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Old Dec 21, 2006, 01:25 PM
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Gyrocopter Aerodynamics

We seem to rediscuss the same aerodynamic issue in this forum. Perhaps we can make a sticky thread that describes some of the common aerodynamic questions to avoid re-doing them for beginners. I am throwing out the first topic. Asymmetric lift and the effect on the rotor. Due to some lay descriptions, some flat errors in some famous books and other factors one myth persists about gyrocopters. The myth is that asymmetric lift causes a rollover. This is not true, asymmetric lift causes a pitch up.

Explanation:
Due to the fact that the rotor is turning, one blade "sees" wind that is the sum of the forward speed and the turning speed. One blade sees the turning speed minus the forward speed. This causes the blade going forward, the advancing blade to have a higher airspeed than the blade going backwards, the retreating blade. A simple look would say that clearly the advancing blade has more lift than the retreating blade, so this must cause a rollover towards the retreating blade. The problem is that even in the stiffest of rotors the blade is attached to the hub in a flexible manner. The centrifugal force of the blade on the hub is the dominant force. Even though the blade sees some instant increase in lift, because the blade angle hasn't changed with the hub this doesn't create any force to tilt the hub (or the model attached to it). For the blade to tilt the model it must tilt up or down so the centrifugal force is no longer in the same direction. Now there is a force that tries to tilt the rotor hub. (You may not like this but you must agree that's it true because a gyrocopter with completely loose hinges will fly and the only possible way the blade can apply a tilting force to the hub in this situation is through centrifugal force.) The question is given that the advancing blade "sees" more lift, when does this lift cause the blade to tilt up and apply some tilt force to the hub? The answer is that with real physical objects, their movement is always behind the application of the force. For example a plane flying along at point A suddenly sees a forward wind gust. It's common sense that the airplane jumps up, but not instantly since that would take an infinite amout of force. What happens is that after the gust the plane climbs to point B. Note that there is no extra wind at point B. This is just how far it climbs from the gust at A.
But suppose we tie our plane to a string and let it fly in a circle. Now if we get the gust at point A we climb up and around the circle to point B. Those that have flown control line know this behavior. The peak altitude from flying control line in wind is not directly into the wind but 90 degrees later.
What's been described is exactly the same behavior as a rotor blade. The advancing blade at point A "sees" more wind because it is advancing. It rises up and around the circle. Now it is at point B, tilted up with respect to the rotor hub. It now is in a position to tilt the rotor hub away from point B. If this were a gyrocopter with a clockwise turning rotor, point A would be the left hand, advancing side, and point B would be over the nose. The end result is that the extra lift on the rotor blade at point A, causes the rotor to tilt up at point B and apply that extra lift to the rotor hub (and aircraft), tilting the nose up. Note that the opposite is true of a tailwind on our plane or the retreating blade. It falls over the tail also trying to tilt the tail down (or nose up).
Net result is that asymmetric lift causes the model to pitch up, not roll over.
Next topic: what happens when the hinge is stiff on the rotor blade.
(please comment if this is worthwhile or throw tomatoes if you could care less)
mick
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Old Dec 21, 2006, 01:55 PM
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Rotor with a stiff flapping hinge.

So what happens when the rotor is more rigidly attached to the hub, or in the case of the plane on the string, say we replace the string with a stiff wire held firmly in the center? What happens is that the plane/rotor doesn't make it a full turn before reaching it's peak. With a completely free hinge the angle is always 90 degrees. (It's called the lag angle.) But with a very rigid rotor this angle may be only 70 degrees or so. (This may give you a clue as to why those little coaxial heliocopters with rigid rotors have the flybars somewhere other than 90 degrees.) In any event the maximum tilt up of the rotor and thus the maximum tilt force applied to the aircraft is not directly over the nose but slightly to the advancing side. 70 degrees is an extreme case, it's more likely that with most rotors the angle is between 80 and 90 degrees. The result is that with a rigid rotor you have a little roll due to asymmetric lift but you still have predominantly a pitch up.

