Item 0940

OTHER: Flight Dynamics - General - Precession - Gyroscopic and Aerodynamic

Positional Statement;

1. Gyroscopic precession (torque-induced precession) explains the activity inside the flapping/teetering hinges.
2. Aerodynamic precession, including non-gyroscopic dynamics, explains the activity outside the flapping/teetering hinges.
3. An exception to 2. is the rigid rotor where, because of the flapping stiffness, some of the blade that is out is of the virtual hinge will partially contribute to the gyroscopic precession.

Therefor;

• Gyroscopic precession has nothing to do with teetering rotors.
• Gyroscopic precession has very little to do with all other rotors.

Elaboration:

The reference to gyroscopic precession was an easy-to-understand method of explaining aerodynamic precession to those who did not need to know the intricacies of the rotor. This was particularly true in the past, when gyrocopters and most helicopters had teetering or gimbaled rotors; and the phase angle was 90º. All modern helicopter rotors have phase angles that are less than 90º.

The rotor of a helicopter has very little inertia for its size. In fact, most pilots would like it to have more inertia during autorotation. I.e. The rotational speed of a helicopter rotor is very slow compared to that of a gyroscope. The mass at the circumference of a helicopter rotor is very small compared to that of a gyroscope.

The following excerpt is the conclusion of a mathematical description about gyroscopic precession;

"Now is the time to confess that there is an implicit assumption buried in our reasoning. We have assumed that the angular momentum was all due to the rotation of the rotor. In fact, the precessional motion also contributes to the total angular momentum. Our analysis is valid only as long as [the precessional frequency] is much smaller than [the angular velocity]. This condition is met when [the angular momentum] is large compared to [the applied torque]. Otherwise, the motion of the gyroscope is much more complicated, as you might observe in an actual experiment where the rotation of the rotor slows down over time. We can see that as the rotor slows, the precessional frequency increases. At some point when the precessional frequency exceeds a critical value, the gyroscope will begin to wobble and eventually tumble in its gimbals."

In other words; the rotational inertia of the helicopter's rotor visa vie, the to the aerodynamic tipping force of the cyclic, is too small for equations of gyroscopic precession to apply.

Overview:

The realignment the rotor disk, due to control input or perturbations can be explained;

1. solely in aerodynamic terms, or
2. in terms of an integrated gyroscopic precession and aerodynamic precession, but
3. not solely in gyroscopic terms.

In 2., the gyroscopic portion can only be related to the rigid portion of the rotor. This rigid portion will consist of the hub and on out to the flapping or lead/lag hinges. Beyond these hinges, aerodynamics and non-gyroscopic dynamics are involved; unless it is a very rigid rotor.

A propeller may be looked at from the perspective of gyroscopic precession because it is a rigid body and there is virtually no tilting of the disk involved. An Absolutely Rigid Rotors (ARR) will involve gyroscopic and aerodynamic precession because there is absolute rigidity in the disk but the complete helicopter 'tilts'.

An Absolutely Rigid Rotor (if such a rotor can be built) will have an aerodynamic phase angle of 0-degrees and a gyroscopic phase angle of 90-degrees. There will be an integration of the two phase angles. The aerodynamic contribution will be the much larger. This mean phase lag will vary during flight depending on forward airspeed, air density etc.

In respect to phase lag, the gyroscopic contribution will always have a phase lag of 90-degrees, whereas the aerodynamic contribution can have any phase lag. It can be greater or less than 90-degress. The aerodynamic phase lag is dependent on the forward velocity, air density and other aerodynamic events at the specific time. The resultant phase lag will again be they result of the contribution of both.

The argument against the use of gyroscopic precession as the sole reason for explaining the phase lag in a helicopter's rotor:

• The gyroscope's precession (phase angle) is 90-degrees; excluding a minor adjustment.
• The phase angle in helicopters can be greater than 90-degrees or less than 90-degrees.
• Therefore, gyroscopic precession is incapable of being the sole contributor to precession in helicopter rotors.

Gyroscopic precession was used as simplistic, but inaccurate, means of explaining the activity in early teetering rotors, gimbal rotors and gyrocopter rotors.

Stability and Gyroscopic Precession ('Absolutely' Rigid Rotors): from Thread on PPRuNe

Coaxial: ~ Will not improve 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 force will cancel each other. The axle can freely yaw but there is now no resistance to pitch and to roll.

_________________________

April 28, 2005, From Chiplight on PPRuNe talking about an experiment by Chuck Beaty. It is now appearing that the gyroscopic processional forces of the two rotors are self-canceling within the power-train frame. In other words, the gyroscopic effect will do nothing for damping.

Different Axis: ~ May?? improve stability ~or~ may it worsen stability by applying cross-couplings?

"If you mount two gyroscopes with their axles at right angles to one another on a platform, and place the platform inside a set of gimbals, the platform will remain completely rigid as the gimbals rotate in any way they please. This is this basis of inertial navigation systems (INS)."

This statement, from the Internet, may mean that the two counterrotating rotors would slightly contribute to the stability of a rigid intermeshing configuration. This is because the masts on the intermeshing UniCopter are at 18º to each other. Do you have any thoughts?

_________________________

"... masts on the intermeshing UniCopter are at 18º to each other."

By Mart (Graviman);
The vertical axis components will cancel, but yes there will be some residual horizontal component. This would give some roll/yaw stability, and accounts for the Flettner direction of rotation - breaststroke is thus equivalent to single gyro going top forwards, bottom backwards. In sideslip the vertical tailplane would input yaw torque, to cause gyro
precession roll as if dihedral. Same sideslip causes downwind rotor to produce more lift, so precession causes yaw towards sideslip (like a tailplane). Don't forget sideslip "dihedral" is being countered, to some extent, by incorrect lift balance of rotors. There is also the yaw effect caused by torque imbalance of downwind rotor seeing more lift, breaststroke rotation causing yaw into wind.

