Helicopter Dynamics: Gyroscopic Precession
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Helicopter Dynamics: Gyroscopic Precession
Only for those with a perversion for the technical.
In some not-so-distant thread, an attempt was made to show that gyroscopic precession is not a factor in the activities of a helicopter's rotor. The bicycle wheel, which is normally used to demonstrate gyroscopic precession, was modified. This modified wheel consisted of only four spokes, a hub and the lose connections between them. The wheel (or what's left of it) now more closely resembles a helicopter's rotor. This wheel combined with the notes of Prouty and the remarks by Nick tends to support the idea of no gyroscopic precession. Current textbooks tend to also hold this position.
_________________
Now for the fiendish part;
I believe that a simple teetering rotor, with no delta3, exhibits a 90-degree phase lag, which is totally caused by the blade flying to position. Perhaps aerodynamic precession, but not gyroscopic precession.
As mechanical restrictions are imposed upon a blade's ability to flap, the phase angle will decrease from 90-degrees. Any increasing of the flapping hinge's offset, or an increasing of the dampening of the flapping hinge, or a stiffening of the blade will result in an even smaller phase angle.
Now consider an airplane's propeller. We know that the propeller is subject to gyroscopic precession. Also, the primary difference between a variable pitch propeller and a helicopter's rotor is their rigidity. I would suggest that it is only the out-of-plane (flapping) rigidity that we are concerned with.
If we take this idea of rotor rigidity to the extreme, we will have a totally rigid rotor and a phase angle of zero degrees. If the maximum pitch is applied on the right side, then the maximum rotor thrust (not flap - because the rigid rotor is rigidly attached to the fuselage) will be exhibited on the right side. The helicopter will obviously roll to the left, but, with trepidation, I feel that it will also want to pitch down slightly at the nose. I believe that this small nose down pitch is the result of gyroscopic precession, which in turn is the result of changing the attitude of this very rigid rotor disk (read as gyroscope disk).
Anyone who read this far, want to tear it apart?
[ 03 August 2001: Message edited by: Dave Jackson ]
In some not-so-distant thread, an attempt was made to show that gyroscopic precession is not a factor in the activities of a helicopter's rotor. The bicycle wheel, which is normally used to demonstrate gyroscopic precession, was modified. This modified wheel consisted of only four spokes, a hub and the lose connections between them. The wheel (or what's left of it) now more closely resembles a helicopter's rotor. This wheel combined with the notes of Prouty and the remarks by Nick tends to support the idea of no gyroscopic precession. Current textbooks tend to also hold this position.
_________________
Now for the fiendish part;
I believe that a simple teetering rotor, with no delta3, exhibits a 90-degree phase lag, which is totally caused by the blade flying to position. Perhaps aerodynamic precession, but not gyroscopic precession.
As mechanical restrictions are imposed upon a blade's ability to flap, the phase angle will decrease from 90-degrees. Any increasing of the flapping hinge's offset, or an increasing of the dampening of the flapping hinge, or a stiffening of the blade will result in an even smaller phase angle.
Now consider an airplane's propeller. We know that the propeller is subject to gyroscopic precession. Also, the primary difference between a variable pitch propeller and a helicopter's rotor is their rigidity. I would suggest that it is only the out-of-plane (flapping) rigidity that we are concerned with.
If we take this idea of rotor rigidity to the extreme, we will have a totally rigid rotor and a phase angle of zero degrees. If the maximum pitch is applied on the right side, then the maximum rotor thrust (not flap - because the rigid rotor is rigidly attached to the fuselage) will be exhibited on the right side. The helicopter will obviously roll to the left, but, with trepidation, I feel that it will also want to pitch down slightly at the nose. I believe that this small nose down pitch is the result of gyroscopic precession, which in turn is the result of changing the attitude of this very rigid rotor disk (read as gyroscope disk).
Anyone who read this far, want to tear it apart?
[ 03 August 2001: Message edited by: Dave Jackson ]
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I think if you take the modified bicycle wheel and do one more modification I may start to catch on.
Of the four metal spokes replace three of them with plastic. (same qualities, flex etc.)
Now, if you input a force to the hub from underneath you would have gyroscopic precession.(while spinning)
In the second case with the spinning "wheel" if you hold a big magnet over a quadrant you would have an approximation of aerodynamic precession.
Am I getting there?
So in the first case we have control forces being transmitted (from "in" to "out"), physically altered by precession, hampered (altered) by hinge offset, resistance etc.
In the second case the control forces are happening already "out" and transmit the pull back to the airframe. (and through the reverse path)
btw, great threads, always enjoy making my brain smoke.
Of the four metal spokes replace three of them with plastic. (same qualities, flex etc.)
Now, if you input a force to the hub from underneath you would have gyroscopic precession.(while spinning)
In the second case with the spinning "wheel" if you hold a big magnet over a quadrant you would have an approximation of aerodynamic precession.
Am I getting there?
So in the first case we have control forces being transmitted (from "in" to "out"), physically altered by precession, hampered (altered) by hinge offset, resistance etc.
In the second case the control forces are happening already "out" and transmit the pull back to the airframe. (and through the reverse path)
btw, great threads, always enjoy making my brain smoke.
Avoid imitations
Now look what you've started!
Imagine two separate simple rotor systems. Both have a central vertically aligned spindle (aka rotor mast) which can be rotated axially and also tilted in any direction by a force acting anywhere at 90 degrees to its axis.
