Aerodynamics - De-cone the Pre-cone

[Dave Jackson]

The Preamble: <img src="frown.gif" border="0">

The hub of a conventional teetering rotor is designed so that the axes of the two spindles (feathering bearings) have a pre-coning angle of 2-3 degrees. The teetering hinge is located an inch or two above these spindles. This undersling is so that the CG of the two blades and the teetering hinge are all inline, under mean disk loading. From their mean position, the blades' CGs will rise and fall (cone), in respect to the teetering hinge, as the disk loading changes.

The Question: <img src="confused.gif" border="0">

Why cannot a rotor be produced where;. .1/ The teetering hinge has no undersling. It is located inline with the feathering bearings.. .2/ The spindles have a small 'downward' coning angle.. .3/ The blades are constructed with a high amount of stiffness and strength. . .Because of the deflection in the blades, under mean disk loading the CGs of the two blades and the teetering hinge are inline, just as they are above. The difference is that now there is no coning angle.

The Perceived Advantages: <img src="smile.gif" border="0">

1/ Large reduction in cross-coupling.. .2/ Less rotor disk flap-back

The Rebuttal: <img src="eek.gif" border="0">

[Grainger]

Dave;. .. .When supporting the weight of the helicopter, the blades must have an upwards cone.. .. .The vertical component of the tension in the blade at the blade root holds the helicopter up against gravity (tension in the blade is therefore many times the weight of the helicopter).. .. .It's the same principle as suspending a weight from the middle of a piece of string and pulling the ends out sideways. No matter how hard you pull the two ends of the string apart, you'll never get the string to stretch out completely straight - it will always have a slight 'V' shape.. .. .If the blades stuck out exactly horizontally as you suggest there would be no vertical force component to lift the helicopter up.. . . . <small>[ 03 March 2002, 17:25: Message edited by: Grainger ]</small>

[Dave Jackson]

Grainger. .. .Thanks for the response. It was beginning to appear that interest in rotorcraft technology had died, with the demise of Lu's (challenging) postings. . .___________________. .. .There is no disagreement with what you say. . .. .I am proposing that the blades (and feathering bearings) have a high level of rigidity. Using your analogy, the string will be replaced by a structural beam. The center of this beam will be attached, by pivoting pin, to the top of the mast. The beam will have a slight bend at the middle so that the 'tips' of the beam are slightly below the pivot point, when at rest. . .. .During flight, these 'tips' will be slightly above the pivot point, because the aerodynamic lift on the beam will deform (cone) the beam slightly.. .. .The end result will be heavier blades with slightly more drag, but, the rotor disk will no longer have a cone.

[Lu Zuckerman]

To: Grainger. .. .Using your argument and applying it to Dave’s’ theory about negative static cone angle he states that the blades will in effect cone but to an angle that is equal to the teeter hinge. This in effect will place the blades in tension and compression to provide the necessary lift (according to what you said).. .. .To: Dave. .. .The primary reason for underslinging the rotorhead is to minimize if not totally eliminate lead and lag. If in the process of coning the CG of the rotor mass is equal to the teeter hinge then that is extra.. .. .Another point that has absolutely nothing to do with your argument is that the pitch change axis does not intersect the center of the mast. In the case of each blade the pitch axis can be ahead of the mast center by ¼” or more. This eliminates or vastly decreases the tendency for spanwise bending of the blades which on some Bell blades is reacted by the drag link at the blade root.. .. .I now take cover from the ICBMs emanating from Connecticut.. . . . <small>[ 03 March 2002, 20:37: Message edited by: Lu Zuckerman ]</small>

[Dave Jackson]

Lu ~~~ Incoming from Vancouver. <img border="0" title="" alt="[Smile]" src="smile.gif" /> . .. .I agree that on teetering rotors, the two blades, basically, lead-lag in unison. The small amount of lack of unison is handled by a strong hub and flexible mast. The undersling is probably an attempt to keep the rotor's mass centralized when the disk tips.. .___________. .. .Regarding your other point, the following R-22 info. may also be of interest;. . . .The R-22 aerodynamic center is probably at 25-27% chord but it has been mentioned that the attachment point is at 40-45% chord.. .. .The R-22 hub's blade-feathering axis is 0,28" ahead of the mast's center of rotation, to reduce the moment carried by the pitch change bearings. . .___________. .. .Edited to remove self-directed personal insult. <img border="0" title="" alt="[Frown]" src="frown.gif" />. . . . <small>[ 03 March 2002, 23:11: Message edited by: Dave Jackson ]</small>

[Lu Zuckerman]

