Coriolis vs Conservation of Angular momentum

[MLH]

The same topic was over-killed decades ago with a similar result:

Certification of Robinson Helicopters (incl post by Frank Robinson)

[[email protected]]

Vessbot - I get the impression you know a lot about physics but very little about helicopters.

Phase lag is governed by Lock number which is a ratio between blade inertia and aerodynamic damping.

A swash plate does not impart an instant or impulse force to a rotor, it builds gradually as a result of turning a rotating motion into a vertical one because you have to change the pitch of the blade to make it climb or descend.

No gyros I have seen have hinges that limit how much the movement of the mass of the gyro can be transmitted to the hub - a rotor system does.

Just because systems exhibit similar behaviours doesn't mean they have the same cause.

[Robbiee]

Originally Posted by MLH

The same topic was over-killed decades ago with a similar result:

Certification of Robinson Helicopters (incl post by Frank Robinson)

Yep, that note from Frank was definitely more than I needed to know,...or could even follow. Glad I don't have to be an engineer, or physicist, to wiggle the stick around.

[Vessbot]

Originally Posted by [email protected]

A swash plate does not impart an instant or impulse force to a rotor, it builds gradually as a result of turning a rotating motion into a vertical one because you have to change the pitch of the blade to make it climb or descend.

It’s true I’m not a helicopter expert, but please give me a little more credit than this. Just a few posts ago, I wrote virtually the same thing: “It's constantly transitioning through 1 sinusoidal cycle of force per rev, and not instant.”

The reason I pointed to the instant-impulse case was to show that the continued presence of a normal force is not required to continue the divergence of the tip path over the 90 degree phase difference; this was in response to another poster who was arguing that such a presence is required.

No gyros I have seen have hinges that limit how much the movement of the mass of the gyro can be transmitted to the hub - a rotor system does.

You Tube

Here’s one, at 6:30 in. The gyro is a cardboard disk with a small hole on a pencil tip, free to swivel about 45 degrees (more than most or all helicopters). Within that range, it transmits no movement to the pencil, and he does a beautiful precession demo within about half of that range.

I’m not seeing the salience of this point, as the phase lag between the input and the resulting tilt of a heli rotor is all about the behavior of the rotor itself, and not any motion that it may or may not pass to the fuselage. I think it’s clear that that step happens with no phase lag - rotor disk tilts forward, helicopter goes forward with it.

Just because systems exhibit similar behaviours doesn't mean they have the same cause.

​Any way that I can see it, the cause here is the same as well. If it’s different, what’s the difference? What fundamental mechanic causes a gyro to behave like a gyro, that’s missing from a helicopter rotor that behaves like a gyro?

(This question isn’t answered by pointing to other mechanics there are present - I know there are many. Offset flapping hinges, delta 3, lead-lag hinges, oscillations of various orders both through hinges and elastic paths that interact in ways that blow minds… yes. I am asking about absence, not presence).

[Ascend Charlie]

What fundamental mechanic causes a gyro to behave like a gyro, that’s missing from a helicopter rotor that behaves like a gyro?

The missing element is Rigidity in Space. Because of all the twisting, flapping, dragging and aerodynamic blade forces, the "disk" is dynamically unstable - and gyroscopes are not. It will not hold its position or orientation, it will diverge and crash, unless the coffee-stabilised pilot stops it from doing so, by playing with the cyclic.

[[email protected]]

What RPM do most gyros rotate at?

Even with his cardboard disc, the precession demonstrated is 90 degrees - as you have already been told, phase lag is frequently not 90 degrees, with some very large variations depending on rotor design blade inertia etc etc - but a gyro is ALWAYS 90 degrees.

Does the angle of gyroscopic precession change with density altitude? Phase lag does change with that variable because of the change in aerodynamic damping - how does that fit with your theory?

The similarity between precession and phase lag is why it has been used as a simple explanation of behaviour of a rotor but many far cleverer people than you and I have said they are not the same and one is not an explanation for the other.

