Delta-3 & Phase Lag

[Dave_Jackson]

This new thread has been started to explain two specific subjects. It is separated from the [Cyclics, Semantics and Teetering Rotors ~ A question] thread so that both can stay on topic, which is/are different.

IMAO (In My Arrogant Opinion) the following is a valid description of these two subjects. Of course, the thread is always open for a scathing rebuttal.

________________________________

The following is an explanation of delta-3, followed by an explanation of phase-lag. It should be noted that these are two different subjects. The action of the rotor's hub, due to delta-3, and the action of control system, due to phase-lag, are then related.

Please note that phase-lag is also used in conjunction with 'flapping hinge offset'; but not in this thread.

Delta-3:

In a conventional teetering rotor, the application of 10º of cyclic stick will result in the swashplate [control plane] having a 10º tilt. This, in turn, will change the plane where an observer sees no variation in cyclic pitch [no feathering plane] so that it will have a 10º tilt. This cyclic pitch of the blades will then result in a 10º tilt of the disk [tip path plane]. It should be noted that the stick input [control plane] and the rotor output [tip path plane] have identical value of 10º. It should also be noted that if the cyclic stick was somehow instantly advanced by 10º then the disk will tilt by 10º within one revolution.

A teetering rotor with delta-3 operates differently. To set the boundaries of delta-3 it should be mentioned that 0º of delta-3 will be the same as no delta-3. In other word, the amount of flap equals the amount of pitch, and the scenario in the previous paragraph will take place. We could say that 100% of the change in cyclic stick pitch gets through to the blades.

If there happened to be 45º of delta-3 then every degree of flap will remove one degree of pitch. This means that none (i.e. 0%) of the change in cyclic stick pitch gets through to the blades

Lets now assume that the rotor has 20º of delta-3. This means that approximately 70% of the cyclic stick pitch get through to the rotor. In other words, the application of 10º of cyclic stick will result in the swashplate [control plane] having a 10º tilt. This, in turn, through the modified pitch horn, will change the plane where an observer sees no variation in cyclic pitch [no feathering plane] so that it will have a 7º tilt. This cyclic pitch of the blades will result in a 7º tilt of the disk [tip path plane]. In other words, the stick input [control plane] and the rotor output [tip path plane] are not identical.

It should be noted that if the cyclic stick was somehow instantly advanced by 10º then the disk will have tilted by 7º within one revolution. There is still a discrepancy of 3º. This means that the tip path plane will tilt 70% of the 3º in the next revolution, which is 2.1º. This means that the tip path plane will tilt 70% of the 2.1º in the next revolution, and on, and on, to infinity. In other words, with delta-3 the tip path plane will have a slower response to the instruction from the control plane.


Phase Angle:

In an articulated rotor, the phase angle is related to the frequency of blade flapping. A greater flapping hinge offset means a shorter blade, which means a higher frequency and a faster flap to position. Because the blades flap to position sooner, the instruction to flap must be delayed, so that orientation of the cyclic stick and the orientation of the disk are in the same direction.

In a teetering rotor, delta-3 does not change the frequency of the blade flap (teeter). All that delta-3 does is reduce the amount of flap (teeter), not the speed at which it flaps. In other words, the teetering hinge with or without delta-3 has a frequency matching that of the rotor. If the phase lag angle is reduce by 20º, from 90º to 70º, then the location of lowest and highest teetering will be 20º further around the mast. There will still be 180º of increased pitch and 180º of decreased pitch.

The following two graphs, which were stolen from Ray Prouty and Shawn Coyle without permission, may help explain the activity.
http://www.UniCopter.com/Pitch_Roll_1.gif http://www.UniCopter.com/Pitch_Roll_2.gif
The graphs are rough approximations but it is interesting to compare them. Both show very little lateral cyclic stick near hover and both show a reasonable amount of left cyclic stick at fast forward speed. The obvious difference between the two is the opposite lateral cyclic at moderate forward speed.

It is assumed that the first graph represents articulated rotors and basic teetering rotors. As the forward velocity increases, the craft will experience 'transverse flow effect' and then the effect of coning. Both effects require the application left lateral cyclic.

It is assumed that the second graph represents a teetering rotor with delta-3, such as the Robinson. In this situation, the phase lag has biased the teetering to left. Therefor at moderate speeds there is a need for a small amount of right lateral cyclic, whereas at fast forward speeds there is a need for a small amount of left lateral cyclic.


Conclusion:

Delta-3 and Phase Lag are two distinctly different functions. Delta-3 'softens' the response of the rotor to the cyclic control. Phase Lag repositions the radial orientation between the cyclic stick and the rotor disk.

In addition, I can see no reason why the delta-3 angle and the reduction in the phase angle need be the same, other than that of keeping the pitch link vertical.

