coriolis effect & static droop
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To: Helisphere
You have finally discovered the secret. Helicopter aerodynamics is taught in the following way.
1) They discuss Bernoulli’s theorem and then address how a venturi works.
2) They apply this to the operation of an airfoil of a fixed wing aircraft and explain how it generates lift
3) They in turn apply this theory to a rotating airfoil and they use the autogyro as an example
4) Without shifting gears they start talking about helicopters and apply the logic of the autogyro to the helicopter and that is where flapping to equality comes from.
I brought this subject up in the Robinson certification thread.
Thanks for bringing it up on this thread.
To: Crab
It looks like we are about the rekindle the war of 1812. If I remember my history the United States defeated the British. Just a bit of humor to get us started.
If I read you correctly you are stating that the lead angle of the pitch horn in your illustration is zero. If I do understand this premise it would appear that everything you say after that point is contrived to fit the basic premise. Also your diagram of the circle and the horizontal line with the vertical lines establishing the angular distance traveled (or in other words the amount of pitch change) is also flawed. If everything in the system is rotating about a fixed point then the angular displacements must be referenced to the point of rotation. That way, you can divide the circle into equal parts and the distance between each two points is equal to the distance between any other two points.
I have in front of me the Sikorsky Blue book. This book is issued to anyone that attends a technical school at Sikorsky whether they are a pilot or a mechanic. On page thirty of the blue book there is an illustration of blade pitch change as the blades rotate 360-degrtees. Although the figures are different from those quoted in my post the angular change of the blade is consistent for each degree of travel around the circular path.
I don’t know if you are familiar with a constant pressure variable delivery hydraulic pump but it too has a swashplate. As the internal mechanism rotates the swashplate action causes pistons to move in and out of a cylinder that resembles the cylinder in a Webley (spelling) revolver. The movement is constant and can be diagrammed just like a sine wave. If the pistons moved in the way you diagrammed the movement by drawing vertical lines from a base line the pump would tear itself apart and if it didn’t your hydraulic system would have to incorporate a pulse damper or, an accumulator. The pump described does not require an accumulator because of the smoothness of the output. Using this same analogy on the rotorhead, if the angular pitch change were not consistent with the degrees of rotation then you would have a constant medium to high frequency vertical beat in your rotor system.
Also, in your illustration of the 0-degree pitch horn the blade would have to be directly over the lowest part of the swashplate (down over the nose) in order to get the maximum pitch change which would place the blade at its’ lowest pitch relative to collective. Assuming it is possible to do this if using gyroscopic theory the disc would tilt to the left when you pushed the cyclic forward. Which way would it tilt using your theory?
The rules are the same for a bell with a 90-degree pitch horn and a Sikorsky using a 45-degree pitch horn and a 45-degree offset of the swashplate. In either case the lead relative to the selected direction of flight is 90-degrees. You stated in a past posting that the Lynx was like the Robinson in that in rigging the helicopter the blades were offset by 15-degrees on the Lynx and I stated that the Robinson blades were offset by 18-degrees. The result of this offset is that the blade will have maximum response 90-degrees later in rotation. My theory about the Robinson is yet to be proved but you had indicated in a previous post that the Lynx without the Auto Control System would roll to the left or 90-degrees later in rotation from the offset position.
In every case, the figure 90-degrees keeps popping up. Why does this figure keep coming up when discussing rotary wing flight? The answer is simple if you are on this side of the pond. It pertains to gyroscopic precession.
Regarding phase lag, it is 90-degrees whether you are addressing a Bell or a Sikorsky. As stated above the Bell pitch horn leads the blade by 90-degrees and on the Sikorsky it leads by 45-degrees and the swashplate tips down 45-degrees ahead of the selected direction of flight. Most helicopters excepting Boeing CH-47s and CH-46s follow this method of cyclic control input. But even on the Boeing helicopters the rotor placement is governed by gyroscopic precession.
Regarding your illustration about the only time that precession would play a part in the displacement of the rotorhead would be in a vacuum. I don't think that would work as the only thing you would do is change the angular setting of the blades but since there is no atmosphere you cant generate the lifting forces that would cause the disc to tilt due to precession.
In your last paragraph you asked me to look at a rotorhead and swashplate and see the tilting of the swashplate relative to where the blade pitch horns are. Assuming a Bell rotor and it is disposed across the lateral axis and the cyclic stick were displaced forward on the center of the rigged axis then the swash plate would move down forward and up aft. (Not on all Bell two blade systems as on some the swash plate moves opposite but the pitch horn is on the rear of the blades so the angular displacement related to blade position would be the same. On a Sikorsky as described above when the cyclic is pushed forward the swashplate will tip down 45-degrees ahead of the longitudinal axis and up 45-degrees ahead of the lateral axis. The blades if disposed over the lateral axis will have minimum pitch on 3:00 and maximum pitch at 9:00 relative to the basic collective pitch setting.
Over.
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The Cat
[This message has been edited by Lu Zuckerman (edited 22 January 2001).]
You have finally discovered the secret. Helicopter aerodynamics is taught in the following way.
1) They discuss Bernoulli’s theorem and then address how a venturi works.
2) They apply this to the operation of an airfoil of a fixed wing aircraft and explain how it generates lift
3) They in turn apply this theory to a rotating airfoil and they use the autogyro as an example
4) Without shifting gears they start talking about helicopters and apply the logic of the autogyro to the helicopter and that is where flapping to equality comes from.
I brought this subject up in the Robinson certification thread.
Thanks for bringing it up on this thread.
To: Crab
It looks like we are about the rekindle the war of 1812. If I remember my history the United States defeated the British. Just a bit of humor to get us started.