What is your explanation for why phase lag is frequently not 90 degrees when gyro precession is always 90 degrees?

If all gyros behave exactly the same way, from the cardboard disc in the video through a spinning bicycle wheel to a proper gyro with a number of degrees of freedom designed to do a specific job, why do helicopter rotors not all follow the same rigid ('scuse the pun) reactions if it really is precession?

AC makes a very valid point about rigidity in space - you can't cherry pick the facets of gyro behaviour - if a rotor obeys one, it should obey all - and it doesn't.

[MeddlMoe]

Originally Posted by [email protected]

Phase lag is governed by Lock number which is a ratio between blade inertia and aerodynamic damping..

This is not correct. The Lock number has very little to do with it.

The critical parameter for the phase shift is the relative flapping hinge offset. This is the ratio between the distance of the flapping hinge from the rotor axis and the blade tip radius. (or the virtual hinge location for a flexbeam rotor).

Due to this distance you get bending moment that tilts the whole helicopter including its rotor shaft axis. This happens at an phase angle smaller than 90° (0° phase angle for a totally rigid rotor with a relative hinge offset equal to 1).
You still have the gyroscopic effect with 90° phase shift for the tilt of the roation axis of the rotor blades (which is then generally not parallel to the rotor shaft axis). The combination of these to tilting effects results in a total tilt at an intermediate phase angle.

[Robbiee]

Hmm, does it matter at all that the book says, that a spinning rotor is "like" a gyro (as opposed to "is" a gyro) and the effect is "approximately" 90° later (as opposed to "is" 90° later)?

I mean, it sounds to me like they are just making a comparison, not literally saying a spinning rotor is a gyroscope.

,...unless you expert physicists are saying that a spinning rotor has absolutely nothing in common with a gyroscope? Is that it,...'cause this thread is hard to follow for us average joes?

[SimFlightTest]

The reason a gyro precesses at 90 deg while some rotors exhibit phase lag less than 90 deg is because rotors with hinge offset (or effective hinge offset) inject an additional moment into the disk that alters the precession angle. This additional moment is a result of the flapped rotor blades being connected to the rotor rotational axis at a location that is not the rotor center (i.e., the offset hinge).

One can use the exact same math to predict phase lag on a rotor as they would to predict how a gyro precesses at 90 deg. We do it all the time in the simulation world. The trick is in properly accounting for all the moments/forces being applied to the disk. Conceptually, you can almost think of a gyro as an infinite number of teetering rotors all spinning around the same axis.

The reason rotor phase lag changes with density altitude is because the magnitude of aero forces from the blades change in relation to the magnitude of the inertial forces from hinge offset. Think of it this way, if you have infinite density, then the blade will perfectly follow the blade pitch, which would result in perfect 90-deg phase lag regardless of the hinge offset. As air density reduces, the aero forces reduce, and the blade can start to deviate from it's pitch angle more and more. With the reduced "stiffness" of the aero forces, the effect of the inertial forces as a result of the hinge offset becomes more dominant, and hence the phase angle increase.

The math explains it all, whether it's a gyro or a rotor. There are no secret physics at play that are peculiar to either case. The two scenarios are entirely consistent with each other.

[[email protected]]

So why does a teetering rotor not exhibit exactly 90 degree phase lag and why does that change with density altitude when there are no hinges or hinge offsets to consider?

[SimFlightTest]

There are subtle effects that can result in a teetering rotor from producing exactly 90 deg phase lag. For example, any of the following will result in a deviation from an exact 90-deg phase lag:
- pitch-flap coupling as a result of a delta3 angle
- friction/damping in teetering hinge
- aerodynamic effects like modifications to blade lift as a result of dynamic operating conditions (varying angle of attack, etc.)
- the rotor hub being underslung
- etc.

