Gyrocopter Aerodynamics - Page 10 - RC Groups
 This thread is privately moderated by mnowell129, who may elect to delete unwanted replies.
Jan 26, 2007, 06:51 AM
I'm not as bad as they say.
Quote:
 Originally Posted by iter I'll have to try that with Ackus blades. They are 20mm wide and 11% at the thickest point. Do you think they are thin enough to twist with ammonia? Ari.
Absolutely
Latest blog entry: AIrcraft I've built.
Jan 26, 2007, 08:51 AM
I'm not as bad as they say.

# Teetering on the edge.

Diagrammed is the basic teetering head. It's basically a box that the blades are mounted on with a pivot. The pivot lets the tips tip up and down, like a teeter totter playground toy, hence the teetering head. Bensen used this with a tilting spindle to implement cyclic pitch in his full sized copters. This design persists today in full sized gyrocopters. The advantage is that you get cyclic pitch without a swashplate and the control loads are low.
In the second and third diagrams you can see why. Tilting the shaft to the left (from behind) clearly puts cyclic pitch into the blades, for when the blades are fore and aft they are tilted, in the third diagram when the blades are side to side the teeter absorbs the tilt and no pitch is applied. Hence cyclic pitch. Because there are only two blades and the teeter absorbs the tilt when the blades are at the sides and the blades resistance to twist is low (refer to the blade balancing post) the control loads are very low. This is the ideal control for a lightweight, low cost homebuilt gyrocopter, that being Bensen's goal.
One problem with the teetering head. The blades are going to cone under load. We know that this happens from the discussion on coning. The result is that the center of mass of the rotor is higher than the teeter point.
As long as the rotor is not tilted this doesn't cause a problem because the rotor mass center is in line with the axis of rotation. However, once the mast tilts, when the blades are at the "sides" and the teeter is absorbing the tilt, the center of mass of the rotor moves off the center of rotation. Hence you get a vibration that happens twice per revolution (2/rev).
The solution is the underslung teeter. You drop the teeter box down by the amount the center of mass moves up due to coning. Now the rotor center of mass is aligned with the teeter pivot and there is no vibration.
Another point is that because the blades are going to cone this causes stress at the arrow and elsewhere in the hub. So knowing this the hub is designed to not have this stress by being "pre-aligned" with the expected coning angle.
This is why you see underslung teetering heads with built in coning. These are not aerodynamic advantages, these are mechanical designs to reduce vibration and stress. Again, the pre-built coning is not for an aerodynamic reason, but a mechanical design to reduce the stresses on something that is known to occur.
The general problem with this head design is that the coning angle changes with rotor rpm, aircraft loading and "g" loads while manuevering. So the underslung height on the teeter is always a compromise. It is correct for exactly one flight condition and less than correct for all the others. Still, it's much better than not making the adjustment at all.
There is one full sized company, Magni I think, that has attacked this problem by, you guessed it, lowering the coning angle. Because coning is the root of the problem. They lower the coning with shorter, heavier higher RPM blades, thus the teeter height is shorter and the compromise teeter height is more correct most of the time.

Why the flapping head doesn't suffer the vibration problem is another installment.

One final note. Why is it that the seemingly simple teetering head hasn't been successful in small models.
The answer is following rate. The undamped teetering rotor has absolutely nothing holding it back from following the control input. The following rate on a 30', 300 RPM full sized rotor is human controllable. When shrunk to 30" and 1000 RPM the following rate goes off the scale for human controllability. Thus the difficulty in making a scale model.
regards
mick

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 Jan 28, 2007, 09:38 AM Thanks Mickey. I finally understand what undersling does Cheers, Rusty (PT Profile ready for first flight)
 Jan 28, 2007, 10:56 AM Registered User Mickey, Thanks for sharing your knowledge. It is truly appreciated.
Jan 29, 2007, 03:06 PM
I'm not as bad as they say.