If I read you correctly you are stating that the lead angle of the pitch horn in your illustration is zero. If I do understand this premise it would appear that everything you say after that point is contrived to fit the basic premise. Also your diagram of the circle and the horizontal line with the vertical lines establishing the angular distance traveled (or in other words the amount of pitch change) is also flawed. If everything in the system is rotating about a fixed point then the angular displacements must be referenced to the point of rotation. That way, you can divide the circle into equal parts and the distance between each two points is equal to the distance between any other two points.
I have in front of me the Sikorsky Blue book. This book is issued to anyone that attends a technical school at Sikorsky whether they are a pilot or a mechanic. On page thirty of the blue book there is an illustration of blade pitch change as the blades rotate 360-degrtees. Although the figures are different from those quoted in my post the angular change of the blade is consistent for each degree of travel around the circular path.
I don’t know if you are familiar with a constant pressure variable delivery hydraulic pump but it too has a swashplate. As the internal mechanism rotates the swashplate action causes pistons to move in and out of a cylinder that resembles the cylinder in a Webley (spelling) revolver. The movement is constant and can be diagrammed just like a sine wave. If the pistons moved in the way you diagrammed the movement by drawing vertical lines from a base line the pump would tear itself apart and if it didn’t your hydraulic system would have to incorporate a pulse damper or, an accumulator. The pump described does not require an accumulator because of the smoothness of the output. Using this same analogy on the rotorhead, if the angular pitch change were not consistent with the degrees of rotation then you would have a constant medium to high frequency vertical beat in your rotor system.
Also, in your illustration of the 0-degree pitch horn the blade would have to be directly over the lowest part of the swashplate (down over the nose) in order to get the maximum pitch change which would place the blade at its’ lowest pitch relative to collective. Assuming it is possible to do this if using gyroscopic theory the disc would tilt to the left when you pushed the cyclic forward. Which way would it tilt using your theory?
The rules are the same for a bell with a 90-degree pitch horn and a Sikorsky using a 45-degree pitch horn and a 45-degree offset of the swashplate. In either case the lead relative to the selected direction of flight is 90-degrees. You stated in a past posting that the Lynx was like the Robinson in that in rigging the helicopter the blades were offset by 15-degrees on the Lynx and I stated that the Robinson blades were offset by 18-degrees. The result of this offset is that the blade will have maximum response 90-degrees later in rotation. My theory about the Robinson is yet to be proved but you had indicated in a previous post that the Lynx without the Auto Control System would roll to the left or 90-degrees later in rotation from the offset position.
In every case, the figure 90-degrees keeps popping up. Why does this figure keep coming up when discussing rotary wing flight? The answer is simple if you are on this side of the pond. It pertains to gyroscopic precession.
Regarding phase lag, it is 90-degrees whether you are addressing a Bell or a Sikorsky. As stated above the Bell pitch horn leads the blade by 90-degrees and on the Sikorsky it leads by 45-degrees and the swashplate tips down 45-degrees ahead of the selected direction of flight. Most helicopters excepting Boeing CH-47s and CH-46s follow this method of cyclic control input. But even on the Boeing helicopters the rotor placement is governed by gyroscopic precession.
Regarding your illustration about the only time that precession would play a part in the displacement of the rotorhead would be in a vacuum. I don't think that would work as the only thing you would do is change the angular setting of the blades but since there is no atmosphere you cant generate the lifting forces that would cause the disc to tilt due to precession.
In your last paragraph you asked me to look at a rotorhead and swashplate and see the tilting of the swashplate relative to where the blade pitch horns are. Assuming a Bell rotor and it is disposed across the lateral axis and the cyclic stick were displaced forward on the center of the rigged axis then the swash plate would move down forward and up aft. (Not on all Bell two blade systems as on some the swash plate moves opposite but the pitch horn is on the rear of the blades so the angular displacement related to blade position would be the same. On a Sikorsky as described above when the cyclic is pushed forward the swashplate will tip down 45-degrees ahead of the longitudinal axis and up 45-degrees ahead of the lateral axis. The blades if disposed over the lateral axis will have minimum pitch on 3:00 and maximum pitch at 9:00 relative to the basic collective pitch setting.
Over.
------------------
The Cat
[This message has been edited by Lu Zuckerman (edited 22 January 2001).]
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Question:
Why does the Lynx have a 75 degree lead on the pitch horn instead of 90? I'm pretty sure I know, but I wonder if there is more to it.
At the risk of taking another name calling from Lu. this is my understanding:
In a two blade teetering rotor, the flapping axis is the same as the rotational axis. Therefore the natural frequency of the blade rotationally is equal to the natural frequency of the blade in flapping. This will put phase lag right at 90 deg. However, in a rotor with offset hinges, or in a rigid rotor or bearingless type, the flapping length of the blade is shorter than the rotational length. This makes the natural frequency in flapping higher than the one for rotation. This means that the blade will flap to its highest or lowest point in less than 90 degrees from the point of highest or lowest blade pitch, in other words the phase lag will be less than 90 deg because the blade will flap faster with a higher natural frequency. Lu mentioned earlier that we need to look at the disk as a whole and not so much at the individual blades. However, when cyclic is input to the rotor, it is the tilting of the rotor thrust vector in relation to the rotor mast that produces a rolling moment. This means that there is a difference in the angle of the tip path plane in relation to the hub and mast IE flapping, and we must consider the higher frequency in flapping when figuring phase lag. Now, this is why I understand that all rotor systems with hinge offset have a phase lag something less than 90 deg although with small hinge offset the amount less than 90 is also small. This does not take into account any affect of delta 3 on phase lag or any other theory for that matter, which is why I post the question. Why does the lynx have 75 deg lead and (according to Lu) all other helicopters have 90 (except Robinson)? I happen to know that the sikorsky S-69 did not have 90 deg phase lag, it was quite small like 60 or 70 some degrees because the blades were so rigid. I know this because I have read the test data. I also know that they adjusted the phase angle at high forward speed but not to alter control reponse but to unload the retreating blades to avoid stall and reduce drag as they were flying at very high advance ratios and most or all of the retreating blade was flying backwards.