Four lengths of scaffolding tube arms (heavy and NON AERODYNAMIC, simply round in section) are attached to each rotor mast by two different methods.
On the first mast, the arms are held in a rigid steel hub so that the arms stick out horizontally like the spokes of a wheel (or the blades of a helicopter), at 90 degrees to each other. This system is rotated at speed. We now have a crude gyroscope. The system will exhibit the two properties of a gyroscope, namely rigidity (it wants to keep spinning in the same plane) and precession (any force applied to the rotor mast in an attempt to tilt the system will appear to act 90 degrees further round to the direction of application until the plane of rotation of the system aligns with the force and it can no longer act).
In the second system, the arms are suspended from the mast, at 90 degrees to each other, by separate lengths of flexible steel cable. At rest the arms hang down alongside the mast. The system is now spun up to speed. As the mast is rotated, the cables attached to it pull round the arms until they fly out at 90 degrees to the mast and 90 degrees to each other. At this stage, the system looks exactly like the first one. Because the rotating arms have the same mass as the other set, they must also act as a gyroscope and must therefore exhibit the same properties of rigidity and precession. A force is now applied to this rotor mast, as before, in an attempt to change the plane of rotation of the system. Because the mast is only connected to the rotating arms by flexible cable, it cannot transmit the force to them. This time the mast moves very easily in the direction away from the force, but the cables merely flex and the rotating arms maintain their plane of rotation. We have a system where the rotor mast can be easily moved, but there is no control over the rotating arms. If the plane of rotation of the arms were to change, there would be no effect on the rotor mast because the forces could not be transmitted through the cables, which would merely flex.
------------------
In the first instance we have a rigid rotor. It can be controlled but the only way to control it is by applying a force through the rotor mast which must move with the system.
In the second instance we have created a fully articulated rotor. We have no practical way of controlling the plane of rotation of this system because we cannot input a force to cause gyroscopic precession to occur.
--------------
We now stop both systems, dismantle them and replace the rotating scaffolding tubes with properly designed rotor blades of identical size and shape. We retain the original methods of attachment, one system rigid apart from simple pitch change bearings and the second still using flexible cables. We also fit a simple system that allows us to change the cyclic pitch angle of the blades. Both systems are spun up to speed with a neutral pitch angle on the blades.
By adjusting the pitch angle of the blades we find that we can fly them around, up and down, changing the plane of rotation of the rotor systems. The Aerodynamic forces generated by the blades overcome the Gyroscopic forces tending to hold the original plane of rotation.
One very noticeable difference between the two systems is that on the rigid system, while the plane of rototation is changing , the rotor mast moves in sympathy. On the second, cable attached system, the rotor mast says rotating along the same axis.
--------------
Applying these two rotor systems to two simple helicopters we find that we can make them both fly by controlling the plane of rotation of the rotors. This is, as we have shown, done aerodynamically by changing their cyclic pitch. The flying characteristics of the two helicopters are however, a little different. The rigid rotor gives us a very responsive helicopter. This is because as soon as the dics tilts, so must the rotor mast, which is now bolted onto the airframe. The airframe rapidly changes direction as the rotor is flown around.
The articulated rotor still flies but the helicopter is reluctant to change direction in sympathy with the rotor system. This is because there are no forces feeding back through to the rotor mast in order to make it tilt.
---------
But this is only part of the story...
Right! Someone else please carry on.
Imagine two separate simple rotor systems. Both have a central vertically aligned spindle (aka rotor mast) which can be rotated axially and also tilted in any direction by a force acting anywhere at 90 degrees to its axis.
Four lengths of scaffolding tube arms (heavy and NON AERODYNAMIC, simply round in section) are attached to each rotor mast by two different methods.
On the first mast, the arms are held in a rigid steel hub so that the arms stick out horizontally like the spokes of a wheel (or the blades of a helicopter), at 90 degrees to each other. This system is rotated at speed. We now have a crude gyroscope. The system will exhibit the two properties of a gyroscope, namely rigidity (it wants to keep spinning in the same plane) and precession (any force applied to the rotor mast in an attempt to tilt the system will appear to act 90 degrees further round to the direction of application until the plane of rotation of the system aligns with the force and it can no longer act).
In the second system, the arms are suspended from the mast, at 90 degrees to each other, by separate lengths of flexible steel cable. At rest the arms hang down alongside the mast. The system is now spun up to speed. As the mast is rotated, the cables attached to it pull round the arms until they fly out at 90 degrees to the mast and 90 degrees to each other. At this stage, the system looks exactly like the first one. Because the rotating arms have the same mass as the other set, they must also act as a gyroscope and must therefore exhibit the same properties of rigidity and precession. A force is now applied to this rotor mast, as before, in an attempt to change the plane of rotation of the system. Because the mast is only connected to the rotating arms by flexible cable, it cannot transmit the force to them. This time the mast moves very easily in the direction away from the force, but the cables merely flex and the rotating arms maintain their plane of rotation. We have a system where the rotor mast can be easily moved, but there is no control over the rotating arms. If the plane of rotation of the arms were to change, there would be no effect on the rotor mast because the forces could not be transmitted through the cables, which would merely flex.
------------------
In the first instance we have a rigid rotor. It can be controlled but the only way to control it is by applying a force through the rotor mast which must move with the system.
In the second instance we have created a fully articulated rotor. We have no practical way of controlling the plane of rotation of this system because we cannot input a force to cause gyroscopic precession to occur.
