Gyroscopic Precession

[ADRidge]

Okay... we're all sitting around the pilot lounge today and I got to wondering WHY gyroscopic precession works. I understand it as much as any CFI does, but we got to thinking about how no matter the RPM of a rotating object (frisbee, rotor disc, toy gyro, whatever) the effect is always noticed roughly 90 degrees after the input is made.

 

Some of us think it has to do with coriolis effect, and the rest of us have no clue other than "it works."

 

What are your thoughts?

[Wally]

Not to promote the competition, but try here:

Nick Lappos at PPrune

 

and elsewhere at that forum for WAY too much scientific PFM.

[ADRidge]

Sweet! I appreciate it. That's an interesting observation. Someone was talking about how at Bell they tell you to forget everything you know about gyroscopic precession. It would seem they're right.

[iChris]

Okay... we're all sitting around the pilot lounge today and I got to wondering WHY gyroscopic precession works. I understand it as much as any CFI does, but we got to thinking about how no matter the RPM of a rotating object (frisbee, rotor disc, toy gyro, whatever) the effect is always noticed roughly 90 degrees after the input is made.

 

Some of us think it has to do with coriolis effect, and the rest of us have no clue other than "it works."

 

What are your thoughts?

 

Gyroscopic Precession of a helicopter rotor system ties-in to the mechanics of Rotational Motion and aerodynamics. It's a deep subject with more factors than can be to cover here. However, the factors you've asked about that can act as forces of the precession are:

 

 

1. Conservation of Angular Momentum

 

2. Coriolis Effect

 

3. Gyroscopic Motion

 

4. Centripetal Force (a.k.a. Centrifugal Force)

 

 

Also note that the effect is not always 90 degrees. Fully articulated rotor systems are less than 90 degrees and decrease with hinge off-set. This is due to centrifugal force acting about the axis of rotation (rotor mast)

 

 

Take a look at the second chart, link below, and you see the many forces and mechanics of Rotational Motion. Click on any that are of interest.

 

 

Rotational Motion & Its Tie-ins

Edited November 29, 2010 by iChris

[Eric Hunt]

Precession is only a way of trying to explain the motion of a rotor head. Sadly, it has been propagated as the reason for phase lag and advance angle.

 

IT AIN'T PRECESSION and the motion isn't always 90 degrees - the R22 is 72 degrees. See the thread on the above-mentioned site by the late Lu Zuckerman, who was asking "Where are the missing 18 degrees?"

Edited November 29, 2010 by Eric Hunt

[NorCalHeliKid]

Precession is only a way of trying to explain the motion of a rotor head. Sadly, it has been propagated as the reason for phase lag and advance angle.

 

IT AIN'T PRECESSION and the motion isn't always 90 degrees - the R22 is 72 degrees. See the thread on the above-mentioned site by the late Lu Zuckerman, who was asking "Where are the missing 18 degrees?"

 

To add to Eric's argument, which i totally agree with, Gyroscopic Precession principle in physics, can only occur in a rigid environment, (rigid rotor systems), so in a semi-rigid system it would only be Phase Lag that occurs, but then the theory falls apart because Phase Lag relies on G/P to exist according to Principles books, so what caused the 72 degree move?

[ADRidge]

Gyroscopic Precession of a helicopter rotor system ties-in to the mechanics of Rotational Motion and aerodynamics. It's a deep subject with more factors than can be to cover here. However, the factors you've asked about that can act as forces of the precession are:

 

 

1. Conservation of Angular Momentum

 

2. Coriolis Effect

 

3. Gyroscopic Motion

 

4. Centripetal Force (a.k.a. Centrifugal Force)

 

 

Also note that the effect is not always 90 degrees. Fully articulated rotor systems are less than 90 degrees and decrease with hinge off-set. This is due to centrifugal force acting about the axis of rotation (rotor mast)

 

 

Take a look at the second chart, link below, and you see the many forces and mechanics of Rotational Motion. Click on any that are of interest.

 

 

Rotational Motion & Its Tie-ins

 

Chris. You rock, man. I appreciate the link. I'll look over it later on in detail. I realize it's a question that likely will never be asked by a student once I've got my CFI certificate, but it's just one of those things about helicopters that always has me wondering.

[Tom22]

Somebody told me one time that a rotor blade has a flapping natural frequency, which is equal to its rotational frequency or pretty close to it – is this true?

[iChris]

Precession is only a way of trying to explain the motion of a rotor head. Sadly, it has been propagated as the reason for phase lag and advance angle.

