View Full Version : Coriolis Force......
05-20-2005, 11:41 AM
I recently finished rotorcraft ground school, and am still having a hard time wrapping my mind around one concept. This concept is how the different rotor systems minimize the effect of Coriolis Force upon them.
The underslung rotor found in semi rigid rotor systems accomplishes this by using the teetering hinge to allow the blades to flap while keeping the center of mass of the rotor relatively unchanged in respect to its reference to the mast.
Here is my question:
How does the drag hinge in a fully articulated rotor system minimize the effect of Coriolis Force on the rotor when it allows for lead and lag, or hunting, in the rotors?
05-20-2005, 12:34 PM
Andrew, congrats on finishing ground school and welcome to the forum. :)
Regarding your question; The blade's center of mass moves inward as it flaps up. (but see the rest of this thread for a more in-depth answer)The Coriolis Force causes the blade to advance as a consequence of moving in a smaller radius.
The lead lag hinge is a way to accommodate this motion which would stress the blade otherwise.
As you say, the underslung teetering rotor does not experience Coriolis forces because you can draw an imaginary line connecting the cg's of the coned rotor and it will pass through the teeter bolt. Thus the center of mass of the combined rotor system is always on the teeter bolt despite flapping.
This can't be accomlished with a fully articulated rotor since the flapping hinges are outboard and the kinematics are very different. Lead lag hinges are required in both gyros and helicopters that have 3 or more blades unless they have fixed pitch and do not flap.
05-20-2005, 01:24 PM
I thought it was established on the old forum that the Coriolis force affecting rotors was pretty much a joke................so is that not true now?
Another thread had links to information that said the Coriolis force is so small that it only affects very large air masses, like huricanes........... :confused:
05-20-2005, 01:37 PM
Michael, the joke was concerning which way the water goes down the drain. The Coriolis force due to earths spin has miniscule effect on the water in the basin compared to the local force of gravity which is 10 million times stronger. The water will go down either way. If you look at a larger mass like a hurricane, then the Coriolis force starts to come into play.
WIth the rotor, the Coriolis force is not from the Earth, it's from the spin of the rotor blades themselves. This is the "ice skater drawing in her arms" scenario. When a blade flaps up, it moves closer to the center and speeds up relative to the other blade.
It is mostly a problem on non teetering rotors as pointed out above.
I think there was some discussion on the old forum concerning whether the Coriolis force was a hoax perpetrated by Cierva to confuse his competitors, but you'd have to ask Chuck Beaty about that. Most rotorcraft books do name the Coriolis force as being important in articulated rotors.
Hooke's joint effect can also explain the effect, and it comes down to frames of reference. Dave Jackson has a write up on it here. http://www.synchrolite.com/B274.html#Coriolis_and_Hooke
The animation below shows the idea. A rotorhead can be thought of as one half of a hooke's joint-the left hand portion in the image below.The block between the two halves appears to rock back and forth in a teetering motion. Notice that it moves like the teeter block on a rotorhead.
05-20-2005, 02:47 PM
ok.........I knew about the skater thing but I didn't realize that was the Coriolis force too.
I really do not think that the coriolis effect has anything to do with it. Earlier in this forum – in http://www.rotaryforum.com/forum/showthread.php?t=961&page=2&highlight=Coriolis Chuck Beaty said that Cierva used this myth to fool his competition! Chuck also wrote: "The Coriolis hoax, ....Was perpetrated by Cierva to bamboozle his competitors.
To have a Coriolis torque, you must have radial movement of mass in a rotating system. The commonest example is to stand at the center of a carousel and walk toward the rim. Your body, as it gains kinetic energy, exerts a torque opposing the rotation of the carousel". In other words: coriolis only has an effect when something moves from the centre of the rotor to the tip or vice versa.
