Coriolis vs Conservation of Angular momentum
 

As I understand it, conservation of angular momentum is what explains the phenomenon of rotor blade acceleration/ deceleration during a corresponding CG change in relation to its axis of rotation. To me, this has nothing to do with Coriolis force, which as I understand it is really just a kinematics term to describe a fictitious force that results in a changing vector on moving reference frame. I am failing to see how this relates to a rotor system. Please enlighten me, am I missing part of the puzzle or are helicopter text books using incorrect terminology?

Things gotta be Trump-ised, or dumbed down, to be understood by the lowest common denominator, the student pilot.

Projecting a 3-D object onto a 2-D horizontal plane produces some funny-looking results - a rotor system, coned upwards with power, and tilted forward for flight, gives the image of the front blade becoming longer and the rear blade becoming shorter. Bring in Kenny Coriolis, and Bob is your mother's brother, it is understandable. You are probably looking at the FAA books online, and last time I looked, they were full of errors of interpretation and of statement. Bring a pinch of salt, and keep your mind open. You seem to have the hang of it.

........absolutely solid gold AC.

The rotor blades are often analyzed in a coordinates system that rotates with the rotor blade, has its origin in the rotor center, and a primary axis parallel to the (coned) pitch axis. In this system you get a coriolis force, propeller moment, etc.

If you actually understand what Coriolis Affect is, you will also understand that it has no affect in a reference space as small as the diameter of a helicopter rotor system.

RMK is correct. The two are related, as the Coriolis is "caused" by movement N/S being closer(or further away) to the perpendicular of Earths axis of rotation, thus being closer to the 'centre of the roundabout'. But over a rotor disc dimension, the effect of Earth's Curvature is beyond negligible. Blade coning, however, will cause an increase in Nr as the diameter will be (slightly) reduced, and therefore angular velocity will increase in order to conserve angular momentum.

Same reason it's funny to get kids to sit at the edge of roundabout as you start pushing it, then get them to try and touch the middle. Hilarious.

if you (and DeltaNg) actually understand what Coriolis Force/Effect is, you will also understand that it applies to all rotating frames of reference, and the example using the earth (typically long range artillery and weather systems) is but one example.

,...but what about Coriolis "Effect"?

If a bolt detaches itself from a blade root whilst the rotor is turning, does it end up along the same blade at the tip? Nope - Coriolis Effect is an apparent deviation in a rotating system, even a rotor disc.

Of course I did not consider the roation of the earth (indeed negledible for a helicopter rotor), but the rotation of the rotor.

The Coriolis force appears in a rotating coordinate system when moving an object in a straight line. This movement in a straigth line (in the rotating system) requires rotational accelerations and decelerations when analyzed in a non-rotating system. The force necessary for these changes in rotational speed, and therfore changes in rotational momentum, is the coriolis force.

Of course this difference in speed changes relative to the two coordinate systems also applies to trajectories other than straight lines, but this is the easiest excample.

As crab said, Coriolis Effect is an apparent deviation. The bolt in his example departs in a straight line as there is no force acting on it to change its path; it is on a radial path to the tip plane; the blade tip was in line with it initially. However, by the time it reaches the tip plane the tip has moved so it does not arrive at the tip of the rotor blade but where it was at the moment of departure. A static observer watching from above will see the bolt on this straight, undeviating path. An observer at the rotor hub looking along the blade and rotating with it will see the bolt apparently lag behind the blade and seem to follow a curved route. CE is not a force and no acceleration occurs.

Conservation of Angular Momentum is the element that applies to a coning rotor disc and there is a mathematical explanation of it that I am not competent to give. The FAA manual is incorrect; I had some interesting discussions with the trainer on my gyro instructors course as he had based his teaching on that book.

I don't know (or care) enough about physics to know if what the FAA is telling me is correct or not. However, if you are correct in that the FAA is not, you should let them know so as to spare future generations of misinformation.

I don't know what the FAA manual says, but in reality a rotor is not demonstrating conservation of angular momentum at all! It can hardly be described as being in a zero torque, frictionless, environment!

Its basically; When a blade flaps up, its center of mass moves inward towards the hub, causing it to accelerate. When the blade flaps down, the center of mass moves outward towards the tip, causing it to decelerate.

Fully-articulated rotors absorb this acceleration and deceleration through the lead/lag hinges. Semi-ridged rotors don't experience it to the extent that fully-articulated rotors do, as the center of mass remains virtually unchanged as the system teeters, due to the underslinging of the blades.

[email protected] Totally agree, however, a departing component from a rotor system is not a normal condition, my point of concern is specific to CG movement during blade coning and the consequential Rrpm change.