 

IT AIN'T PRECESSION and the motion isn't always 90 degrees - the R22 is 72 degrees. See the thread on the above-mentioned site by the late Lu Zuckerman, who was asking "Where are the missing 18 degrees?"

 

That’s correct. The rotor is not a gyro and the rotor flapping is not a pure precession as in “Gyroscopic Precession.” However, the rotor system exhibits similar properties since its part of the same family of mechanics. When a control input is applied that increases the blade pitch at a given point the blade will have its maximum flapping amplitude sometime later in the direction of rotation. The forces that cause this delayed reaction are tied into the mechanics of rotational motion and aerodynamic damping. Mechanics of Rotational Motion (see bottom chart)

 

 

 

Qualitative Discussion of Flapping, Helicopter Performance, Stability, and Control, by: Ray Prouty (Quote Below)

 

“All these flapping characteristics can be explained on the basis that at the flapping hinge (or at the effective flapping hinge in the case of a hinge-less rotor) the summation of moments produced by aerodynamics, centrifugal, weight, inertial, and gyroscopic forces must be zero.”

 

There lie the dynamics: Aerodynamic, Centrifugal, Weight, Inertial, and Gyroscopic Forces

 

Where are the missing 18 degrees? The 18 degree delta-three-angle designed into the upper swashplate. (See link below)

 

R-22 ROTOR SYSTEM: Posting by Frank Robinson Nov. 29, 2000

 

Edited November 30, 2010 by iChris

[iChris]

Somebody told me one time that a rotor blade has a flapping natural frequency, which is equal to its rotational frequency or pretty close to it – is this true?

 

That's true for a hinged rotor without offset; its natural frequency is identically equal to its rotational frequency (system in resonance). If cyclic pitch is applied to a rotor of this type it will have its maximum flapping amplitude near 90 degrees later.

 

If the rotor has hinge offset, the phase angle is less than 90 degrees and the flapping is not numerically equal to the cyclic pitch. As offset is increased the moment due to centrifugal force increases faster than the moment of inertia about the flapping hinge. The natural frequency is higher than the rotational frequency (system is no longer in resonance).

Edited November 30, 2010 by iChris

[iChris]

[Duplicate]

Edited November 30, 2010 by iChris

[iChris]

To add to Eric's argument, which i totally agree with, Gyroscopic Precession principle in physics, can only occur in a rigid environment, (rigid rotor systems), so in a semi-rigid system it would only be Phase Lag that occurs, but then the theory falls apart because Phase Lag relies on G/P to exist according to Principles books, so what caused the 72 degree move?

 

Lets define terms; “Phase lag” is the delay between cause and effect.

 

The Effect:

 

We have a rotor system that responds to our input a time later (delay) after we’ve made them and in a different position ahead of our initial input.

 

The Causes:

 

Aerodynamic Damping, Centrifugal Forces, Weight, Inertial Forces, and Gyroscopic Forces.

 

Gyroscopic Forces are in order because any rotating mass exhibits similar properties to that of a gyro. The rotor disk as a rotating body exhibits an ability to maintain its angular momentum and maintain its direction in space, however weak. In doing so, aerodynamic damping, centrifugal forces, weight, and inertial Force work against linear motion and are the causes of the delayed flapping action.

 

Also, hingeless rotors or rigid rotors may have no single point at which flapping occurs, but an “Effective Hinge Offset” can be determined that will give the same characteristics as a blade with an actual mechanical hinge at that point. Remember, bending and flexing along defined points along the blade accomplishes flapping on a rigid rotor system.

 

 

[Tom22]

If you took away aerodynamic forces, essentially placing a rotor in a vacuum, the rotor would then behave like a gyroscope.

 

Ref:

 

Leishman, J.G. (2006). Principles of helicopter aerodynamics. NY: Cambridge University Press.

Edited November 30, 2010 by Tom22

[Eric Hunt]

Simple physics can explain it a lot.

 

Force = mass x acceleration.

 

Apply a force (increase the pitch on the blade, increase the lifting force) and the mass (blade) will start to accelerate up. It takes time. As the blade flies up, the pitch is decreasing via the swashplate (force decreases) and the acceleration reduces to zero, the blade coasts upwards, and reaches its highest point.

 

While it has been climbing, it has also been turning, so from the front of the aircraft where the upwards force started, the blade has turned through about 180 degrees and reached its highest point above the tail.

 

Now, the force starts acting the other way, accelerating the blade downwards. it reaches its highest rate of downward movement at the abeam position, and its lowest point of movement back at the nose. And it starts again.