--------------
We now stop both systems, dismantle them and replace the rotating scaffolding tubes with properly designed rotor blades of identical size and shape. We retain the original methods of attachment, one system rigid apart from simple pitch change bearings and the second still using flexible cables. We also fit a simple system that allows us to change the cyclic pitch angle of the blades. Both systems are spun up to speed with a neutral pitch angle on the blades.
By adjusting the pitch angle of the blades we find that we can fly them around, up and down, changing the plane of rotation of the rotor systems. The Aerodynamic forces generated by the blades overcome the Gyroscopic forces tending to hold the original plane of rotation.
One very noticeable difference between the two systems is that on the rigid system, while the plane of rototation is changing , the rotor mast moves in sympathy. On the second, cable attached system, the rotor mast says rotating along the same axis.
--------------
Applying these two rotor systems to two simple helicopters we find that we can make them both fly by controlling the plane of rotation of the rotors. This is, as we have shown, done aerodynamically by changing their cyclic pitch. The flying characteristics of the two helicopters are however, a little different. The rigid rotor gives us a very responsive helicopter. This is because as soon as the dics tilts, so must the rotor mast, which is now bolted onto the airframe. The airframe rapidly changes direction as the rotor is flown around.
The articulated rotor still flies but the helicopter is reluctant to change direction in sympathy with the rotor system. This is because there are no forces feeding back through to the rotor mast in order to make it tilt.
---------
But this is only part of the story...
Right! Someone else please carry on.
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To: ShyTorque
A very easy to understand description.
The following is a nit-picking comment and a continuation of your story;
You may wish to slightly modify the following sentence by changing the word 'Gyroscopic' to ' Centripetal'.
>The Aerodynamic forces generated by the blades overcome the Gyroscopic forces tending to hold the original plane of rotation. <.
"Centripetal (center-seeking) force is the constant inward force necessary to maintain circular motion." "Gyroscopic force is the characteristic that causes the gyroscope to react to an applied force at a point 90-degress away from the point of application, in the direction of its rotation."
______________________
To continue your story of the two helicopters;
Assuming that the maximum blade pitch is on the left side of both helicopters, then I believe that the following will take place.
In your first instance, because the rotor is rigidly attached to the helicopter, the mast and helicopter will be pried (rolled) to the right.
In your second instance, because the rotor is teetering, the disk will continue to climb past the left side for another 90-degrees. The tilted disk will then want to change the pitch atitude of the mast and helicopter by dragging them to a new position.
In other words, the first instance has a phase lag of 0-degrees and will roll the helicopter. The second instance has a phase lag of 90-degrees and will pitch the helicopter.
__________________
I think that;
In first instance, the extremely rigid rotor will act like a gyroscope and therefore experience precession. The amount of this gyroscopic precession should be very small though, because;
1/ the rotor has *relatively* little mass,
2/ it must overcome the inertia of the helicopter as well as the rotor, and
3/ no rotor yet (with the possible exception of the V-22) has achieved this high a level of rigidity.
In the second instance, the 'floppy' teetering rotor will not experience any gyroscopic precession.
[ 04 August 2001: Message edited by: Dave Jackson ]
A very easy to understand description.
The following is a nit-picking comment and a continuation of your story;
You may wish to slightly modify the following sentence by changing the word 'Gyroscopic' to ' Centripetal'.
>The Aerodynamic forces generated by the blades overcome the Gyroscopic forces tending to hold the original plane of rotation. <.
"Centripetal (center-seeking) force is the constant inward force necessary to maintain circular motion." "Gyroscopic force is the characteristic that causes the gyroscope to react to an applied force at a point 90-degress away from the point of application, in the direction of its rotation."
______________________
To continue your story of the two helicopters;
Assuming that the maximum blade pitch is on the left side of both helicopters, then I believe that the following will take place.
In your first instance, because the rotor is rigidly attached to the helicopter, the mast and helicopter will be pried (rolled) to the right.
In your second instance, because the rotor is teetering, the disk will continue to climb past the left side for another 90-degrees. The tilted disk will then want to change the pitch atitude of the mast and helicopter by dragging them to a new position.
In other words, the first instance has a phase lag of 0-degrees and will roll the helicopter. The second instance has a phase lag of 90-degrees and will pitch the helicopter.
__________________
I think that;
In first instance, the extremely rigid rotor will act like a gyroscope and therefore experience precession. The amount of this gyroscopic precession should be very small though, because;
1/ the rotor has *relatively* little mass,
2/ it must overcome the inertia of the helicopter as well as the rotor, and
3/ no rotor yet (with the possible exception of the V-22) has achieved this high a level of rigidity.
In the second instance, the 'floppy' teetering rotor will not experience any gyroscopic precession.
[ 04 August 2001: Message edited by: Dave Jackson ]
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To: vorticey
No I didn't see your post.
A number of interesting posts were 'wiped out'; just when the thread was trying to come to a clearer understanding about one small component of rotor activity.
Can you re-post yours on this thread?
No I didn't see your post.
A number of interesting posts were 'wiped out'; just when the thread was trying to come to a clearer understanding about one small component of rotor activity.
Can you re-post yours on this thread?
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Dave, thanks even more.
Please have a bit of patience with me on this, while sorting through it I am having to dispel some previous convictions that I've had. Generally that means I have to understand it all first.