_________________________

My thoughts;

• If the rotating masses are on axes at 0º to each other (coaxial) and rotating in opposite directions there will not be a gyroscopic effect, due to the cancellation within the frame.
• If one of the rotating masses is swung down 90º to the left and the other is swung down 90º to the right (coaxial) there will not be a gyroscopic effect, due to pitch being on the axes of both rotating masses.
• Therefore, if one of the rotating masses is swung down 9º to the left and the other is swung down 9º to the right so that their axes are at 18º to each other there should not be a gyroscopic effect.

• If the rotating masses are on axes at 0º to each other (coaxial) and rotating in opposite directions there will not be a gyroscopic effect, due to the cancellation within the frame.
• If one of the rotating masses is swung down 90º to the left and the other is swung down 90º to the right (coaxial) there will be a gyroscopic effect. Both masses will be rotating in the same direction and this will cause a rotation about the Z-axis.
• Therefore, if one of the rotating masses is swung down 9º to the left and the other is swung down 9º to the right so that their axes are at 18º to each other there should be a gyroscopic effect. Roll will cause some yaw.

• If the rotating masses are on axes at 0º to each other (coaxial) and rotating in opposite directions there will not be a gyroscopic effect, due to the rotation being on the same axes as that of the rotating masses.
• If one of the rotating masses is swung down 90º to the left and the other is swung down 90º to the right (coaxial) there will be a gyroscopic effect. Both masses will be rotating in the same direction and this will cause a rotation about the X-axis.
• Therefore, if one of the rotating masses is swung down 9º to the left and the other is swung down 9º to the right so that their axes are at 18º to each other there should be a gyroscopic effect. Yaw will cause some roll.

Thoughts re the UniCopter:

• I did not notice any sense of gyroscopic precession when pitching, rolling and yawing the arraignment shown in the above picture
• If there are small cross-couplings between the X-axis and the Z-axis due to gyroscopic precession, might any gyroscopic precession from the propeller, and perhaps the engine, reduce these cross-couplings? This might depend on the direction of rotation of the propeller and motor. It should also be noted that the RPM of the propeller will be zero during hover but it will be constant at forward speeds from 50 % of cruise on up. Try to conceptualize this arraignment.

Gyroscopic Precession:

Outside Information:

gyroscopes.org

GYROSCOPIC PRECESSION

[See ~ RW, ch. 4]

Explanation (1) of gyroscopic precession

Explanation (2) of gyroscopic precession

Unique application of gyroscopic precession - the Cheyenne AH56A ~ by Doug Marker

Analytical Classical Dynamics ~ An intermediate level course

Gyroscopic Inertia: The resistance of the gyroscope's spin axis to change in direction.

Nutation is the process of seeking a balance between the rate of tilt, and the rate of precession, two conditions that play upon one another as actions and reactions. As quickly as the balance is reached, nutation (bouncing) stops.

By heedm:

The biggest problem with gyroscopic precession is that the term is used completely inaccurately when describing helicopter flight. It is not a force. It is not an explanation of why a force applied to a spinning object appears to manifest itself 90 degrees later. It is an example of that apparent 90º lag.

When you spin a top, if the surface it's contacting offers little friction, then the top spins about one axis until that axis leans from the vertical. Once it leans from the vertical, gravity tries to pull it over. Instead of falling over, the top continues to spin about it's axis, but the axis rotates in space, or precesses.

That's what gyroscopic precession is.

The top precesses rather than falling over because the force of gravity causes a moment about the contacting point of the top. Since the top is spinning, that moment adds more spin to it, but about a different axis. When these spins are added, the result is the top wants to spin about it's axis while leaning 90 degrees away from the direction that the force was applied. Gravity continues to act on the top, so the top continues to "fall" 90 degrees away from the direction the force was applied. The result is the precession.

Aerodynamic Precession:

Description:

This is the function of the blades flying to position. The blade's pitch change precedes the resultant flap or teeter. In the case of a rotor where the blades are hinged (for out of plane motion. I.e. flapping or teetering) at the center of the mast to aerodynamic precession the phase lag will be 90-degrees, which is the same as the gyroscopic precession. Flapping hinge-offset etc. will reduce the aerodynamic phase lag and an absolutely rigid rotor will have a phase lag of 0-degrees.

General:

See postings in rec.aviation.rotorcraft, started by Doug Marker on April 18, 2000. Subject [Not starting a controversy ---]

Comparison of Aerodynamic and Gyroscopic Precession; using the SynchroLite

Aerodynamic Calculation for Application of 50 pounds of Cyclic Torque at 75% of Rotor Radius:

The following calculations are based on the database's twin rotor calculations, which give a higher horsepower than actual, but the values are good enough for this comparison.

To hover with a gross weight of 545 pounds the collective is 6.55º

To hover at 570 pounds (25 pounds more) will require a pitch of 6.76º

To hover at 520 pounds (25 pounds less) will require a pitch of 6.32º

Distance from mast to center of blade's lift [r] is at 75% of rotor's radius.

The change in pitch to get 50 lb * r cyclic moment arm is [(6.76º - 6.32º = 0.44º) / 2 ] equals a 0.22º change in cyclic pitch. In other words the thrust is still 545 pounds but one side is exerting 50 pounds more, at 75% of R, than the other.

