Helicopter Dynamics: Gyroscopic Precession
 

Only for those with a perversion for the technical.

In some not-so-distant thread, an attempt was made to show that gyroscopic precession is not a factor in the activities of a helicopter's rotor. The bicycle wheel, which is normally used to demonstrate gyroscopic precession, was modified. This modified wheel consisted of only four spokes, a hub and the lose connections between them. The wheel (or what's left of it) now more closely resembles a helicopter's rotor. This wheel combined with the notes of Prouty and the remarks by Nick tends to support the idea of no gyroscopic precession. Current textbooks tend to also hold this position.

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Now for the fiendish part;

I believe that a simple teetering rotor, with no delta3, exhibits a 90-degree phase lag, which is totally caused by the blade flying to position. Perhaps aerodynamic precession, but not gyroscopic precession.

As mechanical restrictions are imposed upon a blade's ability to flap, the phase angle will decrease from 90-degrees. Any increasing of the flapping hinge's offset, or an increasing of the dampening of the flapping hinge, or a stiffening of the blade will result in an even smaller phase angle.

Now consider an airplane's propeller. We know that the propeller is subject to gyroscopic precession. Also, the primary difference between a variable pitch propeller and a helicopter's rotor is their rigidity. I would suggest that it is only the out-of-plane (flapping) rigidity that we are concerned with.

If we take this idea of rotor rigidity to the extreme, we will have a totally rigid rotor and a phase angle of zero degrees. If the maximum pitch is applied on the right side, then the maximum rotor thrust (not flap - because the rigid rotor is rigidly attached to the fuselage) will be exhibited on the right side. The helicopter will obviously roll to the left, but, with trepidation, I feel that it will also want to pitch down slightly at the nose. I believe that this small nose down pitch is the result of gyroscopic precession, which in turn is the result of changing the attitude of this very rigid rotor disk (read as gyroscope disk).


Anyone who read this far, want to tear it apart?

[ 03 August 2001: Message edited by: Dave Jackson ]

AAAHGH !!

I just read the post and my heads on fire !!

AAAHGH

:eek: :eek:

I think if you take the modified bicycle wheel and do one more modification I may start to catch on.

Of the four metal spokes replace three of them with plastic. (same qualities, flex etc.)

Now, if you input a force to the hub from underneath you would have gyroscopic precession.(while spinning)

In the second case with the spinning "wheel" if you hold a big magnet over a quadrant you would have an approximation of aerodynamic precession.

Am I getting there?

So in the first case we have control forces being transmitted (from "in" to "out"), physically altered by precession, hampered (altered) by hinge offset, resistance etc.

In the second case the control forces are happening already "out" and transmit the pull back to the airframe. (and through the reverse path)

btw, great threads, always enjoy making my brain smoke.

:)

Now look what you've started!

Imagine two separate simple rotor systems. Both have a central vertically aligned spindle (aka rotor mast) which can be rotated axially and also tilted in any direction by a force acting anywhere at 90 degrees to its axis.

Four lengths of scaffolding tube arms (heavy and NON AERODYNAMIC, simply round in section) are attached to each rotor mast by two different methods.

On the first mast, the arms are held in a rigid steel hub so that the arms stick out horizontally like the spokes of a wheel (or the blades of a helicopter), at 90 degrees to each other. This system is rotated at speed. We now have a crude gyroscope. The system will exhibit the two properties of a gyroscope, namely rigidity (it wants to keep spinning in the same plane) and precession (any force applied to the rotor mast in an attempt to tilt the system will appear to act 90 degrees further round to the direction of application until the plane of rotation of the system aligns with the force and it can no longer act).

In the second system, the arms are suspended from the mast, at 90 degrees to each other, by separate lengths of flexible steel cable. At rest the arms hang down alongside the mast. The system is now spun up to speed. As the mast is rotated, the cables attached to it pull round the arms until they fly out at 90 degrees to the mast and 90 degrees to each other. At this stage, the system looks exactly like the first one. Because the rotating arms have the same mass as the other set, they must also act as a gyroscope and must therefore exhibit the same properties of rigidity and precession. A force is now applied to this rotor mast, as before, in an attempt to change the plane of rotation of the system. Because the mast is only connected to the rotating arms by flexible cable, it cannot transmit the force to them. This time the mast moves very easily in the direction away from the force, but the cables merely flex and the rotating arms maintain their plane of rotation. We have a system where the rotor mast can be easily moved, but there is no control over the rotating arms. If the plane of rotation of the arms were to change, there would be no effect on the rotor mast because the forces could not be transmitted through the cables, which would merely flex.

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In the first instance we have a rigid rotor. It can be controlled but the only way to control it is by applying a force through the rotor mast which must move with the system.

In the second instance we have created a fully articulated rotor. We have no practical way of controlling the plane of rotation of this system because we cannot input a force to cause gyroscopic precession to occur.

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We now stop both systems, dismantle them and replace the rotating scaffolding tubes with properly designed rotor blades of identical size and shape. We retain the original methods of attachment, one system rigid apart from simple pitch change bearings and the second still using flexible cables. We also fit a simple system that allows us to change the cyclic pitch angle of the blades. Both systems are spun up to speed with a neutral pitch angle on the blades.

By adjusting the pitch angle of the blades we find that we can fly them around, up and down, changing the plane of rotation of the rotor systems. The Aerodynamic forces generated by the blades overcome the Gyroscopic forces tending to hold the original plane of rotation.

One very noticeable difference between the two systems is that on the rigid system, while the plane of rototation is changing , the rotor mast moves in sympathy. On the second, cable attached system, the rotor mast says rotating along the same axis.

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Applying these two rotor systems to two simple helicopters we find that we can make them both fly by controlling the plane of rotation of the rotors. This is, as we have shown, done aerodynamically by changing their cyclic pitch. The flying characteristics of the two helicopters are however, a little different. The rigid rotor gives us a very responsive helicopter. This is because as soon as the dics tilts, so must the rotor mast, which is now bolted onto the airframe. The airframe rapidly changes direction as the rotor is flown around.

The articulated rotor still flies but the helicopter is reluctant to change direction in sympathy with the rotor system. This is because there are no forces feeding back through to the rotor mast in order to make it tilt.

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But this is only part of the story...

Right! Someone else please carry on.

Shytorque,

Thanks, good clean and understandable explanations like that are hard to come by.

Great job !

did you get my last post to you dave! it was a beuty answering the one with Prouty and vacuum? the thred is missing, should have started one before. :(

To: ShyTorque

A very easy to understand description.

The following is a nit-picking comment and a continuation of your story;

You may wish to slightly modify the following sentence by changing the word 'Gyroscopic' to ' Centripetal'.
>The Aerodynamic forces generated by the blades overcome the Gyroscopic forces tending to hold the original plane of rotation. <.
"Centripetal (center-seeking) force is the constant inward force necessary to maintain circular motion." "Gyroscopic force is the characteristic that causes the gyroscope to react to an applied force at a point 90-degress away from the point of application, in the direction of its rotation."
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To continue your story of the two helicopters;

Assuming that the maximum blade pitch is on the left side of both helicopters, then I believe that the following will take place.

In your first instance, because the rotor is rigidly attached to the helicopter, the mast and helicopter will be pried (rolled) to the right.
In your second instance, because the rotor is teetering, the disk will continue to climb past the left side for another 90-degrees. The tilted disk will then want to change the pitch atitude of the mast and helicopter by dragging them to a new position.