Back to the tale of two rotors;
On your rigid rotor you mentioned that with full pitch in the blades on the left side of the aircraft it would roll (pry) right.
I'm wondering.. (uh-oh)
If the blade on the left reached the point of maximum pitch at the exact 90 degree mark wouldn't that force developed take some amount of time to transmit to the fuselage?
While the transmission of force was happening the blades would be changing their relationship to the fuselage.
Actually I think the force devlopedwould be changing it's relationship to the fuselage.
Once again, you guys are putting this into understandable verbage, thanks from everyone.
tom
Please have a bit of patience with me on this, while sorting through it I am having to dispel some previous convictions that I've had. Generally that means I have to understand it all first.
Back to the tale of two rotors;
On your rigid rotor you mentioned that with full pitch in the blades on the left side of the aircraft it would roll (pry) right.
I'm wondering.. (uh-oh)
If the blade on the left reached the point of maximum pitch at the exact 90 degree mark wouldn't that force developed take some amount of time to transmit to the fuselage?
While the transmission of force was happening the blades would be changing their relationship to the fuselage.
Actually I think the force devlopedwould be changing it's relationship to the fuselage.
Once again, you guys are putting this into understandable verbage, thanks from everyone.
tom
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To: Dave Jackson
Sorry to butt into a private thread:
I quote,” 3/ no rotor yet (with the possible exception of the V-22) has achieved this high a level of rigidity".
The V-22 Proprotor is not rigid as it is mounted on a rubber diaphragm that allows both flapping and precession of the Proprotorhead.
Sorry to butt into a private thread:
I quote,” 3/ no rotor yet (with the possible exception of the V-22) has achieved this high a level of rigidity".
The V-22 Proprotor is not rigid as it is mounted on a rubber diaphragm that allows both flapping and precession of the Proprotorhead.
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To support the aerodynamic explanation:
While preventing blade sailing during shutdown, the rotor is controllable down to very low RRPM. Until about 10% RRPM, my inputs to maintain a level disc do not change, only more cyclic into wind is required.
I would find it hard to believe that a rotor at such low RPM is still behaving as a gyro.
This seems to support an aerodynamic cause for the phase lag.
------------
To really analyze this though we will need someone who knows the math behind gyroscopic forces.
While preventing blade sailing during shutdown, the rotor is controllable down to very low RRPM. Until about 10% RRPM, my inputs to maintain a level disc do not change, only more cyclic into wind is required.
I would find it hard to believe that a rotor at such low RPM is still behaving as a gyro.
This seems to support an aerodynamic cause for the phase lag.
------------
To really analyze this though we will need someone who knows the math behind gyroscopic forces.
Avoid imitations
Dave,
You appear to have chosen a French helicopter (with the blades rotating clockwise from above), but no matter either way.
I think the answer is that both systems have a phase lag of 90 degrees. A blade will not move instantly to a new position, whatever force causes the motion. For the aircraft to roll, the cyclic pitch increase would need to be put in as the rotor blades pass the 6 o'clock position of the aircraft.
-----------
With regard to the centripetal force rather than gyroscopic force; you may be more correct. (I did originally include the term but I edited the post many times until my eyes were going crossed).
My understanding is that both forces are a function of the same phenomena. Newton stated that a body tends to move in a straight line unless acted upon by another force. A body / mass forced to rotate around an axis (because it is fixed to it), instead of continuing in its preferred straight line, can do so only by experiencing a force, in this case imparted by the attachment. Newton also stated that every reaction imparts an equal and opposite reaction and so the axis by definition must be experiencing an equal force to the rotating mass. Or vice versa.
The characteristics of gyroscopes can be explained by those two Newton's laws (I'll be very honest here and admit that I can't currently remember which he quoted first second or third!).
Precession is simply a description of the movement of a rotating body out of its plane of rotation by a displacing force acting normal (90 degrees / perpendicular) to the ORIGINAL plane of rotation. The force acts, the rotating body moves in the direction of the force (whilst still rotating around the axis) until the displacing force can no longer act because the plane of rotation has changed so that it is in the same direction as the displacing force; i.e. through 90 degrees but 90 degrees further round the "disk" than where the force was applied.
I probably need a model or a diagram to put that across properly.
ShyT
You appear to have chosen a French helicopter (with the blades rotating clockwise from above), but no matter either way.
I think the answer is that both systems have a phase lag of 90 degrees. A blade will not move instantly to a new position, whatever force causes the motion. For the aircraft to roll, the cyclic pitch increase would need to be put in as the rotor blades pass the 6 o'clock position of the aircraft.
-----------
With regard to the centripetal force rather than gyroscopic force; you may be more correct. (I did originally include the term but I edited the post many times until my eyes were going crossed).
My understanding is that both forces are a function of the same phenomena. Newton stated that a body tends to move in a straight line unless acted upon by another force. A body / mass forced to rotate around an axis (because it is fixed to it), instead of continuing in its preferred straight line, can do so only by experiencing a force, in this case imparted by the attachment. Newton also stated that every reaction imparts an equal and opposite reaction and so the axis by definition must be experiencing an equal force to the rotating mass. Or vice versa.
The characteristics of gyroscopes can be explained by those two Newton's laws (I'll be very honest here and admit that I can't currently remember which he quoted first second or third!).
