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Old Dec 24, 2006, 03:53 AM
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Mickey,

I enjoy reading it at least as much as you seem to enjoy writng it.

Merry Christmas,
Jochen
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Old Dec 24, 2006, 07:45 AM
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Thanks for the feedback guys. Even the tiniest response
helps me stay motivated.
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Old Dec 24, 2006, 07:50 AM
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Quote:
Originally Posted by mnowell129
Ok, here's what we have so far.
The rotor obeys basic physics, that is, nothing happens instantly. We steer the rotor by applying cyclic pitch 90 degrees ahead of where we want something to happen and the rotor responds. Forward motion creates differential velocity on the advancing and retreating blades and if we don't do anything about it the rotor will flap up. To cancel this out we apply down elevator (nick) control. This applies some down blade pitch on the advancing blade and up blade pitch on the retreating blade.

mickey
Hi Mickey,

I think I might be confusing things a bit for myself. For a dc machine; in practice; in order to pitch up you apply a force to tilt the rotor disk up I think? So when you talk about the 90 degrees out of phase are you talking about the individual blades rather than the rotor ?

Sorry for asking a dumb question but I am really interested in understanding this.

Dan

ps Please stay motivated.this is greatly appreciated!
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Old Dec 24, 2006, 08:39 AM
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Quote:
Originally Posted by leadfeather
Hi Mickey,

I think I might be confusing things a bit for myself. For a dc machine; in paractice; in order to pitch up you apply a force to tilt the rotor disk up I think? So when you talk about the 90 degrees out of phase are you talking about the individual blades rather than the rotor ?

Sorry for asking a dumb question but I am really interested in understanding this.

Dan

ps Please stay motivated.this is greatly appreciated!
It's not a dumb question. This is very mind bendingly confusing, it was to me in the beginning and I studied it in college.
But think of it this way. You are not applying a force to move the rotor, you are applying a force to make the rotor move itself.
If you were actually applying the force directly to the rotor by tilting it back, the blades would respond but 90 degrees later and you would get a roll, not a pitch up. Because of the flapping hinge you can't really apply a force to the blades directly, they just hinge when you tilt the shaft. However the blade on the side, the advancing side, gets twisted in pitch, something that the blade has very little resistance to. Since the blade gets twisted it makes more lift and starts to rise, eventually reaching it's peak over the nose. Now that the blade is tilted to a new angle it tilts the total lift vector from the whole rotor backwards and the nose comes up.
Let me know if this helps. I keep searching for the explanation that will make this crystal clear to everyone.
mickey
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Old Dec 24, 2006, 10:36 AM
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What's all the FLAP about?

Okay, I guess we'll deal with flapping.
Cierva (inventor of the Autogiro (trademark)) figured out that he had to deal with asymmetric velocity. His first gyro's had completely rigid rotors. Recall that the rotor responds later in the rotation to the asymmetric velocity and that for a rigid rotor this is less than 90 degrees. Here is where some confusion may arise. Most of the response from asymmetric lift is nose up and in a rigid rotor there is a component of roll. If you were to observe the early attempts at gyro flight the aircraft would simply roll over. It's easy to take the simple first guess and assume that its just the lift acting directly on the blade that is in turn acting directly on the aircraft. We as modern inventors know better. A little more thought gives you a better explanation of what you might have observed. Because the aircraft was long and had the tail firmly planted on the ground and because the landing gear track was quite narrow the small amount of rolling force created by asymmetric velocity on the rigid rotor was enough to roll the aircraft over before it got airborne. Had it have gotten airborne it would have pitched up and rolled over at the same time. How familiar is this to you gyrocopter experimenters to see what looks like basically a snap roll to the retreating blade on takeoff? This is the result of asymmetric velocity applied to a rigid rotor causing rotor tilt aft and to the retreating blade.
Cierva initially tried cyclic feathering to compensate but couldn't overcome the mechanical complexity ( he tried to to do it with cables). So he went to flapping hinges.
How does this work?
In the figure the line A-B-C represents a rigid rotor happily spinning. We know that as this rotor moves along it will try to pitch up. What flapping hinges "apparently" do is just go ahead and let it pitch up, but what happens is a little more sophisticated than that. What we do is put a hinge in the blade root so the blade tip can move up and down freely, or "flap", so its called a flapping hinge. Now when we start moving the rotor flaps up to the line X-B-Y and goes no further. Why does it stop continuing to flap up and reach a stable position? Two reasons. First see that the blade now flies not only around the circle but vertically as well with velocity Vv, Vv is not small if you consider that it is the vertical flap distance in 1/2 of one revolution of the rotor. For a rotor turning 600 rpm this is 10 revs per second, 20 half revs per second or .05 seconds per half rev. If the flap distance is 2 feet this is a vertical velocity of 2ft/.05 seconds = 40 feet per second or 27 mph!

Note that this vertical velocity is 0 at the front and back and peaks at the side. Note that the downgoing blade has the opposite downgoing speed of 27 mph. Perhaps you can see where this is going. The vertical velocity is varying, err..., cyclicly(!) around the circle. A little thought will see that the blades fore and aft have the same velocity at nearly the same angle as before in the non flapped case, but the advancing blade has a new local velocity of the previous velocity plus the vector sum of the vertical flapping. This is shown in the little side diagram. Instead of the blade just having air velocity Vnf (no flapping) it now has velocity Vf (flapping). Note that Vf has a lower angle (because of Vv) than Vnf. And since Vf is lower angle than Vnf clearly this blade has a lower angle of attack and makes less lift. Some thought will prove to you that the retreating, descending blade has a higher angle and thus more lift. The important aspect is that the advancing blade due to flapping has a lower angle of attack, peaking lower at the side position (270) and the retreating blade has an increased angle of attack, peaking at the retreating side position (90). The circle is unbroken now. Flapping is cyclic pitch.
This leads to the following statement. Asymmetric airflow velocity in an autogyro is canceled by cyclic pitch. The cyclic pitch can be implemented with cyclic feathering (either tilting spindle or swashplate) or by blade flapping. A combination of both can be used.
Note that once you allow the blade to flap the component of tilting spindle down cyclic comes into play. This is true whether you move the spindle or it is fixed. (This is a significant fact not to be glossed over. Note that you can and do still have cyclic pitch with a "fixed" spindle. This leads to how you steer a "fixed" head gyrocopter.) Either way, once the rotor flaps back at a higher angle than the spindle/hub a component of cyclic feathering is added to the rotor in addition to the flapping motion. Both of these combine to resolve asymmetric velocity.
Note that flapping rotors will be flapped further back than the angle needed for autorotation. This means in a side by side comparison a flapped rotor will need more tail clearance than a cyclic feathered rotor (either tilting spindle or swashplate).
Other than reducing the tail clearance why not let all rotors flap away? Answer forthcoming.
mickey
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Old Dec 25, 2006, 07:59 AM
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Mickey,
This is great stuff! Thank you for taking the time to explain it in such detail. I have understood everything up to the explanation of flapping. If I understand correctly flapping is introducing cyclic pitch, which assists in reducing asymmetric lift. But what I cannot understand is how the blades hinging at the root can change the angle of attack as they rotate.

In addition, on my PT25 it appears as if the hinge point is not 90 degrees to the leading edge of the blades. It seems to be offset slightly. Does that play a role in changing the angle of attack of the blades as they flap?

Frank
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Old Dec 26, 2006, 06:19 AM
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Mickey.

I think most of this is finally starting to sink in for me, Thank you.

Here is a specific question that I hope is on topic. It is related to something I'm working on at this time. In a rudder only steered single rotor autogyro, how does the yaw roll coupling work with and without a flapping hinge. My limited experience so far indicates that the yaw/roll coupling is not very strong with a rigid rotor.

Dan
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Old Dec 26, 2006, 08:25 AM
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Frank,
I'll try to clarify. When the blades are hinged 90 degrees they don't change their "rigged" angle. That is they don't change the angle at which the blade is attached to the root. But angle of attack is not the mechanical angle that the blades are attached at (this is usually called the incidence angle), it is the angle between the blade and the oncoming air. Think of the oncoming air as coming from a little hand fan that you can move around. If you put the fan in front of the blade, the angle of attack is 0. If you put the fan below the blade the angle of attack is 90 etc.
So lets do a thought experiment. We mount a rotor blade on the car of a ferris wheel that is in the back of a truck. We mount the blades horizontal like they would be sitting across the laps of the riders. With the ferris wheel stopped a rotor blade will have the same angle of attack anywhere around the wheel.
Now lets stop the truck and rotate the ferris wheel. It should be clear that when the blade is on the falling side of the ferris wheel it will have a 90 degree angle with the air its' meeting (angle of attack) and the rising blade will meet the air at -90 degrees.
Now if we spin the wheel and move the truck, the blades experience the combination of the wind from moving and spinning. If the truck speed and the speed the ferris wheel is turning are the same then the blade that is falling "sees" wind from a 45 degree angle from below and has a 45 degree angle of attack. In fact this angle changes based on the ratio of the truck speed and the ferris wheel speed.
So hopefully you can see that the blades now have cyclic pitch even though they are staying horizontal all the time.
Now lets lay the ferris wheel on its side but tilt the front edge up. Let the seats hang vertically so the blade again lay horizontal. Now spin the wheel again. You still have a rising and falling blade, this time not as severe but nevertheless they have a rising and falling airflow. If you move the truck the blades now have the combination of forward movement and up and down movement. This changes the relative incoming air to each blade in a cyclic manner, even though the blades are rigged horizontal. This is cyclic pitch. What the flapping hinge does is allow the blades to rise up and down around the circle just like the tipped ferris wheel. Because the blades rise up and down they have a change in relative incoming airflow that is the cyclic pitch we are looking for.
Does this help?
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Old Dec 26, 2006, 09:09 PM
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Quote:
Originally Posted by Nightnav

In addition, on my PT25 it appears as if the hinge point is not 90 degrees to the leading edge of the blades. It seems to be offset slightly. Does that play a role in changing the angle of attack of the blades as they flap?

Frank
Yes this is called delta-3 hinging.
Delta three is where the hinge line is not exactly 90 degrees with respect to the mast on the flapping hinge.
What this does is make the blade change rigging angle as it flaps. If the delta is negative the blade reduces pitch as it flaps up, and increases pitch as it flaps down. If the delta-3 is positive the reverse is true, the blade increases in pitch as the blade rises.
Negative delta-3 was used in helicopter tailrotors to cut down on the hub stresses. The tail rotor didn't have cyclic pitch, just collective to turn the tail. As the tail rotor was always flying on edge it tended to try to flap back (on its side, but it was basically flapping back). As the tail hubs were rigid this tended to make the tails fail. The solution was to teeter hinge the tail rotor and let it flap, however the flap angle got large. Delta-3 hinging was used in the tail rotor to cut down on the flap angle.
Delta 3 works by virtue of the fact that at the blades lowest point aft it has the highest pitch and as the blade flaps up the pitch reduces, minimizing at the fore position. Note that this isn't the ideal cyclic for cutting down on flapping due to asymmetric velocity as the peak negative is at position 0 not position 270, but it helps. Generally very small delta 3 angles are used usually much less than 10 degrees. Higher delta 3 angles create problems like have the blades oscillate, etc.
Delta 3 has other uses in helicopters as it can make the rotor self stabilizing and correct for gusts. I think in the case of the PT is used to stabilize the rotor and make it less sensitive. It's use to cut down on the amount of flapping is really not important because you have cyclic to do that.
mickey
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Old Dec 26, 2006, 09:19 PM
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Mickey,
Yes, I get it now. After reading over post #20 a few times it finally became evident.
Thanks, I look forward to more.
Frank
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Old Dec 27, 2006, 01:37 PM
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Please enter the cone of silence.....