Of course, any phase lag should be considered in relation to the blade pitch being injected by the swashplate. There are all sorts of geometric/mechanical scenarios that can give the pilot the impression of a phase lag (i.e., flight control mixing, bellcrank geometries, etc.), when in reality the phase lag might be very small.

[[email protected]]

So, unlike a gyro, there are countless other factors that affect flapping - yet people are still adamant a rotor is a gyro?

[SimFlightTest]

Gyros and rotors both obey the same fundamental laws of physics that perfectly describe their behavior. F=MA applies equally to both. The differences lie in the forces that exist and where they get applied to the "disk". If you take a gyro with a mass and rotational inertia that is identical to a rotor, and apply the exact same forces to it that are applied to the rotor, then the gyro will demonstrate the exact same phase lag as the rotor.

There's nothing special about either a gyro or a rotor. They are both just a collection of interconnected masses moving in space. If you choose to define a gyro as something that must operate in a vacuum and have no forces acting on it other than gravity, then yes, a gyro is different than a rotor... but there is nothing in the physics that requires such a limited definition.

[Vessbot]

Originally Posted by [email protected]

What RPM do most gyros rotate at?

Big variance. A flight instrument rotor spins at 10K to 15K RPM, according to Google. A spacecraft in low Earth orbit is at 1 rotation every 90 minutes. It doesn't matter.

Even with his cardboard disc, the precession demonstrated is 90 degrees - as you have already been told, phase lag is frequently not 90 degrees, with some very large variations depending on rotor design blade inertia etc etc - but a gyro is ALWAYS 90 degrees.

This is not true. You can wiggle a toy gyro back and forth in your fingers, and depending on the stiffness you hold it with (in other words, applying other forces), control the amount of precession that occurs. When you're going down the runway in a taildragger airplane, gyro precession will tend to yaw you to the left while raising the tail, and a lot of money, pride, personal safety, and often preservation of historical artifacats, depends on your application of other forces to control this precession to zero degrees.

Does the angle of gyroscopic precession change with density altitude? Phase lag does change with that variable because of the change in aerodynamic damping - how does that fit with your theory?

It fits in by applying other forces (which vary based on circumstances) in addition to the gyroscopic ones, to the object.

What is your explanation for why phase lag is frequently not 90 degrees when gyro precession is always 90 degrees?

Because there are other forces.

This is like asking "what is your explanation for why my car is drifting to the right while I'm holding the steering wheel straight ahead, when a car with the steering wheel straight always goes straight ahead?"

If all gyros behave exactly the same way, from the cardboard disc in the video through a spinning bicycle wheel to a proper gyro with a number of degrees of freedom designed to do a specific job, why do helicopter rotors not all follow the same rigid ('scuse the pun) reactions if it really is precession?

Because there are other forces.

AC makes a very valid point about rigidity in space - you can't cherry pick the facets of gyro behaviour - if a rotor obeys one, it should obey all - and it doesn't.

I really hesitate to open a second rabbit hole when people are struggling so hard with the concept of more than one force acting on an object, and a resulting motion that's a combination of the motions due to the individual forces - but a rotor does have rigidity in space. When you take away rotor-fuselage drag interactions, aerodynamic forces on the blades, etc. the rotor has the same tendency as all rotating mass. Just think of a spinning rotor in a vacuum chamber.

---

Now, I have to ask you again, at a very simple level: what mechanic from a precessing gyro that causes it to precess, is absent from a seemingly precessing rotor?

On a the cardboard gyro, a normal force was applied which deflected the path in that direction, and the new circle had a max offset from the old one 90 degrees later. Yes or no?

On a helicopter rotor, a normal force is applied which deflects the blade path in that direction, and the new circle has a max offset from the old one about 90 degrees later. Yes or no?

[Vessbot]

Originally Posted by [email protected]

So, unlike a gyro, there are countless other factors that affect flapping - yet people are still adamant a rotor is a gyro?