In 90ºs of rotation the 75% point on the blade [r] will have climbed [(pi * 2 * r / 4) * tan (0.22)] = 0.47"

Gyroscopic Calculation for Application of 50 pounds of Cyclic Torque at 75% of Rotor Radius:

The following calculations are from Explanation (2) of gyroscopic precession

Remember that the torque is the rate of change of the angular momentum (dL/dt), so its magnitude is given by: |dL/dt| = TC * g * r

The following table and its calculations have problems. For what appears to be correct see DESIGN: Electrotor-SloMo - Rotor - Disk - Gyroscopic Precession

 SynchroLite: UniCopter:(1) Angular velocity: [ω] (of rotor) 63 73 rad/sec Moment of inertia: [JM] (blades only, hub excluded) from DESIGN: SynchroLite ~ Rotor - Disk - Coning Angle 185.3 * 2 blades * 2 rotors 100 * 3 blades * 2 rotors ft-lb^2 Angular momentum: [L] = JM * ω (of rotor) 46,696 43,800 lb-ft-sec2 The cyclic applied thrust: [TC] 50 50 lbs The acceleration due to gravity: [g] 32.17 32.17 ft/sec^2 The location thrust (75% of R): [r] 8.667' * 0.75 8.333' * 0.75 feet Tc is in # should g be here? Torque: [τ] [tau] = TC * g * r 50 * 32.16 * 6.5 = 10,452 50 * 32.16 * 6.25 = 10,050 ft-lb The above line - modified 50 * 6.5 = 325 50 * 6.25 = 312 ft-lb This looks like it is based on L not Jm The angular frequency of the axis of rotation, called the precessional frequency: [ωp] = τ / JM 10,452 / 46,696 = 0.224 10,050 / 43,800 = 0.229 rad/sec The above line - modified 325 / 741.2 = .438 10,050 / 600 = 16.75 rad/sec 0.224 * 57.28 = 12.8 0.229 * 57.28 = 13.1 deg/sec The above line - modified 0.438 * 57.28 = 25.12 deg/sec A quarter revolution will be made in 1.57 / 63 = 0.025 1.57 / 73 = 0.022 sec. The change in the angle of the blade will be 12.8 * 0.025 = 0.32 13.1 * 0.022 =0.29 degrees The above line - modified 25.12 * 0.025 = 0.628 degrees The climb at [r] is 104" * .75 * sin(0.32) = 0.44 100" * .75 * sin(0.29) = 0.38 inches The above line - modified 104" * .75 * sin(0.628) = 0..85 inches

(1) UniCopter is not used in this comparison.

It looks like the two methods give equal values.

It might be interesting to put the algorithms for calculation by gyroscopic precession and those for calculation by aerodynamics side by side. Then look at the sources of the data for each. This will show what inputs they have in common and what inputs are unique to each.
Another thought is to change the rotor's mass and see if it is possible to get the results from both methods to show a greater discrepancy.
Something for a very very rainy day.

The following is a hugmungous amount of verbiage; to be edited and compressed - some day.

Position Held:

I believe that gyroscopic precession has extremely little, and in some cases absolutely nothing, to do with the activities at a helicopter's rotor-disk.

The bicycle wheel is used as an example of gyroscopic precession. Consider the rotation of this bicycle wheel after we have removed; its tire, its rim, and all but four of the spokes (i.e. 4-blade rotor). Please note that these spokes are 'hinged' at the hub. I do not think that we will now be experiencing gyroscopic precession from this bicycle wheel.

Prouty states that if a shaft is tilted in a vacuum, and there is no hinge offset at the hub (i.e. a teetering rotor), the tip path plane will remain in the original position. Because the bicycle's spokes are hinged at the hub, they will behave as Prouty says. In fact the spokes do have a small offset, and Prouty says that with an offset in a vacuum, and with or without an offset in air, the tip path plane will align itself perpendicular to the shaft. This alignment is the result of centripetal force. If gyroscopic precession was a participant, the bicycle disk would have a tilt at 90-degree to the tilt that the shaft was just given.

The blades do not operate in a vacuum of course, and therefore they should be considered as 'flying' to position. If this is to be called anything, 'aerodynamic precession' might be a more appropriate expression.

Nick Lappos thinks that Gamma [Γ] may change due to air density, and this might be another argument against gyroscopic precession. He feels that "Gyroscopes have nothing to do with it at all!"

Having postulated that there is no gyroscopic precession, the following is a partial retraction:

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 the blades' ability to flap, the phase angle [Γ] will decrease from 90-degrees. In other words, an increasing of the flapping hinge's offset or an increasing of the dampening of the flapping hinge will result in an even smaller phase angle.

Let's now consider an airplane's propeller. We know that the propeller is subject to gyroscopic precession. Also, we know that the primary difference between a variable pitch propeller and a helicopter's rotor is their rigidity. I would suggest that it is this out-of-plane (flapping) rigidity difference, that we are concerned with.

If we take this idea of rotor rigidity to the extreme of a propeller, 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 be a small change in pitch as well. I believe that this small pitch change is the result of gyroscopic precession, which in turn is the result of changing the attitude of an extremely rigid rotor disk (read as gyroscope disk).

Summation:

A 'floppy' teetering rotor will not experience any gyroscopic precession. This is because it is a 2-blade rotor and there is nothing at 90-degrees ahead of the blades to gyroscopically 'precess'.

An absolutely rigid rotor will act like a gyroscope and therefore experience precession. The amount of 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 has achieved this high a level of rigidity

My position at this moment;

There must be out-of-plane stiffness in the rotor for there to be gyroscopic precession present. Teetering rotors will have none whereas rotors with offset and flapping stiffness will have a little.

August 10, 2001 ~ My position just changed see comparison below;

It might be noted that a primary design attribute of the UniCopter is an absolutely rigid rotors.

Probably most of the world, believes that the association between 'gyroscopic precession' and '90-degrees' is a fact. The following excerpt on gyroscopic precession should be of interest.

But first, we must agree that a helicopter's rotor does not rotate as fast as a gyroscope and that the rotor's relative mass is not as great as a gyroscope's relative mass.

