Helicopters and Gyroscopic Precession

[Burgess]

Helicopters and Gyroscopic Precession

There are lots of discussions and explanations about helicopter rotors, how they work, and in some they are referred to as a disk, and through this analogy explain how the disk functions as a gyro and thereby gyroscopic precession enters the explanation. I've always thought the explanation lacking and counter intuitive, and with recall of demonstrations running in visual memory, this thought came to mind. At what point dose a two-bladed rotor head morph into a solid disk?

The answer is, it doesn't! ''

There is an optical illusion of a disk coupled to a theoretical construct. More-so, the mechanical dynamics are different.

Second consideration: With regards to cyclic control input, does gyroscopic precession actually happen?

It's understandable how the theory of gyroscopic precession has been applied to helicopter rotors, however, there is one fundamental difference, a gyroscope has a solid continuous ring of mass, whereas a two-blade rotor head system does not. So the energy is not distributed equally around the perimeter of a theoretical rotor disk, but at two locations 180 degrees apart. So no-matter what the rotational velocity is, the mass is only ever on the line of the blades at any one instance.

If the disk does not exist in three dimensional space, then neither the mass not attributed physics can be applied.
****************************Edit*******************************
That should read "then neither the mass nor attributed physics can be applied."
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Think Centripetal rather than Gyroscopic.

The blades are kept at 180 degree via centripetal force acting on the blades, and with FB system a secondary centripetal force acting on the fly-bar assembly; and their centripetal forces act on that central point of rotation. It's from centripetal forces acting through the teeter action at the seesaw that the fly bar will, always tend towards regaining perpendicularity to the main axis of rotation. If the CG of either the blades or fly bar paddles are not at absolute equidistance, if the heli is held on station, axil precession will set-in and the main axis will describe a conical figure to whatever extent.

The dynamic action of cyclic input.
Assume a Fly-Bar system:
The fly-bar paddle system, Stanley Hiller developed and patented as the "Rotormatic" cyclic control system. It provides an aerodynamic boost to the main rotors, something like power steering on road vehicles.

The blade and paddle angles here are for illustration purposes only. Conditions near still air, sun shining, and no distractions (if only).
The helicopter is on station in steady hover.

The blade angle of attack positive 6 degrees.
With only forward cyclic (forward elevator) input the advancing paddle at 90 degrees to the roll axis, the leading edge of the paddle deflects downward 6 degrees and the retreating paddle upwards 6 degrees.

The main blades at 90 degrees to the pitch axis both with positive 6 degrees angle of attack (pitch). So their lift/drag are in equilibrium so cannot effect a change to the rotor-blades plane of rotation, until the blades aline on the pitch axis. When the advancing blade is 90 degrees to the roll axis it deflects down to positive 3 degrees and the retreating blade deflects up to positive 9 degrees, and the paddles being on the roll axis are both at zero degrees deflection.
The helicopter commences to rotate on the pitch axis, tilting the nose downwards and the tail upwards.

The swash plate connects to the blade-holders via the fly bar mixing arms. So as the paddles deflect from their perpendicular rotational plane the action results in perturbation of the main blade plane of rotation, and an asymmetrical angle of attack of the main blades.
Until centripetal forces equalise and the heli is in steady state forward flight.


Well, I might be wrong...what do you think?

Burgess

[tombo242]

Seems to me that it's a combination of having to apply integral calculus to the rotating mass which leads to a gryoscopic reaction, and the 90º difference of the flybar and rotor blades. We do fly the flybar not the blades and to get a cyclic change in pitch the heli does have to dip, but this dip tends to counter the flybar deflection or the stabilisation would not work.

Even a pendulum will demonstrate gyroscopic action, look at the one in the science museum (London) showing the rotation of the earth. A bee can only hover because the rear wings have shrunken to a pair of knobbed pendulum gyros. It vibrates these to orient itself in space. (All 2 winged flies are the same, dragon flies are still as first evolved.) I believe the same system was used in spatial navigation as it is uneffected by external sources but gives a 3D location within the universe. Certainly the case with some of the craft in the Space Museum at RAF Cranwell where I spent some time.