To: Dave Jackson. .. .“I agree that on teetering rotors, the two blades, basically, lead-lag in unison. The small amount of lack of unison is handled by a strong hub and flexible mast. The undersling is probably an attempt to keep the rotor's mass centralized when the disk tips”.. .. .Response:. .. .On an underslung rotorhead such as that used on a Bell the tendency to lead and lag is minimal because of the underslinging of the head. When the blades teeter the axis of rotation intersects the axis of drive. On a conventional articulated rotor system the axis of rotation deviates from the axis of drive causing leading and lagging to take place. All of this was covered in several other threads. The Robinson rotorhead like the Bell can teeter and it too is underslung. However the blades are free to flap and in doing so the two axes deviate from each other and leading and lagging takes place. But, the blades can’t actually move so the loads are reacted by the cone hinges, the pitch change bearings, the teeter hinge and the rotor mast as well as the blade itself. The tendency to lead and lag can be verified by the inspection of the cone and teeter hinges as they are worn in an elliptical pattern.. .. .“The R-22 aerodynamic center is probably at 25-27% chord but it has been mentioned that the attachment point is at 40-45% chord”.. .. .Response:. .. .If what you say is true then the spanwise bending would be excessive. In an ideal design the pitch change axis, the aerodynamic center and the chordwise CG should all be on the same point. That is why on larger blades the tip weights can be adjusted in order to get them as close as possible. Since it is not possible to get the three points coincident with each other the blades or the blade attachment is designed to react these loads and the loads then go into the rotor head. . . . .. .“The R-22 hub's blade-feathering axis is 0,28" ahead of the mast's center of rotation; to reduce the moment carried by the pitch change bearings”.. .. .Response: . .. .This is what I stated above in my first post. Spanwise bending causes the moment you alluded to. This displacement of the rotor blade relative to the mast centerline is designed into the system because the chordwise CG of the blade is shifted relative to the mast centerline thus minimizing the spanwise bending.. . . . <small>[ 04 March 2002, 02:48: Message edited by: Lu Zuckerman ]</small>

[Buitenzorg]

Not being an engineer my arguments may well get shot down in flames, but I believe what Dave proposes will be impossible to implement in an efficient manner, simply because the strength and stiffness required is too great.. .. .As an illustration, compare Bell and Robinson rotor heads. Bells are pre-coned to a certain angle, a compromise between the ideal angle for a heavy, maneuvering ship, and that for sitting on the ground at 100% Nr at flat pitch. So in the first case the compromise pre-cone angle is too small, causing stresses in the rotor head and the blade roots, and in the second case the pre-cone angle is too large, causing different stresses in these same components. So the rotor heads and blade roots are built stoutly to accommodate said stresses, thus leading to the famous high inertia of Bell rotor systems.. .. .On the other hand, the coning hinges in the Robinson heads allow each blade to seek the ideal angle in any given situation, therefore no bending stresses in blade root and rotor head: these can be built more lightly. Thus leading to the famous low inertia of Robinson rotor systems.. .. .If one were to design as Dave proposes, a rotor system so stiff that it wouldn't cone at all, imagine how much more heavily built that system would have to be, even compared to the products of the Bell Ironworks. Not only that, for adequate stiffnes the blades would have to be pretty thick, probably too thick to be much good at producing lift.. .. .So for rotor systems light enough to get helicopters off the ground, coning is here to stay, and that means two-bladed systems will continue to be underslung.

[Dave Jackson]

Lu. .. .Regarding your first paragraph, I believe that the application of undersling has as much or more to do with minimizing rotor mass misalignment, as it has to do with blade lead-lag. The application of this thread's idea will reduce the misalignments of the blades' centers of mass, aerodynamics, and percussion, etc. etc. There is no argument with your comments about the R-22 head.. .. .I think that the blade attachment is at 40-45% of chord to minimize spanwise bending and/or resist the blade tip's desire to lead. Chordwise, a blade's center of gravity is located ahead of its aerodynamic center; for stability.. .. .President Blowfly:. .. .I totally agree with all that you have said. Stiffening of the blades will definitely add weight to the rotor assembly and for strength, a thicker blade profile will be required, at least near the root. . .. .The bottom line is: Are the disadvantages of a heavier rotor and slightly higher drag worth the advantages that will come from having a reduced mean coning angle plus a reduced range coning angle extremes?. .. .Regarding the R-22 coning hinges, my 'totally unqualified' position is that there should be consideration given for having them physically interlocked. This way they will only perform the function of coning and leave the flapping to the teetering hinge.