So if you've followed along this far the next topic should be easy. Suppose that instead of just having different wind speeds on the blades you changed their angle of attack around the circle, say cyclicly, what effect would that have on the rotor. Thus we get to cyclic pitch, and we're not just talking swashplates but so called "direct control" as well.

mick
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Old Dec 21, 2006, 01:56 PM
Winging it >
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Great information Mickey, keep it coming please!
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Old Dec 21, 2006, 04:45 PM
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Mickey,

do go on.

Jochen
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Old Dec 22, 2006, 10:57 AM
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Steering the gyrocopter

So how do you steer the gyrocopter?
First you must see that the lift from rotor is always at right angles to the disk made by the tips. This is called the tip path plane and all the forces made by the rotor can be modeled as if it was a single force at the center, at right angles (normal to) the tip path plane.
In the first diagram the tip path plane is initially normal to the CG position. The actual blade force numbers from one of my Gyro's is on the diagram. First the centrifugal force on each blade is 16 lbs. The coning angle is 1.79 degrees and the force of the rotor is 1 lb. As long as the rotor force vector is through the CG the model doesn't roll or pitch.
Now suppose that we tip the rotor disk up, assuming we are viewing from the side.
Now the rotor force is not through the CG anymore and is ahead of the CG. This tilts the model nose up, our desired outcome.
So conclusion one is that the model is steered to a large part by making the rotor disk mis-align with the CG in the direction we choose to roll or pitch the model. To a lesser extent the rotor does try to twist against the hub in the direction of tilt so the control is a combination of mis-aligned force and CG and some actual force on the shaft. Note that with a fully teetering rotor there is no component of mast twist, it's all force mis-alignment (clearly the teeter hinge prevents any torque being applied to the mast).
So how do you tilt the rotor?
It's done with cyclic pitch. In the second diagram position 0 is the nose. Suppose we want to go up. We know ahead of time that whatever change we make to a blade to increase or decrease its lift, either increasing its velocity or its angle of attack, that the blade takes a quarter turn to respond. So knowing this we plan ahead. We want to tilt the rotor disk back, to raise the nose. So we increase the pitch at the 270 position. This blade makes more lift, but doesn't move up until position 0. The next statement is really important and the source of a lot of confusion. The blade makes more lift at position 270. So it is true that there is a lift force applied to the blade at this position. However the blade doesn't transfer this force to the aircraft until it tilts up 90 degrees later at position 0.
Similarly the blade at position 90 gets less lift and then applies that less lift to the aircraft 90 degrees later at position 180.
Now that the rotor disk is tilted back from A to B, you should be able to see that the rotor force moves ahead of the CG and this makes the nose rise.
The net result is that to tilt the rotor you have to apply cyclic pitch 90 degrees ahead in the rotation of the direction you want the tilt the rotor.
To tie things together, changing the speed or changing the angle of a blade changes its lift make the rotor tilt 90 degrees later. If you can see that forward flight is applied cyclic lift change to the blades with differential velocity then it is quite natural to see that asymmetric lift is manifested 90 degrees later as a pitch up, not a rolling force as is commonly believed.