[This message has been edited by helisphere (edited 23 January 2001).]
Why does the Lynx have a 75 degree lead on the pitch horn instead of 90? I'm pretty sure I know, but I wonder if there is more to it.
At the risk of taking another name calling from Lu. this is my understanding:
In a two blade teetering rotor, the flapping axis is the same as the rotational axis. Therefore the natural frequency of the blade rotationally is equal to the natural frequency of the blade in flapping. This will put phase lag right at 90 deg. However, in a rotor with offset hinges, or in a rigid rotor or bearingless type, the flapping length of the blade is shorter than the rotational length. This makes the natural frequency in flapping higher than the one for rotation. This means that the blade will flap to its highest or lowest point in less than 90 degrees from the point of highest or lowest blade pitch, in other words the phase lag will be less than 90 deg because the blade will flap faster with a higher natural frequency. Lu mentioned earlier that we need to look at the disk as a whole and not so much at the individual blades. However, when cyclic is input to the rotor, it is the tilting of the rotor thrust vector in relation to the rotor mast that produces a rolling moment. This means that there is a difference in the angle of the tip path plane in relation to the hub and mast IE flapping, and we must consider the higher frequency in flapping when figuring phase lag. Now, this is why I understand that all rotor systems with hinge offset have a phase lag something less than 90 deg although with small hinge offset the amount less than 90 is also small. This does not take into account any affect of delta 3 on phase lag or any other theory for that matter, which is why I post the question. Why does the lynx have 75 deg lead and (according to Lu) all other helicopters have 90 (except Robinson)? I happen to know that the sikorsky S-69 did not have 90 deg phase lag, it was quite small like 60 or 70 some degrees because the blades were so rigid. I know this because I have read the test data. I also know that they adjusted the phase angle at high forward speed but not to alter control reponse but to unload the retreating blades to avoid stall and reduce drag as they were flying at very high advance ratios and most or all of the retreating blade was flying backwards.
[This message has been edited by helisphere (edited 23 January 2001).]
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To: Helisphere
I know absolutely nothing about the S-69 ABS helicopter however I would think that the control system must have been extremely complex to change the pitch of the retreating blade to unload it. But, there are some really tricky mechanical devices in this world.
In my post to Crab I used the Bell and Sikorsky rotor systems as examples, indicating one had a 90-degree lead on the pitch horn, and the other had a 45-degree pitch horn and the swashplate was offset by 45-degrees. This gives a total lead of 90-degrees relative to the direction of cyclic movement. The French helicopters are a bit different but then the French are a bit different.
On the A Star and quite possibly on the other Eurocopters helicopters the pitch horn leads the blade by 60-degrees and the swashplate is offset by 30-degrees which gives a total phase angle of 90-degrees. Whenever you see a helicopter that has pitch horns that do not lead by 90-degrees or, 45-degrees you have to check the layout of the swashplate. I would hazard a guess that the total of the swashplate offset and the pitch horn lead will come out to 90-degrees.
Regarding why the Lynx is the way it is I will yield to Crab.
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The Cat
I know absolutely nothing about the S-69 ABS helicopter however I would think that the control system must have been extremely complex to change the pitch of the retreating blade to unload it. But, there are some really tricky mechanical devices in this world.
In my post to Crab I used the Bell and Sikorsky rotor systems as examples, indicating one had a 90-degree lead on the pitch horn, and the other had a 45-degree pitch horn and the swashplate was offset by 45-degrees. This gives a total lead of 90-degrees relative to the direction of cyclic movement. The French helicopters are a bit different but then the French are a bit different.
On the A Star and quite possibly on the other Eurocopters helicopters the pitch horn leads the blade by 60-degrees and the swashplate is offset by 30-degrees which gives a total phase angle of 90-degrees. Whenever you see a helicopter that has pitch horns that do not lead by 90-degrees or, 45-degrees you have to check the layout of the swashplate. I would hazard a guess that the total of the swashplate offset and the pitch horn lead will come out to 90-degrees.
Regarding why the Lynx is the way it is I will yield to Crab.
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The Cat
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I need to rephrase my question. The Lynx being four bladed probably does not have a PITCH HORN leading 75 degrees or it would be very close to running into the next blade. Either way, what I meant to ask was: Why does the lynx have a PHASE ANGLE lead of 75 degrees as was previously said on the forum?
[This message has been edited by helisphere (edited 23 January 2001).]
[This message has been edited by helisphere (edited 23 January 2001).]
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Lu,
The only mistake I made in my post was regarding where the maximum rate of pitch change occurs. It is in the 30 degree arc either side of the neutral position - the reason the maximum rate of flapping happens at the position of maximum/minimum pitch is because the vertical movement of the pitch operating arms is at it's least 30 degrees either side of this position. This means that the blade spends 60 degrees of it's rotation at or near maximum pitch and 60 at or near minimum pitch. Angle of attack determines lift and therefore flapping so the max rate of flapping is still at max and min pitch positions.
Draw an accurate sine wave - the gradient of the slope is not constant (or it would be a straight line instead of a curve) at the top and bottom of the curve the gradient is least and at the point where the wave crosses the x axis, it is at it's steepest. Converting the rotary motion of the POA s to a vertical motion gives changing rates of pitch change per unit of angular displacement.
If you still don't believe me then get your trigonometry tables out and look at the difference between the sines of 0, 30, 60 and 90 degrees - the change is NOT LINEAR and therfore not constant.
Helisphere - I must go to work but I wil try to answer you question Re Lynx tonight.