:8

[Lu Zuckerman]

To: Dave Jackson

Regarding your comment about the rapid adding of an additional 10-degrees of cyclic the disc will tilt the additional 10-degrees within one revolution. Ask any one that learned to fly in a Bell and they will recount stories about how difficult it is to hover because of the slow reaction of the rotor to control input. In most cases the new pilot will over control by adding more cyclic because the rotor has not yet responded. Based on demonstrated fact the disc will not respond in one revolution.

Quote: “If there happened to be 45º of delta-3 then every degree of flap will remove one degree of pitch. This means that none (i.e. 0%) of the change in cyclic stick pitch gets through to the blades.”

This could only exist in a theoretical situation and it would require changing the pitch horn. On the Bell there is in effect a delta hinge effect but it requires that the pitch link / pitch horn interface be above the teeter hinge. In an Ideal situation if you could maintain this alignment in flight there would be no pitch flap coupling. The same applies to a fully articulated rotor system. On the Sikorsky system (maybe not on the S-76) there is an offset of 45-degrees between the blade and the pitch horn / pitch link interface and, these blades have pitch flap coupling.

Quote: “If the phase lag angle is reduce by 20º, from 90º to 70º, then the location of lowest and highest teetering will be 20º further around the mast. There will still be 180º of increased pitch and 180º of decreased”.

Are you describing what occurs on the Robinson if you are, just change the numbers to 18-degrees and 72-degrees. If you are, are you saying that the disc will tilt down 20-degrees (18-degrees) beyond the mast in the direction of rotation.

I’ll add more when what you have stated fully sinks in or you further explain what you said using mechanic or non engineer speak.


:confused: :hmm:

[Dave_Jackson]

Lu

Re your point #1: I think that they are referring to the response of the helicopter not the disk. Prouty says that a disk will respond within one revolution. Note that he is probably not considering the Robinson.

Re your point #2: Yes. Theoretically, with a delta-3 of 45º, ever degree of positive flap change will result in one degree of negative pitch change. The moving locations of the various flight-control joints, plus dynamic effects, will change this theoretical purity.

Re your point #3: Yes. This is the same as what you have been saying all along. :ok:

[Lu Zuckerman]

Dave if you insist on slowly coming around to my point of view I would suggest you put on a flak jacket. When those individuals on these threads come to the realization that you are espousing the same theories that I did they will attack you just like they did me.

:ouch: :ouch: :ouch: :hmm:

[Spaced]

Just wondering what are the disadvantages of the delta 3 hinge. If it reduces flapping, isnt it a good thing?
I attended a UH-1H ground school a few days ago and the 45 delta hinge is on the tail rotor, are there any helos that use the 45 delta on the main rotor?

[NickLappos]

Dave,

I think you tend to explain things backwards - not wrong, but rather mixing cause and effect. Let me try to straighten things out:

The rotor of a helicopter does not tilt exactly as the cyclic moves, in virtually any case, it moves a few degrees off, depending on a raft of factors. That is documented in many posts on this site. Most helos have a bunch of mixing of long and lat cyclic in an attempt to make the stick feel close to correct. It mostly works. We call that mixing "phase angle" adjustment, and we tell newbies it is for "gyroscopic precession." That fiction works, and most of us sleep at night as a result.

On top of that, we sometimes mix in some delta three, where the flap hinge is not aligned with the pitch horn, so as the blade flaps, it reduces (or increases) blade feathering pitch. Positive delta three makes the blade feather less. Delta three is put in so that the blade delivers less force to the head due to outside disturbences, such as gusts. It acts like automatic cyclic stability, so it is often used to smooth out rotor response to gusts (makes a more stable helicopter). It is also good at making a tail rotor withstand the speed differences between a hover and Vne, so lots of delta three is used on tail rotors.

The angle of delta three is simply the angle between the flap hinge and the blade pitch change horn, relative to the tangent to the rotational axis at the flap hinge location. For a horn that is in front of the flap hinge, if that horn were farther out in raduis from the flap hinge, the delta three would be positive, in that an up flap (caused by an increase in lift) would cause a reduction in blade pitch (and a reduction in the blade lift).


One real effect of delta three is to make the blade flap about a new axis that is not perpendicular to the radius. With delta three, the phase angle is screwed up, so we must adjust it exactly one degree per degree of delta three. Why? The blade actually rises earlier with positive delta three, so it needs less phase angle. The S-76 has 17 degrees of delta three (added for gust alleviation) so the mixing angle is 17 degrees less. This makes the cyclic feel correct, and that the nose goes down with forward stick.

Lu used to think the geometry of the Robinson head made the cyclic behave differently, because he did not understand the delta three correction, I think he has changed since then, but he can tell you that.