In other words, the first instance has a phase lag of 0-degrees and will roll the helicopter. The second instance has a phase lag of 90-degrees and will pitch the helicopter.
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I think that;

In first instance, the extremely rigid rotor will act like a gyroscope and therefore experience precession. The amount of this gyroscopic precession should be very small though, because;
1/ the rotor has *relatively* little mass,
2/ it must overcome the inertia of the helicopter as well as the rotor, and
3/ no rotor yet (with the possible exception of the V-22) has achieved this high a level of rigidity.

In the second instance, the 'floppy' teetering rotor will not experience any gyroscopic precession.

[ 04 August 2001: Message edited by: Dave Jackson ]

To: vorticey

No I didn't see your post.

A number of interesting posts were 'wiped out'; just when the thread was trying to come to a clearer understanding about one small component of rotor activity.

Can you re-post yours on this thread?

Dave, thanks even more.

Please have a bit of patience with me on this, while sorting through it I am having to dispel some previous convictions that I've had. Generally that means I have to understand it all first.

Back to the tale of two rotors;

On your rigid rotor you mentioned that with full pitch in the blades on the left side of the aircraft it would roll (pry) right.

I'm wondering.. (uh-oh)

If the blade on the left reached the point of maximum pitch at the exact 90 degree mark wouldn't that force developed take some amount of time to transmit to the fuselage?

While the transmission of force was happening the blades would be changing their relationship to the fuselage.

Actually I think the force devlopedwould be changing it's relationship to the fuselage.

Once again, you guys are putting this into understandable verbage, thanks from everyone.

tom :D

To: Dave Jackson

Sorry to butt into a private thread:

I quote,” 3/ no rotor yet (with the possible exception of the V-22) has achieved this high a level of rigidity".

The V-22 Proprotor is not rigid as it is mounted on a rubber diaphragm that allows both flapping and precession of the Proprotorhead.

To support the aerodynamic explanation:

While preventing blade sailing during shutdown, the rotor is controllable down to very low RRPM. Until about 10% RRPM, my inputs to maintain a level disc do not change, only more cyclic into wind is required.

I would find it hard to believe that a rotor at such low RPM is still behaving as a gyro.

This seems to support an aerodynamic cause for the phase lag.
------------

To really analyze this though we will need someone who knows the math behind gyroscopic forces.

Dave,

You appear to have chosen a French helicopter (with the blades rotating clockwise from above), but no matter either way.

I think the answer is that both systems have a phase lag of 90 degrees. A blade will not move instantly to a new position, whatever force causes the motion. For the aircraft to roll, the cyclic pitch increase would need to be put in as the rotor blades pass the 6 o'clock position of the aircraft.

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With regard to the centripetal force rather than gyroscopic force; you may be more correct. (I did originally include the term but I edited the post many times until my eyes were going crossed).

My understanding is that both forces are a function of the same phenomena. Newton stated that a body tends to move in a straight line unless acted upon by another force. A body / mass forced to rotate around an axis (because it is fixed to it), instead of continuing in its preferred straight line, can do so only by experiencing a force, in this case imparted by the attachment. Newton also stated that every reaction imparts an equal and opposite reaction and so the axis by definition must be experiencing an equal force to the rotating mass. Or vice versa.

The characteristics of gyroscopes can be explained by those two Newton's laws (I'll be very honest here and admit that I can't currently remember which he quoted first second or third!).

Precession is simply a description of the movement of a rotating body out of its plane of rotation by a displacing force acting normal (90 degrees / perpendicular) to the ORIGINAL plane of rotation. The force acts, the rotating body moves in the direction of the force (whilst still rotating around the axis) until the displacing force can no longer act because the plane of rotation has changed so that it is in the same direction as the displacing force; i.e. through 90 degrees but 90 degrees further round the "disk" than where the force was applied.

I probably need a model or a diagram to put that across properly.

ShyT

To: tgrendl and Shy Torque

tgrendl wrote;

>If the blade on the left reached the point of maximum pitch at the exact 90 degree mark wouldn't that force developed take some amount of time to transmit to the fuselage? <

No. In the case of an absolutely rigid rotor I don't believe this so. In the case of this totally rigid (and hypothetical) rotor, there is no flapping or teetering. This rotor is rigidly coupled to the fuselage, perhaps by what is called a static mast. Therefore, any movement of the rotor, other than rotation about the mast, will cause an immediate and identical movement in the fuselage.

You must consider this really rigid rotor as if it was a large variable pitch propeller mounted vertically. The only movement is rotation about the mast and pitch change. No blade flex. No nothing. No kidding!
_____________________

The following may help to clarify the activity;

We are looking down upon the rotor disks of Shy Torques two helicopters.
On both helicopters;

0-degrees azimuth is straight back.
90-degrees azimuth is the mid-point of the advancing side.
180-degrees azimuth is straight ahead.
270-degrees azimuth is the mid-point of the retreating side.

The X-axis is the longitudinal one.
The Y-axis is the lateral one.
The Z-axis is the vertical one.

Both helicopters are hovering.

Let's consider that by applying the same cyclic to both helicopters, the greatest blade pitch is at azimuth 90, the least pitch is at azimuth 270 and the mean (average) pitch is at azimuths 0 and 180.

We know that the blade pitch and thrust at azimuth 45 is the same as it is at azimuth 135. We also know that the blade pitch and thrust at azimuth 225 is the same as it is at azimuth 315.. We also know that the blade pitches and thrusts at 45 and 135 are greater than they are at 225 and 315.

So far everything has been the same for the two helicopters.


Now, in the case of the helicopter with the teetering rotor, the blades will climb from azimuth 0 to azimuth 180 and descend from azimuth 180 to azimuth 0. The disk will be tipped back. The helicopter will 'eventually' pitch up and fly backwards.


OK so far?

Now for the helicopter with the totally rigid rotor.

Remember that the rotor and fuselage are totally interconnected, except for the rotors rotation about the Z-axis.

The combined thrust at 45 and 135 EXCEEDS the combined thrust at 225 and 315, The rotor and the firmly attached fuselage must therefore roll about the X-axis and sideslip toward the retreating blade side of the craft.

The combined thrust at 45 and 225 EQUALS the combined thrust at 135 and 315, The rotor and the firmly attached fuselage will therefore NOT pitch about the Y-axis nor will the craft move forward or backward.
_____________

We have give both rotors the same amount of blade pitch at the same azimuths but one helicopter is flying backwards and the other is flying sideways.

The only way to get them to fly in the same direction, is by giving the teetering rotor helicopter a 90-degree phase angle and the totally rigid rotor helicopter a 0-degree phase angle.


Hope this makes sense.

____________________


Lu;

Thanks for the information on the V-22 rotor.

:) Dave etc, thanks, I'm getting there.

Did you ever see the TV commercial for "ugly duckling" cars?

The one where the guy is calling from a payphone for help.

His car is in the background and he's telling the service center what kind of "noise" his car was making when it broke.

RRRRR--RRRRRR


And then in the background his old car just explodes.

And he says "RRR-RRRRR Kaboom "

Now that's really what happens to my brain here.

Appreciate any of the extra time you guys take for the people in the back of the class.

Fly safe

Dave Jackson said:
I believe that a simple teetering rotor, with no delta3, exhibits a 90-degree phase lag, which is totally caused by the blade flying to position. Perhaps aerodynamic precession, but not gyroscopic precession.

Nick Sez:
Bravo Dave! You are absolutely correct. The old bugaboo about Gyroscopic Precession is quite mythological, but almost impossible to squelch, because it seems so plausible, and the real issues are so difficult to describe intuitively.