[Grainger]

Stiffening the blades as much as you want won't help as long as they are attached to the mast via a hinge. What you are describing is more like a rigid rotor system, but I don't think this works on a two-bladed system for the lead-lag reasons already given.. .. .To work as you suggest, it would be possible to lift the helicopter via the blades when they were not going round - i.e. you would have to have a rigid connection between the blades and the mast, and blades of sufficient strength to act as a beam. These would be much too heavy.. .. .Vertical force is transmitted to the mast by the blades being in tension. Thus the amount of vertical force transmitted form each blade is equal to [Tension]*[Sin of coning angle]. Coning angle = 0 gives no vertical force transmitted to the mast.

[Vfrpilotpb]

Dave,. .. .Why do Rotor blades on any heli need to be as long as they are, could this length ever be reduce by say half but increase the width of the blade, that way the blade could be made more rigid! could it? <img border="0" title="" alt="[Eek!]" src="eek.gif" />

[Nick Lappos]

Lots of good thoughts tossing around here, some comments:. .. .The blades will cone, regardless of how hard you try to stiffen them, because the limit of materials technology will not allow you to make them stiff enough, unless they become deeply shaped like I beams, which are not exactly good blades.. .. .The blades should not be that stiff or the vibrations they will impart on the aircraft would be very high. The wonder of the articulated head is the vibration and stress relief they allow. Lose the relief and gain what by making the blades so stiff?. .. .Vfrpilotpb raises a good point. The stiffness of a blade is due to its beam properties (its thickness, width and length) the rigidity varies with the cube of the length, so making a shorter blade makes it very much stiffer. But the shorter blade sweeps less disk area, so the disk loading goes up by the square of the length, making the helicopter need very much more power.. .. .One way to make the blade stiffer is to make the centripital (note not centrifugal - Oops, must not feed the troll!) force higher by increasing the rpm. But the tip speed must be subsonic throughout the flight speed range, so that doesn't work.

[Lu Zuckerman]

To: Dave Jackson. .. .Let’s see how much flack this attracts:. .. .I was told by (name on request) that on blades that are symmetrical (NASA 0012 used on early helicopters) the aerodynamic center is located mainly on the blade chord line which makes them stable in flight. However, on cambered blades (like an airplane wing), the aerodynamic center is located outside of the blade, which makes them somewhat unstable. With increased pitch they tend to climb and with decreased pitch they tend to dive and not necessarily where and when the pilot commanded them when he introduced cyclic pitch.. .. .On a conventional control system the blade is firmly anchored and any tendency to climb or dive is reacted by the blade attachment and the pitch horn / pitch link which results in the twisting of the blade. (This is a supposition on my part).. .. .The Apache suffers from this problem because of the unstable attachment of the blade to the head. Using the analogy of a three-legged milking stool it is stable with three legs but if you remove one leg then it becomes unstable. On the Apache the blade is restrained from flying outward by series of straps that are anchored at the rotorhead and attached to the blade at the other end. The only other point of attachment is the pitch horn / pitch link which anchors the system to the swashplate. In the case of the Apache when pitch is added or subtracted the blade will feather by flexing or twisting the attachment straps. The front strap will work against the rotorhead while the rear strap, which is not anchored down, will flex upward. The continued instability of the blade will cause the rear strap to continually strike the rotorhead causing the straps to break. This is a major maintenance driver on the Apache.

[Nick Lappos]

Lu,. .The post will not attract any flack, it is simply all wrong. The aerodynamic center of assymetrical airfoils is not located "outside of the blade". . .. .Write the guy who taught you that and get your money back.

[Lu Zuckerman]

To: Nick Lappos. .. .The individual in question likened the asymmetrical airfoil to that of a wing on an airplane. He indicated that when the control stick is pulled back the aircraft will if the necessary speed is present go into a loop. He indicated that the wing was moving in relation to a theoretical point in space assuming the loop was a perfect circle. He further indicated that an asymmetrical airfoil on a helicopter rotor would want to do the same thing as the aircraft wing. But, it can’t because the blade is restrained by the pitch bearings and the pitch horn / pitch link and because of that the blade will try to climb (outside loop) when pitch is increased. He stated that since it can’t react like a wing then the blade will flex (twist). He also said that this would be the root cause of vibration that did not exist on helicopters using NASA 0012 airfoils. He also said for that reason helicopter blades would always be symmetrical.. .. .Hopefully I got it right because it was a part of a lecture at Sikorsky back in 1956. The man teaching that class was the chief aerodynamicist for Sikorsky.. .. .Evidently he was wrong because just about every helicopter has asymmetrical airfoils but then again modern helicopters have a hell of a lot more vibration than their older cousins do and most have various systems to dampen that vibration.. . . . <small>[ 05 March 2002, 04:36: Message edited by: Lu Zuckerman ]</small>

[Dave Jackson]

