Rigid Rotors & More ~ A challenge
Thread Starter
Joined: Nov 2000
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From: Vancouver, BC, Canada
Hi Lu,
You provoke thought, thanks.
You're hitting on a number of subjects. Here are a couple of answers. I'll get back on the others.
____________________________
The enclosed segment has been moved to [Gyroscopic Precession - Revisited] and is about to be cut from here.
"If you have an infinitely rigid rotor you in effect have a gyroscope."
You have to forget gyroscopic precession & the helicopter rotor. For gyroscopic precession to take place, the rotating device must have considerable [Angular Momentum] A helicopter's rotor does not have enough.
Consider a toy gyroscope on a vertical axis. Bring it up to speed. A minute later it is still spinning, and the disk is still horizontal.
Now lets consider a 'type' of 2-bladed helicopter rotor, which has round 'no lift' blades. We'll make it from a 30-foot long by 2" diameter steel pipe. Drill a hole through both walls at 15-feet from the end and weld in a rod (axle), which extends out both holes. Now spin the horizontal pipe, somehow, on its vertical (rod) axis to about 400 rpm. When released, it will slow and fall over within a second or two.
They ain't the same thing.
____________________________
"If I understand it correctly the advancing blade or rotation on the right side is counter clockwise as viewed from above and the left rotor is rotating clockwise as viewed from above. "
A small point. Flettner originally had them rotating in the direction you mention. He then changed them so that the higher inside blades are advancing. (i.e. Port ~ CCW and Starboard - CW). This was done to give speed stability.
Back with more.
You provoke thought, thanks.
You're hitting on a number of subjects. Here are a couple of answers. I'll get back on the others.
____________________________
The enclosed segment has been moved to [Gyroscopic Precession - Revisited] and is about to be cut from here.
"If you have an infinitely rigid rotor you in effect have a gyroscope."
You have to forget gyroscopic precession & the helicopter rotor. For gyroscopic precession to take place, the rotating device must have considerable [Angular Momentum] A helicopter's rotor does not have enough.
Consider a toy gyroscope on a vertical axis. Bring it up to speed. A minute later it is still spinning, and the disk is still horizontal.
Now lets consider a 'type' of 2-bladed helicopter rotor, which has round 'no lift' blades. We'll make it from a 30-foot long by 2" diameter steel pipe. Drill a hole through both walls at 15-feet from the end and weld in a rod (axle), which extends out both holes. Now spin the horizontal pipe, somehow, on its vertical (rod) axis to about 400 rpm. When released, it will slow and fall over within a second or two.
They ain't the same thing.
____________________________
"If I understand it correctly the advancing blade or rotation on the right side is counter clockwise as viewed from above and the left rotor is rotating clockwise as viewed from above. "
A small point. Flettner originally had them rotating in the direction you mention. He then changed them so that the higher inside blades are advancing. (i.e. Port ~ CCW and Starboard - CW). This was done to give speed stability.
Back with more.
Last edited by Dave Jackson; 26th April 2002 at 17:47.
Iconoclast
Joined: Sep 2000
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From: The home of Dudley Dooright-Where the lead dog is the only one that gets a change of scenery.
To: Dave Jackson
This is a very poor example. A circular body passing through an air stream or an air stream passing over a circular body will initiate what is known as “vortex shedding”. Vortex shedding at 400 rpm will set up such a severe high frequency vibration as to cause the rotating object either to self-destruct or to break away from its’ driving axis. If you rotated the pipe as described but in a vacuum you would not have vortex shedding but you would have a device that would exhibit gyroscopic rigidity in space and gyroscopic precession if you had a means of perturbing the rotating mass. The vibration will be the result of the vortex shedding frequency but mainly due to the vibratory frequencies being different at each station on the rotating pipe.
A propeller on an aircraft is similar to your pipe example and your totally rigid rotorhead but it is rotating about a horizontal axis as opposed to a vertical axis. When the aircraft is maneuvered in any way the movement of the aircraft causes a perturbing force on the rotating mass of the propeller and the propeller wants to precess. It cannot precess because the propeller drive shaft is rigidized by the bearings contained within the crankcase so the blades will bend within their elastic limits.
On the V-22 there is a similar situation. When the aircraft is maneuvered in the airplane mode the Proprotor, which is not rigid will precess (flap). This precessing is detected and electronically corrected by inputs to the servomechanism. You will note that when in the airplane mode there is no advancing and retreating blade and the air stream passing over the Proprotor is uniform so in this case you have to accept gyroscopic precession over aerodynamic precession. Also, since the blades are independent from each other each blade is a part of a rotating mass and as such each blade will individually respond to the perturbing force and although independent from each other they respond as a solid disc.