Ok, so now we have the basics. Cyclic pitch is needed to steer the rotor. How do you implement cyclic pitch.
Lets start with the simplest form of cyclic pitch. It's called tilting spindle cyclic or somewhat confusingly named "direct control".
In diagram three we are viewing a rotor from the 270 position looking down the end of the blade. We tilt the rotor shaft back towards the tail. You can see that the blade at the 270 position that we are looking down has increased pitch equal to the mast tilt. If you imagine turning the rotor 90 degrees you can see that this blade at the 0 position (the front) doesn't have any increased pitch. This is because the shaft tilt is backwards only not side to side. If you mentally follow this blade to the other side it now had decreased pitch. So if you tilt the shaft back you can see that the blade pitch follows exactly the same pattern as diagram 2. Voila! cyclic pitch.
So tilting the spindle creates cyclic pitch, the rotor responds accordingly. Tilt the shaft back, get cyclic at the 270 position, rotor rises a the 0 position, nose goes up. It's all good.
Now a side note.
If the rotor were completely rigid and we apply this aft shaft tilt, we would be attempting to basically force the blade at the 0 position to the line marked NH (no hinge).
The blades are now seperated by distance D1 with 16 lb of force trying to pull them back to the flat position. Clearly any model servo is not going to overcome that force, so what to do? The answer is a flapping hinge. What the flapping hinge does is allow the blades to stay roughly in the same flat plane while cyclic is being applied. So in the example when aft tilt is done to the shaft the hinged blades move to positions H (hinged). Now the distance between the blade forces is only D2. Now the servo has a chance of overcoming the centrifugal forces. Note that the further the hinge is from the hub (it's called the hinge offset distance) the more force has to be applied to overcome the blades in the non-cyclic position to apply to the blades in the cyclic position.(Note that with a teetering rotor the hinge offset is zero and thus the control forces are zero, but model teetering rotors have another problem, that we'll get into later.)
So here's another myth buster. The hinges in a so called "DC" head are not there to resolve asymmetric lift as much as they are there to reduce the force loads on the servos.
But you ask, how is asymmetric lift taken care of? The answer, once you understand cyclic is easy. Since asymmetric lift causes a pitch up, you simply apply a little nose down cyclic. What this does is straightforward. Nose down cyclic reduces the pitch on the advancing blade at position 270. This has the effect of reducing the lift, canceling the increased lift caused by it being the advancing blade. At the 90 position you increase the pitch canceling the effect of the reduced velocity of the retreating blade. Voila! asymmetric lift resolve.
Why this is not obvious is subtle with a DC model. What happens is that the true autorotation angle of the rotor is about 20 degrees aft, but the main mast is not rigged for 20 degrees aft, say it's only 15 degrees aft. The rotor sees forward velocity and flaps back according to asymmetric lift, but since the mast is only tilted 15 degrees back and the rotor is 20 degrees back, the rotor is actually seeing 5 degrees of down cyclic. The rotor reaches a stable point automatically because it will continue to tilt back from asymmetric lift until the correct amount of down cyclic is formed by the misalignment with the mast. This explains why in a DC gyro you hold nose up to get the rotor spinning at the true autorotation angle but as the model speeds up and asymmetric velocity happens you relax the nose up elevator to allow the correct down trim to compensate for asymmetric lift on the blades. Clever!
All for now.
mick