Robbiee, the FAA have been miss-describing information for many years. They are not perfect, however, I have noticed they are receptive to change. VRS terminology being a great example, but i don't want to go down that rabbit hole.

212man Correct, Angular momentum is not applicable when there is a torque applied, however, consider the rotor system in autorotation or rapid descent (power on or off), this is when conservation of angular momentum is prevalent.

dickmct couldn't agree more

Robbiee correct, however the principle you are describing is conservation of angular momentum, and not Coriolis effect. Conservation of angular momentum is just one part of the formula that describes the theoretical / fictitious Corilis effect

Just checked my Dr. Henry Velkoff text, and the phenomenon is just as AC described it! 😂

Thing is, the FAA gave me a license to fly helicopters, not to design them, so what they want me to know about the physics behind that design is good enough for me.

However, if someone can prove to me that the FAA's definition of Coriolis Effect will cause me to crash my helicopter, then I'd be more than happy to discover the "truth".

Until then, I'll just sit Corilois Effect on the shelf next to Settling with Power, Loss of Tail Rotor Effectiveness,...and any other titles that we give to things that the rest of you don't like,...that don't effect how I fly, or my odds of crashing anyway.

The opposite would happen if an inward-shooting bolt cannon at the blade tip, shoots a bolt initially toward the hub. An observer at the cannon would see the bolt curve forward and to the right, while an outside observer would see it go in a straight line (yet still forward of the blade). This is Coriolis force, and it is a direct result of the conservation of angular momentum. They're not two different things. Check out this video, skip to the 7 minute mark:
The difference between the free particle that is our inward-shot bolt (or a water droplet in the experiment in the video, or an air parcel on a large scale wind on a rotating planet) vs. a piece of rotor blade in the middle of coning in, is that it's not free but rather rigidly mounted to the rest of the blade. So it pulls the blade forward and RPM goes up.

How does this "apparent" deviation result in an actual force/torque? Seems like a something-for-nothing deal, which we know isn't possible. From an energy budget perspective, we know that angular momentum was conserved: for a free particle, decreased radius converts to a higher angular speed. This can also be put in terms of straight-ahead plain old momentum: Actual speed stays the same, which means that the distance per time stays the same. Which means that the same distance (per time) wrapped around a smaller circle, covers more angle (per time). So the "apparent" path deviation to the right (to an observer rotating to the left with the system) is still a very real angular speed deviation, pulling the rotor forward.

He thought we were talking about the Coriolis force of the planet, not the rotor.

A rotor, being part of the real universe, obeys all of its laws of physics, including the conservation of angular momentum.

A rotor at constant RPM is in a state of zero net torque: the forward torque applied by the engine equals the reverse torque applied by the drag of the air, the friction of the mountings/mechanisms, etc. An increase or decrease of one of these opposite torques, unbalances the sum from zero, and a change in RPM (or, rotational acceleration) occurs.

If RPM changes due to the above things, momentum is not conserved (within the rotor system), it's being taken from or given to the outside world (in from fuel energy, out to turbulence due to lift/drag, etc.) If RPM changes due to the inward mass shift due to coning, (figure skater effect) it's due to the conservation of angular momentum. You just have to be meticulous with your accounting when multiple effects may be happening at the same time.

Pilotmike, the topple of a childs spinning top is due to gyroscopic precession, not coriolis. Indeed, the properties of gyro instruments are due to both rigidity and precession, and are not related to Coriolis.

You are right to use the word 'effect' because there is no such thing as coriolis force, it is merely an apparent effect - the path of an object (straight line) relative to a rotating observer. The observer sees the object curving. It is not curving, the observer is! There is no 'Force'.

Coriolis effect can be apparent on any sized rotating system. (Not including the sub-atomic!!).

You're right about this.

These effects, or fictitious forces, are not forces at the basic definition that satisfies F=ma, but act like forces to our perception so strongly and consistently, that there's gotta be something to it. We can either yell at people not to call them forces until we're blue in the face, but also we can (as long as we're being careful about it) expand our definition to a higher more general order, that our previous more basic definition becomes a more specific case of. If we're only considering unaccelerated reference frames, then F=ma. However, we act in accelerated reference frames so often, that it's really more convenient to go ahead and use those frames, and account for them in the definition. So, the "a" of the frame, ends up being a fictitious/apparent "F" within the frame. And we end up with our familiar (and often wrangled over) centrifugal force. If I'm pulling 10 G's in an aerobatic plane (let's disregard Earth's gravity for simplicity), there's sure as hell a force that I can both feel in my body and measure with a force meter. What's happening?