The only mistake I made in my post was regarding where the maximum rate of pitch change occurs. It is in the 30 degree arc either side of the neutral position - the reason the maximum rate of flapping happens at the position of maximum/minimum pitch is because the vertical movement of the pitch operating arms is at it's least 30 degrees either side of this position. This means that the blade spends 60 degrees of it's rotation at or near maximum pitch and 60 at or near minimum pitch. Angle of attack determines lift and therefore flapping so the max rate of flapping is still at max and min pitch positions.
Draw an accurate sine wave - the gradient of the slope is not constant (or it would be a straight line instead of a curve) at the top and bottom of the curve the gradient is least and at the point where the wave crosses the x axis, it is at it's steepest. Converting the rotary motion of the POA s to a vertical motion gives changing rates of pitch change per unit of angular displacement.
If you still don't believe me then get your trigonometry tables out and look at the difference between the sines of 0, 30, 60 and 90 degrees - the change is NOT LINEAR and therfore not constant.
Helisphere - I must go to work but I wil try to answer you question Re Lynx tonight.
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To: Crab
We may be talking about two different things. One is flapping and the other is rate of pitch change. Using a pictorial analogy draw a circle. Divide the circle into four equal parts. The upper edge of the circle is the direction of flight. Where the right end of the horizontal centerline meets the outer edge of the circle mark that as point A=12-degrees. The opposite point on the circle is C=24-degrees. The top point is B=18-degrees and the bottom point is D= 18-degrees.
Addressing rate of pitch change; According to Sikorsky, if you broke the individual quadrants down to smaller elements which all meet at the center of the circle, and each of the smaller units were all equal, they say that the rate of pitch change from 12-degrees to 18-degrees is constant. And, if measured at the circumference of the circle the rate of change between elements of the circle would also be constant. The same would be true for points B-C, C-D and D-A.
Now draw three parallel lines spaced equally. The bottom left edge of the line is identified as 12-degrees and point A. Now draw a vertical line from that point to the edge of the top line. Now draw similar vertical lines spaced equally (2” apart). Draw a line from point A to the point where the second vertical line intersects the top horizontal line. Mark this as point C. Where the line intersects the middle line mark that as point B Now, draw a line from point C to the bottom of the second vertical line. Where the two lines meet mark this as point A. Where the line you made from point C to point A intersects the centerline mark that as point D. You can keep on going but the point I am trying to make is that the rate of pitch change is constant and that by graphing it out it can be seen that there is no sinusoidal curve. The line is straight.
Addressing rate of flap; First a couple of assumptions. You have a multi-blade rotor head that is fully articulated. The interlock number is much less than less than 1 so the rotorhead does not couple up with the disc path. Now, an analogy. When you shoot a bullet into the air it will go up and at some point that bullet will come to a complete stop just prior to reversing its’ course and start falling to the ground. Without scientific instruments it must be assumed that it did not fully stop and that the propulsive force just sort of faded away and gravity took over. I’ll try to apply this to the rotor and flapping.
Back to the drawing board. Draw a T. The top of the T should be 1-2” long. The vertical line should be the same length. At each end of the top of the T, make a large dot. That represents the offset hinges. From those dots draw a line about 3-4’ in length. These are your blades.
Now, draw the blades in a shallow V. These are your blades in a hover. Now, tilt the shallow V to the left. One blade will rise relative to the shallow V and the other will lower in relation to the shallow V. These are you blades when you are flying in any given direction. Using the circular reference above, mark the highest point on the shallow V as point D. The lowest point on the shallow V is marked point B. Connect the two points. This is your tip path. So, in flapping from point D to point B the blades are moving at a constant speed and discounting Coriolis forces and any drag forces the tip speed from point D to point B is also constant. The fastest rate of flap positional change would be between points D and A because when the blade reaches point A it is already changing pitch to a more positive angle. Regarding the bullet analogy the change of flap down to flap up although happening several hundred times a minute is gradual and not instantaneous.
Now, if "that" is what you said then I agree with you.
The only thing we don’t agree on is what caused the disc to tilt.
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The Cat
[This message has been edited by Lu Zuckerman (edited 23 January 2001).]
We may be talking about two different things. One is flapping and the other is rate of pitch change. Using a pictorial analogy draw a circle. Divide the circle into four equal parts. The upper edge of the circle is the direction of flight. Where the right end of the horizontal centerline meets the outer edge of the circle mark that as point A=12-degrees. The opposite point on the circle is C=24-degrees. The top point is B=18-degrees and the bottom point is D= 18-degrees.
Addressing rate of pitch change; According to Sikorsky, if you broke the individual quadrants down to smaller elements which all meet at the center of the circle, and each of the smaller units were all equal, they say that the rate of pitch change from 12-degrees to 18-degrees is constant. And, if measured at the circumference of the circle the rate of change between elements of the circle would also be constant. The same would be true for points B-C, C-D and D-A.
Now draw three parallel lines spaced equally. The bottom left edge of the line is identified as 12-degrees and point A. Now draw a vertical line from that point to the edge of the top line. Now draw similar vertical lines spaced equally (2” apart). Draw a line from point A to the point where the second vertical line intersects the top horizontal line. Mark this as point C. Where the line intersects the middle line mark that as point B Now, draw a line from point C to the bottom of the second vertical line. Where the two lines meet mark this as point A. Where the line you made from point C to point A intersects the centerline mark that as point D. You can keep on going but the point I am trying to make is that the rate of pitch change is constant and that by graphing it out it can be seen that there is no sinusoidal curve. The line is straight.