# Teetering closer to the edge, Swash out!

Now that we have the teetering head sorted out and we see the basic cyclic pitch that takes place, we can actually go backwards in development to the swashplate. The two bladed teetering head was made popular by Bensen, who created it to have an easy to build cyclic system for homebuilders. But cyclic was already being done in helicopters and gyrocopters with a swashplate going back to Raoul Haffner in the early part of the century.
Examining a teetering head we see again the cyclic motion created by tilting the shaft. In this case a roll left as viewed from behind. When the blade is pointed aft (out of the page) it gets nose down cyclic, as the blades turn to parallel to the page the teeter absorbs the cyclic.
To get to a swashplate we add one more teeter joint. We add a ring inside the teeter with another teeter at 90 degrees to it. This makes a universal joint kind of arrangement where the rotor is free to teeter and now it is free to feather on the second axis.
We now attach the rotor to a rotating cam called a swashplate. The attachment is such that the pushrod can make the rotor feather but doesn't stop the rotor from teetering. The swashplate is two "plate"s connected by a bearing. The lower plate doesn't turn. The upper plate has a portion that extends down through the bearing. The whole upper portion and the extending tube, turn with the shaft. The inner portion has a relief in it to allow the swashplate to tilt in any direction.
Now we tilt the swashplate in the direction that we want to go. Notice that as the blades are fore and aft, the tilted swashplate is connected by linkage to tilt the rotor on it's feather axis. Later when the blades are side to side the part of the swashplate that is lined up with the linkage doesn't have any tilt. This is providing the same cyclic pitch to the rotor as the tilting spindle.
The disadvantage to the swashplate is the head is more complicated and the swashplate is more difficult to manufacture than the mechanism to tilt the whole spindle, so it's not as easy for home building.
The advantage to the swashplate is that the spindle isn't controlled by the pilot/servos so all the resulting mechanism can be lighter and take less power. The rotor loads are transferred directly to the fuselage without going through the control system.

Note that you don't see models with swashplates and these kinds of heads for the same reasons as two bladed teetering rotors, the following rate is just too high for human control.
The answer to the swashplate controlled teetering rotor following rate problem is to use a gyroscopically stabilized control system called the flybar.
mickey

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 Jan 29, 2007, 05:00 PM Registered User Well, when the time comes, and I can get all the parts together for a 3 bladed, flybarless, swashplate controlled autogyro head, I'll be real interested in how sensitive that is. So please, lets hear about multibladed heads.
Jan 30, 2007, 05:25 PM
I'm not as bad as they say.

# Hinge offset, what's the flap about?

Lets compare the teetering head to a flapping hinge head. In the first row of the diagram is a non-underslung teetering head. When the rotor is tilted the coned up CG is tilted off the turning axis and the vibration results. The teetering rotor once tilted actually is turning around the tilted axis. Note that distance 1 and 2 are the same but the whole mass center of the rotor is no longer in line with the shaft and it vibrates. This is review from a previous post.
Another point about the offset hinge is illustrated in the last figure. Because the hinges are not in the center the blades can now exert a torque on the shaft. In this case we are tilting the mast to the left, but the blades, not having moved yet, are opposing the tilt. Note that if you have only two blades then as the rotor comes around this force goes away and the mast is free to tilt easily, twice per revolution. But if you have 3 or more blades there is always at least one blade opposing the mast tilt. Thus the multibladed head provides more opposition to control input than the two blader.
Further because the blades exert a torque on the mast the opposite is true, the mast opposes the blade from flapping up or down in contrast to the teetering head where there is no such resistance.
So in the end the three or more bladed rotor doesn't follow the controls as quickly as a two bladed teetering rotor or even a two bladed offset hinge (flapping) rotor. Thus explaining the success of the 3 bladed direct control head model autogyros.

One final note. If you do a flapping head with a very stiff flapping hinge or make it rigid, the blade has a very long lever arm with which to fight your control inputs (with 0 offset in the teetering rotor it has none, the further out the flapping hinge, the more opposing torque the blade has, a rigid rotor acts like a flapping rotor with a very large hinge offset). So the reason you have a flapping hinge on a DC gyro is not to have flapping to alleviate asymmetric lift (you're accomplishing that with cyclic pitch by tilting the spindle) its to allow the servo to apply the mast tilt against the centrifugal force of the blades.
The tricky part of designing this kind of head is that you need to get the hinging correct so that you get enough damping to get the following rate down, but not so much that you overpower the servos. A good reason to build a known good design.
Emilio has made a different choice and made a two bladed flapping rotor ( http://www.rcuniverse.com/forum/m_3405617/tm.htm ) (it's not teetering like the forum thread says and text opens with, its got a stiff flapping hinge with offset.) But to get the following rate down he used tip weights instead of a third blade. The advantage here is that you reduce the servo loads without always having one blade opposing the tilt all the way around the circle.
regards
mick

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 Jan 30, 2007, 07:38 PM Winging it Ò> Good stuff once again Mickey. Thanks! How do we make your online lessons a sticky? Dan
Jan 30, 2007, 08:13 PM
I'm not as bad as they say.
Quote:
 Originally Posted by leadfeather Good stuff once again Mickey. Thanks! How do we make your online lessons a sticky? Dan
I think I have to make a request to the moderator...

Last edited by mnowell129; Jan 30, 2007 at 08:15 PM. Reason: update
 Jan 31, 2007, 11:30 AM Registered User Mickey, well done. Jochen
Feb 01, 2007, 10:13 AM
I'm not as bad as they say.