Now lets consider a 'type' of 2-bladed helicopter rotor, which has round 'no lift' blades. We'll make it from a 30-foot long by 2" diameter steel pipe. Drill a hole through both walls at 15-feet from the end and weld in a rod (axle), which extends out both holes. Now spin the horizontal pipe, somehow, on its vertical (rod) axis to about 400 rpm. When released, it will slow and fall over within a second or two.
A propeller on an aircraft is similar to your pipe example and your totally rigid rotorhead but it is rotating about a horizontal axis as opposed to a vertical axis. When the aircraft is maneuvered in any way the movement of the aircraft causes a perturbing force on the rotating mass of the propeller and the propeller wants to precess. It cannot precess because the propeller drive shaft is rigidized by the bearings contained within the crankcase so the blades will bend within their elastic limits.
On the V-22 there is a similar situation. When the aircraft is maneuvered in the airplane mode the Proprotor, which is not rigid will precess (flap). This precessing is detected and electronically corrected by inputs to the servomechanism. You will note that when in the airplane mode there is no advancing and retreating blade and the air stream passing over the Proprotor is uniform so in this case you have to accept gyroscopic precession over aerodynamic precession. Also, since the blades are independent from each other each blade is a part of a rotating mass and as such each blade will individually respond to the perturbing force and although independent from each other they respond as a solid disc.
Last edited by Lu Zuckerman; 25th April 2002 at 21:25.
Thread Starter
Joined: Nov 2000
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From: Vancouver, BC, Canada
Lu,
I don't disagree with your remarks about the propeller.
Previously mentioned was, " For gyroscopic precession to take place, the rotating device must have considerable [Angular Momentum]. A helicopter's rotor does not have enough."
This [Angular momentum] involves RPM and mass. A propeller has a much higher RPM and, proportionately, a much higher mass than the helicopter rotor.
______________
I actually hope that the UniCopter's two counterrotating rigid rotors do exhibit a little gyroscopic precession. This is desired to give the craft dynamic stability in pitch and roll.
Counterrotating Gyroscopes (Dynamic Stability):
Assume that the rotational part of a gyroscope is mounted on a stationary vertical axle. Assume, also, that we are looking down at the gyroscope (plan view) and that the locations of interest are the four primary points of the compass.
If the gyroscope was rotated CW an upward force on the West will cause the North to rise and the South to lower, due to precession. If the gyroscope was then rotated CCW the same upward force on the West will now cause the South to rise and the North to lower.
If we put two counterrotating gyroscopes on the same rigid axle and again apply an upward force on the West the opposing North and South forces will cancel each other. The axle can freely yaw but there is resistance to pitch and to roll.
_____________
If you want to pursue gyroscopic precession further, we should go to the [Gyroscopic Precession - Revisited] thread, so that other can beat up on you, also.
Now to tackle your main point.
Dave J
I don't disagree with your remarks about the propeller.
Previously mentioned was, " For gyroscopic precession to take place, the rotating device must have considerable [Angular Momentum]. A helicopter's rotor does not have enough."
This [Angular momentum] involves RPM and mass. A propeller has a much higher RPM and, proportionately, a much higher mass than the helicopter rotor.
______________
I actually hope that the UniCopter's two counterrotating rigid rotors do exhibit a little gyroscopic precession. This is desired to give the craft dynamic stability in pitch and roll.
Counterrotating Gyroscopes (Dynamic Stability):
Assume that the rotational part of a gyroscope is mounted on a stationary vertical axle. Assume, also, that we are looking down at the gyroscope (plan view) and that the locations of interest are the four primary points of the compass.
If the gyroscope was rotated CW an upward force on the West will cause the North to rise and the South to lower, due to precession. If the gyroscope was then rotated CCW the same upward force on the West will now cause the South to rise and the North to lower.
If we put two counterrotating gyroscopes on the same rigid axle and again apply an upward force on the West the opposing North and South forces will cancel each other. The axle can freely yaw but there is resistance to pitch and to roll.
_____________
If you want to pursue gyroscopic precession further, we should go to the [Gyroscopic Precession - Revisited] thread, so that other can beat up on you, also.
Now to tackle your main point.
Dave J
Last edited by Dave Jackson; 26th April 2002 at 00:14.
Thread Starter
Joined: Nov 2000
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From: Vancouver, BC, Canada
Lu,
"If you move the cyclic forward from a hover (assuming zero wind) the greater lift will be on the retreating side. This will generate a perturbing force on the two rotors causing them to move as a gyroscopic rotor 90-degrees later in rotation, which will cause the nose to fall and the tail to rise because of the 100% interlock between the rotors and the fuselage. At least I think that is what will happen."