In the old (Norm's) forum, Al Hammer was quick to point our the fallacy of my thinking: ]“It is not Coriolis, but rather hookes joint effect that causes a cyclic speed variation in the rotorhead[/COLOR]” (Sorry Al you goofed again by bringing coriolis forces,into the discussion. In fact I am shuddering to argue with to one with your knowledge, but I really think you are wrong, or as Chuck said earlier : "The Coriolis (is a) hoax, ...perpetrated by Cierva to bamboozle his competitors".)
To understand what is going on, with undersling, please see again http://www.rotaryforum.com/forum/showthread.php?t=961&page=2&highlight=Coriolis
Actually, what I have to do one day is to paste the whole explanation that Al gave me on the old Forum, with graphics and all.
After learning from Al and talking this over with my engineer son, I am totally convinced that the coriolis effect, as it is used within Giro circles is, as Chuck said, a hoax.
05-20-2005, 06:46 PM
I stand by those earlier comments on Norm's forum, and I'm honored that you saved them.
However, I think it can be argued that there are times when it is useful to use fictitious forces to help analyze a system.
The Coriolis force is an apparent force that would go away if you chose the right reference frame.
But then consider that the Coriolis force that moves hurricanes is also a fictitious force. Nothing pushes the air mass in a circle. The motion is a result of the mass moving in a smaller circle around the earth as it moves away from the equator. From an outside , non rotating reference point, it appears as if a force exists and this force is given a name, just like centrifugal force is a useful fiction to describe what happens in a rotating system when mass is forced to change direction.
That's why I am not jumping up and down to correct someone who speaks of the Coriolis force.
I did try to slip in the concept of the Hookes (or Cardan ) joint at the end, to cover my butt, so I left some wiggle room for both points of view. :D
05-21-2005, 01:39 PM
I am not sure how to word this but what we are really talking about is conservation of angular momentum. As the blade on a fully articulated rotor system flaps up the distance from the center is reduced. As the blade flaps down the distance is increased.
To be more exact without using sums or calculus and keeping things easy
I = momentum
m = mass
r = radius or distance
v = velocity or speed
the equation looks like this
v = I/(mr)
and we have a constant I and m in our system so the velocity v and the distance r are inversely correlated. In other words , conservation of angular momentum says that a decrease in the distance r must be accompanied by an increase in velocity v, and vice versa.
05-21-2005, 01:51 PM
I should have been complete in my previous reply but…
The lead lag hinges are needed in order to reduce the torque on the rotor hub. If one blade flaps up and another flaps down then there will be a speed difference on each of the blades. This would result in torque and the eventual destruction of the rotor head if it were not for the lead lag hinge or the ability of the blade to flex.
05-21-2005, 03:15 PM
Here's the problem; That formula presumes that the blade is moving about the spin axis of the rotor head. The blades, durung flapping, are moving in a plane of rotation that has its own axis. After all, flapping is a condition where the rotor is tilted with respect to the spin axis.
If you measure the movement of the blades' cg relative to that axis, then the radial motion disappears, so there is no need for a change of angular speed.
The blades do indeed need to advance and retreat about the lead lag hinges, but it is because of geometry, or kinematics, just like in the animation of the universal joint I posted above.
By your reasoning, Micheal, a blade speeds up or slows down because of conservation of momentum.
If a mass moves to 1/2 the radius, the angular speed doubles, acording to your formula.
But we know that centrifugal force should also double, since it is proportional to speed squared and inversely proportional to radius.
CF=(2)² X (1/2)= 2
Do you believe that the centrifugal force increases on the rising blade and decreases on the falling blade? Is energy expended to draw in the mass of the spinning blade just as a skater expends energy to draw in her arms?
I think the answer to these questions is no.
The accepted fiction is to teach that the blade speeds up because of Coriolis force, or conservation of momentum because its easier to grasp than some complicated model of a hinged multi-axis spinning mess.
You'll notice I started giving the "Coriolis" BS when Andrew asked the original question, but since its not just students who might be reading this, I am backing away from the easy answer. :)
05-21-2005, 08:49 PM
Yes well I did mention that I wanted it to be simple and easy not a bunch of calc, or sums of forces. It is however a conservation of rotational energy. When analized it is a complex system. However if we expect to be able to talk about it in a general and understand able way...