Addressing rate of flap; First a couple of assumptions. You have a multi-blade rotor head that is fully articulated. The interlock number is much less than less than 1 so the rotorhead does not couple up with the disc path. Now, an analogy. When you shoot a bullet into the air it will go up and at some point that bullet will come to a complete stop just prior to reversing its’ course and start falling to the ground. Without scientific instruments it must be assumed that it did not fully stop and that the propulsive force just sort of faded away and gravity took over. I’ll try to apply this to the rotor and flapping.
Back to the drawing board. Draw a T. The top of the T should be 1-2” long. The vertical line should be the same length. At each end of the top of the T, make a large dot. That represents the offset hinges. From those dots draw a line about 3-4’ in length. These are your blades.
Now, draw the blades in a shallow V. These are your blades in a hover. Now, tilt the shallow V to the left. One blade will rise relative to the shallow V and the other will lower in relation to the shallow V. These are you blades when you are flying in any given direction. Using the circular reference above, mark the highest point on the shallow V as point D. The lowest point on the shallow V is marked point B. Connect the two points. This is your tip path. So, in flapping from point D to point B the blades are moving at a constant speed and discounting Coriolis forces and any drag forces the tip speed from point D to point B is also constant. The fastest rate of flap positional change would be between points D and A because when the blade reaches point A it is already changing pitch to a more positive angle. Regarding the bullet analogy the change of flap down to flap up although happening several hundred times a minute is gradual and not instantaneous.
Now, if "that" is what you said then I agree with you.
The only thing we don’t agree on is what caused the disc to tilt.
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The Cat
[This message has been edited by Lu Zuckerman (edited 23 January 2001).]
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Lu: your 'triangular sawtoothed wave' arises from the sinusiodal element being eliminated by having a horizontal axis which is non-linear (sinusiodally) and eliminates the sinusoidal nature of pitch change in your graphical representation.
Try plotting against phase! (instead of longditudinal position as you have done and wrongly interpreted the data)
Now all YOU have to understand is what makes the disc tilt...
(hope that saved you the trouble, Crab ...
)
[This message has been edited by JoePilot (edited 23 January 2001).]
Try plotting against phase! (instead of longditudinal position as you have done and wrongly interpreted the data)
Now all YOU have to understand is what makes the disc tilt...
(hope that saved you the trouble, Crab ...
)[This message has been edited by JoePilot (edited 23 January 2001).]
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I have got well behind the gist and I am having trouble following the discussion but:
Lu,
Are you saying that in the USA, helicopter rotor systems are controlled by applying forces to cause gyroscopic precession and that aerodynamic forces do not directly play a part in we in the UK call "flapping to equality"?
Lu,
Are you saying that in the USA, helicopter rotor systems are controlled by applying forces to cause gyroscopic precession and that aerodynamic forces do not directly play a part in we in the UK call "flapping to equality"?
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To: Joe Pilot and Crab
If you were to use a true sinusoidal wave it would mean that the closer you got to the peak of the wave either + or – the rate of change would decrease. And it would begin to speed up as you went on the downward side of the wave and then slow down as it approached the bottom end of the wave. That would mean that the rate of pitch change is not constant around the tip path. I was just graphing out what Sikorsky has been teaching for the last fifty years. They say that the rate of change + and – is constant. If you want to disagree with that please contact Sikorsky.
The fact that the description involved a saw toothed diagram instead of a true sinusoidal wave does not mean that the effects of the saw tooth wave will cause some sort of calamitous reaction in the tip path plane because, it doesn’t. The pitch change around the disc is seamless, as is the flapping around the disc. Assuming there are no mechanical defects in the blades or the rotor system these things happen and you are not aware of them because that’s the way the designers wanted it.
Now if you want to discuss the vibrations that result from flapping that is the subject of another thread. Most production helicopters have a means of combating that type of vibration.
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The Cat
If you were to use a true sinusoidal wave it would mean that the closer you got to the peak of the wave either + or – the rate of change would decrease. And it would begin to speed up as you went on the downward side of the wave and then slow down as it approached the bottom end of the wave. That would mean that the rate of pitch change is not constant around the tip path. I was just graphing out what Sikorsky has been teaching for the last fifty years. They say that the rate of change + and – is constant. If you want to disagree with that please contact Sikorsky.
The fact that the description involved a saw toothed diagram instead of a true sinusoidal wave does not mean that the effects of the saw tooth wave will cause some sort of calamitous reaction in the tip path plane because, it doesn’t. The pitch change around the disc is seamless, as is the flapping around the disc. Assuming there are no mechanical defects in the blades or the rotor system these things happen and you are not aware of them because that’s the way the designers wanted it.
Now if you want to discuss the vibrations that result from flapping that is the subject of another thread. Most production helicopters have a means of combating that type of vibration.
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The Cat
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To: ShyTorque
Go to page 4 of this thread and several posts from the bottom is a post by Helisphere. Read that and then go to the top of this page and read my response to his post. Plain and simple, Flapping to equality is a term that is applied to Autogyros and it for some unknown reason has been carried over into the teaching of helicopter aerodynamics.
In the USA they teach that when the pilot pushes cyclic he creates an imbalance of lift across the disc. This imbalance is strongest over the left side of a counterclockwise rotor system. This perturbing force causes the disc to tip up over the tail and down over the nose. Aerodynamics initiated the force change but the actual movement was cause by the gyroscopic turning moment of the rotating disc.
If you look at retreating blade stall the cause and effect are the same. The left side of the disc is generating less lift than the right side. This imbalance will first cause the helicopter to roll left due to the disymmetry of lift and if you don’t catch it in time the disc will flap back or blow back pick one or the other. In either case you are dead or close to it.
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The Cat
Go to page 4 of this thread and several posts from the bottom is a post by Helisphere. Read that and then go to the top of this page and read my response to his post. Plain and simple, Flapping to equality is a term that is applied to Autogyros and it for some unknown reason has been carried over into the teaching of helicopter aerodynamics.