Precession is simply a description of the movement of a rotating body out of its plane of rotation by a displacing force acting normal (90 degrees / perpendicular) to the ORIGINAL plane of rotation. The force acts, the rotating body moves in the direction of the force (whilst still rotating around the axis) until the displacing force can no longer act because the plane of rotation has changed so that it is in the same direction as the displacing force; i.e. through 90 degrees but 90 degrees further round the "disk" than where the force was applied.
I probably need a model or a diagram to put that across properly.
ShyT
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To: tgrendl and Shy Torque
tgrendl wrote;
>If the blade on the left reached the point of maximum pitch at the exact 90 degree mark wouldn't that force developed take some amount of time to transmit to the fuselage? <
No. In the case of an absolutely rigid rotor I don't believe this so. In the case of this totally rigid (and hypothetical) rotor, there is no flapping or teetering. This rotor is rigidly coupled to the fuselage, perhaps by what is called a static mast. Therefore, any movement of the rotor, other than rotation about the mast, will cause an immediate and identical movement in the fuselage.
You must consider this really rigid rotor as if it was a large variable pitch propeller mounted vertically. The only movement is rotation about the mast and pitch change. No blade flex. No nothing. No kidding!
_____________________
The following may help to clarify the activity;
We are looking down upon the rotor disks of Shy Torques two helicopters.
On both helicopters;
0-degrees azimuth is straight back.
90-degrees azimuth is the mid-point of the advancing side.
180-degrees azimuth is straight ahead.
270-degrees azimuth is the mid-point of the retreating side.
The X-axis is the longitudinal one.
The Y-axis is the lateral one.
The Z-axis is the vertical one.
Both helicopters are hovering.
Let's consider that by applying the same cyclic to both helicopters, the greatest blade pitch is at azimuth 90, the least pitch is at azimuth 270 and the mean (average) pitch is at azimuths 0 and 180.
We know that the blade pitch and thrust at azimuth 45 is the same as it is at azimuth 135. We also know that the blade pitch and thrust at azimuth 225 is the same as it is at azimuth 315.. We also know that the blade pitches and thrusts at 45 and 135 are greater than they are at 225 and 315.
So far everything has been the same for the two helicopters.
Now, in the case of the helicopter with the teetering rotor, the blades will climb from azimuth 0 to azimuth 180 and descend from azimuth 180 to azimuth 0. The disk will be tipped back. The helicopter will 'eventually' pitch up and fly backwards.
OK so far?
Now for the helicopter with the totally rigid rotor.
Remember that the rotor and fuselage are totally interconnected, except for the rotors rotation about the Z-axis.
The combined thrust at 45 and 135 EXCEEDS the combined thrust at 225 and 315, The rotor and the firmly attached fuselage must therefore roll about the X-axis and sideslip toward the retreating blade side of the craft.
The combined thrust at 45 and 225 EQUALS the combined thrust at 135 and 315, The rotor and the firmly attached fuselage will therefore NOT pitch about the Y-axis nor will the craft move forward or backward.
_____________
We have give both rotors the same amount of blade pitch at the same azimuths but one helicopter is flying backwards and the other is flying sideways.
The only way to get them to fly in the same direction, is by giving the teetering rotor helicopter a 90-degree phase angle and the totally rigid rotor helicopter a 0-degree phase angle.
Hope this makes sense.
____________________
Lu;
Thanks for the information on the V-22 rotor.
tgrendl wrote;
>If the blade on the left reached the point of maximum pitch at the exact 90 degree mark wouldn't that force developed take some amount of time to transmit to the fuselage? <
No. In the case of an absolutely rigid rotor I don't believe this so. In the case of this totally rigid (and hypothetical) rotor, there is no flapping or teetering. This rotor is rigidly coupled to the fuselage, perhaps by what is called a static mast. Therefore, any movement of the rotor, other than rotation about the mast, will cause an immediate and identical movement in the fuselage.
You must consider this really rigid rotor as if it was a large variable pitch propeller mounted vertically. The only movement is rotation about the mast and pitch change. No blade flex. No nothing. No kidding!
_____________________
The following may help to clarify the activity;
We are looking down upon the rotor disks of Shy Torques two helicopters.
On both helicopters;
0-degrees azimuth is straight back.
90-degrees azimuth is the mid-point of the advancing side.
180-degrees azimuth is straight ahead.
270-degrees azimuth is the mid-point of the retreating side.
The X-axis is the longitudinal one.
The Y-axis is the lateral one.
The Z-axis is the vertical one.
Both helicopters are hovering.
Let's consider that by applying the same cyclic to both helicopters, the greatest blade pitch is at azimuth 90, the least pitch is at azimuth 270 and the mean (average) pitch is at azimuths 0 and 180.
We know that the blade pitch and thrust at azimuth 45 is the same as it is at azimuth 135. We also know that the blade pitch and thrust at azimuth 225 is the same as it is at azimuth 315.. We also know that the blade pitches and thrusts at 45 and 135 are greater than they are at 225 and 315.
So far everything has been the same for the two helicopters.
Now, in the case of the helicopter with the teetering rotor, the blades will climb from azimuth 0 to azimuth 180 and descend from azimuth 180 to azimuth 0. The disk will be tipped back. The helicopter will 'eventually' pitch up and fly backwards.
OK so far?
Now for the helicopter with the totally rigid rotor.
Remember that the rotor and fuselage are totally interconnected, except for the rotors rotation about the Z-axis.