# She's a real barfly...

Ok, so the problem with the teetering head in general is that it has a very high following rate (among other things such as low control power, but that's another story). So how do you tame the following rate. If you go back to the following rate information you will recall that the following rate increases with rpm, increases with blade area, increases with diameter and decreases with blade mass.
The RPM is kinda fixed by the size of gyrocopter, number of blades etc, so you can't change that much. But you can mess with the other things. So if you make a very small blade and put it out on a stick at a fairly small radius you get a rotor with a slow following rate. In fact you can adjust the following rate by the area, weight and radius of the rotor to your liking.
So in the diagram we've done that. We now have a rotor that is comfortable to fly, only it's not big enough to lift our copter. What to do? What we do is allow this little rotor (called a flybar in modern terms) actually control the main rotor. It turns out that the main rotor will move at exactly the same rate as the control rotor when you do this. So a main teetering rotor that would have an extremely high following rate by itself, adopts the following rate of the flybar and the system is flyable by a human. A side benefit is that if you don't put any control in the small rotor it behaves like a gyroscope so that if your copter body gets shoved around by the wind, the control rotor tries to stay put and automatically stabilizes your aircraft. (Note that if you leave the control rotor blades off and just make them weights ala blade CX, et al, the control rotor becomes a pure stabilizer.)
The only tricky part is following the cyclic, but the good news for you is that the only thing you have to understand is the 90° lag of the rotating objects to respond to pitch changes. It's helpful to have a model heli around to watch this take place, but here's how it works.
Suppose in the figure you are going in the direction of the arrow and you want to roll left. You apply cyclic (it doesn't have to be swashplate, you could conceivably use a tilting spindle on the flybar, it's been done, pics somewhere on the web that I can't find) so that the flybar rotor has pitch in front, 90° later the flybar tilts up, just like a rotor should. But now since the flybar frame is tied to the rotor, the tilting of the flybar applies pitch to the rotor blade that is front. Happy to oblige 90° later, the rotor blade tips up, tilting the whole rotor to the left and away you go.

Note that I've simplified the whole head to the basic, fixed pitch rotor head and drawn it with a very clumsy obivous construction. Most heads are more clever in design. And I've left off more complicated features like collective pitch and bell-hiller mixing, but you can easily find references to that on the web.
So here we are.
Some summary points:
Rotors turn by using cyclic pitch, period. The manner in which the cyclic pitch is applied can be varied, you can tilt or yaw the aircraft body which tilts the spindle which applies the cyclic. You can tilt the spindle directly or you can tilt a virtual spindle with a swashplate. But the end result is that somewhere, somehow you have to apply cyclic to get the rotor to move the way you want to go (unless you are just happy skidding around turns, but then you don't really have a three axis control aircraft).

Asymmetric lift on a flapping rotor causes the rotor to flap back, not roll over. You resolve asymmetric lift with cyclic pitch, either flapping or feathering cyclic, but cyclic nevertheless. Asymmetric lift on a very rigid rotor causes it to both flap up and roll over due to the less than 90° phase lag of the rotor response.

Model rotors have additional problems that full sized rotors don't. Namely the mast angle is further back and the blade pitch is more negative due to scaling (reynolds number) effects. The following rate on model rotors is higher making effective control more difficult.

Providing good control with an acceptable following rate is probably the single biggest challenge with model gyrocopters. A good understanding of this is probably useful in designing/improving your model. The confusion caused by having most model rotors be too controllable has probably been the reason that gyrocopters are the last aircraft type to be widely seen in modeldom.
Maybe we can change this.

regards

cheater

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 Feb 01, 2007, 11:18 AM I'm not as bad as they say. Spindle controlled flybar cyclic: https://www.rcgroups.com/forums/show...ghlight=flybar Latest blog entry: AIrcraft I've built.
Feb 04, 2007, 12:16 AM
Registered User

I can't wait to get started on my BEGI.

Wildman
Feb 04, 2007, 06:02 AM
Registered User

# position of cg

hello for all
Mnowell can you tell us more about the position of CG and about
the moment done by the lift(in a previous post you just talk of
moment of drag and motor thrust)
I have a book about autogyro that say : with a pusher the cg
must be aft the mast of rotor , then the lift create a pitch up moment counterbalancing the pitch down moment of motor thrusline.
Can you draw a full view of all the forces (lift ,drag ,thrust)with
cg before and aft of the mast and what it does in flight pitch?
Thank you
Feb 06, 2007, 09:49 AM
I'm not as bad as they say.
Quote:
 Originally Posted by Wildman I have read this sticky but I can't find anything on Disk loading and number of blades 3 blades are better than 2 but can I increase the load or shorten the blades with 3 and why not 4 or 5 blades? I can't wait to get started on my BEGI. Wildman
I use a disk loading estimate of 1.25 ounces per blade per square foot of disk area. This turns into 2.5 ounces/sq foot for two blades, 3.75 ounces/sq foot for 3 blades and 5 ounces/sq foot for 4 blades. So yes you can increase the load with more blades.