Nick,. .. .You've brought up some excellent concerns, particularly since they're founded in hands-on experience.. .. .The minimization of the coning angle may be achievable by a combination of blade stiffness, plus blade anhedral (not just tip anhedral) or negative pre-cone. . .. .Your point about high loading and vibration is very much of a concern. As well, I question whether Higher Harmonic Control or Active Blade Control will be able to overcome the blades inertia about the feathering axis, at rates of 1/4 or 1/8th or 1/16th of a rotor's revolution. . .. .The theoretical objective of all this 'stiffness' is to improve the response of the craft to cyclic inputs.. .. ._____________. .`. .`. .`. . <img src="http://www.unicopter.com/super_hug.gif" alt="" /> . .. .Keeping Nick and Lu at arms length ~ or is it ~ Nick and Lu making up?. .`. .`. ._____________. .. .Lu;. .. .Probably very few people have a comprehensive understanding of rotor blade aerodynamics and I certainly don't; but for the heck of it, here goes a little;. . . .Looking at a cross section of a blade (profile), the chord line is a straight line that runs from the leading edge to the trailing edge. On the symmetrical NACA 0012 airfoil the 'Center of Pressure' is located at 25% of chord (25% back from the leading edge). As the blade's angle of attack is varied, the Center of Pressure will not move along the chord line.. .. .On an asymmetrical (cambered) airfoil, the Center of Pressure at zero lift can be ahead or far back from the 25% location (forward or aft camber). As the blade's angle of attack is increased, the Center of Pressure will move, and hence the instability.. .. .A light coverage of this subject is located at; <a href="http://www.cybercom.net/~copters/aero/pressure_patterns.html" target="_blank">http://www.cybercom.net/~copters/aero/pressure_patterns.html</a>. .. .To use the NACA 0012 as an example, the center of mass is in front of the Center of Pressure. If a gust should lift the blade, the inertia of the forward-located mass will want to reduce the blade's pitch angle.. .. .This is starting to move off the topic of fat heavy blades ------ <img border="0" title="" alt="[Smile]" src="smile.gif" />

[Nick Lappos]

Only Lu can mis-remember a lecture from 1956, and then blame the instructor when he screws it all up.. .. .Give us a break, no aerodynamicist gave you that wrong info Lu (the aerodynamic center is outside of the blade), but you would NEVER, EVER admit a mistake so I give up.

[Vfrpilotpb]

Dave, and Nick L,. .. .As far as my question about the length of blades, why do Heli rotor blades seem to follow the convention of lots of length plus very little twist, compared with a Prop from a Fixed wing which is shorter wider and has a pronounced twist to create Pull/push power, if the osprey can have a big aircraft type Prop cum Rotor why would this sort of design not be able to be used in other heli configs, which if it could be used would create a far more rigid system, or is it purely down to the osprey type design of prop would then weigh more than would be ecomnomic for the Heli type design?

[Grainger]

vfr: It's down to energy consumption.. .. .To get the same reaction, you can change the momentum of a large mass of air by a small amount, or you can take a small mass of air and change its momentum by a large amount.. .. .Since momentum = mv but kinetic energy = 1/2 mv^2, the second method uses much more energy to achieve the same amount of lift.. .. .The most extreme example of this is the Harrier, which shoves a tiny mass of air out of the nozzles at very high speed - but you'll run out of fuel after just a few minutes' hover.. .. .In forward flight, the Osprey and Harrier use the wings to deflect a larger amount of air, improving fuel efficiency. . .. .In a helicopter you need a large diameter rotor disc to achieve the same efficiency.

[Nick Lappos]

Grainger has it exactly right. If the disk is small for the weight of the machine (high disk loading) the power needed to hover goes up. That is why a tilt rotor needs about 40% more power than a helicopter to do its job, its rotors are proportionately smaller and more highly loaded.. .. .Down wash velocity is also part of the problem. As disk loading increases, the speed of the air that supports the helicopter must go up, and downwash velocity increases. Big helicopters do not make higher downwash velocities because they are bigger, it is disk loading that makes the difference.

[Lu Zuckerman]

To: Vfrpilotpb. .. .One of the reasons for not using a smaller diameter rotor such as the Proprotor on the V-22 on a helicopter is its’ inability to sustain lift during autorotation. On a conventional helicopter at least those that I worked on the rate of descent is around 1,400 feet per minute with a forward speed of around 70 miles per hour. If you place the V-22 into an autorotation in the helicopter mode the rate of descent is 4-6000 feet per minute and it can’t be arrested like in a conventional helicopter.. .. .It is my personal belief that this is the reason the FAA has elected to certify this type of aircraft as a powered lift aircraft and not under the helicopter certification requirements.