".............. Otherwise the motion of the gyroscope is much more complicated, as you might observe in an actual experiment where the rotation of the rotor slows down over time. We can see that as the rotor slows, the precessional frequency increases. At some point when the precessional frequency exceeds a critical value, the gyroscope will begin to wobble and eventually tumble in its gimbals." From; Explanation (2) of gyroscopic precession [My change to bold].

Gyroscopic precession has *virtually* nothing to do with a helicopter's rotor.

Gyroscopic precession is little more than a simplistic means of describing the [i]basic[/i] end result at the rotor, after the application of a cyclic input. (i.e. 90-degrees later ~ [i]basically[/i]). It is no good for explaining the 'how'.

The simplest argument against the use of 'gyroscopic precession' is to look at its algorithm. Mass and rotational velocity are the predominant variables. The relative mass and rpm in a gyroscope are humoungeous. The relative mass and rpm in a rotor disk are negligible.

The helicopter's rotor disk 'flies' to position. The eventual demise of the sinusoidal swashplate will result in rotor blades that can fly to position in 12.3-degrees or 123-degrees.

The results of gyroscopic precession and aerodynamic precession are the same for a basic teetering rotor, but the result of gyroscopic precession is easier to see. It therefore is a quick way to explain precession to mechanics and pilots who have to work with it but do not necessarily have to know its 'innards'. If a pilot or mechanic want to fully understand precession then to continue to explain it in terms of gyroscope precession only becomes a problem.

I am not saying "that gyroscopic precession has nothing to do with helicopter rotors". It plays a role, but its direct roll is a very small one and its indirect role is exactly that ~ 'indirect'.

A gyroscope (gyroscopic precession) functions because of high mass and high rpm. Aerodynamic plays no significant role.

A rotor (aerodynamic precession) functions because of aerodynamic forces. Mass and high rpm play no significant role

Direct role:

I believe the magnitude of gyroscopic precession's direct role in aircraft is dependent upon the rigidity, mass and speed of the device. A propeller will have a reasonable amount of gyroscopic precession, whereas a teetering rotor will have very little.

Indirect role:

Nick mentioned "The wheel is rigid, of course, so each part of it cannot move relative to any other.". What he is saying [I think :) ]is that a force at one location on the rigid wheel is creating forces at all locations on the rigid wheel. If a force at 90-degrees azimuth results in an upward force of 5 lbs at that location then there will be a force of -5 lbs at 270-degrees. There will be a sine(45) * 5-lb force at 45 and 135-degrees. There will be a 0-lb force at 0 and 180-degrees, etc,etc. The culmination of all the upward forces is at 180-degrees, and this is the high point. . The culmination of all the downward forces is at 0-degrees, and this is the low point.

Nick is talking about a singular force being distributed around the circumference due to the rigidity of the circumference. As he said, he is describing gyroscopic precession.

The helicopter rotor does not have this rigid ring at its circumference. It also does not have a singular force at one location. The pitch of its blades is providing a force directly to all the locations.

For these reasons, I believe that aerodynamic precession is a cleaner description.

_______________

Gyroscopic precession and aerodynamic precession only give the same results because the swashplate and gyroscopic precession produces a sinusoidal curve. When the swashplate (pure sinusoidal curve) is replaced, gyroscopic precession must fly out the window. This is because the new pitch controllers will be able to put into the blade any pitch at any azimuth they want to. I.e. no longer pure sinusoidal.

In the case of an intermeshing or coaxial helicopter, it may be possible to add a little additional short-term pitch to the lower blade as it passes through the downwash of the upper blade.

From PPRuNe ~ Nov 2001

Nick Lappos

Gyroscopic precession is a mysterious force, until you look at the fundamental physics behind it. The best way to figure it out is to look it up in a Physics text, or an Engineering Mechanics text.

The underlying principles are basic. The gyro has a fixed angular momentum due to the spinning mass. This is a set quantity, and(like linear momentum) must be preserved. If you try to rotate the gyro, you are adding to the angular momentum (because the rotation of the whole gyro in another plane induces a change to the total angular momentum). The faster the rotation you impart, the more the momentum change that you request. As a total system, the momentum must be constant, when you disturb the angular momentum balance, the extra rotation 90 degrees out results.

One way of describing it is to picture a wheel spinning free in space. Imagine it in front of you spinning with its axle pointing at you, rotating clockwise (top to the right). It is happy to spin there, undisturbed, until you push on the top rim (12 o'clock position)in a direction away from you. The wheel is rigid, of course, so each part of it cannot move relative to any other. Because you start it moving away from you, the piece of the wheel at the top has two components of its velocity, one to the right, and one directly away from you. This means that you have tried to disturb its velocity, relative to the rest of the wheel. Because the rototion you called for (top away, bottom toward you) has no rotational speed at the sides of the wheel (the 3 and 9 o'clock pieces of the wheel see no translation due to your push), the mass has the confusing need to have more energy at the top and bottom (more total speed) than it does at the sides (3 and 9 o'clock) The "precession" of the gyro is simply the motion that the gyro makes that rotates this 3 and 9 o'clock part to EXACTLY match the 12 and 6 o'clock part. The speed of rotation imparted on the wheel is proportional to the force you exert on the wheel, and its angular momentum (speed of rotation, basically). The slower it spins, the faster the precessional speed to make up for the larger disturbance you caused.

Dave Jackson

Gyroscopic precession has *virtually* nothing to do with a helicopter's rotor.

Gyroscopic precession is little more than a simplistic means of describing the basic end result at the rotor, after the application of a cyclic input. (i.e. 90-degrees later ~ basically). It is no good for explaining the 'how'.