Basically, the whirling blade flaps at a natural frequency that depends on the centrifugal force to return it to its normal position. Picture the blade with a strong pair of springs, one below and one above the blade that oppose its flapping motion. If we pull the blade tip down, and let go, it will bounce a bunch of times like a diving board. Gor a helicopter, there are no springs, (an elastomeric rotor has such little spring force it changes this not a bit) but there is a strong centrifugal force that opposes a flapping motion. This force is a spring term that acts just like that diving board.

It turns out (in math that gets pretty stinky) that the blade resonates at 1 per rev, because the centrifugal spring changes its force with rpm, so it always allows the blade to resonate at its whirling rpm frequency. It also turns out that the phase relationship between the cyclic pitch (swash plate angle) and the tip path is about 90 degrees, depending on a bunch of blade properties.

Gyroscopes have nothing to do with it at all!

I just reaffirmed my understanding by re-reading a good source (for science and engineering pros):

Stepniewski & Keys - ROTARY - WING AERODYNAMICS
New York: Dover Pub.

dave
in the other tread you talked about blades in a vacuum, but in a vacuum or not the rotor axis must be changed to get precesion.
the mast or its hinges have nothing to do with it, they have there own precesion.
to change the axis we use pitch to put an up and down force on the blades,this over comes inercia and the disk starts to move but because the axis is changing, gyroscopic precession will TRY to take the movement ahead in rotation. a little cyclic will stop this happening.
i recon that if you on the ground with the rotors spining you might be able to notice it if you pushed the cyclic forward then hold that atitude. while the rotors are coming down they might be infront of the input but when they stop at the bottom it should be lined up with the input ;)

Nick;

Thanks for your elaboration of the teetering rotor
and your mention of Rotary-Wing Aerodynamics.
You just came up with tonight's reading.

It's surprising what one can learn from a textbook. :)


By the way, it is because of your previous postings that I have acquired (hopefully?) a better understanding of things like; static mast, anhedral, plus, plus.
Thanks.

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vorticey;

It appears that you want to disassociate the blade's activities from the rest of the rotor's activities. I do not believe that the activities of an individual blade can be related to gyroscopic precession.

In fact, I would guess that the association of gyroscopic precession and the helicopter rotor has come about because people have been thinking in terms of the rotor disk. They envision the rotor-disk as some sort of structural entity, where in reality, it's mostly a bunch of (hot) air.

Gyroscopic precession is probably only active in a rotating body that has absolute rigidity. When one starts to think of the rotor disk as a rotating body, then their thinking starts to get a little tipsy.

If you think that the above is hot air as well, fire back.

To: Dave Jackson

When the Cheyenne Helicopter was first built it flew quite well. I don’t know if you are familiar with the rotor system on the Cheyenne or not. The Cheyenne had a rigid rotor system that was free to feather but was rigid in plane and flapped by flexing the blade and the arms of the rotorhead. In order to introduce pitch change into the blades the pilot would move the cyclic and caused a servo to move. This servo was attached to a horseshoe shaped spring, which was compressed. The spring compression was transmitted via control linkage to a gyro that was mounted above the rotorhead. This gyro which consisted of four arms disposed at 90-degrees to each other and each arm had a very heavy weight at the end. This produced a gyroscope rotor that was capable of imparting a great deal of force. The individual arms were attached to the pitch horns on the blades. When the pilot input cyclic movement and the gyro would displace 90-degrees later inputting a pitch change into the blades and the rotor system like a gyro would displace 90-degrees in the direction of rotation.

As the design progressed the Army kept adding weight to the Helicopter. Lockheed indicated that the helicopter could no longer meet its’ performance guarantees and Lockheed requested a change in the rotor diameter to regain the necessary lift. The Army said no so Lockheed went back to the drawing board. What they came up with was a bastard design that not only had negative twist like other helicopters they also included a camber which added a degree of instability. Then they did something that was quite novel and they painted themselves into a corner in the process. Not only was the blade cambered it had a different camber at different blade stations so from the root to the tip the blade had constantly changing in its’ cross section.

This design in concert with the blades inherent stiffness caused major problems as the blade would not fly or precess to the position commanded by the pilots’ cyclic input. The first time this problem manifested itself a pilot was lost, as was the helicopter. The next time it happened it took out the wind tunnel at Ames labs in California.

The problem was eventually solved but the solution was so complex that it became sensitive to a single point failure that would cause loss of the helicopter. The solution although complex worked similar to the electronic system on the Lynx helicopter that corrects for a 15-degree coupling in the cyclic control.

Now, way back then when I learned how the system worked Ray Prouty indicated that there were two gyroscopic elements. The control gyro which precessed and the gyroscopic precession of the rotor. It seems that that assumption is no longer valid.

Lu, what's with the permanent thumbs down mate?

Regarding your comment about the gyroscopic pitch change mechanism on the Cheyenne(although I haven't seen it), it sounds a lot like a stabilising device.

Some gyroscopic forces must certainly be associated with whirling massive components, but as Nick Lappos pointed out above, the actual movement of rotor blades is fundamentally an aerodynamic thing.

Harking back to the old Huey again, the pitch change is accomplished by hooking up the pitch change rods from the swash plate to the stab bar (you may already know about this so apologies if it's telling you how to suck eggs) which is the rod mounted at 90 degrees to the rotor blades, and connected to them via the pitch change links and an oil-filled damper.

Basically, the stab bar whirls around and tries to remain rigid in space, and if the rotor blades are perturbed by turbulent air, the design of the connecting rods in the system leads to a pitch input to correct the disturbance.

For pilot-induced cyclic pitch changes, the swash plate moves the control tubes which act through the stab bar system to the pitch change links, leading to cyclic pitch changes on the blades causing them to fly to the new desired position.

So I guess what I'm saying is, gyroscopics have a place in rotor design, but aerodynamic forces are what makes the blades fly as they do. What you're talking about above sounds like it's designed as a stablilising system, and the pitch inputs to the blades are still what lead to disc movement.

To Dave Jackson et al, enjoying reading your posts. A bit of constructive discussion is a good thing!

[ 06 August 2001: Message edited by: Arm out the window ]

Lu;

Thanks for the information on the Cheyenne rotor. The following web page, by Doug Marker, may also be of interest. It describes some of what you said and adds some of its own.
http://www.internetage.com.au/cartercopters/pics9.htm


A year ago, Doug started a thread on rec.aviation.rotorcraft, in which participants discussed gyroscopic precession. His intent was to display the conclusion after all the information was is.
He may have never been able to come to a conclusion :eek:, whatever, an e-mail was sent to him earlier today.
_________________

Regarding Prouty and gyroscopic precession:

I just came across the following two excerpts from 'Helicopter Performance, Stability and Control'. "... the summation of the moments produced by aerodynamic, centrifugal, weight, inertial and gyroscopic forces must equal zero." and "... the rotor disk acts as a gyroscopic and remains in its original plane".

Perhaps it is in reference to a small amount of gyroscopic precession that may be present in rotors with offset and flapping hinge stiffness.

[ 06 August 2001: Message edited by: Dave Jackson ]

I think Arm out the window has hit the nail on the head, and perhaps summarised previous posts succinctly. The UH-1H stab bar exihibts gyroscopic tendencies to adjust the rotor system sensitivity to both pilot and gust inputs. It is rigid.

Here is the summary: the Stab bar acts as a Gyro because it is rigid, the rotor aerodynamically precesses because it is not!

Does this satisfy? I think that is the gist of things thus far.

