This is Forum Notes.... Page Three



From Ralph Kalb:

Basically, increasing the solidity of a rotor decreases that rotors RPM (and therefore increases its cone angle and roll/pitch stability).

Bill: The "frontal area" of a disc is the area of the disc multiplied by the sine of the tiltback angle (back to the trig book.    However, with a cone angle as large as you described, the best bet would seem to be to treat the rotor as two seperate parts... one ahead of the pivot and one behind, and add the two areas up. In other words, the half ahead of the axis would be (disc area /2)*sin(tilt+cone) and behind would be (disc area/2)*sin(tilt-cone).
I wouldn't want to comment on the co-ax vs the side by side rotors, except to say that with side by side, basically you have two gyros flying side by side (but with one body!), and one would expect the total rotor drag to be twice that of one rotor. With the coax, that rotors interact with each other, and all bets are off!
Someday when you have time, could you move the wind tunnel test stand outside in the breeze and measure the VERTICAL lift at larger angles than were done on the wind tunnel test data? I need data from about 10 degrees tiltback to at least the PEAK lift angle (where the lift starts dropping off). Drag data would be useful also, but not vital. Wind speed is not critical, but should be reasonably constant.    Thanks....Ralph

Steve: Let me recapitulate the saga of the lead/lag rotor blades and see if I understand.....
The blades are drilled for the retaining strap bolt in line with the blades CG. The retaining straps are identical. The hub holes for mounting the retaining straps are equally spaced. So far, so good?
Statically, the rotor is in balance. At very low RPM the rotor is in balance. OK so far?
After a high RPM run, the blades are found to have shifted their angular position from the original to a leading angle for blades that originally balanced at 25% chord and a lagging position for blades originally balanced at a 30% position, and the rotor is now out of balance.   The blades are acting as though the drag on each blade is less on the 25% blades and greater on the 30% blades OR the force causing the blade to rotate is greater for the 25% blades, and less for the 30% blades, or both effects acting together.   This could be caused by the fact that the difference in the distance to the reflex bevel is causing more "nose-up" twist on the 25% blades and less on the 30% blades. The reflex bevel you have mentioned (@ 45 degrees) is a rather radical departure from what I consider a reflex... a smoooooth contour change from a flat bottom to a slightly upturned trailing edge.
One way of checking out this theory is to make a 4 bladed rotor having 2 25% blades mounted at 180 degrees from each other, and 2 30% blades mounted at right angles to them. The rotor should remain in balance after running but the angle between the blades should change from 90 degrees to 90 +/- ?? degrees if this is a true theory. First "swing wing rotor" ever flown!!!
Actually, Steve, monorotors are a lot of fun   Ralph

Steve: Re the lead of a 25% chord balanced blade and the lag of a 30% chord balanced blade.... I have to make some assumptions... correct me if they aren't right!   I am going to assume the pivot point of the blade to the hub is on the 25% chord line (if one were there!).   I am also going to assume that Sherlock Holmes was right when he said "Eliminate the impossible, and what's left (however improbable) must be the cause".  Sounds like a good place to start.
With either set of blades (25% or 30%), when you "hand prop" them to start, you either push on that one blade (which gives a severe unbalance + that blade has a leading angle momentarily) or you push on the hub, and all blades swing back into lag (momentarily).    If we could imagine somehow "magically" putting the revolving rotor into outer space (no air!), we would find that the CGs of both rotors, both pivot points and the hub axis would line up under the influence of centrifugal force! (If you can't get a quick shuttle launch scheduled, you can always fake it by hanging a 2 bladed rotor from one CG and note the same thing).
If we place a lead weight on the blade on each LE, the CG will switch from the 25% chord to (perhaps) the 10% chord, but the blade axis will be LAGGING. Putting the lead weight on the TE, the CG will switch from the 25% chord to (perhaps) the 50% point, and the blade axis will be leading! Sort of bass-ackwards of what you are seeing, so it doesn't seem to be a mechanical problem, rather aerodynamic.
About 2 years ago, you mentioned that you were always finding your blades "leading" when they spun down, and I attributed it to the plades "pulling the hub around" as opposed to a heli whose "hub pulled the blades around", producing a lagging force. Gotta think some more!   Ralph


Looking at it closely, the denominator can be written ((n^3 x d^3} x d^2 x density ratio), where n x d = Prop Tip Speed (TSR) * 60/pi. Thus with a fixed TSR (825 to 925 '/sec) the Cp basically depends on the HP of the engine, the TSR selected, and d^2.  
There is the rub: the engine HP rated by the manufacturer is the HP at the RPM of the prop if directly coupled, and they don't perform anywhere near what the manufacturer says is peak RPM. By the time one adds all the "goodies" (prop, muffler, etc), the engine is only putting out about half of its "rated" (published) HP.
In addition, the TSR suggested (825-925 '/sec) is getting right up there with the speed of sound (1040'/sec) and tip noise is a problem... not at an airport, but if you got neighbors????. Most R/C'rs run typically 500 '/sec or so and a means of using a reduction gear would be a big advantage, allowing a higher engine RPM and a lower tip speed to generate more static thrust quietly!    Ralph