Dan, will get to yaw-roll coupling. But for now, coning.
Coning is the condition where the blades are tilted up from the mast above 90 degrees.
Please don't confuse coning with the dihedral of two wingtip rotors, we'll deal with that when we talk about turning.
Coning results because the blades cannot be infinitely stiff, nor can the hub be infinitely strong. When the blade starts making lift it will climb up until something stops it. The something is generally centrifugal force. Note in the first diagram that the blade force tries to make the blade cone, the centrifugal force tries to make it flat. Hub stiffness affects the coning angle as well. Note that if the hub is stiff that the blade will still bend under load and create coning another way. Failure to allow for coning in a full sized aircraft results in very high hub stresses and early failures.
Airplane wings do the same thing under load, they experience a slight amount of dihedral under load. For very stiff wings this may be measured in the .001" but it still happens. So coning is a direct result of the rotor being loaded.
The question is what are the effects of coning and are they desirable. Coning looks like dihedral in an airplane so it seems that it should do the same thing. However it doesn't.
It's a little sideways to the explanation but lets quickly describe dihedral in a wing. The "v" from dihedral works to stabilize an airplane because when an airplane is disturbed from level flight it tends to slide sideways (slip). The "V" made by the wings geometry forces the wing that is forward in the slip to have a higher angle of attack than the wing that is backwards in the slip. This difference raises the lower, forward slipping wing back to level.
So lets return to a coned rotor in the second figure. The coned rotor is traveling right to left. Note that the two blades at position E, on the left and right sides, have the same angle of attack as they had without coning. It's not that they have the same angle as each other because we know flapping and asymmetric velocity are both affecting each blade differently, but they have the same angle of attack that they would have if not coned. The blades for and aft are a different story. The blade leading is much like the leading wing in a dihedraled plane. If you break down the incoming airflow from aircraft motion (Vf) it has two parts, a part horizontal to the blade (Vh) and a part that is vertical to the blade (Vv). The aft blade has the same Vf but this breaks down, in this case, to a horizontal part and a small negative vertical part. It should be clear that the forward blade has a much higher relative angle attack to its local airflow than the aft blade does. Note that the side blades have the same old angles they had before but the front going blade now goes from zero to some increased angle back to zero at the retreating side. Oh my, we already know what this is, cyclic pitch. So the front blade has increased lift applied to it and 90 degrees later it flaps up and applies that increased lift to the aircraft and the net result is a roll towards the advancing blade.
So this behavior is not very intuitive to the average observer. To see the model pitch up and roll to the advancing side makes no sense until you see the whole combined picture. Making the model move creates asymmetric velocity. Asymmetric velocity causes the rotor to flap back until flapping and/or cyclic stop the flap. Once the rotor is loaded up with the weight of the model at takeoff the rotor cones and promptly rolls to the advancing blade. The problem is that the cone induced roll doesn't happen in your hand, it doesn't kick in until the weight of the model is on the rotor. So in the first case coning is definitely problematic.
How about the similarity to dihedral.
Suppose the model is flying along level. It then gets bumped off to the side. What happens then is one blade is pointed down hill just like the dihedral wing. You used to believe that this would just pick that side of the rotor up, but now you know better. Because the aircraft responds 90 degrees behind the rotor the net effect of the aircraft slipping sideways with coning is that it makes the aircraft pitch, not correct in roll. Worse yet is if the slip is to the advancing blade the pitch is nose up and if the slip is to the retreating blade, the pitch is nose down. So not only does the coning not provide the desired roll correction, it creates a nasty pitch result.
So does coning have to happen, yes. Do we have to allow for it in full sized rotors, yes. Can we ignore it in models with much stronger materials in the hub and blades relatively speaking, yes. Does it stabilize like dihedral, no. Does it create roll coupling with forward flight, yes.
So the idea is to reduce coning.
There are a couple ways, one is to increase the overall rotor stiffness. Another way is to increase the RPM of the rotor (but this increases the following rate, and raises all the stresses on the rotor). Another is to shift the CG of the blade further out so the the centfigual forces are more effective in reducing coning (tip weight).
There you have it. Coning is a necessary evil. It has nasty side effects and is not stabilizing. There are ways to reduce coning, the most common being the use of tip weight.

Everyone hanging in there with this?
mickey
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Old Dec 27, 2006, 03:56 PM
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There is another way to deal with effects of coning: use negative coning. These "UFO" toys are so stable precisely because they have so much negative coning.

Ari.

http://www.raidentech.com/rcufo.html
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Old Dec 27, 2006, 04:52 PM
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Not to mention the rather large gyroscopically stable outer ring below the CG.
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Old Dec 28, 2006, 01:02 AM
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Mickey,

With cyclical controls (assume very flexible flapping hinge), is the gyroscopic precession of the rotor disk from control inputs eliminated?

Dan
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Old Dec 28, 2006, 04:51 AM
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Mickey,

your posts are just great!! Please keep them coming, I find them extremely instructive and well written.

A question about the relationship between flapping and coning: Doesn't flapping rotors allow for more coning automatically? In other words, if you don't allow coning, won't the flapping be gone, too?

Edi
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