It does seem that there may be more to a non-circular gyro than at first thought, I'm working on it but don't hold your breath, I now prefer flying models to maths.

(I could be wrong too!)

Tom.

[ferretmaster]

Cutting to the chase.....(is that saying only understood in the USA?)

I move the stick on the transmitter and the heli moves too.

Good enough for me.

[Burgess]

[admiral]

Who said flying RC helicopters isn't educational?

"Cut to the chase is a saying that means to get to the point without wasting time.

The phrase originated from early silent films. It was a favorite of, and thought to have been coined by, Hal Roach Sr (January 14, 1892 – November 2, 1992). Films, particularly comedies, often climaxed in chase scenes to add to film time."

I learnt something today about a saying I've used for years.

Sorry Burgess, it has nothing to do with Gyroscopes.

[ferretmaster]

Five points for the Admiral!

Silent movies was the genesis of that little verbal gem.

Back on track....

When I was an Air Force mechanic on the F-106 back in the late '60s, we had a trick we would play on the new green mechanics that was loved by all but the recipient.

There was an item called the "stable table" that was the actual gyro for the flight controls and provided reference data for the weapons system. It was completely sealed in a 20"x 20"x 20" block box, spun on precision bearing (gimbles) that were near silent even at full speed and weighed about 70 lbs and spun at ungodly rpm's. It took about 45 min to an hour to spin down to a stop after removing power.

On the "A" model of the "Six" the table was located in the hell-hole located in the belly of the aircraft just forward of the armament bay doors. Access was by a swing down door about 24" x 24" (~0.7m?) and the fuselage edge was about waist high on the average airman.

As mentioned above, it took quite a while to spin down and standard procedure was to NOT perform maintenance on/remove the stable table for at least an hour after flight, or the last time power was applied on the ground whichever came last.

The humor began by ignoring the above procedure and back three of the four mounting bolts WAY out so they could be removed quickly and there was just one bolt left to remove. Speed here was critical as it took a lot of time to remove these bolts if not loose initially. Turn power back on long enough to get the gyro up to speed and cut power again. The idea was to have as much rotating speed left in the gyro as possible when you sent the rookie into the "hell-hole" to finish the removal of the "table" and set it on the ground.

The results for those familiar with the Gyroscopic Precession Burgess started this thread discussion about was predictable and (we felt at the time) hilarious. The PDB (Poor Dumb Ba$tard) would almost beat himself to death first trying to lift the table, then move it into his chest so as to fit down and out of the small opening and lower himself and the rapidly spinning gyro to the ground. Bloody knuckles were the usual minimum reward and the occasional good knock on the head or other upper body part were icing on the cake!

Not at all sure I would try that type of stunt today. but sure was fun at the time!

Thought you might enjoy this little story.

Dave

[Burgess]

Tom,

Google Doodle celebrates Léon Foucault's 194th birthday with Foucault pendulum tribute.
He also used a classic gyroscope for his demonstrations.
http://www.cleonis.nl/physics/phys256/gyroscope_physics.php

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Dave

I heard a similar story back in the 1960s while I was an RAF cadet.

From what your saying, it's a good job that old jet fighter guidance gyroscopes aren't needed for small RC helicopter rotor systems. You'd never be able to get then out of the mail box, especially if one of those PDBs now works for the U.S. Mail.

Try this link
http://www.pprune.org/archive/index.php/t-51070.html

The contents reads...

"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.

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? "


So, I'm not the only one to question the theory.

Burgess

[nick_onelove]

Awesome, thought-provoking read: thanks Burgess.

Helicopter aerodynamics are so fascinating; it's like they narrowly cheat the laws of physics.