To Lu: I believe the device fitted to the Cheyeene was merely a pitch change mechanism thus mounted to help with the aerobatic capabilities of the aircraft and has nothing to do with gyroscopics. Nick will know for sure, but I believe this aircraft was the first aerobatic helicopter. Damn pretty too.

As for Mr Prouty, I have been a long time fan, and some what of a devotee to his explanations, but....and I will strap on the armour now....we are all entitled to our imperfections. I would find it thoroughly benefitial for his input on the topic at hand, but, I cannot subscribe to this particular statement of his. Lu, he is a pal of yours, can you encourage him on line?

Check the date on that publication Dave.....

To all of us Nerds :) ,

I think the Cheyenne gyro was actually intended as a true gyro, that is certainly how it is described in one of Prouty's books, added to modify the rotor response and stability. It was a heavy ring , first mounted below the rotor but later moved to above it. As Lu said, it was an ongoing project, many major mods were carried out as it ran (stumbled?) along, before being cancelled for a number of reasons.

We should all realise that, as indicated by the Lockheed designers having all these problems, we really are talking about a complex issue here!

Dave,

One thing that occurred to me earlier is that a "rigid" rotor is not actually completely rigid in the literal sense so perhaps we have all been slightly barking up the wrong tree. The term "rigid rotor" actually means that there are no flapping or lead /lag hinges but there is an inherent flexibility in the system, either within the blades themselves or on the rotor head, like on the Lynx.

Juan de la Cierva did originally attempt to fly an autogyro with a truly rigid rotor by fitting bracing wires between rotor head and the blades. He did this because when he scaled up to full size from a model he was alarmed how much the blades drooped at rest. It rolled over on takeoff. He later realised that his models' blades had inherent flexibility, allowing them to flap to equality. Bracing up the full-size blades caused aerodynamic loads to be fed back into the fuselage, giving a massive rolling force that the pilot could not overcome.

Lu, please note, that accident was put down to inflow roll, an aerodynamic, rather than gyroscopic phenomenon.

ShyT

Below is a very lengthy explanation of gyroscopic precession. I tried to make it so that everyone on this thread could fully comprehend it, but I did gloss over some points. I tried explaining this to other groups at different times, and it has only worked after much dialogue afterwards. Feel free to ask for clarification either privately or in this thread.

Keep in mind, I'm trying to address only gyroscopic precession in helicopter rotors. I do understand that the truth is much more complex and that there are factors that affect gamma other than what I will be discussing.

There are responses to posts made by Dave, ShyTorque, Lu, HeloTeacher, and Nick following this lengthy explanation

__________________


I'm not an expert in helicopter theory, but I do have a solid understanding of rotational dynamics. It seems consensus in this group that gyroscopic precession does not cause a 90 degree phase lag in helicopter rotors. I agree. It also seems evident from your posts that most of you don't fully understand what gyroscopic precession is. I'll try help with that and with other terms. I think I can illustrate why experts in this industry don't agree whether or not gyroscopic precession actually applies.

First of all, if you wanted to describe how hard a non-rotating hockey puck was about to hit me, you could give me it's velocity and it's kinetic energy for me to fully understand what kind of hit to expect. Or you could give it's mass and velocity, or it's momentum and kinetic energy, or it's mass and momentum, etc. The point is many of the words that we use to describe physical processes are functionally redundant. Functionally because in some instances alternate descriptions are easier to understand or apply. I believe that this is one of the reasons why gyroscopic precession is being dropped from basic helicopter theory: other quantities give a more understandable description and, in fact, more accurate.

A review of the concepts we need to understand gyroscopic precession. Conservation of momentum is a law of physics that deal with bodies in motion. Simply put, conservation of momentum is Newton's First Law of Motion, "Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon." (Motte's 1729 translation of Philosophiae Naturalis Principia Mathematica, Sir Isaac Newton).

Conservation of angular momentum is an identical concept except that it applies for objects rotating rather than objects in linear motion.

We understand easily how to conserve linear momentum. If a hockey puck is travelling north and we leave it alone, it keeps on travelling north. If a hockey stick imparts a force on it towards the east, we know that the puck will then travel in approximately a northeasterly direction. Since we can all do wind triangles, we can add vectors to come up with a resultant vector for this hockey puck.

If we hang that puck on a string connected at it's center and begin to spin it counter clockwise when viewed from above, it will keep on spinning if we leave it alone (ignore the torsion in the string, air friction, etc.) If we stop the puck spinning about the vertical axis, it will continue to not spin. If we impart a downwards force on the southernmost part of the non-spinning puck, that puck will want to rotate about the east-west axis counter-clockwise when viewed from the east. This should all seem intuitive. The next bit is harder to comprehend.

We now impart a force on the southernmost point of the SPINNING puck. That force wants to cause the puck to spin about the east-west axis, but the puck already has a spin. In the same way we add vectors to figure out what the hockey stick does to the moving puck, we must add these spins to get the resultant spin.

Consider the point of your right index finger to be the southernmost part of the hockey puck. Hold that finger behind your head, level with your nose, and practice the motion that would result in the case of a non-spinning puck, a rotation around the ear-ear axis going from behind your head, to your neck, your nose, your scalp, etc. You probably just did a universal hand signal to indicate madness. Haha. Now move your right index finger around your head slowly in the ear-ear-nose plane to simulate the revolution of the spinning puck prior to the force being impressed upon it, go from back of head, to right ear, to nose, left ear, etc.

Now you must add those two spins. Starting at the back of your head, the original spin starts moving your finger towards your right ear, but the rotation due to the force wants to move your finger down towards your neck, so the initial information we get on the resultant spin is that from the back of your head your finger wants to move down and right. What we don't yet know is how much to spin around the ear-to-ear axis and how much to spin about the vertical axis.

An easy way to relate to this motion is a small mass on a string, spinning around the vertical axis. If you were sitting on that mass and unaware of the spinning, you would feel a force away from where the string is attached, a centrifugal force. In fact, you would feel like you are on a pendulum with the restoring force being the centrifugal force (for a clock pendulum gravity is normally the restoring force).

When you perturb a pendulum, it swings one way, slows down, swings the other way, etc. It's initial velocity depends on the strength of the force that perturbs it, as does the amplitude of the swing. However, the time required for a full cycle, called the pendulum's period, is always the same for a given pendulum, independent of the perturbation. For our mass on a string it is given as the square root of the length of the pendulum divided by the acceleration due to the restoring force [P=(l/a)^.5 , if you like formulas]. It’s important to note that the period of these oscillations is independent of the mass.

The acceleration due to the centrifugal force is given by the radius of the rotation times the square of the angular velocity (how fast it's spinning), [a=rw^2 for the formula inclined]. Since the length of the pendulum is the same as the radius of the rotation then the period of the perturbed mass oscillations equals the inverse of the angular velocity.

This means the pendulum does one full cycle for every rotation about the vertical axis.

You now know enough to complete the motion of your right finger. You know that the downwards force on the south point now is just a perturbation of a pendulum, that the pendulum wants to drop down some, return to middle, go up some, and return to middle while your finger goes once around your head. The amount that it goes down (pendulum's amplitude) is dependant on the strength of the perturbing force, so lets keep that force small enough to cause a maximum two inch displacement. Your finger now starts at the back of your head, swings towards the right and down to a point two inches below your right ear, continues to the front of your head and to your nose, around to the left side and two inches above your left ear, and towards the back and down to the starting position.