Also not all of the mass is at the tips of the blades so a calc problem is at hand.
I don't beleive or contend that all of the blade motion can be explaned by this conservation of rotational energy equation as it is just a simple one mass one distance one velocity equation.
If we want to go there we can but I dont think it will help.
I still think the best way to describe it is to use the simple way and then mention that it is just that. Most pilots dont expect to do calc problems in order to be able to understand and fly the bird. LOL
I respect your understanding of the system and did not target my responce to you Al My goal was as I stated to make it easy and not use any "extra math".
Also note that I never used that BS term to describe the motion.
Now for the bad stuff so just put on the waders and plug the nose in case it gets too high or a bit ripe.
The rotor model would need to describe the dynamics of each blade with coupled flap, lag, and torsion. A finite element formulation could be used to model the blade, coupled with a modal coordinate transformation to reduce the number of degree of freedom and, therefore, the number of equations describing the blade dynamics. Then the blade equations would need to be written to take into account arbitrary hub motions; and the blade elastic deformations which may not be small. When commbined With rigid-body fuselage equations, and the blade dynamics equations, the result would be a system of coupled differential equations for the rotor and fuselage that might come close.
I dont take myself serious why should you. :)
05-21-2005, 10:33 PM
Well put, Michael. We shouldn't take ourselves too seriously.
05-22-2005, 08:57 AM
Imagine a shallow sheet metal cone with an included angle of 174º driven at its apex by a constant velocity universal joint (rotor blades typically fly at a coning angle of 3º; thus, the included angle is 174º).
If the driveshaft should be at some angle to the cone axis, would any atom of metal in the cone be subjected to a force that would make it speed up or slow down? A spot on the cone surface is at times nearer to the shaft axis and at other times, farther away, so why not?
The answer is simple; the atom of metal rotates at uniform angular velocity about its own axis and the driveshaft axis is irrelevant.
A 3-blade rotor with flap and drag hinges does the same. The rotor blades rotate at uniform angular velocity about an axis unrelated to the rotorhead axis. Flap and drag hinges are a kinematic necessity that permits the rotor to spin about its own axis.
Floating hub rotors are an exact equivalent of the sheet metal cone and don’t ordinarily utilize flap or drag hinges.
In this instance, the rotorhead is mounted on gimbel pivots and is permitted to self align with the rotor axis.
Some floating hub helicopters have been the Doblhoff tip jet helicopter, the Doman helicopter and the McDonnell (St. Louis) series of helicopters.
Coriolis theory extends conservation of energy principles to rotating bodies that are subjected to radial movement of masses.
Sure enough, a pirouetting ice skater’s spin rate increases as he tucks in and slows when spreading out. But unrelated to rotor principles.
05-23-2005, 07:07 AM
Confusion can arise if we picture the rotor blades as rising above their plane of rotation and then falling down below it as they proceed around. This faulty image is similar to one of those amusment park rides that looks like a huge steel tarantula, with arms the rise and fall individually as they travel around in a circle. Sort of a circular roller coaster ride.
In the amusement park ride, a dedicated hydraulic mechanism lifts and lowers the arms. No such thing exists in a spinning rotor. Cyclic pitch changes that are fed to the blades via the flap hinges equalize the lift on each blade as the blade goes from retreating to advancing and back again. As a result, there's no periodic change in lift that would cause the blades to rise and fall. Without a periodic force to cause excursions from their plane of rotation, the blades coast around a simple conical path. That's why Chuck's analogy to a tin funnel works.
Since the blades' CGs don't move in and out relative to the BLADES' own center of rotation, there's no Coriolis effect in normal flight. Math buffs can, if they want, describe the flight of the blades as a mutation of simple circular flight around the spindle axis, with rising and falling blades, Coriolis effect and all. With great effort, using this point of reference, you can still prove that it all cancels out, if you really want to!