Now for your conclusions, delta three does soften out cyclic so we need more cyclic range to get the same control. This is not all bad, but the head geometry must be designed with this in mind. Delta three softens out the aircraft's response to gusts, so it acts like a stability augmentation system, a powerful one.

Delta three does make a change in gamma (phase angle0 and must be accounted for in the rotor design, or else the cyclic will feel funny, in that forward will produce some roll.

The cyclic plots you show are quite representative of common helos, but don't think that the rotor head is the only way that moments are produced. The lateral stick shift can be a product of the delta three (its angle is the reason why the first plot moves off to the right) but it also follows the lateral balance of the aircraft, which can be changes thru CG or through the horizontal tail. A left side tail will produce a strong download at speed, and require some right stick to balance (and vice-versa).

[Dave_Jackson]

Spaced,

The incorporation of delta-3 into a main rotor may be a good thing. It is one of many, many arraignments that have been tried. Delta-3 is used in the Robinson and the K-Max, and both are still being built, whereas most of the other ideas have come and gone.

A delta-3 angle of 45º on a tail rotor means that all flap will be opposed by an equal and opposite pitch, so as to maintain the blade in its 'home' position. On a main rotor the same thing will take place. In other words, the cyclic stick will be useless because a delta-3 angle of 45º not allow the blade to leave its 'home' position. On a tail rotor, of course, there is no cyclic control and there is no desire to tilt the disk.


Nick,

You and Lu have mentioned some of the nuances of delta-3 and phase lag where I haven't, but we appear to be pretty well in agreement on the major points.

One area might do with some clarification. You said; "I think you tend to explain things backwards - not wrong, but rather mixing cause and effect. " Here we differ. Your emphasis seems to be on gust alleviation, and that is what delta-3 in the tail rotor is all about. The technical discussions about delta-3 and the main rotor, that I have read, tend to put the emphasis on the cyclic control input and the mention of gust alleviation is sort of a by-product.

Consider the following two distinctly different activities;

Delta-3:
A tail rotor does not have cyclic control input (from the pilot). It would therefore be meaningless to discuss phase angle when discussing the tail rotor because there is no phase lag. There is only a specific angle of delta-3, which was selected by the designer to give a specific speed of response to gusts etc.

Phase Angle:
Exclude delta-3 from the consideration. A phase lag can be decreased by rotating the pitch links to the blade's pitch horn by 20º CW or by rotating the swashplates inputs from the mixed box by 20º CCW.

You said that; "The blade actually rises earlier with positive delta three, so it needs less phase angle." On this point, I disagree. I think that this explanation is backwards. It is the Phase Angle that determines the timing of the 'blade rise'. Delta-3's responsibility is only to reduce the amount of the blade rise. In other words, if the pitch link was not vertical, the delta-3 would still pull pitch, but it would be uncoordinated with the phasing.

This is why I think that Lu is correct when he questions where did 17º of the 180º go. In an articulated rotor, the blades will flap to position in less than 90º and thus the control plane and the tip path plane will be coplanar in less than 90º. In a rotor with delta-3, the location of maximum flap will be 90º after the azimuth where the control plane asked for maximum pitch.

Edited to lighten an erroneous statement.

[NickLappos]

Dave,

You and Lu wonder where the 18 degrees go because you don't concieve of the way delta three changes the flapping geometry of the head. No matter how you two wonder, the head knows, that's why the controls must be phased differently, and that's why the S-76 and Robinson have appropriate phase angles, even if they seem wrong to you and Lu.
Every degree of positive delta three reduces the phase angle of the rotor by that same amount. That is a physical fact. The blade operates about an equivilent flapping hinge (the dual pivot points of the flap hinge and the blade pitch change horn) that allows it to flap earlier. You mix the concepts of blade movement with the concept of blade lift (thrust). We are talking about flapping as a physical movement of the blade. If the blade rises, it is moving, regardless if it produces any lift while doing so. Thus, when the blade rises earlier, it needs less phase angle.
The controls of the S-76 are almost perfect in regrad to phase angle, and the phase angle is about 57 degrees.

The use of delta three in the main rotor is almost always to reduce aircraft disturbence to those gusts and to relieve blade stress at the head due to gusts. I know this is true for the S-76 because I was one of those who helped introduce delta three into its design, back in 1974. We specifically chose it so that the ride was more stable, and it works that way, admirably. It also flattens out the cyclic pitch sensitivity, and makes things harder for the designer, who must figure out how to get more feathering angle for the blade because the delta three washes it out.

For the tail rotor, the delta three is not for gust alleviation. If the tail rotor had no delta three, it would build enormous flapping forces as the aircraft built up speed, due to dysymetry of lift, where the forward sweeping blade would have very high thrust, and would introduce very strong moment into the head and shaft. Delta three acts like an automatic stress relief for the tail rotor, that is why most tail rotors have about 45 degrees of delta three. This means that flapping of the tail blade reduces the increase in blade lift to almost nothing.