Mickey:  If I'm not mistaken, lift dysymmetry will cause a precession of the rotor disc rearward, not a rolling force in a teetering head design. With a Cierva head, the rising blade produces a sideways force, since it is inclined higher than the retreating blade producing a rolling force toward the retreating blade (neutralized by tilting the mast, moving it toward the retreating blade, or moving the CG toward the advancing blade)...   Ralph

Steve:  I believe you are right about the KK and the stiff blades.  If one could mill the blades out of solid 6061-T6, it probably wouldn't make any difference where they were hooked up to the hub .  However, in this "best of all possible worlds", a non-symmetrical airfoil will have a pitching moment, and the thinner, blades make the situation all the worse unless .....nbsp;
Basically, a rotor blade is like a flying wing in many respects, and although we may hold it in the right position at the hub, waaaaay out there on the tip (where it is going the fastest!), unless it is torsionally rigid (like the 6061 rotor) or the pitching moment is compensated for with a reflex in the case of a rotor or an elevator trimmed to push the tail down in a fixed winger.
This pitching action can be demonstrated by sticking a rotor out a car window at high speed... if things are wrong, it will flutter like mad....   Ralph

Bill: Re the hinges....  I think I covered that in the PhARTS 1 booklet, but lets go over it again.... 
If one has offset (ie spaced) hinges, centrifugal force will keep the blades rotating in the same disc plane, and if the fuse is swung to one side, EACH BLADE will continue to stay at the same angle to the horizon BUT each blade will be displaced vertically from the other. This displacement forms a "couple" and a large rotational force results which sets the fuse straight. Ya gotta draw it to see it, I'm afraid!
As a "hands on" experiment, cut a piece of paper or light cardboard 6" long and 1" wide... this will be your "rotor".  Using heavy pressure on a ball point pen, form hinges by marking the paper 2" in from each end on both sides, and crease the paper by folding both "blades" up and down a few times.  Mark and punch a tiny hole in the center of the paper (this will be the "hub") and slip in a toothpick (this will be the shaft/mast). With the "blades" and "hub" lined up and parallel, the "mast" should be vertical if your fingers try to pull the blades apart (centrifugal force).  With your third hand angle the hub so the toothpick "mast" is angled away from vertical, releasung some of the "centrifugal force" of your fingers.  This then represents the body being swung away from the vertical for some reason. Note that the "blades" are still parallel but seperated from each other.  Increasing the "centrifugal force" will immediatly cause the "mast" to return to vertical due to the moments of the offset "hinge".  This restoring force is in addition to the normal pendulum restoration due to the gyros CG being below the rotor CG, and gives increased stability. ...   Ralph


From Mickey Nowell:  in reply to the following question:
"If I'm not mistaken, lift dysymmetry will cause a precession of the rotor disc rearward"

Depends on which side. If it is on the retreating side it will precess forward. This is exactly the way cyclic works.  I still believe that lift dysymmetry is a transient condition. The rotor, once in a stable plane of rotation will exhibit a force at the center, perpindicular to the tip path plane. A disturbing condition, such as a gust, fuselage wiggle, cyclic, intentional pitch, roll or yaw by the tail, constitutes a momentary condition in which the rotor will precess to a new, stable, centered condition.  It goes back to a simple idea that no one has yet to refute here:
A teetering rotor or a hinged rotor cannot apply a torque to the rotor shaft.
The blade or teeter can only apply a force that pulls on the hinge pin(s).
Once the rotor is steady state the force applied is zero measured parallel to the tip path plane. The rotor is thus producing a thrust perpindicular to the tip path plane. I don't believe in any lift dysymmetry, it is I believe that the thrust vector does not go through the CG and thus produces a roll or pitch or both. This has to be trimmed out. The trim can be tilt or offset, the net result being the lift vector is through the CG.
i've been proved wrong many times so please keep me honest....    Mickey


More from Ralph Kalb:

Bill: The basic vector analysis on any "flying machine" says that for a constant altitude, constant airspeed flight, Lift = Weight and Drag = Thrust.  When this condition is met, all is right with the world!  
Talking about "power" reguires a knowledge of airspeed, since the power available for a gyros flight changes with airspeed.   Example: 1 HP = 550 ft #/second.   Written another way, 1 HP = (#) x (ft/sec), where # is thrust and ft/sec is velocity.
The Prop Coefficent calculations are based on Hollnann's book "Designing the Gyroplane" and come from a way of estimating the static thrust of a 2 bladed prop, tip speed 825-925 '/sec that Hamilton Standard came up with, using a graphical conversion in the book.   What you end up with is the expected static thrust (AS = zero), and from that you can determine the "effective" HP the engine is putting to work at any given airspeed, and then comparing that "effective" HP to what a gyro requires at the same airspeed.  If the "effective" HP is less than that required, "she no fly"; if greater, the difference can be expressed as PAFC or Power Available For Climb.     Ralph


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updated 5-30-00..jb