The simplest argument against the use of 'gyroscopic precession' is to look at its algorithm. Mass and rotational velocity are the predominant variables. The relative mass and rpm in a gyroscope are humoungeous. The relative mass and rpm in a rotor disk are negligible.

The helicopter's rotor disk 'flies' to position. The eventual demise of the sinusoidal swashplate will result in rotor blades that can fly to position in 12.3-degrees or 123-degrees.

Dave Jackson

The results of gyroscopic precession and aerodynamic precession are the same, but the result of gyroscopic precession is easier to see. It therefore is a quick way to explain precession to mechanics and pilots who have to work with it but do not necessarily have to know its 'innards'. If a pilot or mechanic want to fully understand precession then to continue to explain it in terms of gyroscope precession becomes a problem.

I am not saying "that gyroscopic precession has nothing to do with helicopter rotors". It plays a role, but its direct roll is a very small one and its indirect role is exactly that ~ 'indirect'.

A gyroscope (gyroscopic precession) functions because of high mass and high rpm. Aerodynamic plays no significant role.
A rotor (aerodynamic precession) functions because of aerodynamic forces. Mass and high rpm play no significant role

Direct role:

I believe the magnitude of gyroscopic precession's direct role in aircraft is dependent upon the rigidity, mass and speed of the device. A propeller will have a reasonable amount of gyroscopic precession, whereas a teetering rotor will have very little.

Indirect role:

Nick mentioned "The wheel is rigid, of course, so each part of it cannot move relative to any other.". What he is saying [I think]is that a force at one location on the rigid wheel is creating forces at all locations on the rigid wheel. If a force at 90-degrees azimuth results in an upward force of 5 lbs at that location then there will be a force of -5 lbs at 270-degrees. There will be a sine(45) * 5-lb force at 45 and 135-degrees. There will be a 0-lb force at 0 and 180-degrees, etc,etc. The culmination of all the upward forces is at 180-degrees, and this is the high point. . The culmination of all the downward forces is at 0-degrees, and this is the low point.

Nick is talking about a singular force being distributed around the circumference due to the rigidity of the circumference. As he said, he is describing gyroscopic precession.

The helicopter rotor does not have this rigid ring at its circumference. It also does not have a singular force at one location. The pitch of its blades is providing a force directly to all the locations.

For these reasons, I believe that aerodynamic precession is a cleaner description.
_______________

Gyroscopic precession and aerodynamic precession only give the same results because the swashplate and gyroscopic precession produces a sinusoidal curve. When the swashplate (pure sinusoidal curve) is replaced, gyroscopic precession must fly out the window. This is because the new pitch controllers will be able to put into the blade any pitch at any azimuth they want to. I.e. no longer pure sinusoidal.

In the case of an intermeshing or coaxial helicopter, it may be possible to add a little additional short-term pitch to the lower blade as it passes through the downwash of the upper blade.
_______________

Phase lag, Gamma, offset and delta-3 are subjects for other future threads.

heedm

Nick's right when he talks about summing the spins. The energy argument is a little mixed up, and it actually applies to special cases only. One important point, the angular momentum is not constant, it is conserved. If you apply a moment to a spinning object you change the angular momentum in magnitude, direction, or both.

In the past I've found that many don't accept some of the jumps in a rotational dynamics based description of gyroscopic precession, or they don't have the background to understand it. If you want a fairly complete attempt at explaining gyroscopic precession, I put one on page two of the Helicopter Dynamics: Gyroscopic Precession thread. I warn you, it's long.

Don't believe what Dave says about a gyroscope requiring high mass and high rpm. Gyroscopic effects happen on all rotating systems. Read my previous message in this thread.

Dave Jackson

Heedm

>"I think you'll find that the theory behind it is the same for gyroscopic precession and aerodynamic precession ."<

I have always agreed with you on this. In fact, during the previous set of postings I did the math to verify it.
________________

The following is another reason for using 'Aerodynamic non-relativistic rotational kinematics' in preference to 'Gyroscopic non-relativistic rotational kinematics'.

The swashplate and also the basic Bell, 2-blade, teetering (normal to span) rotor exhibit exactly the same characteristic as a gyroscope. I.e. 90-phase offset.

All rotorheads with a flapping hinge offset have a phase offset that is less than 90-degrees. 'Gyroscopic non-relativistic rotational kinematics' cannot represent this (at least not easily). 'Aerodynamic non-relativistic rotational kinematics' (blade flying to position) can.

Would you agree to this?

Kyrilian

Dave,
Perhaps you need a quantitative way to describe your definitioin of 'relative'. How about the Lock number (gamma = rho*c*cla*R^4/Ib where rho is density, c is chord, cla is the lift curve slope, R is rotor radius and Ib is the blade moment of inertia)? So what you're arguing is that gamma is much larger than 1 (and I think a reasonable number for argument's sake would be 8--more for most articulated and teetering rotors, and less for rigid rotors).

heedm

Edited stuff in italics

Dave, I was a bit confused about what you meant by the relative mass and rpm. The only significant comparison between the two of which I'm aware is angular momentum. I think helicopter rotors have more angular momentum than the average gyroscope.

There are many other relationships that include mass and rpm. Rotational Kinetic Energy is one of the obvious ones. I didn't consider including more concepts to be useful.

As far as what type of non-relativistic rotational kinematics to use, drop the terms "gyroscopic" and "aerodynamic" and I'll agree with you.

The flapping hinge offset is described by basic physics quite easily. This is a very small part of the explanation. There are aerodynamic and control geometry effects that have a much larger effect on gamma. I alluded to this in my long post on gyroscopic precession. The natural frequency of the blade becomes less than the 1/rev of a blade with the flapping hinge coincident with the center of rotation. Because of this, the blade wants to flap in a full cycle in less time it turns through a complete revolution, so when it's finished a 1/4 cycle (max displacement) then blade has rotated less than 90 degrees (gamma less than 90).