P.S. this is a complicated step, please let me hear from you guys that I'm making it clear enough.
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Old Dec 22, 2006, 02:54 PM
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Mickey,

everything is fine except for the last 7 lines. You lost me there, but that may be language difficulties.

I suppose with 'autoration angle' you mean the angle where, at a given speed, the rotor goes from 'windmilling' to 'lift producing' and not something to do with powerless flight? And what do you mean by 'asymmetric velocity'?

This is - as usual - very interesting.

Jochen
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Old Dec 22, 2006, 03:07 PM
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Quote:
Originally Posted by JochenK
Mickey,

everything is fine except for the last 7 lines. You lost me there, but that may be language difficulties.

I suppose with 'autoration angle' you mean the angle where, at a given speed, the rotor goes from 'windmilling' to 'lift producing' and not something to do with powerless flight? And what do you mean by 'asymmetric velocity'?

This is - as usual - very interesting.

Jochen
What is meant is that a rotor won't autorotate at less than ~20 degrees tilt back. If you hold rotor at 90 degrees to the wind it will autorotate. If you rotate it forward it will maintain autorotation to about ~20 degrees. Any shallower and the rotor just comes to a stop. In other words if you put in down trim so that the rotor goes below ~20 degrees with respect to the airflow in forward flight the rotor will stop.
Asymmetric velocity is the condition of the advancing rotor blade having a local velocity of the rotation speed plus the forward airspeed and the retreating blade having the local velocity of the rotation speed minus the forward airspeed. Thus the velocity of the advancing and retreating blades is asymmetric. This asymmetric velocity is what causes the asymmetric lift that causes the rotor to flap back in response. I chose the term asymmetric velocity to counter with the down cyclic pitch to point out that the differential cyclic (down on the advancing blade, up on the retreating blade) cancels the lift caused by the asymmetric local velocity vectors. So with proper down cyclic, asymmetric lift is canceled by reducing (increasing on the retreating side) the local angle of attack (via cyclic) in proportion to the local increase (decrease on the retreating side) in velocity, even though asymmetric velocity remains.
When I get a chance I'll diagram the DC head in a trimmed condition.
mickey
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Old Dec 22, 2006, 04:46 PM
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Mickey,

where did you get the 20 value? When I had a closer look at the teetering head Micromum video I decided to take out one frame to eveluate the coning. And while I was at it, I evaluted the rotor angle, too: 17. The gyro was more ore less flying horizontal and at that time I was pulling pitch to break it down.

Jochen
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Old Dec 22, 2006, 05:24 PM
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There were NACA and RAE studies in the early 20th century when autogiros were of interest.
The study is quoted in a paper by J. Gordon Leishman
http://www.glue.umd.edu/~leishman/Ae...giro_paper.pdf
The graph on page 6 shows that at somewhere around 15-20 degrees autorotation quits working. The angle changes with reynolds number, airfoil performance etc. but is generally around that 15-20 degree point. My eyeball measurement is usually around ~ 20 degrees for a good guesstimate number. Your value of 17 degrees is certainly in the right range. If you were descending even 1 or 2 degrees the angle would be the 18-19 degrees which agrees quite closely with the NACA test values.
Note that in the graph it is of the hub plane angle not the tip path plane angle, the tip path plane angle being higher due to flapping as discussed below the graph.
Note that on page 8 of the paper Leishman points out the Cierva actually tried cyclic pitch to handle asymmetric lift, but while the idea was correct his implementation with cables was not practical.
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Old Dec 23, 2006, 03:26 AM
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Mickey,

based on my own experiences and in spite of all those studies, I'd judge the autorotation angle of my Micromums to be in the region of about 10 rather than 20. Take a look at this:
http://www.rcgroups.com/forums/attac...hmentid=716953
What you see are traces in the snow of my Micromum v3 taking off. What you can also see is that the tail ski is taking off first.

When the Micromum with skis is sitting on a flat surface, the angle of attack of the tail boom is about 5 (see: http://www.rcgroups.com/forums/attac...mentid=828681). Adding the mast tilt of 8 to that value, the rotor hub's angle of attack is 13. Now, when the gyro lifted its tail for take-off, this angle had to be smaller than 13 and the rotor was spinning fast enough get the Micromum airborne.

But we may be taking about different speed ranges. My Micromums surely were never as slow as my G3P0. Which is why I made the latest modifications, which have in effect increased the rotor's angle of attack.

Another point. I think your remarks about the forces acting on the servos are only valid when you hold the gyro in your hand. Once it is airborne, the servos will not try to hold the rotor in its relative position to the fuse, they'll hold the fuse, which only weighs a few ounces, in its relative position to the rotor, thereby shifting the cg. And then gravity steps in and does the heavy work. You don't really need metal gear servos when flying a dc head gyro, you need them when the gyro touches ground again - at any imaginable angle and velocity.

Can't wait for the next installment.

Jochen
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Old Dec 23, 2006, 07:51 AM
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Your hub angle may be 13 but due to flap the rotor angle may be higher. I'm not trying to argue the exact angle, just that the flap back of the rotor compared to the hub angle is creating effective down cyclic to compensate for asymmetric velocity. Your in flight measurement of 17 of the rotor vs 13 hub angle reinforces my point.