I believe that you previously accepted the fact that an teetering rotor has a precession of 90-degrees and that a rotor with some rigidity (flapping hinge offset) has a precession of less than 90-degrees. If you increase this rigidity all the way to 'absolute' rigidity you will reduced the precession all the way to 0-degrees.
For further information on this, see my paragraph to CRAN a few postings back and his subsequent agreement.
__________
Here's a little mental analogy, for the fun of it. Take a toy gyroscope and with its axle vertical and 'weld' the axle to the top of a can of beer.
If you try to roll this assembly to the right when the gyro is not rotating, the assembly will roll to the right.
Now drink all the beer so that the can is very light and spin the gyro up to a zilloin rpm CCW. If you now try to roll this assembly to the right, the assembly will roll forward. [Gyroscopic precession]
Now **** the beer back into the can, file most of the mass off of the gyro and only spin it at 60 rpm.
If you try to roll this assembly to the right which way will it go?
This is the analogy with the Unicopter. The full can of beer is the heavy fuselage, the filed down gyro is the light rotor(s) and the 60 rpm is the slow rotor rotation.
If you don't buy this, I'm having a beer.
"If you move the cyclic forward from a hover (assuming zero wind) the greater lift will be on the retreating side. This will generate a perturbing force on the two rotors causing them to move as a gyroscopic rotor 90-degrees later in rotation, which will cause the nose to fall and the tail to rise because of the 100% interlock between the rotors and the fuselage. At least I think that is what will happen."
I believe that you previously accepted the fact that an teetering rotor has a precession of 90-degrees and that a rotor with some rigidity (flapping hinge offset) has a precession of less than 90-degrees. If you increase this rigidity all the way to 'absolute' rigidity you will reduced the precession all the way to 0-degrees.
For further information on this, see my paragraph to CRAN a few postings back and his subsequent agreement.
__________
Here's a little mental analogy, for the fun of it. Take a toy gyroscope and with its axle vertical and 'weld' the axle to the top of a can of beer.
If you try to roll this assembly to the right when the gyro is not rotating, the assembly will roll to the right.
Now drink all the beer so that the can is very light and spin the gyro up to a zilloin rpm CCW. If you now try to roll this assembly to the right, the assembly will roll forward. [Gyroscopic precession]
Now **** the beer back into the can, file most of the mass off of the gyro and only spin it at 60 rpm.
If you try to roll this assembly to the right which way will it go?
This is the analogy with the Unicopter. The full can of beer is the heavy fuselage, the filed down gyro is the light rotor(s) and the 60 rpm is the slow rotor rotation.
If you don't buy this, I'm having a beer.
Iconoclast
Joined: Sep 2000
Posts: 2,132
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From: The home of Dudley Dooright-Where the lead dog is the only one that gets a change of scenery.
To: Dave Jackson,
You stated:
"Now **** the beer back into the can, file most of the mass off of the gyro and only spin it at 60 rpm.
If you try to roll this assembly to the right which way will it go?
This is the analogy with the Unicopter. The full can of beer is the heavy fuselage, the filed down gyro is the light rotor(s) and the 60 rpm is the slow rotor rotation".
My response:
It will most likely assume the position that you moved it to. (Rolled the can to the right). There are two reasons for this:
1) By filing the weight off of the rotor you have decreased the mass of the gyro rotor thus severely reducing any precessional energy contained within the spinning mass
2) At 60 RPM there would be minimal energy in the spinning mass even if you had not filed most of the weight from the rotor.
In a previous posting they mentioned a toy gyroscope that can maintain rigidity in space as long as the rotor is turning at or above the minimal speed to maintain that rigidity. As the rotor spins down due to friction the energy decreases allowing the gyro to tumble. However there is still sufficient energy to respond to a perturbing force which is what causes the gyro toy to rotate in the direction of rotor rotation although some of this can be attributed to friction.
Are you stating that your conceptual helicopter has a totally rigid head(s) that rotate at only 60 RPM? If that is the case, then you will have to defy the laws of aerodynamics and physics to get the helicopter off the ground and then to respond to control inputs.
Care for a Labatts Blue?
You stated:
"Now **** the beer back into the can, file most of the mass off of the gyro and only spin it at 60 rpm.
If you try to roll this assembly to the right which way will it go?
This is the analogy with the Unicopter. The full can of beer is the heavy fuselage, the filed down gyro is the light rotor(s) and the 60 rpm is the slow rotor rotation".