 

Nothing to do with gyroscopes, just F=mA

[Runon]

It helps to think of it, instead of applying a force downward on a certain area of the disc, to think of it more acting like a brake in one plane and an accelerator in another plane (90 degrees off).

 

Looking from above - How far would you have to roll a helicopter to no longer see a counterclockwise rotating horizontal disc and turn it into a straight line chopping vertically (like a table saw)..... 90 degrees.

 

You stopped all angular momentum in the horizontal direction and accelerated it all in the vertical direction.

 

But really you are borrowing just the smallest LITTLE BIT of the rotational energy in the horizontal plane and using it to tilt the disc in the vertical plane.

[Tom22]

Well, in response to my second post.

 

If the rotor was operating in a vacuum (without aerodynamic forces), the flapping equation has a general solution as the following:

β= β_(1c ) cos⁡〖ψ+ β_1s 〗 sin⁡ψ

 

Where

β Blade flapping angle positive up

β_(1c ) Longitudinal flapping angle

β_1s Lateral flapping angle

ψ Azimuth angle

 

With the absence of aerodynamic force the rotor will take up an arbitrary orientation in inertial space thus in effect acts like a gyroscope. Key word being acts.

Ref:

 

Leishman, J.G. (2006). Principles of helicopter aerodynamics. NY: Cambridge University Press

 

See attachment for proper format of equation.

Edited December 1, 2010 by Tom22

[Tom22]

Duplicate

Blade Flapping.pdf

Edited December 1, 2010 by Tom22

[iChris]

Simple physics can explain it a lot. Force = mass x acceleration. Apply a force (increase the pitch on the blade, increase the lifting force) and the mass (blade) will start to accelerate up. It takes time. As the blade flies up, the pitch is decreasing via the swashplate (force decreases) and the acceleration reduces to zero, the blade coasts upwards, and reaches its highest point. While it has been climbing, it has also been turning, so from the front of the aircraft where the upwards force started, the blade has turned through about 180 degrees and reached its highest point above the tail. Now, the force starts acting the other way, accelerating the blade downwards. it reaches its highest rate of downward movement at the abeam position, and its lowest point of movement back at the nose. And it starts again. Nothing to do with gyroscopes, just F=mA

 

I wish it were that simpl. If you look at figure 3.33 (don't worry about the math) you'll see the forces acting on the blade that account for its flapping action. Figure 7.8 shows the same for a blades with hinge offset. Lets list them again:

 

1. Aerodynamic forces

 

2. Weight forces

 

3. Inertia forces

 

4. Centrifugal forces.

 

When we say "Gyroscopic Forces" lets list some:

 

1. Weight (mass)

 

2. Inertia forces

 

3. Centrifugal Forces

 

Even our rotor system shares some of the same forces. So don't get hung-up on that. The rotor system, I say again, is not a gyroscope. Blade flapping is result of the forces in figure 3.33 and 7.8.

 

TOM22 was correct in writing:

 

If you took away aerodynamic forces, essentially placing a rotor in a vacuum, the rotor would then behave like a gyroscope.

 

Lets do essentially that. If we were to redraw figure 3.33 and pin the blade perpendicular to the mast and eliminate the aerodynamic forces we would have in effect a spinning mass that would respond like a Gyroscope with Precession.

 

Here's a section from the Army's Fundamentals of Flight, Field Manual, FM 3-04.203, 2007. (pg. 1-17)

 

GYROSCOPIC PRECESSION

 

1-40. The phenomenon of precession occurs in rotating bodies that manifest an applied force 90 degrees after application in the direction of rotation. Although precession is not a dominant force in rotary-wing aerodynamics, aviators and designers must consider it, as turning rotor systems exhibit some of the characteristics of a gyro. Figure 1-25 illustrates effects of precession on a typical rotor disk when force is applied at a given point. A downward force applied to the disk at point A results in a downward movement of the disk at point B.

 

Force = mass x acceleration alone dose not address the effects of circular or rotational motion. You're hung-up on the Newton's second law side of the mechanics. You need to also consider the mechanics of rotational motion.

 

Edited December 2, 2010 by iChris

[Tom22]

Hey Chris what book is that one...just curious?

[iChris]

Hey Chris what book is that one...just curious?

 

Here you go...

 

Helicopter Performance, Stability, and Control, By:Ray Prouty (Amazon)

 

 

 

[Tom22]

Thanks! I might have to add that one to my library.

[Tom22]

ADRidge,

Attached is an encyclopedia article on precession.

Edited December 3, 2010 by Tom22