The combined thrust at 45 and 135 EXCEEDS the combined thrust at 225 and 315, The rotor and the firmly attached fuselage must therefore roll about the X-axis and sideslip toward the retreating blade side of the craft.
The combined thrust at 45 and 225 EQUALS the combined thrust at 135 and 315, The rotor and the firmly attached fuselage will therefore NOT pitch about the Y-axis nor will the craft move forward or backward.
_____________
We have give both rotors the same amount of blade pitch at the same azimuths but one helicopter is flying backwards and the other is flying sideways.
The only way to get them to fly in the same direction, is by giving the teetering rotor helicopter a 90-degree phase angle and the totally rigid rotor helicopter a 0-degree phase angle.
Hope this makes sense.
____________________
Lu;
Thanks for the information on the V-22 rotor.
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Dave etc, thanks, I'm getting there.Did you ever see the TV commercial for "ugly duckling" cars?
The one where the guy is calling from a payphone for help.
His car is in the background and he's telling the service center what kind of "noise" his car was making when it broke.
RRRRR--RRRRRR
And then in the background his old car just explodes.
And he says "RRR-RRRRR Kaboom "
Now that's really what happens to my brain here.
Appreciate any of the extra time you guys take for the people in the back of the class.
Fly safe
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Dave Jackson said:
I believe that a simple teetering rotor, with no delta3, exhibits a 90-degree phase lag, which is totally caused by the blade flying to position. Perhaps aerodynamic precession, but not gyroscopic precession.
Nick Sez:
Bravo Dave! You are absolutely correct. The old bugaboo about Gyroscopic Precession is quite mythological, but almost impossible to squelch, because it seems so plausible, and the real issues are so difficult to describe intuitively.
Basically, the whirling blade flaps at a natural frequency that depends on the centrifugal force to return it to its normal position. Picture the blade with a strong pair of springs, one below and one above the blade that oppose its flapping motion. If we pull the blade tip down, and let go, it will bounce a bunch of times like a diving board. Gor a helicopter, there are no springs, (an elastomeric rotor has such little spring force it changes this not a bit) but there is a strong centrifugal force that opposes a flapping motion. This force is a spring term that acts just like that diving board.
It turns out (in math that gets pretty stinky) that the blade resonates at 1 per rev, because the centrifugal spring changes its force with rpm, so it always allows the blade to resonate at its whirling rpm frequency. It also turns out that the phase relationship between the cyclic pitch (swash plate angle) and the tip path is about 90 degrees, depending on a bunch of blade properties.
Gyroscopes have nothing to do with it at all!
I just reaffirmed my understanding by re-reading a good source (for science and engineering pros):
Stepniewski & Keys - ROTARY - WING AERODYNAMICS
New York: Dover Pub.
I believe that a simple teetering rotor, with no delta3, exhibits a 90-degree phase lag, which is totally caused by the blade flying to position. Perhaps aerodynamic precession, but not gyroscopic precession.
Nick Sez:
Bravo Dave! You are absolutely correct. The old bugaboo about Gyroscopic Precession is quite mythological, but almost impossible to squelch, because it seems so plausible, and the real issues are so difficult to describe intuitively.
Basically, the whirling blade flaps at a natural frequency that depends on the centrifugal force to return it to its normal position. Picture the blade with a strong pair of springs, one below and one above the blade that oppose its flapping motion. If we pull the blade tip down, and let go, it will bounce a bunch of times like a diving board. Gor a helicopter, there are no springs, (an elastomeric rotor has such little spring force it changes this not a bit) but there is a strong centrifugal force that opposes a flapping motion. This force is a spring term that acts just like that diving board.
It turns out (in math that gets pretty stinky) that the blade resonates at 1 per rev, because the centrifugal spring changes its force with rpm, so it always allows the blade to resonate at its whirling rpm frequency. It also turns out that the phase relationship between the cyclic pitch (swash plate angle) and the tip path is about 90 degrees, depending on a bunch of blade properties.
Gyroscopes have nothing to do with it at all!
I just reaffirmed my understanding by re-reading a good source (for science and engineering pros):
Stepniewski & Keys - ROTARY - WING AERODYNAMICS
New York: Dover Pub.
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dave
in the other tread you talked about blades in a vacuum, but in a vacuum or not the rotor axis must be changed to get precesion.
the mast or its hinges have nothing to do with it, they have there own precesion.
to change the axis we use pitch to put an up and down force on the blades,this over comes inercia and the disk starts to move but because the axis is changing, gyroscopic precession will TRY to take the movement ahead in rotation. a little cyclic will stop this happening.
i recon that if you on the ground with the rotors spining you might be able to notice it if you pushed the cyclic forward then hold that atitude. while the rotors are coming down they might be infront of the input but when they stop at the bottom it should be lined up with the input
in the other tread you talked about blades in a vacuum, but in a vacuum or not the rotor axis must be changed to get precesion.
the mast or its hinges have nothing to do with it, they have there own precesion.
to change the axis we use pitch to put an up and down force on the blades,this over comes inercia and the disk starts to move but because the axis is changing, gyroscopic precession will TRY to take the movement ahead in rotation. a little cyclic will stop this happening.
i recon that if you on the ground with the rotors spining you might be able to notice it if you pushed the cyclic forward then hold that atitude. while the rotors are coming down they might be infront of the input but when they stop at the bottom it should be lined up with the input
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Nick;
Thanks for your elaboration of the teetering rotor
and your mention of Rotary-Wing Aerodynamics.