Were it not for a driving force that is mechanically in phase to rotation of the blade (via swashplate) then the blade's motion could be quite erratic.

Dave Jackson

Thanks Kyrilian

The Lock number could be a perfect way to scale the rotor.
It might also be usable for scaling the gyroscope, by using '1' as a constant for 'density x lift curve slope'
______________

Heedm

>"As far as what type of non-relativistic rotational kinematics to use, drop the terms "gyroscopic" and "aerodynamic" and I'll agree with you.

I'm happy to drop the term 'gyroscopic'. It is a good one for holding a spinning bicycle wheel in your hand and saying "Wow". It is also a valid analogy for describing a basic teetering rotor head, which is used in conjunction with a 90-degree offset pitch horn and a swashplate.

I believe that the analogy with the gyroscope starts to loose its validity as delta-3, flapping hinge offset and rigid rotors are introduced. It will probably loose more of its validity as 'smart materials' are incorporated into the rotor blades. An expert in the field has stated that the swashplate is no longer totally compatible with many current rotorhead designs.

The helicopter rotor is an aerodynamic device. I believe that the best way to describe its operation, is aerodynamically (I.e. the blade flies to position), now and even more so in the future.

heedm

Dave said, "I believe that the analogy with the gyroscope starts to loose its validity as delta-3, flapping hinge offset and rigid rotors are introduced. It will probably loose more of its validity as 'smart materials' are incorporated into the rotor blades."

If you apply a moment to a rotating body, the result must be a vector sum of the original angular momentum and the impressed angular momentum. Doesn't matter if there is an unusual control geometry, aerodynamic effects, etc. Gyroscopic precession is actually an illustration of that effect. Many basic helicopter texts use gyroscopic precession to mean that effect. If you use this latter definition, then it's valid as long as the rotors are turning.

"The helicopter rotor is an aerodynamic device. I believe that the best way to describe its operation...."

I try to talk only about the motion of the rotors due to a force being impressed upon them. Yes, some of those forces are generated aerodynamically. How they are generated does not change the effect they have on the system.

Rotors are also accelerated by an internal combustion engine. Should that be in a theory on why rotors lag by 90 degrees?

I really don't care what you want to call it. To me, rotational dynamics says it all. So does many other terms. I don't see that specifying the origin of these forces creates any deeper understanding of the concepts, rather it may confuse.

I'm sure given the budget we could build a model of a rotor system that generates "lift" through magnetism or something other than aerodynamics. It would exhibit a 90 degree lag as well.

Dave Jackson

Lu

>"Why do you feel that a Bell rotor system emulates the qualities of a gyroscope just because it has a 90-degree pitch horn?"<

I don't.

The following statement is from an aerodynamist, who's name I've forgotten. "For blades freely articulated at the center of rotation, or teetering rotors, the response is lagged by exactly 90-degrees in hover".

The pitch horn does not make the rotor emulate the gyroscope. The pitch horn only aligns the cyclic control stick with the rotor.
____________________

>"Yet you totally discount the Sikorsky and all of the other multi blade helicopters. "<

I don't discount the Sikorsky. Its only that I, you and perhaps a few others are having difficulty understanding the basics, so it is probably a little premature to introduce additional complexities.

Dave Jackson

>"If you apply a moment to a rotating body, the result must be a vector sum of the original angular momentum and the impressed angular momentum."<
>"I don't see that specifying the origin of these forces creates any deeper understanding of the concepts, rather it may confuse."<

Why talk about "impressed angular momentum' when one can eliminate the middlemen, go right to the source and just say 'thrust'?
________________

>"Yes, some of those forces are generated aerodynamically. "<
>"Rotors are also accelerated by an internal combustion engine. Should that be in a theory on why rotors lag by 90 degrees? "<

There is only one force that is of interest. It is the only one that is variable and it is aerodynamic. The "original angular momentum" is an uninteresting constant. Or at least the RRPM better be a constant or there are serious problems.
__________

As previously mentioned, we are talking about the same thing. I prefer looking at it aerodynamically and use aerodynamic algorithms, where as you prefer to look at it dynamically and use dynamic algorithms. Are these fair statements?

heedm

Dave said, The aerodynamicist will collect a large number of variable, such as; pitch, angle of attack, RRPM, forward velocity, air density, chord, airfoil profile centrifugal (centripetal) force etc., etc. etc. He will then calculate [the height that the blade will fly to], at the azimuths of interest.

Thank you. We agree. Since NONE of our discussions mentioned pitch, angle of attack, forward velocity, air density, chord, or airfoil profile then obviously we weren't discussing this from an aerodynamics point of view.

Aerodynamics is "The dynamics of bodies moving relative to gases, especially the interaction of moving objects with the atmosphere." (The American Heritage® Dictionary of the English Language, Fourth Edition)

We weren't discussing anything about aerodynamics. What we were talking about were the effects of forces that we all took for granted, forces that are generated aerodynamically.

Dave said, "Why talk about "impressed angular momentum' when one can eliminate the middlemen, go right to the source and just say 'thrust'?" Because the two are different. You add thrust to angular momentum the same way you add oranges to anecdotes...you can't. Besides, thrust is an intermediary. The thrust produced by the blade is mostly used to hold the helicopter off the ground. A small part of the thrust is used to create a moment on the blade which imparts angular momentum to that blade, which is summed with the angular momentum the blade already has, .... are you getting it now?

Dave said, "There is only one force that is of interest. It is the only one that is variable and it is aerodynamic. The "original angular momentum" is an uninteresting constant. Or at least the RRPM better be a constant or there are serious problems."

You may find it uninteresting, but just like high school geometry, you can't do without it. The mass of planets doesn't change considerably, but if NASA ignored that uninteresting constant, those rockets just wouldn't get anywhere.