The work above is just for a point mass on a string. The hockey puck can be split into many point masses. Since the puck is solid, the perturbing force is spread out to the whole puck and each point mass gets a perturbation whose direction and magnitude is based on its location in the puck. This can be shown easily but exhaustively. To convince yourself, first turn the point mass into a barbell by adding an opposing point mass, then keep adding more point masses.

Phew. We just added two spins. Physicists just add vectors. We draw a vector perpendicular to the disk of revolution to represent spin. It's direction is such that it points the same way as your right thumb if your right fingers were curled around it in the direction of rotation. The vectors length represents the speed of the spin (ie rpm).

For our hockey puck it originally spins ccw from above so it gets a big up vector. Our force imparted on the south point causes a slow rotation about the east-west axis so that gets a small vector pointing east. Do a vector sum and you get a big vector pointing up but leaning to the east, which is consistent with a disk spinning fast in a plane that is tipped from the horizontal down towards the east. (Note that the magnitude of the vector has slightly increased. This is very small for these types of perturbations.) Isn’t that much easier than all that pendulum and finger around the head stuff?

Back to the original purpose: gyroscopic precession...what is it? It is just a manifestation of conservation of angular momentum with a few stipulations. We talk about a 90 degree phase lag of movement from an applied force. In fact, the force creates a moment about the center of rotation, which causes a rotation. That rotation is immediate...there is no lag. We say that there is a lag because our inability to easily perceive rotational dynamics causes us to fall back on linear dynamics.

"I push here, disk should go down here. Disk goes down over there instead. Therefore that disk lags." nope. "I push here, disc rotates. Disk is already rotating, so it IMMEDIATELY changes it's plane and magnitude of rotation." yup.

What are these stipulations? One of them is that the perturbations aren’t that large. As you get larger perturbations, other factors cause the resulting motion to be even more complex, but still based on conservation of angular momentum. Since the magnitude of the perturbations depends on the relative size of the perturbations to the spin, gyroscopic precession isn’t seen when the angular velocities are slowed considerably and perturbations are the same size.

Another stipulation is that the radius in the centrifugal acceleration equation is the same as the length of the pendulum. This automatically holds true for solid objects that are free to rotate on all axes through one point, but more complex objects may induce restraints. An example would be a helicopter rotor that flaps about a hinge that is far from the mast. Except for rigid rotors and teetering rotors, this is the case. What happens, going back to my equations is l<r so the period of the pendulum (blade flapping) is less than the period of the spin (rotor rpm). This would reduce the apparent lag, but since cyclic forces have the same period as the rotor, this effect is only noticed by a change in gamma.

There are other stipulations. A general solution for a solid spinning object subjected to external forces would be much too complicated to explain on this forum, or anywhere for that matter. Because it is so complex, assumptions that are valid for the problem at hand are made. The assumptions in the case of gyroscopic precession are these stipulations.


That’s gyroscopic precession. Question that remains is this. Does it apply to helicopter theory?


Yes, if you accept that there are stipulations. But No, to be completely accurate. Truth is we aren’t completely accurate anyhow.

In my opinion, in basic helicopter theory, we should explain conservation of angular momentum well enough to understand what I’ve written, use gyroscopic precession as an example of a very specific manifestation of conservation of angular momentum, and then state where helicopter rotors differ. I don’t think we should say helicopter rotors have a phase lag because of gyroscopic precession, but I do think we should say that the reasons that gyroscopic precession occurs are also reasons that explain why helicopter rotors behave they way they do, but it’s not that simple.

As I mentioned, I’m not an expert in helicopter theory. I don’t know fully how they fly. I do know some of the physics behind it and that except for very specific cases gyroscopic precession does not really apply. Why it doesn’t apply is because the rotor system does not meet the stipulations that must define a gyroscope. It’s got nothing to do with whether aerodynamic forces are stronger or if the proper explanation is called aerodynamic precession. I recognize that the truth is much more encompassing than what I've written here, but I believe many have misled themselves by discounting gyroscopic precession and not knowing how to conserve angular momentum.


Matthew.
_______________________

Responses to individual posts follow (for all to read):


_______________________


Dave said, “I believe that a simple teetering rotor, with no delta3, exhibits a 90-degree phase lag, which is totally caused by the blade flying to position. Perhaps aerodynamic precession, but not gyroscopic precession.”

You’re right in a way, because you can demonstrate this type of movement with pure kinematics. However, conservation of angular momentum is buried inside those kinematics, same as you can determine mass and velocity of an object if given it’s kinetic energy and momentum. You’ll find that the work leads you to the simplified explanation of the spinning pendulum that I gave.

Also, “In [ShyTorque’s] first instance, because the rotor is rigidly attached to the helicopter, the mast and helicopter will be pried (rolled) to the right”

Actually, gyroscopic precession is a very good way of describing the rigid rotor. The mast and the helicopter would roll right only if the rotor wasn’t turning. With the rotor turning, everything pitches nose down.

Finally, “I do not believe that the activities of an individual blade can be related to gyroscopic precession.”

As a point mass can show gyroscopic precession, so can a single blade. If you have a bunch of blades connected to one hub, they don’t have to react to each other because they each generate their own perturbing forces. In effect you have a number of gyroscopes spinning in close formation. (Of course, I say a single blade can do this, but the blade must be built within the mentioned stipulations. Most blades do not exhibit true gyroscopic precession.)


ShyTorque, I enjoyed your analogy. It does make things clear. However, you seem to be considering that gyroscopic precession somehow needs the force to be exerted through the mast. The force only has to result in a moment about the center of revolution. You can do this by torquing the mast, blowing on the tubes, using a magnet, etc.

You mentioned that your rigid system, “…will exhibit the two properties of a gyroscope, namely rigidity (it wants to keep spinning in the same plane) and precession (any force applied to the rotor mast in an attempt to tilt the system will appear to act 90 degrees further round to the direction of application until the plane of rotation of the system aligns with the force and it can no longer act).”

It is true that rigidity and precession are qualities of a gyroscope but they are also both direct results of conservation of angular momentum.

Lu, I hope this isn’t a private thread…I wasn’t invited. Please comment on what I’ve written.

HeloTeacher, as the blades slow down, the perturbations have to be even smaller to stop other conservation of angular momentum effects from dominating. The obvious test of this is dangerous and destructive…comparing the effects of large cyclic inputs at different rotor RPMs. I think leaving this to models and engineers is a better plan than any of us trying it ourselves. But I suspect that is part of the reason why cautions have arisen for cyclic inputs at low Nr.

Nick Sezzed, “The old bugaboo about Gyroscopic Precession is quite mythological, but almost impossible to squelch, because it seems so plausible, and the real issues are so difficult to describe intuitively.”

Correct, but it’s not really mythological and conveniently plausible, it’s just close and based on the exact same concepts as the truth.

And, “It turns out (in math that gets pretty stinky) that the blade resonates at 1 per rev, because the centrifugal spring changes its force with rpm, so it always allows the blade to resonate at its whirling rpm frequency.”

Actually, for small amplitudes, the natural frequency doesn’t depend on the centrifugal force or the rpm. The resonant frequency is dependant only on mass distribution in the blade, and the center of rotation. For larger amplitudes the one per rev doesn't hold. I doubt if large enough blade movements occur.

The math you’re talking about that describes the truth about helicopter rotors is simplified in this post, but here it describes gyroscopic precession. That’s not just coincidence. Gyroscopic precession really is quite close.