[Lu Zuckerman]

To: NickLappos

Picture this. The Bell and the Robinson control inputs are the same in that the swashplate will move in the same direction as cyclic input. On the Bell when the rotor is laterally disposed the pitch horn is over the longitudinal centerline of the helicopter so the advancing blade has the lower pitch and the retreating blade has the higher pitch. This is because the pitch horn leads the blade by 90-degrees.

On the Robinson when the blades are laterally disposed the pitch horn has not reached the maximum travel relative to the swashplate displacement. In fact the blade must travel an additional 18-degrees before the blades have maximum input +/-. As the blade travels from the laterally disposed position to the point where the pitch horn has maximum input the blade is changing pitch. Minus for the advancing blade and plus for the advancing blade. The blades do not have maximum input until the blades are disposed 18-degrees ahead of the mast (advancing) and 18-degree behind the mast (retreating).

Getting back to the slight change in pitch between the laterally disposed position and the point where the pitch horn is at its’ maximum displacement the blade is flapping down towards the nose because the pitch horn is following the swashplate tilt. However the blade does not reach its’ maximum pitch change until the blade is 18-degrees ahead of the mast (see above) which means if you subscribe to the phase angle theory the blade will reach its’ maximum displacement in 72-degrees so that it is full down flap over the nose. However if you subscribe to the precession theory (Aerodynamic/Gyroscopic) the blade will have maximum down flap 18-degrees past dead center.

If the blade flap takes place within the 72-degree phase angle please describe the disc plane relative to the horizon.

:confused: Please use language that stupid people like me can understand.

[Dave_Jackson]

Nick,

Yes, there is difficulty understanding some of your points, but, your statement "No matter how you two wonder, the [delta-3] head knows" can not be implying that a dozen pieces of metal in a delta-3 hinge has a higher cognitive ability than Lu or I. ;) Or does it? :(
___________________________

You say; " the S-76 and Robinson have appropriate phase angles, even if they seem wrong to you and Lu"

Now you've really gone and done it. :eek: Who said that the phase angle was wrong. Hell, I've never even said that Robinson's use of delta-3 is wrong. The other thread is currently an attempt to understand his first reason for using it.

___________________________

You say; "The use of delta three in the main rotor is almost always to reduce aircraft disturbance to those gusts and to relieve blade stress at the head due to gusts."

Now you've gone and got yourself into an argument with Frank Robinson. :*

He says; " The R22 rotor system was designed with 18 degrees of delta-three to eliminate two minor undesirable characteristics ..... [1] In a steady no-wind hover, when forward cyclic pitch is applied, the 90-degree rotor disc will end up tilted in the forward direction ....... [2] The other undesirable characteristic in rotor systems having 90-degree pitch links is the lateral stick travel required with airspeed changes ..."
__________________________

You say; "The blade operates about an equivalent flapping hinge ... that allows it to flap earlier."

I disagree on this point. The rotor's delta-3 is working in conjunction with the swashplate's phase-lag. The Robinson's blade will start to flap (teeter) 18º later.

To use an application of forward cyclic as the example, the control plane (swashplate) will be highest at 0º azimuth (the back) and lowest at 180º azimuth. This is in agreement with FR's statement; "The lower non-rotating swashplate is aligned with the aircraft's centerline and always tilts in the same direction as the cyclic stick."

On a Bell-47, with its phase angle of 90º, it means that the blades minimum pitch will occur when the pitch-link - swashplate joint is at 180º azimuth and the blade is at 90º azimuth.

On the Robinson, with its phase angle of 72º, it means that the blades minimum pitch will occur when the pitch-link - swashplate joint is at 180º azimuth and the blade is at 108º azimuth.

In other words, all cyclic control (pilot) induced activity at the blade will take place 18º later on the Robinson than it will on the Bell.

In addition to what the swashplate's phase lag has done, the rotor's delta-3 will decrease the strength (angle) of that which was requested by the cyclic input.


Phase lag is used in conjunction with flapping hinge offset and with delta-3, but I believe that flapping hinge offset and delta-3 are two quite distinctly different activities. An example of this distinction is the fact that flapping hinge offset will reorient the disk faster then a basic teetering rotor, whereas delta-3 will take considerably longer then a basic teetering rotor.

___________________________

No argument with your last paragraph. My use of the word 'gust' was a lousy way of saying 'aerodynamic input'

[Lu Zuckerman]

To: Dave Jackson

"No matter how you two wonder, the [delta-3] head knows" can not be implying that a dozen pieces of metal in a delta-3 hinge has a higher cognitive ability than Lu or I. Or does it?