Also, there is not only one force that is variable. Drag is variable. Weight is variable (remember weight is a vector, it's direction changes as the attitude of the blade and/or helicopter changes). Depending on how you choose to label all the interactions the rotors have with their environment, there can be many more changing forces. Of course, it doesn't matter how you label them, they all have to be considered no matter how much they interest you.

Yes, we do agree on most of this stuff. You still seem to hold aerodynamic precession as a very special concept. I'm not sure exactly what your theory is, and as Lu was wondering, how it explains what the apparent lag is. A more general theory from a dynamics point of view (keep in mind that aerodynamics is a subset of dynamics) does explain that apparent lag, and it doesn't need to know the air density to explain it.

aerotech

Hi guys,just felt a need to throw in a couple of comments.I've never worked on two bladed heads so most of my experience comes from 3,4 and 5 bladed heads. The comments i've been reading about pitch horn offset seem to miss the point as i understand it which is that the pitch on the blade will reach it maximum deviation 90degs before the effect is felt.so the pitch horn offset can be ignored because it is the position of the blade centre line that is important as the response is at 90degs to this.
Somebody mentioned the control spider on a lynx (sorry forgot who) and said that with system the sinusoidal nature of the swashplate can be overcome, this however is not the case.The end result of the spider is exactly the same as a swashplate. Another point made about the lynx head is that it is rigid and will suffer the effects of procession more so than fully articulated head,although the head is semi-rigid the articulation is achieved in the flex of the titanium sleeves and central star,so the blades still flap,lead and lag the same as any other helicopter and so shouldn't feel procession more or less than any other helicopter.
If i've misunderstood any of the above comments i'm sure somebody will put me right

Grey Area

Gentlemen, especially believers in precession. A point to ponder for you.

The Autogyro (yes I've flown those as well). The control of the rotor in simple autogyros is direct movement of the teetering hub; this input is in phase with the disk movement.

Lets look at the forces applied when commanding the disk to tilt forward.

1. An upward force is applied at the BACK of the disk (6 o'clock).

2. A tiny movement of the disk causes the advancing blade to experience an instantaneous reduction in effective pitch angle reducing the angle of attack. The disk begins to move, does it:

A. Tilt up on the side of the advancing blade (3 o'clock [for example]) following the laws of precession?

Or

B. Tilt forward.

Given that we already know that the controls are rigged in phase we know that the effects of precession are not noticeable to the pilot and the disk tilts forward.

Now imagine if you used a swashplate instead. Where would you want to reduce the pitch if you wanted the disk to tilt forward (teetering, undamped head)?

GA

PS. With over 1500 helicopter deck landings I can assure you that the disk follows the helicopter, which follows the deck, at normal rotor speeds no matter what the pitch or roll. Why? Because if it didn't it would experience a change in its' attitude relative to the control orbit which would return the disk to its'original position as though the pilot had commanded the disk to level itself with respect to the aircraft. However gust of wind, or turbulence, especially with a vertical component alter the induced velocity and disturb the disk, at low rotor rpm the blade sail can be quite significant and tip strikes on the deck are not unheard of.

PPS Heedm - In response to an earlier post of yours, the Robinson you saw hovering tilted to one side was experiencing an effect called "Tail Rotor Roll", more or less all conventional single rotor helicopters experience this, it has nothing to do with gyroscopes.

Nick Lappos

I thought I'd toss in my 2cents about gyroscopic precession and helicopter swashplate rigging angles. Kirilian laid out the factors that describe how a rotor does not obey the gyroscopic precession rules (because it is not a gyroscope in any real way). The swashplate rigging angle is affected by many factors, and is never really 90 degrees in any helicopter!

Before all the mechanics jump up and describe (accurately) that their helicopter is rigged exactly at 90 degrees (forward stick makes the swashplate tilt exactly to the right), let me clarify one point:

The rigging of the helicopter is the offset put in to phase the cyclic exactly to match the motion of the aircraft. The test of perfection is that the pilot moves the cyclic forward and the nose goes down, with no roll at all (and vice-versa). Well, that never really is achieved! We compromise in two important ways:

1) Speed changes the rigging angle (we call it Gamma) so that there is a big change between hover and Vne. As I recall, high speed needs less Gamma, hover needs to most. The difference for the S-76 was about 10 degrees, for the Comanche it is even more! We usually compromise at a Vcruise setting and let it go. The S-76 flew with 3 different sets of mixing bellcranks, and we picked the "best" set to match our opinions. For Comanche, with the Fly By Wire, we tune the Gamma to match each flight condition.

2) There is a rotor tilt for short term, medium term and long term that is different. The short term is seen in big stick inputs done fast, and washes out quickly. This one is usually under-mixed, since it is seen only in abrupt, unusual maneuvers (unless you are dogfighting in a Comanche). The BO-105 folks know this one when they pull load factor and there is a big need to retrim roll.

The meduim term slow response is there as the "constant" term and is the one we address with mechanical mixing in most helos. This is the one that sets Gamma. You find this if you ask for 5 degrees per second roll rate, and look to see if any pitch retrim is needed.

The longest term is the roll and pitch retrim needed for changes in airspeed, which we do not set up mechanically, we let the auto-pilot or pilot worry about this. This one sets the S-76 and Robinson stick somewhat to the right as speed increases, about 1" or so from hover to cruise. Don't be confused by this one, at any point in the flight, if the pilot pushes the stick forward, the nose goes down with almost no roll, even though the stick is moving with airspeed in a slightly rightward direction.

Let me forwarn LU, I will answer no questions he asks on this subject, as he has read all this before and has NEVER understood a word of it. If any other ppruners have a question or disagreement, fire away!