I totally agree with what Doug and Chuck have just said.
It is worth-while to read Doug’s comment again: “Confusion can arise if we picture the rotor blades as rising above their plane of rotation and then falling down below it as they proceed around. This faulty image is similar to one of those amusement park rides that looks like a huge steel tarantula, with arms the rise and fall individually as they travel around in a circle. Sort of a circular roller coaster ride.” It is worth while to download the short movie at the left hand bottom of http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml — This has to do with coriolis, but shows how one's viewpoint can confuse you.
Although it may seem as if the blades are flapping up and down, they are, in fact, moving around a simple conical path. What Chuck said is important: The blades “rotates at uniform angular velocity about its own axis and the driveshaft axis is irrelevant”
I also totally agree with Al that the Coriolis force that moves hurricanes is a fictitious force.
We therefore should rather call it the “coriolis effect”. Al is also correct in saying that: “Nothing pushes the air mass in a circle.”
Yet, as Chuck observed, “you must have radial movement of mass” on a rotating mass to cause this effect. In our rotors there is no radial movement.
Maybe I am wrong but my fear is that as long as we talk about the coriolis effect in regards to rotors, people are still not going to understand leading, lagging and undersling.
Please refer to http://www.physics.orst.edu/~mcintyre/coriolis/TT_QT.html for more on the coriolis effect. Very interesting!! This effect even has a name: Fennell’s Law.
Hurricanes that Al mentioned are just large movements of air. The coriolis effect on Hurricane Andrew can clearly be seen in my attachment. You can even see the area where the air spins out of and the low pressure there it is spinning into. Just look at the size of this storm! Must have a diameter of about 5000 km and a circumference of over 15 000 km. Even if winds blow at 400km per hour it will take almost 40 hours to blow once around the edge of the storm. In this time the earth has spun almost twice around its axis. – That may explain the secondary whirlwinds that one finds in these storms.
To explain that’s going on in our rotors, let’s leave coriolis behind and concentrate on Hooke’s joint effect. Todd, thanks for the editing button. I changed this after Doug showed me my mistake. Thanks Doug! (By the way, he, Hooke and Isaac Newton were enemies.) :D :D
05-24-2005, 08:48 AM
Jim, do you perhaps mean the Hookes-joint effect?
If memory serves, Hooke's law has to do with stretching and bending stuff. It says that strain is proportional to stress within the elastic limit.
05-24-2005, 10:24 AM
Here's another view of the teetering rotor as a Hooke's joint.
Since the rotor is powered by the air, the "driven" shaft is the green one and it changes speed twice per rev according to the Hookes joint model.
The variation gets greater as the angle between the shafts gets greater. The angle in this case, is the flapping angle, or teetering angle.
Actually, with a two-bladed rotor, the blades speed up and slow down together, so this model doesn't allow us to do away with the Coriolis explanation which predicts that one blade speeds up and one slows down, so introducing the Hooke's joint may not be a substitute for the Coriolis force explanation.
In any case, the Coriolis explanation is only needed when you try to pretend that the blades are rotating about the vertical axis instead of realizing that they rotate about a tilted axis(the tip-plane axis.) The center of mass of each blade stays at the same distance from that axis(which is on the yellow shaft.)
There you go Al! :)
Finally we are starting to get you warmed up! ;)
Keep going! Tell the folks what you told on the old forum. I am sure they cannot wait to hear! :rolleyes: :rolleyes:
Seriously — you have much to offer. - But I do not just want to paste your old stuff here -- want to see what new I can learn!