Matthew Parsons
[email protected]

[ 06 August 2001: Message edited by: heedm ]

heedm
please read my post at the top of the 2nd page, do you think the experiment should work? you would 'see' the Gyroscopic precession before the disc came to rest at a nose down atitude. i dont have access to a chopper at the moment otherwise i would know.

dave
you:When one starts to think of the rotor disk as a rotating body, then their thinking starts to get a little tipsy.
the rotor disk is a rotating body(disc) using air to change its axis! hic'up! :p

Matthew Parsons presented some cogent arguments about precession.

Some proofs for your consideration that the blade is bouncing up and down, and not precessing:

The blade changes its gamma based on its inertia, its flapping hinge geometry, its forward speed, its hinge offset and its aerodynamic damping. We can make major changes to the phase of the rotor with these terms. We can even change gamma by putting a weight somewhere on the span of the blade!

A gyroscope changes its 90 degree precession angle only if you move it to the Bizarro Universe, where there is another Law of Conservation of Angular Momentum. If someone can show me a Gyroscope that changes its precession angle, I'm listening.

The equations of motion of the rotor blade flap behavior contain terms for the rotational speed, and certainly account for the change in CF as the principle term that automatically "retunes" the blade to resonate at 1 per rev. It is the dynamic response of the blade's flapping as opposed by the restoring CF that makes it resonate. No CF, no resonance.

The Bifilar pendulum absorbers on many Sikorsky rotors (and inside many older recip engines) is a lag resonant device that behaves exactly as the rotor blade does, except it does it in the in-plane direction. It also self tunes to the operating rpm of the rotor.

heedm,

Thanks for your reply. In my analogy of the fully articulated rotor head, I was just trying to make the point that in this particular case we had a rotor head that could not be controlled through the rotor mast, unlike the previous "rigid" rotor, because the simple articulation by cables would not transmit a force to the gyroscopic arms. Of course, as you state, any displacement of the arms by other means would result in precession of the rotor system but would not affect the mast. This is my main point. A helicopter rotor produces gyroscopic behaviour, but as a by-product of aerodynamic reactions on the blades and not by the pilot's controls causing gyroscopic precession directly. However, it is the latter forces, "feeding back" through the aircraft structure that cause the hull to follow the rotor.

I think this entire discussion (previously an argument, on another thread) actually started because of a disagreement over "cause and effect", namely does gyroscopic precession result in aerodynamic effects or rather aerodynamic effects resulting in gyroscopic precession?

I strongly favour the latter as far as helicopter control is concerned.

ShyT

I’ll reiterate. I am not an expert on helicopter theory. My explanation was merely a description of gyroscopic precession. I discussed helicopters just to illustrate where the gyroscopic precession breaks down.

vorticey, I suspect your theory would work on some helicopters and not on others. Many things that affect gamma are dynamic and do not apply to steady state conditions. Delta 3 appears to be one of them, it comes into play only when the tip path plane and swashplate are not parallel. I’m definitely not the one to ask for this.

Nick said, “Some proofs for your consideration that the blade is bouncing up and down, and not precessing”

You’re right, the blade is bouncing up and down. At some point prior to max upwards deflection, the blade pitch is at a maximum. This is obvious if you think about it. We apply a force to a blade that causes an acceleration, which in turn causes displacement. Although it is an instantaneous process, we don’t see what we consider to be the full result of the maximum force until a number of degrees later.

The blades are rotating. They are constrained to either pivot about a flapping hinge or to bend over their length when subject to forces parallel to the rotor axis. Because of this you can’t just push on the blades and expect them to move under your finger. They will start moving immediately, but you won’t see max deflection until later on. It won’t always be 90 degrees because of the geometry of the system, notably the flapping hinge, and because of the complexity of rotors.

The blade doesn’t “spin…with a motion in which the axis of rotation sweeps out a cone” (Encarta World English Dictionary) so by definition it does not precess.

The ways that you can change gamma are consistent with what I’ve written. Adding the mass to the blade changes the moment of inertia of the blade which changes it’s resonant frequency. That will definitely change gamma. Keep in mind that all the forces on the blade are not necessarily in phase with cyclic input. The net result could change gamma even on a system that exhibits a true 90 degree phase lag.

I can give you a fairly simple rotating system that shows a precession of 45 degrees, and can be adjusted for other precession angles. However, it doesn’t fit into the definition of a gyroscope so it doesn’t qualify as a gyroscope that changes it’s precession angle. You’re right that you’d have to go to Bizarro world to see that.

I’m not sure what you mean when you discussed the dynamic response and the blades resonating. The equations of motion can fully describe the motion of the blades without ever talking about conservation of angular momentum. That does not negate what I’ve said. Conservation of angular momentum is buried inside the equations of motion. Also, the resonant frequency of the blade is dependant on geometry and mass distribution, not any dynamic factors.

For the bifilar pendulum dampers, I bow to your knowledge.

ShyTorque said, “…does gyroscopic precession result in aerodynamic effects or rather aerodynamic effects resulting in gyroscopic precession?”

Neither. Aerodynamic effects control the rotors. Gyroscopic precession is a close explanation of why the aerodynamic forces appear to be out of phase with their result.

I need a good helicopter aerodynamics textbook. Anyone have a recommendation?

Matthew.


"In this philosophy particular propositions are inferred from the phenomena and afterwards rendered general by induction.", Sir Isaac Newton

[ 06 August 2001: Message edited by: heedm ]

ShyTorque:

>One thing that occurred to me earlier is that a "rigid" rotor is not actually completely rigid in the literal sense <
Agreed. My description was not expressed clearly enough. The use of the expressions "totally rigid rotor" and "really rigid rotor" are intended to represent a non-existent and theoretical rotor. A rotor that is able to achieve absolute rigidity. This theoretical rotor should exhibit gyroscopic precession. As a rotor's rigidity decreases from this absolute state, so will the amount of gyroscopic precession that it exhibits.

At the other extreme, we have the teetering rotor that probably exhibits no gyroscopic precession. Between these two extremes will be the so-called rigid rotors.

_____________________

heedm;

Thanks for a very elaborate description of gyroscopic precession.

>>Also, “In [ShyTorque’s] first instance, because the rotor is rigidly attached to the helicopter, the mast and helicopter will be pried (rolled) to the right” <<
>Actually, gyroscopic precession is a very good way of describing the rigid rotor. The mast and the helicopter would roll right only if the rotor wasn’t turning. With the rotor turning, everything pitches nose down. <

Like ShyTorque, perhaps your statement above is also based on my unclear description of 'absolute rigidity'. The rotor above must be turning to obtain both aerodynamic precession and gyroscopic precession. I agree that gyroscopic precession will pitch the nose down. But also, because this extremely rigid rotor does not flap, aerodynamic precession (maximum downward force on the right, assisted by maximum lift on the left) will want to roll the craft to the right.

_____________

There appears to be one major difference between the gyroscope and the rotor of a helicopter. The gyroscope has a large amount of relative mass and its moment arm is approximately 98% of its radius. The helicopter has a very small amount of relative mass and its moment arm is approximately 45% of its radius. To me, this implies that, if gyroscopic precession does play a part in rotor dynamics, its part will be very small.

The following is a graph that has been used by Prouty and by Stepniewski & Keys. http://www.synchrolite.com/0941.html#Phase_Angle It shows that as the rotor's stiffness increases, the phase angle of the rotor decreases. The hypothetical absolutely rigid rotor that is mentioned above, can be seen to have a theoretical phase angle of 0-degrees.

To achieve this rigidity, the weight of the rotor will be quite heavy and therefore gyroscopic precession must become a factor. The aerodynamic precession of 0-degrees will work in conjunction with the gyroscopic precession of 90-degrees and a resultant phase angle of say 4-degrees will result.