You just came up with tonight's reading.
It's surprising what one can learn from a textbook.
By the way, it is because of your previous postings that I have acquired (hopefully?) a better understanding of things like; static mast, anhedral, plus, plus.
Thanks.
___________________
vorticey;
It appears that you want to disassociate the blade's activities from the rest of the rotor's activities. I do not believe that the activities of an individual blade can be related to gyroscopic precession.
In fact, I would guess that the association of gyroscopic precession and the helicopter rotor has come about because people have been thinking in terms of the rotor disk. They envision the rotor-disk as some sort of structural entity, where in reality, it's mostly a bunch of (hot) air.
Gyroscopic precession is probably only active in a rotating body that has absolute rigidity. When one starts to think of the rotor disk as a rotating body, then their thinking starts to get a little tipsy.
If you think that the above is hot air as well, fire back.
Thanks for your elaboration of the teetering rotor
and your mention of Rotary-Wing Aerodynamics.
You just came up with tonight's reading.
It's surprising what one can learn from a textbook.
By the way, it is because of your previous postings that I have acquired (hopefully?) a better understanding of things like; static mast, anhedral, plus, plus.
Thanks.
___________________
vorticey;
It appears that you want to disassociate the blade's activities from the rest of the rotor's activities. I do not believe that the activities of an individual blade can be related to gyroscopic precession.
In fact, I would guess that the association of gyroscopic precession and the helicopter rotor has come about because people have been thinking in terms of the rotor disk. They envision the rotor-disk as some sort of structural entity, where in reality, it's mostly a bunch of (hot) air.
Gyroscopic precession is probably only active in a rotating body that has absolute rigidity. When one starts to think of the rotor disk as a rotating body, then their thinking starts to get a little tipsy.
If you think that the above is hot air as well, fire back.
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To: Dave Jackson
When the Cheyenne Helicopter was first built it flew quite well. I don’t know if you are familiar with the rotor system on the Cheyenne or not. The Cheyenne had a rigid rotor system that was free to feather but was rigid in plane and flapped by flexing the blade and the arms of the rotorhead. In order to introduce pitch change into the blades the pilot would move the cyclic and caused a servo to move. This servo was attached to a horseshoe shaped spring, which was compressed. The spring compression was transmitted via control linkage to a gyro that was mounted above the rotorhead. This gyro which consisted of four arms disposed at 90-degrees to each other and each arm had a very heavy weight at the end. This produced a gyroscope rotor that was capable of imparting a great deal of force. The individual arms were attached to the pitch horns on the blades. When the pilot input cyclic movement and the gyro would displace 90-degrees later inputting a pitch change into the blades and the rotor system like a gyro would displace 90-degrees in the direction of rotation.
As the design progressed the Army kept adding weight to the Helicopter. Lockheed indicated that the helicopter could no longer meet its’ performance guarantees and Lockheed requested a change in the rotor diameter to regain the necessary lift. The Army said no so Lockheed went back to the drawing board. What they came up with was a bastard design that not only had negative twist like other helicopters they also included a camber which added a degree of instability. Then they did something that was quite novel and they painted themselves into a corner in the process. Not only was the blade cambered it had a different camber at different blade stations so from the root to the tip the blade had constantly changing in its’ cross section.
This design in concert with the blades inherent stiffness caused major problems as the blade would not fly or precess to the position commanded by the pilots’ cyclic input. The first time this problem manifested itself a pilot was lost, as was the helicopter. The next time it happened it took out the wind tunnel at Ames labs in California.
The problem was eventually solved but the solution was so complex that it became sensitive to a single point failure that would cause loss of the helicopter. The solution although complex worked similar to the electronic system on the Lynx helicopter that corrects for a 15-degree coupling in the cyclic control.
Now, way back then when I learned how the system worked Ray Prouty indicated that there were two gyroscopic elements. The control gyro which precessed and the gyroscopic precession of the rotor. It seems that that assumption is no longer valid.
When the Cheyenne Helicopter was first built it flew quite well. I don’t know if you are familiar with the rotor system on the Cheyenne or not. The Cheyenne had a rigid rotor system that was free to feather but was rigid in plane and flapped by flexing the blade and the arms of the rotorhead. In order to introduce pitch change into the blades the pilot would move the cyclic and caused a servo to move. This servo was attached to a horseshoe shaped spring, which was compressed. The spring compression was transmitted via control linkage to a gyro that was mounted above the rotorhead. This gyro which consisted of four arms disposed at 90-degrees to each other and each arm had a very heavy weight at the end. This produced a gyroscope rotor that was capable of imparting a great deal of force. The individual arms were attached to the pitch horns on the blades. When the pilot input cyclic movement and the gyro would displace 90-degrees later inputting a pitch change into the blades and the rotor system like a gyro would displace 90-degrees in the direction of rotation.
As the design progressed the Army kept adding weight to the Helicopter. Lockheed indicated that the helicopter could no longer meet its’ performance guarantees and Lockheed requested a change in the rotor diameter to regain the necessary lift. The Army said no so Lockheed went back to the drawing board. What they came up with was a bastard design that not only had negative twist like other helicopters they also included a camber which added a degree of instability. Then they did something that was quite novel and they painted themselves into a corner in the process. Not only was the blade cambered it had a different camber at different blade stations so from the root to the tip the blade had constantly changing in its’ cross section.