Unaccelerated reference frame (aka inertial reference frame, aka outside observer, aka absolute reality, as much as there can be one):

The airplane is accelerating around the curve toward the center (centripetal acceleration), and applying a force equal to that times my body's mass, to my body.

Accelerated reference frame (observer inside the plane):

I am feeling a force away from the center of the curve (centrifugal force), toward the floor of the airplane. If I drop an object, it will accelerate at an acceleration equal to the weight of that object divided by its mass.

In both cases, F=ma. But in the first case the a is the motion of the body within the frame, while in the second case it is the motion of the frame itself. Like many problems, it's really an issue of definitions and accounting. It's gerrymandering the border around what you consider to be a part of the system, vs. outside of it.

Vesspot, couldn't have put it as well as you.

Vessbot Thanks for your input. The video is a great representation of the Coriolis effect, however, it really doesn't focus on the law in question; conservation of angular momentum.

Coriolis Effect and conservation of angular momentum are absolutely different! Stating that Coriolis effect is the same as conservation of angular momentum is like saying distance is the same as speed in the old speed, distance, time formula.

It is important to remember that two different physical principles are involved when defining Coriolis 'force', namely, conservation of absolute angular momentum and centrifugal accelerations felt in the rotating frame.

Coriolis effect is reserved for describing the fictitious deflection of a moving object in an a non-inertial rotating frame of reference. It is nothing more than a method to quantify the magnitude of the fictitious force. However, in the case of a rotor system there is nothing 'fictitious' about a rotor rpm speed change, it is actually happening. This phenomena is the direct result of conservation of angular momentum. The formula that defines the rpm change:L=R x MV
where R =radius, m =Mass, V = linear velocity
So, with or without the genius Mr. Coriolis' calculation of the apparent deviation, the blade rpm change is going to happen. Why not call it what it actually is?

As stated before, "like Gyroscopic effect" helps to explain phase lag, but has absolutely nothing to do with the physics.

Gyroscopic precession,...thank you! I knew there was another term we use that got your guys' knickers in a twist, but just couldn't pin it down. :ok:

Well it seems we're in complete agreement on why the coning-in rotor speeds up, but disagree on the nomenclature. L = rmv, L and m are each conserved, therefore r and v are inverse. It leads to an actual RPM change. So far, we're together. But you use the presence or absence of this actual RPM change, as the discriminator of whether the conservation of angular momentum is what's happening. Well in the inward sprinkler experiment, the RPM of the water droplets alsoactually changes, so it meets your own standard. Then why do you say the video doesn't "focus" on this law?

Yes conservation of angular momentum and Coriolis aren't exactly the same thing, but the latter is merely an example of an effect, directly caused, by the former.

If the water droplet was somehow attached to the tube, then their diverging motions through this attachment would create a force, and through it the forward-accelerating droplet would pull the tube forward. How, then, would the setup be different from a coning in rotor or figure skater? (This was described in the rotating frame. In the outside frame, the droplet moves in a straight line, but the section of tube that it's closest to, moves backward. Same relative motion, caused by the same difference in the physical world: straightline-moving droplet, decreasing-radius along the tube.)

I'm OK with calling it other things, but I take exception to that calling it an example of Coriolis is incorrect, or that it and the conservation of angular momentum are "absolutely different."

Are phase lag and gyroscopic precession not the same thing? How are the physics different?

Jeez, Vessbot, I hope you are just being a troll and that you don't actually believe in helicopters having precession.

"Precession" is an easily accepted idea that it takes time for the force of a control input to accelerate a blade mass and make it move to where you want it, and while that time is elapsing, the blade is rotating around the mast. Usually it takes between 72 and 90 degrees of turn before the rotor gets to the desired position, but by then it is already receiving signals to get back to where it was, or go even further the other way.

A gyroscope it ain't. And it doesn't take exactly 90 degrees to take effect, like a real gyroscope would. The late Lu Zuckerman, when shooting down the Gyroscope Gang, would ask "where is the missing 18 degrees?" when he spoke of the R22, which displayed a phase lag of 72 degrees.