Dave you have just opened the flood gates of caustic criticism.

:rolleyes:

[NickLappos]

Dave,
I am responding to your first assertion, that phase angle and delta three are not related. You wrote: "In addition, I can see no reason why the delta-3 angle and the reduction in the phase angle need be the same, other than that of keeping the pitch link vertical."

As I have tried to say, the delta three will change the phase angle, so if you took a hypothetical helicopter, with the proper phase angle, and then modified the head with some degrees of positive delta three, you would discover that the phase angle was now wrong by exactly that number of degrees.

This is a simple fact of head geometry, as I have tried to state. Both you and Lu seem to think otherwise, and you are not correct.

When we added the delta three to the S-76, we had to change the mixing to account for the different phase angle. Most 76 pilots know about the "analog beam phase shifter" on the upper deck, which was added to get gamma back to the right setting.

You are correct, however, in that the delta three can be used to straighten out the cyclic, as positive delta three will make the cyclic go to the right with speed, so if is was going to the left, some delta three would straighten it out. Seems like a complex way to do it, however. The angle of the cyclic stick travel would also be exactly the delta three angle.

[Lu Zuckerman]

To: NickLappos

Can you now return to my post above (An honest question) and please respond. Thank you.

:O

[Dave_Jackson]

This posting completely replaces a previous posting that was totally wrong.


Lu,

It looks like Nick got us, again. :ouch:

Delta-3 is a little more complex than we thought. Wayne Johnson in 'Helicopter Theory' explains it in depth, using some weird language called mathematics. He also, very kindly, explains it in the single embarrassing sentence; "Thus pitch-flap coupling introduces an aerodynamic spring that increases the effective natural frequency of the flapping motion ...."

OOPS. Perhaps a dozen pieces of metal in a delta-3 hinge do have a higher cognitive ability we do.


Nick,

You are right. Thanks for the knowledge and for taking the time to drive this to a correct conclusion. :ok:

[Lu Zuckerman]

Dave:

That is all well and good but I am still waiting for NickLappos to respond to my post. Maybe his response will put it to bed for me as well.

:ok:

[NickLappos]

Lu,
Sorry that I didn't specifically answer your question, but here goes:

If you push the stick forward in a robbie, or an S-76, the disk will tilt almost perfectly forward, even though those aircraft have phase mixing that is not 90 degrees. The phase mixing that they have is exactly what they need to make the cyclic behave as desired, and varies from 90 degrees because it must.

Delta three is the biggest contributer, but also blade Locke number is a driver, where the phase angle varies from 90 degrees because of the natural "spring"of the blade (a balance of the aerodynamic forces, and kinematic forces that determine the natural resonance frequency of the flapping axis).

Hope that helps!

[Dave_Jackson]

This is an about-face to nullify the previous about-face. All mea culpas are off.

Nick, Forget my apology. ;)

Lu, You da man. At least, for da moment. :ok:


Both of you guys have made mention of many nuances. We've now got a delta-3 rotor that's pushing more nuances than air molecules. Someone once said that the swashplate is only ideal for a basic teetering rotor and as rotor technology advances, the swashplate becomes less and less capable of providing a satisfactory control input.


Nick,

This whole situation cries out for an 'Absolutely Rigid Rotor'. :D

Seriously, I do not argue with what you say. You and Wayne Johnson are knowledgeable people and you are in agreement; but Lu's questioning does raise an interesting concern.

Forgetting the nuances and accepting the given; Both 'delta-3' and 'flapping hinge offset' introduce a spring, which increases the effective natural frequency of the flapping motion.

This higher frequency will remove the discrepancy between the control plane and the tip path plane in less rotor rotation than it takes a basic teetering hinge rotor to remove it. Therefore, when Lu asks what happens during the remaining, say 18º, nothing happens because the two planes are now coplanar.

Here is the problem, as I see it. A rotor with 'flapping hinge offset' will cause the control plane and the tip path plane to become coplanar well within a single revolution. But, on a rotor with 'delta-3' we have previously said that; " if the cyclic stick was somehow instantly advanced by 10º then the disk will have tilted by 7º within one revolution. There is still a discrepancy of 3º. etc. etc. etc." and that "Delta three softens out the aircraft's response to gusts, so it acts like a stability augmentation system,". Therefore with delta-3 there is a residual discrepancy between the control plane and the tip path plane during the remaining 18º for a number of revolutions.

Perhaps the stick is moved so slowly, in relationship to the speed of the rotor, that Lu concern becomes just another nuance in a bag full of nuances.

[NickLappos]

Dave,
There is no remaining 18 degrees. The rotor flaps so that it is exactly in tune with the pilot's cyclic input, and this is because it moves in concert with the lesser phase angle.