In the USA they teach that when the pilot pushes cyclic he creates an imbalance of lift across the disc. This imbalance is strongest over the left side of a counterclockwise rotor system. This perturbing force causes the disc to tip up over the tail and down over the nose. Aerodynamics initiated the force change but the actual movement was cause by the gyroscopic turning moment of the rotating disc.
If you look at retreating blade stall the cause and effect are the same. The left side of the disc is generating less lift than the right side. This imbalance will first cause the helicopter to roll left due to the disymmetry of lift and if you don’t catch it in time the disc will flap back or blow back pick one or the other. In either case you are dead or close to it.
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The Cat
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>>This imbalance will first cause the helicopter to roll left due to the disymmetry of lift and if you don’t catch it in time the disc will flap back or blow back pick one or the other. In either case you are dead or close to it.<<
Well you got one out of three right.
First, you will have vibes, then usually you have a pitchup of the nose and a roll, either both at the same time or one before the other.
One can recover, as you have to be really ignorant of the developing vibes prior to the actual stall reactions in pitch and roll.
[This message has been edited by RW-1 (edited 23 January 2001).]
Well you got one out of three right.
First, you will have vibes, then usually you have a pitchup of the nose and a roll, either both at the same time or one before the other.
One can recover, as you have to be really ignorant of the developing vibes prior to the actual stall reactions in pitch and roll.
[This message has been edited by RW-1 (edited 23 January 2001).]
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Lu, complete bo**ocks on two counts.
1. Having initiated a change in pitch cyclicly by pushing the cyclic that tilts the swash plate etc. the blades as they flap are seeking to recover the equal AoA they had before the cyclic pitch was applied. If cyclic pitch is removed then the AoA is reduced and the blade flaps down - in flapping down it increases the AOA back towards the original value. THIS IS FLAPPING TO EQUALITY - the equality is that of AoA. The disc assumes its new position with the tip path plane tilted forwards and stays in this new plane until something else (that is a gust or another control input and not the preaceesion fairy) changes the equality of lift(AOA) around the disc..
Moving into forward flight produces dissymmetry of lift because the advancing blade sees a change in rotational velocity which causes and increase in AoA - on the retreating side the opposite is happening - guess what... the advancing side flaps up with a high point at the front and the retreating blade flaps down with a low point at the back ----THIS IS FLAPBACK and is a result of flapping to equality. The pilot overcomes this with forward cyclic -something you can do in a helicopter but not in an autogyro - that is the difference.
2. Retreating Blade Stall - continuing from the above argument - as the forward speed is increased so the difference in AoA between advancing and retreating blades increases and to equalise the AoA the retreating blade has to flap down more and more as it's rotational speed is least. Eventually it reaches its stalling angle, has a rapid increase in drag and decrease in lift and flaps down. The effect is most pronounced due to the max rate of flapping between the 9:00 and 7:00 position so when lift is lost the aircraft pitches up and rolls left - THAT IS RETREATING BLADE STALL.
PS apparently one degree of cyclic pitch change produces about one degree of flapping.
1. Having initiated a change in pitch cyclicly by pushing the cyclic that tilts the swash plate etc. the blades as they flap are seeking to recover the equal AoA they had before the cyclic pitch was applied. If cyclic pitch is removed then the AoA is reduced and the blade flaps down - in flapping down it increases the AOA back towards the original value. THIS IS FLAPPING TO EQUALITY - the equality is that of AoA. The disc assumes its new position with the tip path plane tilted forwards and stays in this new plane until something else (that is a gust or another control input and not the preaceesion fairy) changes the equality of lift(AOA) around the disc..
Moving into forward flight produces dissymmetry of lift because the advancing blade sees a change in rotational velocity which causes and increase in AoA - on the retreating side the opposite is happening - guess what... the advancing side flaps up with a high point at the front and the retreating blade flaps down with a low point at the back ----THIS IS FLAPBACK and is a result of flapping to equality. The pilot overcomes this with forward cyclic -something you can do in a helicopter but not in an autogyro - that is the difference.
2. Retreating Blade Stall - continuing from the above argument - as the forward speed is increased so the difference in AoA between advancing and retreating blades increases and to equalise the AoA the retreating blade has to flap down more and more as it's rotational speed is least. Eventually it reaches its stalling angle, has a rapid increase in drag and decrease in lift and flaps down. The effect is most pronounced due to the max rate of flapping between the 9:00 and 7:00 position so when lift is lost the aircraft pitches up and rolls left - THAT IS RETREATING BLADE STALL.
PS apparently one degree of cyclic pitch change produces about one degree of flapping.
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To: Crab
This is another point where we must agree to disagree. You are 100% correct. But only on the eastern end of the Atlantic. If you came to the States to attend a class at Sikorsky you would have a very hard time to understand what the instructor was trying to teach because it would be totally alien to you. I have taught aerodynamics to US Army helicopter pilots and mechanics and I have taught in two A&P schools. They didn't have any problems understanding what I was trying to teach them. However if one of our guys came over to the UK to attend a course at Westland on the EH 101 and they taught principles of flight the way you are describing them they would have an equally hard time to comprehend the instructor because his words would be alien to him as well. Besides he would most likely be speaking in a midlands accent which doesn’t help matters much.
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The Cat
This is another point where we must agree to disagree. You are 100% correct. But only on the eastern end of the Atlantic. If you came to the States to attend a class at Sikorsky you would have a very hard time to understand what the instructor was trying to teach because it would be totally alien to you. I have taught aerodynamics to US Army helicopter pilots and mechanics and I have taught in two A&P schools. They didn't have any problems understanding what I was trying to teach them. However if one of our guys came over to the UK to attend a course at Westland on the EH 101 and they taught principles of flight the way you are describing them they would have an equally hard time to comprehend the instructor because his words would be alien to him as well. Besides he would most likely be speaking in a midlands accent which doesn’t help matters much.