Theoretically speaking.

[ 07 August 2001: Message edited by: Dave Jackson ]

To: Dave Jackson

I read the article about the Cheyenne and the author got it almost perfect. However his reference in comparing the stabilizer bar on the Bell to the control gyro on the Cheyenne is incorrect. He properly states that the control gyro in its’ precession of 90-degrees is the motivating force in changing the pitch of the blades to cause a gyroscopic reaction 90-degrees later. He properly indicates that the pilots initial input to the swashplate and the compression springs is 180-degrees out of phase with the direction the pilot wants to fly. The input is made into the control gyro and it responds 90-degrees later and the blade disc responds 90-degrees after the control gyro change the pitch in the advancing and retreating blades.

One point he left out in his addressing blade response to control input is that the Cheyenne flies like a fixed wing aircraft. On a conventional helicopter the helicopter will continue to fly in a given direction as long as the cyclic is maintained in a given position that relates to the direction being flown. On the Cheyenne as soon as the pilot gets the desired attitude or direction he moves the cyclic stick back to neutral. The gyro having rigidity in space maintains the position the pilot had commanded it to and it continues the pitch change input necessary to maintain the direction or attitude of flight.

Here is a point to consider when looking at the crash of the first Cheyenne and the breakup in the wind tunnel. Once the helicopter attains sufficient speed so that the wings are lifting the helicopter the pilot lowers the collective and the helicopter flies like an autogyro. One problem with an autogyro is that it flies in low pitch and the blades in this condition are extremely sensitive to cyclic pitch input. Under the proper conditions the introduction of cyclic cause the blade to go unstable and maybe this was a contributing factor in the loss of the two helicopters and the death of the test pilot.

Regarding a comment referencing Ray Proutys’ explanation of the Cheyenne rotor system the Ring gyro was mounted on the proof of concept vehicle and only on that vehicle. The others used a gyro similar to that used on the Cheyenne.

Here is another point that he did not address. When sitting on the ground all cyclic input is locked out which immobilizes the stick. If the stick were displaced on the ground the helicopter would tip over.

If you will allow me to repeat myself, I asked that this thread be created so that individuals could expound on their theories relative to gyroscopic precession and when all inputs were made to compare notes and see if you could agree on a common and acceptable theory. Comparisons were made to spinning hockey pucks, bicycle wheel, bicycle wheels with only four spokes and several other strange concepts that were all equally difficult to follow.

Since most of you are pilots why can’t you reference the gyros that are spinning at great speed just a foot or two in front of your nose. Or, why can’t you reference a gimbaled gyroscope that most of us have seen in science class or flight or mechanics school.

[ 08 August 2001: Message edited by: Lu Zuckerman ]

[ 08 August 2001: Message edited by: Lu Zuckerman ]

Lu;

The gentleman who wrote the article on the Cheyenne is Doug Marker. Doug appears to be the marketing point man for the CarterCopter. He would probable take great interest in the comparisons between the Cheyenne and gyrocopters.

He has not yet responded to my e-mail, about his previous thread on gyroscopic precession. You may wish to e-mail him at [email protected] to see if he wishes to comment on your points, or participate in this thread.


There would be no reason for discussions if there weren't differences of opinions. How boring.

Lu said, "Since most of you are pilots why can’t you reference the gyros that are spinning at great speed just a foot or two in front of your nose. Or, why can’t you reference a gimbaled gyroscope that most of us have seen in science class or flight or mechanics school."


Reread my post, where you see "hockey puck" insert the words "gimballed gyroscope".

The point is that attitude indicators, toy gyroscopes, science class gyroscopes, suspended hockey pucks, etc. all fit into the constraints that I identified. Most rotor systems do not.

Matthew.

To: heedm

You have just expressed your opinion and it differs from mine. Opinions are like a$$ h***s. Everybody has one. Because your opinion differs from mine does not make you right and me wrong. We differ in the details and you say that gyroscopic precession has nothing to do with helicopters but everything to do with spinning hockey pucks and toy gyroscopes. If you want to believe that and it works for you then it’s OK with me. Just accept that there are alternate theories for every subject. That’s why there are so many scientists and engineers. If there were only one theory to cover a given area of science we would still be trying to make gold from lead.

To: All

In the Sikorsky Blue Book (Sikorsky Helicopter Flight Theory for Pilots and Mechanics) they discuss the aerodynamic theory proposed by members of the forum that are based in the UK and several of its’ Colonies and it is incomplete agreement with them. In this theory the pitch is changed in the blades cyclically and as pitch is removed from the blades they dive and if pitch is added to the blades they climb. If they didn’t carry the theory beyond this point then it would be true that Lu Zuckerman is full of crap. However they didn’t stop there as several pages later they added the following:

“We have stated that by means of cyclic pitch change, we make the blades climb from point A to point B and then dive from point B to point A. In doing so we effectively tilt the rotor in the direction of desired flight. In order for the blades to pass through points A and B it is obvious that the blades must flap up and down on a hinge.

One might be led to think that at point A the blades are at their lowest flapping point they would also be at their lowest pitch. And that at point B where they are at their highest flapping, they would also be at their highest pitch. If only aerodynamic considerations were involved in this statement it could be considered to be true. A Rotor system however has the qualifications necessary to take on certain properties of the gyroscope.

While we are not necessarily interested in the gyroscopes’ property of rigidity in space, we are interested in its’ property of precession.

Gyroscopic precession is an inherent quality of rotating bodies in which an applied force is manifested 90-degrees in the direction of rotation from the point where the force is applied.

Considering a rotating disc turning in a counter clockwise as shown in the illustration a downward force to the side of the disc would cause the disc to tilt downward 90-degrees in rotation from where the force was applied. Thus, to achieve a forward rotor tilt in a counter clockwise rotor system the force causing the blades to flap downward over the nose must be applied to the rotor on the right side of the helicopter while the force causing the blades to flap upward over the tail must be applied on the left side of the helicopter. 90-degrees of rotation from where the forces were applied, the blades will flap to their highest and lowest position. The text goes on describing the mechanics of the system that input pitch in the blades at the specific time in their period of rotation.

This is what is being taught at the Sikorsky Service School and based on what is contained in my Bell and Boeing helicopter training manuals it is also taught in those schools as well.

Based on the text in the Blue Book if you only read certain pages then The UK and OZ types could claim victory. However if you read several more pages in that same text you will see that gyroscopic precession is what is taught in the factory schools in the United States. If some of you might remember that on a long ago post I asked several members from the UK how they reconciled the different approaches to teaching the subject when they attended a US sponsored school. From what I understand the subject is not even covered in the Robinson schools.

Lu said:
Based on the text in the Blue Book if you only read certain pages then The UK and OZ types could claim victory. However if you read several more pages in that same text you will see that gyroscopic precession is what is taught in the factory schools in the United States.

Nick sez:
I guess if we wanted to just have the book read to us, we could have asked Nicole Kidman and enjoyed it more.

These books that Lu quotes were written as a sort of Classics Illustrated comic book version for mechanics and electricians to get enough of the basics to keep from crushing their fingers as they turned the wrenches. Any semblence between them and a reasonable engineering understanding of the underlying physics is almost coincidental, Lu.

You are at it again, Lu. To paraphrase your interminable posts, "Anytime I appeared to be wrong it was because someone told me to say the wrong thing, and anytime I am right, it is because I have been around since Christ flew crew changes on the Arc."

"One might be led to think that at point A the blades are at their lowest flapping point they would also be at their lowest pitch. And that at point B where they are at their highest flapping, they would also be at their highest pitch. If only aerodynamic considerations were involved in this statement it could be considered to be true."


