to describe it in practical terms that rely on the behavior of any simple harmonic system. Max acceleration always preceeds max velocity and zero acceleration happens at max (or min) velocity, and that includes up/down flapping. [For the mathematically inclined, the derivative of any sinusoid will be 1/4 period out of phase with the original function.]

 

[XXavier]

That is a great diagram, I didn't realize he came up with the delta hinge angle in fig. 4.

In the text of the patent, Cierva writes that its purpose is (...) to achieve the automatic variation of the aerodynamic incidence of the blades as they rise and drop during the rotation (...) In this way, the amplitude of the variation of incidence in a full revolution is reduced, with the corresponding increase in efficiency.

 

[Aerofoam]

Yes, the delta 3 hinge line actually changes the pitch of the blades as they change in the plane of rotation.
I designed this feature into the first RC model I built (Basically a teetering Cierva), but I thought it was a modern development.
It worked very well and was very responsive despite only being controlled by rudder and elevator.
it could actually do big sloppy rolls... It had stub wings with dihedral at the tips. They worked well too...

 

[llwindy]

For example, imagine that you push your gyro's stick forward. As you have observed, because of the teeter hinge, this action does not "muscle" the spinning rotor forward. Instead, it causes the rotor to experience a cyclic pitch change as it swings through the 9 o'clock - 3 o'clock position in its rotational cycle. If the rotor spins counterclockwise viewed from above, then the blade passing through the 3 o'clock position pitches down (relative to the plane of the rotor disk), while the blade passing through 9 o'clock experiences an increase in pitch. Because of precession lag, the 3 o'clock blade begins to descend as soon as it "feels" the decreased pitch, but its descent maxes out at the 12 o'clock position. The 9 o'clock blade behaves in the same lagged fashion, reaching its maximum upward excursion as it reaches 6 o'clock. IOW, both blades experience a 90-degree precession lag.

I agree on the system being one in resonance. And I fully understand it when for example there is a gust which influences the advancing-retreating balance and even when one changes the advance ratio (change in wake shape).
However, still I do not see why it does not require (much) force to change the blade's position when in situation B of my figure. Regardless of the cyclic pitch behavior, there is no degree of freedom in the direction where I am moving the axis and blades. If I still persist to move the blade at exactly that position, it is moving because of the physical coupling. In that view, I do not see a difference with trying to move a hingeless rotor i.e. as if it is a gyroscope!

 

[llwindy]

However, it's also true that Cierva patented –in 1926– the semi-rigid rotor:

View attachment 1157591

Xavier, what is the exact patent number of this one? It seems very interesting.

 

[XXavier]

Xavier, what is the exact patent number of this one? It seems very interesting.

This is the complete document. Patent 16484 of 7.12.1926:

 

[Jean Claude]

However, still I do not see why it does not require (much) force to change the blade's position when in situation B of my figure.

To change the pitch in position B, it is enough to overcome the inertia of the beam around the axis of the span. This inertia is very small.

 

[llwindy]

To change the pitch in position B, it is enough to overcome the inertia of the beam around the axis of the span. This inertia is very small.

But at exactly that point, it acts as a gyroscope. Thus, the reaction will be a roll depending on the rotor's angular momentum, and the torque you apply to tilt the rotor, right? However, it is then the direction where the hinge degree of freedom is. So, will there be a roll velocity, or not?

 

[Vance]

But at exactly that point, it acts as a gyroscope. Thus, the reaction will be a roll depending on the rotor's angular momentum, and the torque you apply to tilt the rotor, right? However, it is then the direction where the hinge degree of freedom is. So, will there be a roll velocity, or not?

I found how a gyroplane rotor is controlled very confusing and slowly became confused on a higher level.

When I teach how a rotor works I have the learner stand in front of the gyroplane and watch the rotor that is at 90 degrees to our direction of travel as I move the cyclic front to back.

Most can see that when I move the cyclic forward the advancing blade pitches down and the retreating blade pitches up so the rotor disk will tilt forward aerodynamically. It is a process and doesn’t happen all at once.

The learner can see nothing happens when I move the cyclic left to right.

I find this demonstration helpful to most learners.

 

[Aerofoam]

I found how a gyroplane rotor is controlled very confusing and slowly became confused on a higher level.

That is the best statement I have heard in a long time!

Vance, I am going to steal it and apply it to other things as well!!!

 

[Jean Claude]

and the torque you apply to tilt the rotor, right?

No torque is apply by the stick. just a cyclic pitch relatively to the tip path plane.
It is the blades wich produces the required momentum thank to own cyclic lift
Please, loock here: https://www.rotaryforum.com/threads/quantifying-the-effectiveness-of-direct-control.1147577/

 

[kolibri282]

The basic misconception is, that a rotor is NOT a gyroscope, so a rotor does not exhibit any precession, since this is a term solely used for gyroscopes, a rotor exhibits phase lag (see below). You can easily see that a rotor is NOT a gyroscope if you imagine the spinning rotor in a vacuum: no matter how hard you stir your stick around (even as hard as stirring Bond's Martini...;-), the blades will will NOT AT ALL change their plane of rotation, they will only change their angle wrt. the plane of rotation and so no resultant force will act upon the air frame in the vacuum (actually at this point we assume zero height of the teeter tower, to keep things simple). This is totally different from a gyroscope, e.g. the ubiquitous bicycle wheel with handles on each side of the axle. If you change the orientation of the axle a resultant moment (i.e. a force acting on a lever arm) will be exerted according to a right hand rule, i.e. the moment generated will be perpendicular to the plane spanned by the axis of rotation and the direction about which the axis is rotated. This happens anywhere, in a vacuum or in air. A rotary wing rotor on the other hand exhibits a lag in response, called "phase lag", because a rotor is a SECOND ORDER SYSTEM IN RESONANCE !!!! acted upon by aerodynamic forces (that is, why it does NOT work in vacuum!). I should, perhaps, add, that the phase lag for a second order system in resonance is 90°. Let us assume the rotor rotates counter clock wise seen from above (US helo) and that the angle of rotation starts over the tail. If you want the helicopter/gyro to slow down you increase the blade angle of attack in the 90° position, i.e. when the advancing blade is at right angles on the starboard side. Due to the 90° phase lag the blade will reach the maximum upward deflection over the nose of the aircraft and the rotor plane is tilted backwards.

The late Raymond Prouty has shown all this in a brilliantly concise way in his book "Helicopter Performance, Stability and Control", the lines in the attachment a from page 150f.

 

[XXavier]

Thanks, Juergen, for your post. Let me add the full printed pages 150...153 of the book that you quote: