Gyroscopic Precession - Revisited

[Dave Jackson]

helmet fire raised the question of gyroscopic precession on another thread and since this was a separate topic a few months ago it seems only fair that it should be again. :eek:

helmet fire is also is responsible for my lack of sleep last night, while trying to think of a logical reason why gyroscopic precession has very very little to do with the helicopter rotor :)


Eureka!!! An answer. Better yet; The answer. http://www.unicopter.com/7up.gif

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 applied aerodynamic torque from the cyclic, is toooo small for equations of gyroscopic precession to apply.

Anyone want an argument? :mad: ;)

[Lu Zuckerman]

To: Dave Jackson

Dave I would strongly advise to put your affairs in order and make out a will because you are going to get killed on this one. You have awakened two sleeping giants. One giant represents the believers in aerodynamic precession over gyroscopic precession. And, the other giant represents the believers in gyroscopic precession being the cause of the disc tilting in respect to cyclic input with no or minimal input from aerodynamics other than that force developed aerodynamically that causes the rotor (gyro) to nutate.

:eek:

[heedm]

gyroscopic precession has very very little to do with the helicopter rotor

I disagree. I say gyroscopic precession has nothing to do with the helicopter rotor, if you're a purist.

Avoid discussing gyroscopic precession and avoid discussing aerodynamic precession. In fact, they are precisely the same. They are each special conditions of a much broader generalized theory. I'll try write that down for you in a later post.


As far as relative inertias, torques, etc. helicopter rotors don't get large enough torques to noticeably exhibit the higher order actions of rotating bodies. They're there all right, and some theorists/designers may need them in the calculations, but in general they aren't significant. Why? Because for most of the flight the rotor doesn't change noticeably. A large input will cause you problems, but only until the quasi-equilibrium state occurs.

If you want to see that effect, go to the toy store and buy a spinning top. Get it in a stable spin. Poke it. It moves. Poke it harder. The axis starts gyrating like crazy. The second order effects are best noticed when the spin axis is far from the vertical, it draws a cone but it also circles the surface of the cone that it draws. Gyroscopic precession is actually drawing the cone, the higher order effects of GP are encircling the surface of the cone. It's all very simple when you describe it with Vector Calculus.

[[email protected]]

Put a rotor system in a vacuum and it will probably display gyro behaviour and precess in reponse to a torque input in spite of the low mass and speed of rotation.
Since rotors fly in air and are subject to the far more powerful aerodynamic forces of lift and drag, it is these that determine the response of the rotors and not precession.
Gyros can't flap to equality but a rotor system can which gives us all the problems of inflow roll, flapback, retreating blade stall etc to overcome (all aerodynamic in origin).
If the rotor simply precessed then factors like Lock number (blade inertia and aerodynamic damping factor) and phase lag changing with hinge offset and altitude would not be around to complicate the designers ordered lives.

[vorticey]

dave:
yes the disc axis is changed by the blades flying into place!
yes the axis would try to advance as the disc was tilting!
(gyro. press.)
yes the pitch on the blades would change as the disc started advancing from the attitude induced by the pilot.
and when the gyroscpic precesion = the attitude pressure, from the blades trying to bring the disc back to the pilot induced attitude, it becomes nutral.

lu:
if the disc used gyroscopic procession to change the attidude, when the axis stopped changing, gyroscopic precession stops(forward flight) you would have a 90deg adjustment to make??

hows my theory

[Lu Zuckerman]

To: vorticey

You stated:

dave:
yes the disc axis is changed by the blades flying into place!
yes the axis would try to advance as the disc was tilting!
(gyro. press.)
yes the pitch on the blades would change as the disc started advancing from the attitude induced by the pilot.
and when the gyroscpic precesion = the attitude pressure, from the blades trying to bring the disc back to the pilot induced attitude, it becomes nutral.

lu:
if the disc used gyroscopic procession to change the attidude, when the axis stopped changing, gyroscopic precession stops(forward flight) you would have a 90deg adjustment to make??

hows my theory


My response:


I can’t disagree with your first point it is that I don’t understand exactly what you said. It is true on an articulated rotor system there is a deviation between the driving axis of the rotor shaft and the driven axis of the blade rotational plane. This shifting of the relationship between the two axes is what causes leading and lagging. These same forces are present in a rigid rotor system but the lead and lag is absorbed in the blades and the head. The newer Bell rotors and the French helicopters have soft in plane lead lag dampers but even though there is no actual flapping hinge there is still an apparent difference between the driving axis and the driven axis. On a two blade system there is a similar deviation but since the rotorheads are underslung the tendency to lead and lag is minimized.



Whether you espouse the aerodynamic precession theory or the gyroscopic precession theory the 90-degree adjustment you mentioned is taken care of by the relationship between where the swashplate is moved by the cyclic and where the blade is when it receives the maximum input.

To my knowledge the only two helicopters that vary from what I am about to say are the Robinson and the S-76. The 90-degree adjustment relates to the pitch horn relative to the blade and the maximum deflection of the swashplate. On most Sikorsky helicopters the swashplate tips 45-degrees in advance of desired flight and the pitch horn leads the blades by 45-degrees = 90-degrees. On Aerospatial helicopters it is 60-degrees plus 30-degrees = 90-degrees. On two blade Bell helicopters it is 90-degrees

[Dave Jackson]

The following was cut & pasted from another thread.
___________________________

Lu said
"If you have an infinitely rigid rotor you in effect have a gyroscope."

You have to forget gyroscopic precession & the helicopter rotor. For gyroscopic precession to take place, the rotating device must have considerable [Angular Momentum] A helicopter's rotor does not have enough.

Consider a toy gyroscope on a vertical axis. Bring it up to speed. A minute later it is still spinning, and the disk is still horizontal.

Now lets consider a 'type' of 2-bladed helicopter rotor, which has round 'no lift' blades. We'll make it from a 30-foot long by 2" diameter steel pipe. Drill a hole through both walls at 15-feet from the end and weld in a rod (axle), which extends out both holes. Now spin the horizontal pipe, somehow, on its vertical (rod) axis to about 400 rpm. When released, it will slow and fall over within a second or two.

They ain't the same thing.

[vorticey]

lu>
i think it was you that believed that gyroscopic procession is the reason for the 90deg phase angle.
and to make my explination clearer:
gyroscopic procession only happends when the disc is tilting.
so when the disc acheives an attitude and holds it, gyroscopic procession will have stopped aswell as the need for the 90deg phase angle.
:- gyroscopic procession must not be the reason phase angle is needed.
sorry if you already know this, my computer has been of line for a while.

dave>
Now lets consider a 'type' of 2-bladed helicopter rotor, which has round 'no lift' blades. We'll make it from a 30-foot long by 2" diameter steel pipe. Drill a hole through both walls at 15-feet from the end and weld in a rod (axle), which extends out both holes. Now spin the horizontal pipe, somehow, on its vertical (rod) axis to about 400 rpm. When released, it will slow and fall over within a second or two.

but put a stand under it to spin in (a helicopter)

i think the drag effect is the problem with your egsample dave.
if it was a flat bit of steel, this would spin for longer.
also theres all the wheight on one axis and it would fall over, but 3 or four blades is a different storey

angular momentum must be the spinning speed heh? the speed and wheight would be directionaly proportional to the amount gyroscopic procession pressure

[Dave Jackson]

vorticey,

"i think the drag effect is the problem with your egsample dave. if it was a flat bit of steel, this would spin for longer."

You're correct. The pipe was used so that there would be profile drag but no lift.