Delta-3 & Phase Lag
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Keeping the pot stirred.
With all of the dialog going back and forth and the explanations provided I have only one question. Where did my 18-degrees go?
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Just the facts
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.
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.
Last edited by Dave_Jackson; 3rd Aug 2003 at 09:30.
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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.
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.
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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.
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.
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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.
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.
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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.
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.
Last edited by Dave_Jackson; 3rd Aug 2003 at 12:50.
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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!
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!
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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.
p.s. I know you meant 72 degrees vice 78.
Matthew.
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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
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An honest question.
To: NickLappos
I hate to be hard nosed or hard headed (take your pick) but what angle is that?
In the case of the 72 (thanks!) degree phase of a robbie, the swash plate actually tilts at that angle
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heedm, Lu; and Nick, if we are still talking. 
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.
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.
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.
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.
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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.
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.
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!
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!
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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 , 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.
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 , 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.