Vessbot Thanks again for your input, I think I'm with you now. The conservation of angular momentum accounts for the rpm change, but the 'puzzle' doesn't end quite yet. You could go a step further to analyze the rotor system once the rpm change has actually taken effect, which would be the blade mass deflection perpendicular to direction of rotation, when viewing the rotor system from the non-inertial frame of reference, i.e. Coriolis effect. I think we are on the same page, but that comprehension is about the extent of my brain power. I need to take note from Ascend Charlie

To answer your question, no. Gyroscopic precession and phase lag are not the same. There is no doubt that a rotating rotor system serves as a gyro, however, gyroscopic precession is only a small part of the Phase lag 'ingredients'. Phase lag varies greatly in helicopter rotor designs. I've heard numbers from as little as 50 degrees to over 100 degrees. Unlike a typical gyro, a rotor system experiences not only dynamic inertial inputs but also aerodynamic inputs. Blade hinge offset and design plays a a big role too.

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Originally Posted by Ascend Charlie (Post 10948107)

Jeez, Vessbot, I hope you are just being a troll and that you don't actually believe in helicopters having precession.

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Given that every other rotating body in the universe exhibits this property, why wouldn't a helicopter rotor?

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"Precession" is an easily accepted idea that allows Trump-brains to grasp the idea that it takes time for the force of a control input to accelerate a blade mass and make it move to where you want it, and while that time is elapsing, the blade is rotating around the mast. Usually it takes between 72 and 90 degrees of turn before the rotor gets to the desired position, but by then it is already receiving signals to get back to where it was, or go even further the other way.

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Why would it take any time? Hint, it has nothing to do with inertia or slow acceleration. It would happen the same even if the force was applied in a single impulse, a knock rather than a push; and the resulting deflection of the blade was instantaneous. The answer is that it is impossible for the blade to teleport to a position higher than it currently is, which is what would be required for the disk to tilt with no phase lag. The best that can happen (again, even with instantaneous knock and deflection) is that the path of the blade is changed upward, reaching a maximum 90 degrees later.

For another visualization, say you have a spacecraft in an Eastbound orbit, perfectly tracing the equator. When crossing the prime meridian, you fire the engine for a brief moment with the nose pointed North. What's gonna happen? You'll change the flight path from purely Eastward, to slightly Northeast. At which point along your new orbit will you reach the highest North latitude? Not over the prime meridian, again that would require teleportation. You only began your new path at the intersection of the equator and the prime meridian; the maximum North latitude you'll reach is at 90 degrees East longitude.

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A gyroscope it ain't. And it doesn't take exactly 90 degrees to take effect, like a real gyroscope would. The late Lu Zuckerman, when shooting down the Gyroscope Gang, would ask "where is the missing 18 degrees?" when he spoke of the R22, which displayed a phase lag of 72 degrees.

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There are higher order effects stacked on top of the basic 90 degree one, changing the final outcome slightly. I wouldn't mistake this for the basic effect underneath lacking a behavior fundamental to all rotating bodies. See what I wrote earlier about careful accounting of multiple effects happening simultaneously.

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F=mA.

Apply some pitch from the cyclic via the swash plate. The increased AoA produces lift, a Force. This lift acts on the mass of the blade, and accelerates it upwards. But that acceleration takes time for the blade to change position. The maximum force applied, Lift, is around 90 degrees in advance of the maximum deflection of the blade. It took time, and the blade rotated around 90 degrees in that time. Lighter blades, like the R22, move a little quicker, and only need 78 degrees of advance angle. Each blade has its own forces and movements, and (in multi-blade systems) acts almost independently of its mates. The "disk" is the visual blur to our eyes, it isn't a real disk or a gyroscope.

A gyroscope is a rigid, solid thing, no hinges, no flexing, nothing that moves, other than a heavy mass spinning on an axis. A rotor system has feathering hinges, offset flapping hinges, drag dampers, the blades flex and twist, and all sorts of reasons why it only LOOKS like a gyroscope. Gurgle up Nick Lappos and read his "Helicopter Urban Myths", he has a bit more knowledge than most of us on Proon combined. Read John Dixson too.

You said it takes time in your last post, I asked you why it takes time, and you didn't say why, but just repeated that it takes time again. (You also ignored where I explained why.)

If you're suggesting that the lag is because of the gradual application of the force (and overcoming of the blade's inertia), that doesn't explain the phenomenon because the same thing happens to the spacecraft performing the crosstrack maneuver with an instantaneous rather than gradual force; and for the entirety of the 90 degree lag, the craft is not undergoing a force, nor is it accelerating, upward. So it must be something other than the graduality of the force or inertia.

You also differentiate a gyroscope from a rotor based on being rigid vs not, but that doesn't explain your distinction because the same behavior happens with the spacecraft orbit, which is not only not rigid, but there is no matter even there, except an infinitesimally small bit out at the periphery. So, "not rigid" fails as an escape from gyroscopic behavior.