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The Cat
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Lu,
I have read same again, however I am still unsure if we are singing off the same hymnsheet or not. Please excuse me stating a few basics from a pilot's point of view.
Regarding the autogyro case, the disc flaps to equality as has been stated because it must be allowed to do so. As I understand, Cierva originally built small models from lightweight materials; they flew well. The blades were mounted directly onto the head, like sails on a windmill. When he went upscale to a full-size machine he used strong bracing wires above and below to control drooping and flapping of the blades due to their inherent mass / flexibility which he saw as a structural problem. He had unwittingly just designed a rigid rotor with no lateral cyclic control.
Unfortunately this was not the thing to do and feedback forces to the head and fuselage caused the aircraft to roll over during take off. He then realised that the small model's blades were so flexible they naturally flapped to equality by aerodynamic effects, without any hinging as such, which meant there was little or no rolling force fed back. He removed the bracing from the big aircraft and the fault was cured - it flew, with the characteristic back-tilted disc and the whole shooting match dragged along against its will by a big engine and propellor.
A helicopter disc will also flap to equality in exactly the same way if left to its own devices. Unlike the autogyro which has a separate forward thrust motor of some sort, the resulting flapback would cause the aircraft to go forwards for only a short time. The (now) rearwards horizontal rotor disc thrust component would now cause a reversal of aircraft direction. Obviously the pilot wishes to make forward progress and so makes cyclic inputs to make the disc FLY to where it needs to go to keep the horizontal rotor thrust component pointing forwards. With the cyclic held / trimmed forwards, forces are fed back through the swash plate to the fuselage resulting in a nose-down tilt to the aircraft.
Do you agree with this? If you don't then maybe there really is a fundamental difference of teaching depending on which school one attends.
BTW, I have no axe to grind here but having been taught and passsed on to many others the "British" way I am intrigued by all this argument over the very basics of how our machines fly. There will therefore be nil off-slagging from me!
I have read same again, however I am still unsure if we are singing off the same hymnsheet or not. Please excuse me stating a few basics from a pilot's point of view.
Regarding the autogyro case, the disc flaps to equality as has been stated because it must be allowed to do so. As I understand, Cierva originally built small models from lightweight materials; they flew well. The blades were mounted directly onto the head, like sails on a windmill. When he went upscale to a full-size machine he used strong bracing wires above and below to control drooping and flapping of the blades due to their inherent mass / flexibility which he saw as a structural problem. He had unwittingly just designed a rigid rotor with no lateral cyclic control.
Unfortunately this was not the thing to do and feedback forces to the head and fuselage caused the aircraft to roll over during take off. He then realised that the small model's blades were so flexible they naturally flapped to equality by aerodynamic effects, without any hinging as such, which meant there was little or no rolling force fed back. He removed the bracing from the big aircraft and the fault was cured - it flew, with the characteristic back-tilted disc and the whole shooting match dragged along against its will by a big engine and propellor.
A helicopter disc will also flap to equality in exactly the same way if left to its own devices. Unlike the autogyro which has a separate forward thrust motor of some sort, the resulting flapback would cause the aircraft to go forwards for only a short time. The (now) rearwards horizontal rotor disc thrust component would now cause a reversal of aircraft direction. Obviously the pilot wishes to make forward progress and so makes cyclic inputs to make the disc FLY to where it needs to go to keep the horizontal rotor thrust component pointing forwards. With the cyclic held / trimmed forwards, forces are fed back through the swash plate to the fuselage resulting in a nose-down tilt to the aircraft.
Do you agree with this? If you don't then maybe there really is a fundamental difference of teaching depending on which school one attends.
BTW, I have no axe to grind here but having been taught and passsed on to many others the "British" way I am intrigued by all this argument over the very basics of how our machines fly. There will therefore be nil off-slagging from me!
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Lu: Sinusoidal With Respect to PHASE
Lu:"If you were to use a true sinusoidal wave it would mean that the closer you got to the peak of the wave either + or – the rate of change would decrease. And it would begin to speed up as you went on the downward side of the wave and then slow down as it approached the bottom end of the wave. That would mean that the rate of pitch change is not constant around the tip path. "
That's right - now you are learning! ... I think if we came to an American school we would have no problem in understanding that the plot which you say the Sikorsky school uses is against LONGDITUDINAL POSITION - which you are just misinterpreting... simple really.
Crab and Shy express the other point well, try re-reading it with an open mind - then you'll learn more...
(There's just a slightly subtle error with crab ... the AoA's aren't actually equalised ... because the airspeeds are different Clv2 same thing really tho')
Helicopters still fly in the US because none of this really matters....
Lu:"If you were to use a true sinusoidal wave it would mean that the closer you got to the peak of the wave either + or – the rate of change would decrease. And it would begin to speed up as you went on the downward side of the wave and then slow down as it approached the bottom end of the wave. That would mean that the rate of pitch change is not constant around the tip path. "
That's right - now you are learning! ... I think if we came to an American school we would have no problem in understanding that the plot which you say the Sikorsky school uses is against LONGDITUDINAL POSITION - which you are just misinterpreting... simple really.
Crab and Shy express the other point well, try re-reading it with an open mind - then you'll learn more...
(There's just a slightly subtle error with crab ... the AoA's aren't actually equalised ... because the airspeeds are different Clv2 same thing really tho')
Helicopters still fly in the US because none of this really matters....