Jim :) :)
06-14-2005, 12:59 AM
Interesting discussion where I love to join in to give some theoretical points of view. Yes there is a difference between teetering rotors and rotors with more than two blades concerning the effect of flapping to the leading end legging (hunting and dragging, advancing and retarding) of the individual blade and the effect it has on the rotor and the individual blade(s). Coriolis forces give indeed the tendency to the blades to accellerate when the centre of gravity is moving towards the mast and V.V. But the blades are actually in another position than you might expect due to the (indeed twisting and bending)Hookes Joint Effect: One blade (F.I. the forward) is given a pitch input slightly before 90° earlyer so that it flaps down in front of the craft and another blade is forced to flap up at the rear, the circular movement of the tips is shifted forward, while the mast the centre of rotation. Therefore the forward moving down flapping bladetip is forced to follow the new tip path and thus will advance, while the coriolis effect will retard the blade due to the outward moving of the C.G. So you see these forces are opposites! And yes these forces are olmost reduced when the hub is again paralell with the tip path plane, the disc between the tip paths. Mostly by tilting of the fuselage when gaining speed. Then the forward airspeed will effect the rotor by effecting the "forward" turning blade with more v so it will flap up almost 90° later (flap back effect). To counteract you must increase the steering input or your airspeed will reduce. On top of that with a tilted forward rotor speeding through air the blade with highest position will have a greater angle of attack than the lower blade in front, so this will effect some 90° later by a roll! Two bladed rotors the blades are useally connected by a beam but are subjected to all of these forces.The blade connection reduces some of the effect because a flap up of one blade and a simultanious flape down of the opposite automatically tilt the beam along over the cardanic bearing. A three bladed rotor needs dampers for the advancing and retarding blades for they live a life at their own. Mind you, some four bladed rotors there are fully articulated ones with dampers but f.i. the Bell 412 has two sets of rotorblades slightly above each other! I hope the drawing will help..
06-14-2005, 03:48 PM
The rotor is subjected to a Coriolis effect when the coning angle changes.
The rotor is subjected to a cyclical Coriolis effect when the disk tilts. The cyclical Coriolis effect and the Hooke's joint effect are two ways of mathematically explaining and conceptualizing the same activity.
If the pitch change in the blades is of no interest, the above activity should be considered as a Knuckle joint effect not a Hooke's joint effect. For reference, in Al's last picture, the lower hinge is the teetering hinge and the upper hinge is the cyclical blade pitch hinge.
The use of the term 'Gimbal Joint' appears to be a confusing one, at least to me it is.
The Universal joint, the Hooke's joint and the Cardan joint are three names for the same device. The word 'Gimbal' also refers to this device. However, it appears that some people may be applying the word 'Gimbal' to the Constant Velocity Joint.
The three helicopters, which Chuck mentioned, are interesting.
The rotors of the Doblhoff WN-342 and the McDonnell XV-1 are driven by pressure-jet units at the blade tips.
The rotorhub the Doblhoff WN-342 appears to be mounted on a Self-aligning Ball Bearing. The inner race of this bearing is mounted on a fixed post The only axis of rotation is the Tip-path axis therefore there is no cyclical Coriolis.
The rotorhub of the McDonnell XV-1 is mounted to a universal joint, which allows flapping on the longitudinal and lateral axii. The inside of this universal joint is attached to a stub mast. The bottom of the stub mast is mounted to a horizontal ball bearing to allow rotation of the rotor. When the tip path axis of this rotor is not aligned with the mast axis (i.e. flapped rotor) The stub mast will oscillate twice per revolution due to the cyclical Coriolis effect. However, this is not a problem because the bottom end of the mast is not attached to anything except the bearing.
The rotor on the Doman LZ-1A is driven by the mast, like a conventional helicopter.
The rotorhub of the Doman LZ-1A is similar to the McDonnell XV-1 in that it is mounted to a universal joint, which allows flapping on the longitudinal and lateral axii. This joint handles all forces between the rotor and the helicopter except for the rotational force turning the rotor. A constant velocity joint is used to transmit the engines torque and this CVJ does not create the 2/rev oscillation, which a Hooke's joint would. Doman LZ-1A Rotorhub (http://www.unicopter.com/Doman_LZ-1A.html)
This subject is one of the two reasons for the creation of Rotor - Hub - 3-blade - CVJ+HS (http://www.unicopter.com/S_Hub_CVJ.html)
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