Yes the "disk" is a visual blur (in addition to a useful abstraction in other respects) but my point still stands that if the individual blade is knocked upward at a certain point, if it is to assume the flap position that corresponds with that pitch/roll input with no phase lag, teleportation would be required. For example, in an American-turning rotor, a left roll input (trying to tilt the disk to the left) that knocks the blade up at the 3 o'clock position can not possibly move the blade up at that position, regardless of blade mass or amount of force, or inertia, or anything. The best that can possibly happen is that it begins to move upward at that position, reaching a peak at some later point.

They are not. Phase lag is "around 90°" but not exactly, and varies for every helicopter. The exact angle has to do with the relationship between the resonance of the flapping behaviour of the blades compared to the rpm of the rotor system as a whole. Offset flapping hinges (or apparent offset 'hinges' such as in rigid rotor systems) increase the flapping resonance so that it is slightly higher than 1/revolution meaning that for an applied force, the peak of the flapping oscillation will occur slightly less than 90° later.

To be quite honest, most of the maths is far beyond me, but if you're keen to dig deeper on the fundamental and raw physics of rotating blade motion then Leishman, Principles of Helicopter Aerodynamics, 2nd Ed. 2006, p171-188 will be of interest to you. The book is quite expensive, so maybe this fragmented preview will be enough.

You're arguing in circles mate. It takes time to move? Of course it takes time. Start with zero displacement, and apply a force. The item accelerates while the force is present, and displacement increases at a greater rate. To reach its maximum displacement, use s+ut + 1/2 a t *2 and t = TIME.

Couldn't give 2 twopenny stuffs about a spacecraft in orbit, it has zero to do with a rotor in motion.

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Originally Posted by Ascend Charlie (Post 10948225)

You're arguing in circles mate.

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You're arguing that a phenomenon (max displacement approx. 90 degrees after the force) happens because of a thing (s+ut + 1/2 a t ^2), but I'm pointing out that the same phenomenon happens without that thing. If it happens without the thing, the thing can't really be the reason can it?

I gave you an example that boils away every possible confounding factor and leaves the simplest possible arrangement that shows the behavior of rotating matter, with perfect 90 degree phase lag but with no s+ut + 1/2 a t ^2, so maybe you should give a twopenny about it.

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Originally Posted by ApolloHeli (Post 10948224)

They are not. Phase lag is "around 90°" but not exactly, and varies for every helicopter. The exact angle has to do with the relationship between the resonance of the flapping behaviour of the blades compared to the rpm of the rotor system as a whole. Offset flapping hinges (or apparent offset 'hinges' such as in rigid rotor systems) increase the flapping resonance so that it is slightly higher than 1/revolution meaning that for an applied force, the peak of the flapping oscillation will occur slightly less than 90° later.

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I was wrong to call them "the same thing," but how about the chief "ingredient" (to use heliman500's word, even though he says it's a small ingredient). Yes, all manner of complicated hinge arrangements and various forces modify the phase lag, but why is the base value that is modified, the same as what a simple rotating body (gyroscope) does?

All the complications happen near the center, leaving most of the motion dominated by simple rotation. (Now if the offset of the flapping hinge was something like at 90% of the radius, it would be a different story.) When a basic motion is modified by higher order effects to add up to the final result, it doesn't disappear and is still there underneath. And in this case, enough of it is there to be not only clearly recognizable, but the main driver of the motion.

For a clear-cut example (I mean a general example of superposed motions and the contributions of their causes, not a specific example of gyroscopic motion), look at the Earth's rotation. Measured to the accuracy available to today's instruments, it has its own precession, nutation, and God knows what else, and they're not even constant. They're affected by tectonic movement, ocean currents, celestial bodies, and other things, which change the rotation rate as well. Leap seconds have to be added at irregular intervals to account for this. Looking at all this, you wouldn't say that the Earth is not a rotating ball, and you have to calculate all these mind-boggling stacked motions every time you describe the Earth's movements. No, the simple rotation is still there underneath, dominating the total motion, so a constant-rate spinning ball is still a correct first-order approximation that serves just fine as a model. (And ultimately everything we talk about is models, unless you endeavor to calculate the individual movement of all the atoms of the messy system, every time you talk about anything.)

Well, the chief test pilot at Sikorsky wrote these, I tend to follow his thoughts rather than yours:

I think you've hit the nail on the head there mate. We all agree that saying phase lag happens due to gyroscopic precession or that helicopters behave like gyroscopes is close enough for the average student, but it's still an approximation. After all, it's getting the concept and theory across in a digestible and understandable form for the student that matters. "Lies to children" as Scott Manley would put it.