Lu; Where did you say this came from???

If a person believes this statement, then they will believe anything, such as the very next statement.


"A Rotor system however has the qualifications necessary to take on certain properties of the gyroscope."

To: Dave jackson and Nick Lappos

Dave, this material that I quoted came from the text used in the Sikorsky service school and it covers all aspects of rotary wing flight as it applies mainly to Sikorsky helicopters and can be applied to any helicopter with an articulated rotorhead. The basic theory applies to all helicopters including Bell, Aerospatial and Boelkow rigid rotors.

Nick I believe you have done your own company a disservice in describing the Blue book as a comic book presentation that is designed to keep mechanics from crushing their fingers. The diagrams found in the Bluebook can also be found in many engineering texts covering the subject. Using your position to describe the Bluebook as a comic book will give those on these threads the idea that the material should be discounted because it is presented in a childlike way. I would strongly suggest you go over to the service school and pick up a copy. If you feel the information is incorrect then give them sh!t and not me for quoting from what many in the industry consider to be the bible.

Here should be the title of your book:

LZ: I am the cheese!

Another chance lost due to ignorance and arrogance to try to place yourself way above where you really are.

Wannabe.

You can talk about different theories all day long, but your opponants are talking from facts, and there is a big difference between the two.

You saying that there can be many theories is just another excuse to not throw out yours, since it has been proven wrong.

You can preach it any way you want, but each and every time you have brought it up, it has been shot down. You can continue to bring it up, but that will not turn that Theory into FACT.

Since you have not brought anything new to it, as with any other theory, then you either change it and see if what it predicts is true, or you discard it.

Now, above you tell Heedm that it is now an opinion differential, WELL WHICH IS IT?

Or do you now accept that as a theory it is trash, and to now use the label of opinion you may continue to drivel it to everyone?

We should petition Capt PPRUNE to place the following disclaimer on your title block:

I am the Lu Zuckerman.
I am not a pilot.
I am not an engineer.
I am not involved, nor have experience with
rotor head design/aerodynamics to be making any type of assertions to those who do on this forum.
I am simply a wannabe guru.
I am never wrong.

My heli post's are for entertainment purposes only, and should not be used or considered in actual flight operations/planning.

[ 10 August 2001: Message edited by: RW-1 ]

Lu said, "[Matthew has] just expressed [his] opinion and it differs from mine."

Lu, our opinions differ in how helicopter theory should be taught, but the information I gave about gyroscopic precession is fact not opinion.

I'll restate my position for you. Gyroscopic precession is a good way of teaching helicopter theory, but it is not completely accurate. I believe that a more fundamental look into rotational dynamics is better. Use gyroscopic precession as an example but don't teach it as the be all end all theory that it is sometimes presented as.

The point I was trying to illustrate is that all these theories are actually snippets of the same theory. The math that Nick referred to that substantiates the blade flying to position theory is the same math I used to derive gyroscopic precession in a very simple rotating body (that's why I used a hockey puck rather than AI or gimballed gyro).


I would be careful in substantiating a theory in helicopter dynamics by stating that it is the way that it is taught in training schools. That, to me, is like saying an introduction to computer science gives you enough theory to design a workstation. Facts are often somewhat inaccurate on purpose when being presented to non-experts. This is because the full story is far too complicated for the scope of the crowd, and a close enough description creates better understanding in general. This is why I see teaching helicopter dynamics using gyroscopic precession to be valid. Doesn't mean it's right.


In a different post, Lu said, "One might be led to think that at point A the blades are at their lowest flapping point they would also be at their lowest pitch."

Even if you ignore all the rotationally related theories, it is still obvious that the blade is moving (descending) prior to arriving at it's lowest point of flapping. The blade doesn't just magically stop there, the "brakes" are put on prior to arriving there. This means that pitch must be increased from it's lowest value prior to arriving at the blade's lowest point of flapping.

Lu also said, "If there were only one theory to cover a given area of science we would still be trying to make gold from lead."

It can be done, it's just not economically feasible.

Matthew.

To: heedm

Granted, the blades do fly to their assigned disc position due to the introduction of cyclic pitch, which substantiates the theories proposed by many individuals on this forum. Many of these individuals discount the theory of gyroscopic precession being involved in any displacement of the blades / disc with the introduction of cyclic input. If gyroscopic precession plays no part in the tilting of the disc either as a single entity or as individual blades then please explain this.

Lets assume that the optimum phase angle is 90-degrees although with what Nick indicated this is not always true. However for the purposes of this explanation we will accept 90-degrees as the phase angle for the helicopter systems being discussed. When Sikorsky helicopters were designed it was assumed that the phase angle was 90-degrees and to accommodate pitch input and proper pitch response they offset the servos by 45-degrees and the pitch horn led the blades by 45-degrees. When the pilot pushed forward cyclic the fore and aft servo moved downward. Assuming that the advancing blade was disposed over the right side of the helicopter it would be at the minimum pitch position. The opposite blade would be at the highest pitch position. 90-degrees later the blade on the right side would be at the low flap position and the blade that was over the left side would be at the high flap position. However as the advancing blade approached the longitudinal axis it would already be increasing in pitch. The opposite would be true for the blade passing over the longitudinal axis over the tail.

A similar situation exists on the Bell rotor but in the Bell the pitch horn leads by 90-degrees and the cyclic pitch activity would be the same as that on the Sikorsky. All other helicopters are similar in that the pitch change is maximum 90-degrees prior to where the maximum result will take place. The only two helicopters that I know of that do not have a 90-degree offset in the controls are the Lynx and the Robinson. Now, maybe Nick might be aware of others that don’t have a 90-degree phase angle at least in the way the controls are set up. One that Nick mentioned was the S-76 and the reason the controls were not set up in the normal Sikorsky design concept was depending on who tells the story due to an engineering screw-up. Sikorsky had to do a lot of test flying to design compensation into the mixing unit in order to counter the lack of a 90-degree offset in the control system.

In the light of the above I ask why the 90-degrees if gyroscopic precession is not involved. Why couldn’t they just put the control inputs anywhere and just let the blades seek their own position.

LU. Here we go again.....

You said: >>Assuming that the advancing blade was disposed over the right side of the helicopter it would be at the minimum pitch position. The opposite blade would be at the highest pitch position. 90-degrees later the blade on the right side would be at the low flap position and the blade that was over the left side would be at the high flap position. However as the advancing blade approached the longitudinal axis it would already be increasing in pitch. The opposite would be true for the blade passing over the longitudinal axis over the tail.<<

NOT TRUE (but getting closer)

Please, as I have said before, go back and learn about flapping to equality. While you are at it, try cyclic feathering, and the terms pitch and Angle of attack too. Arm out the window gave you an excellent description of flapping to equality in your last thread, yet you totally ignored it.


As I posted in the other thread, (in a suggestion you totally avoided confronting) you need to go back to these fundamental POF in order to attain the basic background required to try and understand the theories (and REALITIES) discussed on the forum.

There is no better evidence of your need to do this than your question at the end of your last post:

You asked: >>In the light of the above I ask why the 90-degrees if gyroscopic precession is not involved. Why couldn’t they just put the control inputs anywhere and just let the blades seek their own position.<<

Why? Because of flapping to equality and cyclic feathering!!

Arm out the window: can you post an explanation as the start of another thread for Lu's (and my) benefit? Sorry to pick on you but your previous brief explanation was great.

Mine helmut ist now schmoldering.........