Let me use an analogy. You are always shooting a 30 cal rifle with a 180 grain slug that travels at 3000 feet per second. When you shoot you aim 3 inches high at 100 yards. Everybody always said that they aim 3 inches high at 100 yards. The books said that all rifles require that you aim 3 inches high at 100 yards. We call that normal, it is taught in all the books, and it is gospel.

Somebody comes along with a rifle that shoots a faster bullet, which only needs 1 inch of elevation at 100 yards.

Where did that lost 2 inches go?

If the rotor flaps faster, the flap occurs sooner in the rotation, so the rotor phase needs fewer leading degrees. Is this really that complex??

[Dave_Jackson]

Nick, you asked the question "Is this really that complex??" and the answer, at this point in time, is yes. That is why my former post has been replaced with this one,

You say; "If the rotor flaps faster, the flap occurs sooner in the rotation, so the rotor phase needs fewer leading degrees.". The answer here is also yes, if the rotor flaps faster. However, I see nothing that will cause the rotor to flap faster. Any advantage derived from delta-3 in one 90º sector is a disadvantage in the next sector.

From my [b]current perspective, there are two possible scenarios.

~ One is as you say. The amount of angler flap within a single revolution equals the angular difference between the control plane and the tip path plane. There is nothing left to be done in the remaining 18º and Lu is up the creak without a paddle.

~ In the other, the amount of angler of flap in a single revolution equals the angular difference between the control plane and the no-feathering plane. In this scenario, it takes a number of revolutions for the control plane to become coplanar with the tip path plane. Therefore something must be happening during these 18ºs and Lu has a point. This is the same argument that I made in my previous posting, but in different words.

Currently, I tend to favor the latter.

[NickLappos]

Dave,
With all due respect to your attempts to determine how a blade flaps, you are boggled right here:

"However, I see nothing that will cause the rotor to flap faster."

What exactly DO you know about what makes a blade flap at a given angle? Frankly, not much. Now don't be angry, I don't know much either (I am one fact ahead of you on this!) In fact, the best brains at Sikorsky knew so little about this for the S-76 that we made three sets of mixing bellcranks for the cyclic, and tried them out in flight, and settled on the best compromise for production. I know exactly how the S-76 cyclic behaves, and it is just about right, even though the cyclic phase angle is 57 degrees (33 degrees wrong by the Lu-Dave math).

The belief that the real phase angle is 90 degrees is where you and Lu are stuck. Just when you see the light that this is NOT TRUE, the blade DOES NOT FLAP at 90 DEGREES, your old, solid, comfortable belief kicks in, and you go back around the circle.

OK what can I say? The fact that you don't see why is a puzzle for you. You believe that it must flap at exactly 90 degrees, so all those poor sods at Sikorsky and Robinson who make these machines at the "wrong" angle must be on drugs.

Oh well, I guess it's time for me to give up, but I'll try one more time:

1) The required phase angle is a number that often differs from 90 degrees. The books are wrong when they call it gyroscopic precession.

2) The real phase angle depends on the flapping inertia of the blade, its chord, its rpm, its hinge offset, and several other factors. The real phase angle changes up to 5 degrees, depending on the speed of the helicopter, for pete's sake.

3) The real phase angle has been as much as 135 degrees on some helos, and as little as 57 on others, and these helos all flew nicely, and the cyclics worked like cyclics should.

4) On a robbie it is 72 degrees, on an S-76 it is 57 degrees.

5) The robbie and S-76 cyclic behave properly.

6) Lu and Dave cannot see WHY these statements are true, so they disbelieve them.

7) Nick has reached a nice place to sign off. Adios!

[Lu Zuckerman]

With all of the dialog going back and forth and the explanations provided I have only one question. Where did my 18-degrees go?

:rolleyes: :confused: :rolleyes: :confused: :ouch: :ouch: :ouch:

[Dave_Jackson]

Nick,

I truly appreciate and respect your vast knowledge. You provide information and you provoke thought. During the course of this thread, I have tended to vacillate; it has been an oscillation between the strength of your spoken word versus research, logic and reason.

IMNSHO your conceptualization of delta-3 is wrong. You don't understand delta-3 and you don't understand what I am saying.

You have just said;
" The belief that the real phase angle is 90 degrees is where you and Lu are stuck."
" You believe that it must flap at exactly 90 degrees."

Don't put words in my mouth. Other than in reference to a basic teetering rotor, I have NEVER EVER said that a phase angle must or should be 90-degrees.

Lu's concern about the missing 18-degrees can be discussed later. Furthermore, it is easily explained, if you understand delta-3.

If you want to disseminate false information and then run away with a " Nick has reached a nice place to sign off. Adios!" that's your decision.