True that the servo forces are higher in your hand, but two things: This also applies to on the ground taxiing for takeoff and waggling the fuselage around for weight shift is a non insignficant servo load, especially when you include g forces during manuevering. My point is that applying cyclic to a direct control head involves some torque, whereas other methods don't take the same amount of servo torque. Also, another point is that the role of the flapping hinge is much different from what is commonly believed.
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Old Dec 23, 2006, 11:24 AM
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Nicely done, Mickey. Its always a pleasure to read your explanations of how an auto works.
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Old Dec 23, 2006, 10:28 PM
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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.
So called "direct control" (shaft tilt cyclic) is actually cyclic pitch, and very cleverly trims itself out for asymmetric lift.
Flapping hinges are needed on a direct control gyro to allow the servo to overcome the centrifugal forces of the blades when they are off-axis from the cyclic input.
Why did spindle tilt die off (it was later revived by Igor Bensen, where it lives in the homebuilt gyrocopter market)? The answer is that the tilting spindle can create high control forces back to the pilot, and further complicates things like collective pitch and rotor pre-spin. The last stages of gyrocopter development in the 1930's were toward jump takeoff gyrocopters to meet an army requirement to clear a 50' obstacle just ahead of the gyrocopter. Any way I digress.
Whereas Cierva couldn't make cyclic feathering work right and chose flapping hinges (more later) a guy named Willet eventually made a rigid rotor gyroplane with only cyclic pitch to cancel asymmetric lift. Cyclic pitch using a swashplate and feathering bearings became the norm for helicopters because of the lower control forces and lower mechanical complexity once you start driving the rotor and using collective pitch. Also the large spherical bearing for a tilting shaft head becomes a significant problem in larger aircraft. So how does swashplate controlled cyclic feathering work?
In the diagram we are applying nose down cyclic pitch. The blade is now mounted on a feathering bearing, one that turns parallel to the blade axis rather then at right angles to it. A lever arm is attached to the feathering shaft which can rotate the blade on its axis. Because airfoils have very little resistance (0 resistance for symmetrical blades) to being twisted at the quarter chord point this is a low force. This arm is connected to a swashplate. A swashplate is two "plates" connected by a bearing. The upper half moves with the rotor, the lower half doesn't turn. In practice the swashplate can pitch and roll, in this case it's pitched nose down. Note that when happens and because of the way the linkages are set, a nose down swashplate movement creates nose down pitch in the blade in the 270 or advancing position. If you mentally turn the rotor a quarter turn you can see that because the swashplate is not rolled, just pitched, that there is no pitch change over the nose. Around at 90 the linkage causes the blade to be pitched up and again at 180 there is no pitch change. Note that this now identical to the cyclic that would be input if the hub were tilted down in a spindle tilt cyclic arrangement. So swashplate controlled cyclic and spindle tilt cyclic create exactly the same motion in the blades and in this case tilt the rotor nose down, the desired effect.
Note that centrifugal forces don't come into play here. The feathering bearing carries all the centrifugal forces and all the control inputs have to overcome is the twisting force along the length of the blade, which is very low.
Note that with a teetering two bladed head the control forces are also low and the mechanical complexity is simpler than a swashplate, this being the reason that Igor Bensen chose the tilting spindle form of cyclic for his homebuilt gyrocopters.
Now some of you are probably fuming at this point because you know that Cierva used flapping hinges and not cyclic, and he must have been right because his aircraft work, etc. etc. So I'll get to that next. But be warned, flapping is cyclic, and Cierva knew it.
I guess after that I'll go into how yawing a gyrocopter can make it turn in the absence of coning. The answer is again, cyclic. Other topics we need to touch on are stabilty, control response (following rate), and why a small scale teetering rotor is so difficult (if not impossible).
Merry Christmas to all. Hope your all enjoying my rambling!
mickey
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Old Dec 23, 2006, 11:58 PM
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Hope your all enjoying my rambling!
We enjoy learning from you Mickey!

Ari.
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Old Dec 24, 2006, 12:20 AM
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Mickey,

Excellent stuff. Please do go on.

Mike Smith
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