This design in concert with the blades inherent stiffness caused major problems as the blade would not fly or precess to the position commanded by the pilots’ cyclic input. The first time this problem manifested itself a pilot was lost, as was the helicopter. The next time it happened it took out the wind tunnel at Ames labs in California.
The problem was eventually solved but the solution was so complex that it became sensitive to a single point failure that would cause loss of the helicopter. The solution although complex worked similar to the electronic system on the Lynx helicopter that corrects for a 15-degree coupling in the cyclic control.
Now, way back then when I learned how the system worked Ray Prouty indicated that there were two gyroscopic elements. The control gyro which precessed and the gyroscopic precession of the rotor. It seems that that assumption is no longer valid.
Lu, what's with the permanent thumbs down mate?
Regarding your comment about the gyroscopic pitch change mechanism on the Cheyenne(although I haven't seen it), it sounds a lot like a stabilising device.
Some gyroscopic forces must certainly be associated with whirling massive components, but as Nick Lappos pointed out above, the actual movement of rotor blades is fundamentally an aerodynamic thing.
Harking back to the old Huey again, the pitch change is accomplished by hooking up the pitch change rods from the swash plate to the stab bar (you may already know about this so apologies if it's telling you how to suck eggs) which is the rod mounted at 90 degrees to the rotor blades, and connected to them via the pitch change links and an oil-filled damper.
Basically, the stab bar whirls around and tries to remain rigid in space, and if the rotor blades are perturbed by turbulent air, the design of the connecting rods in the system leads to a pitch input to correct the disturbance.
For pilot-induced cyclic pitch changes, the swash plate moves the control tubes which act through the stab bar system to the pitch change links, leading to cyclic pitch changes on the blades causing them to fly to the new desired position.
So I guess what I'm saying is, gyroscopics have a place in rotor design, but aerodynamic forces are what makes the blades fly as they do. What you're talking about above sounds like it's designed as a stablilising system, and the pitch inputs to the blades are still what lead to disc movement.
To Dave Jackson et al, enjoying reading your posts. A bit of constructive discussion is a good thing!
[ 06 August 2001: Message edited by: Arm out the window ]
Regarding your comment about the gyroscopic pitch change mechanism on the Cheyenne(although I haven't seen it), it sounds a lot like a stabilising device.
Some gyroscopic forces must certainly be associated with whirling massive components, but as Nick Lappos pointed out above, the actual movement of rotor blades is fundamentally an aerodynamic thing.
Harking back to the old Huey again, the pitch change is accomplished by hooking up the pitch change rods from the swash plate to the stab bar (you may already know about this so apologies if it's telling you how to suck eggs) which is the rod mounted at 90 degrees to the rotor blades, and connected to them via the pitch change links and an oil-filled damper.
Basically, the stab bar whirls around and tries to remain rigid in space, and if the rotor blades are perturbed by turbulent air, the design of the connecting rods in the system leads to a pitch input to correct the disturbance.
For pilot-induced cyclic pitch changes, the swash plate moves the control tubes which act through the stab bar system to the pitch change links, leading to cyclic pitch changes on the blades causing them to fly to the new desired position.
So I guess what I'm saying is, gyroscopics have a place in rotor design, but aerodynamic forces are what makes the blades fly as they do. What you're talking about above sounds like it's designed as a stablilising system, and the pitch inputs to the blades are still what lead to disc movement.
To Dave Jackson et al, enjoying reading your posts. A bit of constructive discussion is a good thing!
[ 06 August 2001: Message edited by: Arm out the window ]
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Lu;
Thanks for the information on the Cheyenne rotor. The following web page, by Doug Marker, may also be of interest. It describes some of what you said and adds some of its own.
http://www.internetage.com.au/cartercopters/pics9.htm
A year ago, Doug started a thread on rec.aviation.rotorcraft, in which participants discussed gyroscopic precession. His intent was to display the conclusion after all the information was is.
He may have never been able to come to a conclusion
, whatever, an e-mail was sent to him earlier today.
_________________
Regarding Prouty and gyroscopic precession:
I just came across the following two excerpts from 'Helicopter Performance, Stability and Control'. "... the summation of the moments produced by aerodynamic, centrifugal, weight, inertial and gyroscopic forces must equal zero." and "... the rotor disk acts as a gyroscopic and remains in its original plane".
Perhaps it is in reference to a small amount of gyroscopic precession that may be present in rotors with offset and flapping hinge stiffness.
[ 06 August 2001: Message edited by: Dave Jackson ]
Thanks for the information on the Cheyenne rotor. The following web page, by Doug Marker, may also be of interest. It describes some of what you said and adds some of its own.
http://www.internetage.com.au/cartercopters/pics9.htm
A year ago, Doug started a thread on rec.aviation.rotorcraft, in which participants discussed gyroscopic precession. His intent was to display the conclusion after all the information was is.
He may have never been able to come to a conclusion
, whatever, an e-mail was sent to him earlier today._________________
Regarding Prouty and gyroscopic precession:
I just came across the following two excerpts from 'Helicopter Performance, Stability and Control'. "... the summation of the moments produced by aerodynamic, centrifugal, weight, inertial and gyroscopic forces must equal zero." and "... the rotor disk acts as a gyroscopic and remains in its original plane".
Perhaps it is in reference to a small amount of gyroscopic precession that may be present in rotors with offset and flapping hinge stiffness.
[ 06 August 2001: Message edited by: Dave Jackson ]