I'm adamant that the factor that moves the new tip path 90 degrees after the input, is the same as the one that does the same thing in gyros. And it seems to be the dominant factor in a rotor, when stacked together with all the others, since the result is only modified slightly.

[[email protected]]

Big variance. A flight instrument rotor spins at 10K to 15K RPM, according to Google. A spacecraft in low Earth orbit is at 1 rotation every 90 minutes. It doesn't matter.

If a toy gyro isn't rotating at high speed it falls over so it does matter.

This is not true. You can wiggle a toy gyro back and forth in your fingers,

Of course you can but that is just applying additional torques and muddying the waters of what is discussed here

The big difference between your last two lines is that one is 90 degrees and the other is 'about' 90 degrees - can you show me a gyro that doesn't precess at 90 degrees? That would be far more beneficial to your argument.

On a rotor, the mechanical input is the start of the process, the next stage is the aerodynamic forces that are a result of the mechanical change in pitch to the blades - these accelerate the blades, assisted by the mechanical input and governed by the laws of aerodynamics - the movement eventually cancels itself out when the lift produced is negated by the braking/damping effect of the air and the reducing mechanical input.

[Vessbot]

Originally Posted by [email protected]

that is just applying additional torques

Yes! Yess!!

I have to go so I'll be back later with a normal post, but please ruminate on this for a bit.

[SimFlightTest]

From a physics standpoint, a "gyro" can be defined as an object whose effects due to rotational motion dominate the behavior of the object. In this regard, a rotor is a gyro because the effects of rotation dominate. Whether or not a "gyro" is a disk, or a ring with spokes, or just spokes, or a slender rod rotating about it's mid point (like a teetering rotor) is irrelevant.

To go further, at some point even a gyro is no longer considered a gyro. Take a gyro and slow it down. Any rotational effects become less dominant. Same with a rotor. Now slow it down again... and again... and again. At some point, the effects due to rotation are negligible, and neither object behaves in a manner that is comparable to their rotating states.

It's all simply masses moving around a center point. You can define "gyro" and "rotor" any way you want... but you can not imply that the same physics do not apply to each.

[MeddlMoe]

Originally Posted by [email protected]

Vessbot - I get the impression you know a lot about physics but very little about helicopters.

Phase lag is governed by Lock number which is a ratio between blade inertia and aerodynamic damping.

A swash plate does not impart an instant or impulse force to a rotor, it builds gradually as a result of turning a rotating motion into a vertical one because you have to change the pitch of the blade to make it climb or descend.

No gyros I have seen have hinges that limit how much the movement of the mass of the gyro can be transmitted to the hub - a rotor system does.

Just because systems exhibit similar behaviours doesn't mean they have the same cause.

The lock number has very little influence on the phase lag. (It is also not the delta 3 angle, as somebody else claimed)

The phase lag is predominantly determined by the flapping hinge offset. This is the ratio between the distance from the rotor axis to the flapping hinge and the distance from the rotor axis to the blade tip.

Then you get two effects that occur simultaneously and therefore overlap:

1. The gyroscopic effect leads to a maximum deflection at 90° phase shift from the maximum lift force. This effect does not affect the orientation of the rotor shaft. This means that the rotor blades rotate about a (slightly) different axis as the rotor shaft.

2. The non-zero flapping hinge offset leads to bending moments in the rotor shaft due to the deflection. This leads to a rolling or pitching moment of the entire helicopter, which then turns according to the magnitude of this bending moment and its inertia. This leads to a change of the orientation of the rotor shaft axis. The phase shift of this effect smaller than 90° depending on the hinge offset.

These two tilts of rotation axes combined lead to a combined phase shift, that is smaller than 90°.

Note that also flexbeam rotors have a hinge offset, which is determined for the equivalent ratio between blade deflection and bending moment at the rotor shaft.

[MLH]

SFT,

Thanks for the clarity, game over. I'm curious as to your background on the subject.