My response:
It will most likely assume the position that you moved it to. (Rolled the can to the right). There are two reasons for this:
1) By filing the weight off of the rotor you have decreased the mass of the gyro rotor thus severely reducing any precessional energy contained within the spinning mass
2) At 60 RPM there would be minimal energy in the spinning mass even if you had not filed most of the weight from the rotor.
In a previous posting they mentioned a toy gyroscope that can maintain rigidity in space as long as the rotor is turning at or above the minimal speed to maintain that rigidity. As the rotor spins down due to friction the energy decreases allowing the gyro to tumble. However there is still sufficient energy to respond to a perturbing force which is what causes the gyro toy to rotate in the direction of rotor rotation although some of this can be attributed to friction.
Are you stating that your conceptual helicopter has a totally rigid head(s) that rotate at only 60 RPM? If that is the case, then you will have to defy the laws of aerodynamics and physics to get the helicopter off the ground and then to respond to control inputs.
Care for a Labatts Blue?
Joined: Jan 2001
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From: AB, Canada
Dave,
Everything rotating body will display "gyroscopic precession". Doesn't matter how fast/slow it turns, doesn't matter it's mass, mass distribution, etc.
It gets too complicated when multiple bodies get together to form a rotating system, so it's best to ignore GP. In fact also ignore aerodynamic precession...it just confuses the issue by generating argument about which precession theory applies to helicopters. Neither one does. They are both convenient explanations.
Examine the theory behind GP or AP. You will find it is the same rotational dynamics behind each. The blade wants to flap at it's natural frequency. If the natural frequency is the same as the rpm of the rotor, then the apparent lag is 90 degrees. If the natural frequency is higher, the lag is lower.
A gyroscope can be considered to be a bunch of point masses that are spinning around an axle and are free to "flap". Each point mass is just like a high school physics pendulum. The natural frequency depends on the length and the restoring force, sq. rt. of g/l in high school physics. Since the restoring force for the point mass is the centrifugal force (it's okay to use centrifugal force...just not a real force) then the force depends on the distance from the center, and the speed of rotation. In the end, we find each point mass has a natural frequency that is exactly the same as the rotational speed of the gyroscope. Reading the above paragraph, that means the apparent lag on a gyroscope is exactly 90 degrees. This shows that GP is just a special case of the blade frequency theory that is a much better way of looking at helicopters. QED
_____________
The full beer can with a slowly spinning gyro will do what you want, but it will require a small corrective force to keep the intended tilt in the right direction. That small corrective force corrects the gyroscopes reaction to the impressed moment.
______________
Lu, with the propellor example, the engine moves in response to the planes movement, that energy is absorbed by mounts, but some still transmitted to the aircraft. IIRC there are some aircraft with reversing gears between the engine and propellor to get closer to a zero angular momentum condition.
Everything rotating body will display "gyroscopic precession". Doesn't matter how fast/slow it turns, doesn't matter it's mass, mass distribution, etc.
It gets too complicated when multiple bodies get together to form a rotating system, so it's best to ignore GP. In fact also ignore aerodynamic precession...it just confuses the issue by generating argument about which precession theory applies to helicopters. Neither one does. They are both convenient explanations.
Examine the theory behind GP or AP. You will find it is the same rotational dynamics behind each. The blade wants to flap at it's natural frequency. If the natural frequency is the same as the rpm of the rotor, then the apparent lag is 90 degrees. If the natural frequency is higher, the lag is lower.
A gyroscope can be considered to be a bunch of point masses that are spinning around an axle and are free to "flap". Each point mass is just like a high school physics pendulum. The natural frequency depends on the length and the restoring force, sq. rt. of g/l in high school physics. Since the restoring force for the point mass is the centrifugal force (it's okay to use centrifugal force...just not a real force) then the force depends on the distance from the center, and the speed of rotation. In the end, we find each point mass has a natural frequency that is exactly the same as the rotational speed of the gyroscope. Reading the above paragraph, that means the apparent lag on a gyroscope is exactly 90 degrees. This shows that GP is just a special case of the blade frequency theory that is a much better way of looking at helicopters. QED
_____________
The full beer can with a slowly spinning gyro will do what you want, but it will require a small corrective force to keep the intended tilt in the right direction. That small corrective force corrects the gyroscopes reaction to the impressed moment.
______________
Lu, with the propellor example, the engine moves in response to the planes movement, that energy is absorbed by mounts, but some still transmitted to the aircraft. IIRC there are some aircraft with reversing gears between the engine and propellor to get closer to a zero angular momentum condition.
Thread Starter
Joined: Nov 2000
Posts: 452
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From: Vancouver, BC, Canada
heedm
Thanks for your more detailed explanation.
"Everything rotating body will display "gyroscopic precession". Doesn't matter how fast/slow it turns, doesn't matter it's mass, mass distribution, etc."