Dave Jackson

Heedm

>>""Why talk about 'impressed angular momentum' when one can eliminate the middlemen, go right to the source and just say 'thrust'?"< Because the two are different."<.

True, but force (or torque) changes the state of rotational inertia and rotational inertia is a component of angular momentum.

>"Also, there is not only one force that is variable. Drag is variable. Weight is variable."<

True again, but for conceptual simplicity, it is easier to consider them as being constants.

>"You still seem to hold aerodynamic precession as a very special concept. I'm not sure exactly what your theory is, and ..... how it explains what the apparent lag is."<

Phase lag is one of the reasons why I like this hypothetical aerodynamic precession. For me, it is easier to aerodynamically envision the relative phasing between the control plane and the tip path plane, when considering a blade that is flying to position in less than 180-degrees.

If phase lag is to be discussed, others might prefer that it be on a new thread.

I agree with all you say 100%. Well; not to go overboard [as in ditching], lets say 99.9%.
Whatever. This discussion is certainly thought provoking and educational, for me at least.
_____________

In a hypothetical world, one could have a teetering rotor, with absolute rigidity between the blades (to resist coning), and no mass.

There is no 'original angular momentum' in this hypothetical world since the rotor has no mass. If the engine stops, the rotor will immediately stop revolving, since there is nothing to oppose the drag.

In this hypothetical aerodynamic world, it will still be possible to fly the rotor disk to position, whereas it will be impossible to move it to position by gyroscopic forces.

Now; if helicopter designers can continue to reduce the mass of helicopters far enough, gyroscopic precession will take its last flight - out the window.
_____________

Nick

Thank you ~ again.

Your explanation of Gamma is very timely. I have been reading and rereading documents on Gamma in the Sikorsky ABC. As you know from flying the craft, it had an in-flight variable Gamma from less than 20-degrees to greater than 60-degrees. The graphs show the results of different Gamma at different forward speeds. It has been difficult to understand, but interesting.

Your current description of Gamma and forward speed is making things easier. Thanks.

heedm

heedm,

We in the industry tell everyone it is gyroscopic precession to keep the troops in line and fool them, but it really is the phase angle between the forcing function (the controls) and the rotor flapping resonance (the disk tilt).

The phase angle for the S-76 is about 56 degrees, which would make Newton roll over in his grave, gyroscopically. Most helos would not be rigged (yes, Lu, rigged, rigged rigged, get used to it) at 90 degrees if we tried to perfect their controls, but pilots are wonderfully adaptive fellows, and quickly get the phase angle just right even if the manufacturer did not. The Benson and De Cierva gyrocopters are examples, where the cyclic stick is directly attached to the swashplate, so pushing forward stick achieves something approximating a left roll, I think (any gyrocopter pilots here to help me out?). Ouch, but it works.

This is similar to a motorcycle, where the way to turn left at speed is to tweek the handlebars rightward, and cause the bike to lean left to make the banked turn. Not natural, but easily learned and quickly second nature.

I'll respond to everyone in one post.

Nick, thank you for that practical discussion. While I enjoy getting into the theory, I don't lose sight of the fact that the pilot makes the finesse corrections as the flight parameters change. I don't mind going head-to-head with you on physics but for cockpit knowledge, I bow to your training and experience.

You said, "Kirilian laid out the factors that describe how a rotor does not obey the gyroscopic precession rules...." Was that the Lock's number post, or did I miss something?

I agree that many factors will affect this angle, but no matter how many factors there are, basic physics still applies. If the rotor flapping hinge is coincident with the axis of rotation, then an angle of precisely 90 degrees is measured between a maximum force and maximum displacement. If the hinge is offset, then the angle will reduce.

Jed A1, I do a two day HUET and EBS course every 3-5 years. I've always been comfortable in the water, but I learnt on day one that I would have not escaped an upsidedown ditching without the training and confidence that that course gave me. You're right to recommend it.

Grey Area, first of all, I was kidding about that left turning Robinson. Part of a long discussion.

Secondly, the forward movement of the stick in the autogyro with a teetering head doesn't directly put an upwards force on the disk at 6 o'clock. It's a teetering head, so when a blade is at 6 o'clock, the hinge is normal to the force. Consider what would happen with the blade at 6 o'clock but the rotors not turning. What I believe does happen is the forward movement of the stick causes less pitch at the 3 o'clock and more pitch at the 9 o'clock. The process from here follows the apparent 90 degree lag discussions.

Kyrilian what is the gamma that is in Lock's formula? The way gamma has been used here is that it is the phase angle between blade pitch and blade displacement (don't know the precise definition of that angle).

Dave, If you can email those articles on the ABC, I'd really appreciate it. If they're not on the computer yet, just point me in the right direction.

Problem with your massless rotor is if you attempt to fly it to position, you will apply a force to the blade. A force applied to massless matter (not possible, but I'll follow it through) will cause infinite acceleration, and your attempt to fly to position will result in catastrophic failure.

Dave Jackson

>'A force applied to massless matter (not possible, but I'll follow it through) will cause infinite acceleration, ...."<

The blade is being flown to position in air. If the ascending flap velocity were to exceed the commanded rate, the angle of attack will move to above the blade and force it back down. The same thing will occur if the tip path plane was to travel beyond the control plane.

In the case of a (hypothetical) absolutely rigid rotor, I believe that;

• the 'aerodynamic precession' will be exactly 0-degrees,
• the 'gyroscopic precession' will be exactly 90-degrees,
• and the resultant of the combined precessions will be around 10-degrees.

In all other rotors the 'aerodynamic precession' component will be greater than 0-degrees.

with gyrocopters and early Bell helicopters having one of 90-degrees.

This is an overview and is subject to 'fine tuning' by many details.

Related Information;

Last Revised: November 15, 2011