But, while you are running, here is a little thing to ponder;

You question the statement; "However, I see nothing that will cause the rotor to flap faster." This statement was made in respect to a rotor with delta-3, NOT a rotor with flapping hinge offset.

Consider these facts;
The swashplate determines the blade pitch.
The blade pitch determines the blade flap.
In a basic teetering hinge rotor, the ration of pitch to flap is 1 to 1.
Delta-3 is located between the swashplate and the blade pitch.
Delta-3 removes pitch.

Please explain how the hell a delta-3 rotor can flap further or faster than a basic teetering rotor. ????

It can't, and Wayne Johnson in 'Helicopter Theory' will be happy to mathematically explain it all to you.

[heedm]

What is the exact definition of the phase angle. I'd be happy if everyone answered because I'm concerned that some definitions are different.

I'm pretty sure Nick's assertion that the phase angle is reduced precisely by the amount of delta 3 will become clear if the phase angle is defined properly.

Matthew.

[Dave_Jackson]

Lu.

It's coming. Consider;

With an offset flapping hinge, there is no 'remaining 18-degrees'. This is because the swashplate and the tip path plane became coplanar in 72-degrees.

With delta-3, the rotor must revolve a number of times before the swashplate and the tip path plane become coplanar. Here those 18-degrees do have an effect and the magic words just might be 'washed-out coupling effect' and 'Wee-wa'.


heedm

The phase angle is the number of radial degrees between two events. In the case of a rotor it is the input (pitch) and the output (flap).

You are correct. " the phase angle is reduced precisely by the amount of delta 3"

On a rotor with flapping hinge offset, the blades fly to position faster. Therefor the phase angle (phase lag) is less than 90-degrees. On a delta-3 rotor, the phase angle is also less, but for a very different, and more complex reason.

[heedm]

Dave, the definition I was looking for needs more detail. I don't want to put words into anyone's mouths because I want to see if there is actually consensus. But for a hint, is the angle measured along the span of the blade, along the mean azimuthal position (when able to lead and lag), etc. Also, is this just a rigging angle decided by the engineers, or is it a complex aerodynamic result of the design of the entire system that allows a predictable and intuitive stick plot?

As far as the delta 3 reducing phase angle, I thought you weren't convinced of that point and that is why I started with this questioning. The natural frequency of the blade (speed at which it flaps) is only one consideration that decides phase angle. It is a fairly significant one as it considers many attributes of the blade and the rotor, but not the only one.

Changing delta 3 should change phase angle even if all other factors (including blade freq) stay the same. Understanding delta 3 requires understanding what phase angle precisely is, and understanding the movement the blades make whilst flapping (especially with some delta 3).

Matthew.

[Dave_Jackson]

heedm,

You appear to be going into phase angle much deep than I am capably of going. You may also be bringing in variables that are not necessary to understand the actions of delta three.

The following is a simplistic description; but it does describe the activity.

Let's say that we want 10º of flap at 180º azimuth. To get this we must input 10º into the swashplate. For simplicity, when the cyclic stick inputs this 10º, it is done instantly. In addition, let's say that the phase angle is 72º in both examples.

1/ ~ Offset flapping hinge causes a faster flap to position, so the input of 10º from the cyclic stick can be done later than it would need to be done in a basic teetering rotor. In approximately 72º of rotation we have the desired 10º flap.

2/ ~ Delta-3 is located between the swashplate and the blade pitch. In addition, as the blade flaps, delta-3 removes some of the pitch that is input from the swashplate. This means that when the blade gets to 180º azimuth the flap is not 10º. The flap is the swashplate's 10º input minus the delta-3 reduction. The blade has not flapped faster, it has flapped a smaller angle, and, it has done this in 72º of rotation.

Now remember that the swashplate is still asking for 10º of flap at 180º azimuth. So the rotor must go around again to get the flap closer to 10º. After half a dozen rotations, the flap eventually get to 10º.

_________________________

The summation is that the offset flapping hinge only needs 72º because it travels the flapping angle faster. Delta-3 only needs 72º because it travels a smaller flapping angle.


Summation added.

[NickLappos]

heedem,

Phase angle is the term we use to describe the relationship between the input (swashplate tilt angle) and the ouput (tip path angle) for a dynamic occurence. It is literally the difference in rotation angle between the place where the swashplate tilts and the place where the rotor ends up tilting. People who build helicopters call that angle Gamma.

The guys seem to have a great deal of confusion over this, especially Lu, who asks that plaintive refrain, "Where did the 18 degrees go?" The 18 degrees is the difference between his mythological wish that phase angles are always 90 degrees, and the reality of the robbie's rotor head, where the phase angle is 78 degrees. If you subtract the real phase angle (78) from Lu's erroneous wish (90) you get the 18 degrees, and you confuse Lu.