"The full beer can with a slowly spinning gyro will do what you want, but it will require a small corrective force to keep the intended tilt in the right direction. That small corrective force corrects the gyroscopes reaction to the impressed moment."
Agreed. In the UniCopter, it should not be a very strong force and therefore when integrated with the other rotors opposite "gyroscopic precession", it should dampen any oscillations in pitch and roll. [I previously erred and called it static stability when it is actually dynamic stability]
Thanks for your more detailed explanation.
"Everything rotating body will display "gyroscopic precession". Doesn't matter how fast/slow it turns, doesn't matter it's mass, mass distribution, etc."
"The full beer can with a slowly spinning gyro will do what you want, but it will require a small corrective force to keep the intended tilt in the right direction. That small corrective force corrects the gyroscopes reaction to the impressed moment."
Agreed. In the UniCopter, it should not be a very strong force and therefore when integrated with the other rotors opposite "gyroscopic precession", it should dampen any oscillations in pitch and roll. [I previously erred and called it static stability when it is actually dynamic stability]
Iconoclast
Joined: Sep 2000
Posts: 2,132
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From: The home of Dudley Dooright-Where the lead dog is the only one that gets a change of scenery.
To: heedm
Let's see how many people object to this statement.
Early on in discussions about gyroscopic precession I mentioned exactly the same thing (but in my words) regarding a book I read while working at Boeing (V-22) and the gyroscopic rotor you described above was illustrated and explained in the book. When I mentioned it I was crucified but those were the days everyone was preaching aerodynamic precession and flapping to equality. Terms that I was totally unfamiliar with.
A gyroscope can be considered to be a bunch of point masses that are spinning around an axle and are free to "flap". Each point mass is just like a high school physics pendulum. The natural frequency depends on the length and the restoring force, sq. rt. of g/l in high school physics. Since the restoring force for the point mass is the centrifugal force (it's okay to use centrifugal force...just not a real force) then the force depends on the distance from the center, and the speed of rotation. In the end, we find each point mass has a natural frequency that is exactly the same as the rotational speed of the gyroscope. Reading the above paragraph, that means the apparent lag on a gyroscope is exactly 90 degrees. This shows that GP is just a special case of the blade frequency theory that is a much better way of looking at helicopters. QED
Early on in discussions about gyroscopic precession I mentioned exactly the same thing (but in my words) regarding a book I read while working at Boeing (V-22) and the gyroscopic rotor you described above was illustrated and explained in the book. When I mentioned it I was crucified but those were the days everyone was preaching aerodynamic precession and flapping to equality. Terms that I was totally unfamiliar with.
Thread Starter
Joined: Nov 2000
Posts: 452
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From: Vancouver, BC, Canada
Lu & Heedm,
Help!!! The original theme of this thread has been stolen.
I'm moving my first 'precession' comments to [Gyroscopic Precession - Revisited]. If you guys want to cut and past in sequence, we can rebuild the conversation over there.
Lu. You're next
Help!!! The original theme of this thread has been stolen.
I'm moving my first 'precession' comments to [Gyroscopic Precession - Revisited]. If you guys want to cut and past in sequence, we can rebuild the conversation over there.
Lu. You're next
Last edited by Dave Jackson; 26th April 2002 at 17:44.
Thread Starter
Joined: Nov 2000
Posts: 452
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From: Vancouver, BC, Canada
Hi CRAN,
However an absolutely rigid rotor is physically unrealizable and therefore some flapping and hence 'some' flap-back will occur (the exact nature of it being dependent on the blade dynamics). The extent of this flapping will depend on how stiff you can make the rotor and still get off the ground."
I agree that absolute rigidity is unrealizable. My thinking is to make the blade as rigid as is feasible, then; a/ mold it with a slight downward curvature, or, b/ give the tip some anhedral, or, c/ give the pitch bearings a slight negative pre-cone.
The intent is to give the disk a zero coning angle when it is hovering at gross weight and then accept the small deviation (+ & - coning) during flight.
However an absolutely rigid rotor is physically unrealizable and therefore some flapping and hence 'some' flap-back will occur (the exact nature of it being dependent on the blade dynamics). The extent of this flapping will depend on how stiff you can make the rotor and still get off the ground."
I agree that absolute rigidity is unrealizable. My thinking is to make the blade as rigid as is feasible, then; a/ mold it with a slight downward curvature, or, b/ give the tip some anhedral, or, c/ give the pitch bearings a slight negative pre-cone.
The intent is to give the disk a zero coning angle when it is hovering at gross weight and then accept the small deviation (+ & - coning) during flight.