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Lu, as ever, you have misinterpreted a diagram designed to highlight the fact that pitch changes throughout the 360 degree orbit and guessed that they really meant to show you that pitch change was constant. If that was what Sikorsky had meant to show, they would probably have used a 44 sided shape and not a circle. The 44 sided shape with pitch change constant would produce your saw-tooth wave when drawn - the circle produces a sine wave which for the second time does not have a constant gradient and is therefore not linear and does not give constant rate of pitch change.
As a further counter to your precession theory - you happily accept that phase lag changes with hinge offset - Lynx and BO105 have phase lag of between 75 and 80 degrees - now show me a gyro that precesses at anything less than 90 degrees!!! Oh no you can't.
Furthermore I have just been looking at a book that is imaginatively titled FM 1-203; it is produced by the US Army and is the fundamentals of flight manual issued at Ft Rucker. It has pages and pages of flapping to equality, non-uniform rates of pitch change around a control orbit, blowback etc etc etc and one 5 line paragraph about precession. So much for vive la difference across the Atlantic then. Are you sure the book you read was written after the Wright Brothers got airborne at Kittyhawk?
PS try explaining why the coriolis force effect that deflect air moving in the Northern Hemisphere to the right is negligible at the Equator and increases as you increase Latitude......hmmm, might it have something to do with Sine of the Latitude changing non linearly?
As a further counter to your precession theory - you happily accept that phase lag changes with hinge offset - Lynx and BO105 have phase lag of between 75 and 80 degrees - now show me a gyro that precesses at anything less than 90 degrees!!! Oh no you can't.
Furthermore I have just been looking at a book that is imaginatively titled FM 1-203; it is produced by the US Army and is the fundamentals of flight manual issued at Ft Rucker. It has pages and pages of flapping to equality, non-uniform rates of pitch change around a control orbit, blowback etc etc etc and one 5 line paragraph about precession. So much for vive la difference across the Atlantic then. Are you sure the book you read was written after the Wright Brothers got airborne at Kittyhawk?
PS try explaining why the coriolis force effect that deflect air moving in the Northern Hemisphere to the right is negligible at the Equator and increases as you increase Latitude......hmmm, might it have something to do with Sine of the Latitude changing non linearly?
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I have been following the last few entries with a little eye brow raising. The one thing that I have seen that gives concern is the use of the terms 'pitch change RATE' and 'pitch change ANGLE'. One or other of the two will infact be constant while the other will change throughout each revolution.
Are you sure that you are not getting the two mixed up? You may be arguing the same point.
Are you sure that you are not getting the two mixed up? You may be arguing the same point.
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Lu,
Do you think the piston in a car engine moves from top dead centre to bottom dead centre at a constant rate? Of course not - the rapid burning of the fuel expands the air and ACCELERATES the piston downwards - the piston stops moving vertically at the top and bottom of each stroke - WITHOUT tearing the engine apart.
To use your hydraulic pump analogy - the fuel pump in the Wessex was exactly the same with pistons moving up and down following the swash plate; the angle of the swash plate determined the stroke of the piston and thus the output. My point here is that the rate of stroke of the piston is not constant - it is accelerated downwards as a very efficient method of compressing the fluid - fuel in this case. As a piston on one side of the swash plate is accelerating downwards, the corresponding piston 180 degrees out is accelerating upwards so the net effect is balanced and the pump does not tear itself apart. The piston begins to move downwards at the beginning of the stroke, reaches its maximum rate of movement mid stroke and then reduces its rate until at its low point where the reverse process begins.
Back to helicopters - the Lynx disc is low at the front when you push the cyclic forward - the advance angle is 15 degrees - the pitch actuator is mounted 15 degrees ahead of the lateral line through the rotor mast - this is because the phase lag is approximately 75 degrees (15+75 =90) ie it only takes 75 degrees of angular rotation from the application of the force to achieve its high or low point - CAN A GYRO DO THIS?
The Lynx head does not have a mechanical flapping hinge - the titanium forging flexes to allow the flapping to occur and gives an effective hinge offset of between 12 and 17% depending on who's book you read. The fact that phase lag reduces as hinge offset increases is well documented - WHY this happens I do not fully understand as I am allergic to greek flute music and have to take a day off if I see more than one variable in a formula. I am sure you will have a lengthy explanation.
Do you think the piston in a car engine moves from top dead centre to bottom dead centre at a constant rate? Of course not - the rapid burning of the fuel expands the air and ACCELERATES the piston downwards - the piston stops moving vertically at the top and bottom of each stroke - WITHOUT tearing the engine apart.
To use your hydraulic pump analogy - the fuel pump in the Wessex was exactly the same with pistons moving up and down following the swash plate; the angle of the swash plate determined the stroke of the piston and thus the output. My point here is that the rate of stroke of the piston is not constant - it is accelerated downwards as a very efficient method of compressing the fluid - fuel in this case. As a piston on one side of the swash plate is accelerating downwards, the corresponding piston 180 degrees out is accelerating upwards so the net effect is balanced and the pump does not tear itself apart. The piston begins to move downwards at the beginning of the stroke, reaches its maximum rate of movement mid stroke and then reduces its rate until at its low point where the reverse process begins.
Back to helicopters - the Lynx disc is low at the front when you push the cyclic forward - the advance angle is 15 degrees - the pitch actuator is mounted 15 degrees ahead of the lateral line through the rotor mast - this is because the phase lag is approximately 75 degrees (15+75 =90) ie it only takes 75 degrees of angular rotation from the application of the force to achieve its high or low point - CAN A GYRO DO THIS?
The Lynx head does not have a mechanical flapping hinge - the titanium forging flexes to allow the flapping to occur and gives an effective hinge offset of between 12 and 17% depending on who's book you read. The fact that phase lag reduces as hinge offset increases is well documented - WHY this happens I do not fully understand as I am allergic to greek flute music and have to take a day off if I see more than one variable in a formula. I am sure you will have a lengthy explanation.