The rotor is actually a dynamically tuned device, where the blades resonate in the flap axis. By resonate, I mean that the blades oscillate up and down in flapping at one full cycle per revolution of the rotor. A swing resonates at a specific frequency, and the child learns to lean back at exactly the same timing as the resonant frequency, so the swing applies the child's energy very efficiently during the resonant cycle. That is why a weak child can pick herself up to such heights while swinging. It is alo why the cyclic can so powerfully move the massive rotor with so little force. The rotor wants to flap to help you!

[heedm]

Nick, the swashplate does not consider the extra angle provided by pitch arms. Gamma needs to be defined with this in mind. I'm not just being picky here, I understand the concept but in order to fully state my belief in how delta 3 affects Gamma, I need a very precise definition.

p.s. I know you meant 72 degrees vice 78.

Matthew.

[NickLappos]

Gamma is the difference between the swashplate tilt angle and the place where the blades finally tilt to thier maximum (and the place where the cyclic stick goes in that direction). In other words, if straight ahead is 0 degrees as a reference, you push the cyclic 2 inches forward = 2'' at 0 degrees. The rotor would be observed tilting about 6 or 7 inches down at 0 degrees (each inch of cyclic might be about 3 degrees of cyclic pitch). The swash plate would have tilted to the right (US convention) a lot to the right and some forward, with the lowest point 18 degrees forwrd of the right side. It is actually hard to find the blade tilt angle, we do it in flight test. If the rotor flaps earlier than the theoretical 90 degrees, then gamma is less than 90. In the case of the 72 (thanks!) degree phase of a robbie, the swash plate actually tilts at that angle

[Lu Zuckerman]

To: NickLappos

In the case of the 72 (thanks!) degree phase of a robbie, the swash plate actually tilts at that angle

I hate to be hard nosed or hard headed (take your pick) but what angle is that?

:confused:

[Dave_Jackson]

heedm, Lu; and Nick, if we are still talking. :D

The following is a plot of a basic teetering rotor and one with a delta3 of 18º. The 18º was selected because it is the Robinson's angle. Please note that phase-lag is not considered until the end.

If necessary, here is a clarification of the various planes. (http://www.unicopter.com/B329.html#Axes_Systems_Rotor)

http://www.unicopter.com/0941.gif

Some considerations re this graph;

The [control plane] and the [tip path plane w/o delta3] are representative of a basic teetering rotor. I.e. a 1 to 1 ration between pitch and flap.
The [control plane] plus the remaining three lines are representative of a delta3 rotor.

The [delta3 pitch change] is derived from [tip path plane w/o delta3] times an 18º delta3.
The [no-feathering plane] is the sum of the [control plane] and the [delta3 pitch change].
The [tip path plane w/ delta3] is based on this line reaching 90º azimuth at the flap angle where the [no-feathering plane] pitch changes from positive to negative.

There is an interdependency between the last three lines, and this will change their true location from that which is depicted in the graph. However, I believe that the [no-feathering plane] will remain on the same side of the [control plane], and that the [tip path plane w/ delta3] will remain on the same side of the [tip path plane w/o delta3].

Should this be correct, then two conclusions can be drawn from the graph.
1/ The blade pitch will reach 0º before the blade reaches 90º azimuth. I.e. a phase angle of less than 90º is required.
2/ The blade pitch will reach 90º azimuth before all the flap has been pulled out of it. I.e. additional rotations will be required before the [control plane] and the [tip path plane w/ delta3] are coplanar.

[Rich Lee]

Consider an elastic beam of thickness a bent to a radius of curvature R, such that R >>a, the bending moment M is given by
M=EI/R
where E is Young’s modulus for the material of the beam and I is the second moment of area of the cross-section of the beam about an axis which is normal to the plane of bending and passes through the neutral plane. For a beam of thickness a and width b, the expression for I is
I = ba3/12.

[Winnie]

Just a quick question from Newfoundland,
Is Lu's missing 18 degrees, what we are said to teach as advance angle?

I thought the two: Phase Lag and Advance Angle were interconnected. It is a little hard to follow when one cannot read Wayne Johnson's book because it is way too technical for a lowlife instructor like me!

Otherwise though, good posts, very informative and interesting, almost like sitting at Ray Prouty's seminar again!;) :ok:

[Dave_Jackson]

Winnie,

God knows what the 'advance angle' is. Could you be thinking of 'advance ratio' (tip speed ratio)?

Lu,

It's only the delta-3 rotor, that you're concerned about, isn't it?
___________________________

A bit of trivia;

A couple of years ago, John Uptigrove, the builder of the Mosquito (http://www.innovatortech.ca/) , rotated the bottom (only) of the pitch links on his helicopter approximately 10 to 15-degrees. As I recall, he said that it made no discernible difference to flight.