Twisted questions (again)...

[darrellwittke]

Does the positive twist of Dragon Wings at the tips cause any increase in H-force (or two per rev shake)?

Does the elliptical pattern caused by the two per rev differ from positively tip twisted blades to straight untwisted tip blades?

Is my understanding accurate and can engineers put calculated numbers on the following: I understand positive twist blades allow the rotor to have 5-7%? more efficiency. I think this comes from having more driving area (say 75%? of the length of the rotor blade versus 70%? for non-twisted blades) to turn the driven (or lifting) section which operates at a higher angle of attack and can thereby turn at a lower speed while still producing the same amount of lift. Since aerodynamic drag increases exponentially with speed, I assume this is probaly the main producer of the increase in efficiency of positively twisted rotor blades. Is this correct?

(I know this has been discussed before but the light bulb just went off in my head how the tip speed is the efficiency gain key, just recently, still ahead of Paul B. though. :) )

Other questions:

How does the efficiency gains compare from positively twisted rotor blades to composite tapered rotor blades (lets say Patroney's current tapering 8H12 blades)? I would guess their increased performance comes primarily from the larger inboard (drive) section being more adapted to flying forward with the reduced airspeeds it sees compared to farther out towards the tip. I would guess the driven section is probaly shifted outwards also (say the same 75%? ratio as positively twisted blades) and I would guess the blades run at a higher speed thereby giving up the exponential drag reduction of the slower turning positive twist blades, so where does the increase in efficiency come from? (I do believe they are more efficient ie. "tons of lift" but where does the increase in efficiency come from?) Is it because the optimized driving section rams the tapered driven section through the air faster, which imparts higher inertia which can be translated into "tons of lift"?

The ideal blade (I believe Chuck B. stated) would be of uniform construction (density, weight and smoothness) with an varying airfoil shape (optimized to the airspeed it will see) along the whole length of the rotor blade, with a positive twist on the end, and perhaps (if you desire the slower speed range to be slightly optimized) droop tips at the end of the blades. Is this correct?

I suspect such rotor blades require the resources of a large aerospace company (ie. Boeing) to produce due to composite engineering and experience required as well as the manufacturing capability to very tight tolerances. Is this correct?

Please forgive me as some of this has been discussed ( I can't find the relative threads or I am not using the search function correctly) but if technical experts can answer some or all of the above questions, it would be greatly appreciated (as always!) Thanks, darrellwittke

[quadrirotor]

From rotor rooter:
http://www.unicopter.com/0864.html

[darrellwittke]

As Udi replied (in the hot/cold blade thread) that the gain in efficiency of positively twisted blades comes primarily from increasing the driving section, my core question now is "How does the performance gain from tapered blades (re Patroney) compare to positively twisted blades (re Dragon Wings?) The tapered blades also increase the driving section by reducing angle of attack, correct?

I suspect it would be math intensive to analyze and answer all the above questions, so if engineer types do not want to spend the time, that's fine (as always.) Any discussion on this comparison (even generally speaking) would be helpful, however, to resolve my curiosity. Thanks. darrellwittke

[Doug Riley]

Long post!

The intended effect of twist in a rotating airfoil, whether on a window fan, a prop, a helo rotor or a gyro rotor, is to allow as much of the wing section as possible to operate at its most efficient angle of attack. Airfoils, like many devices, are most efficient at a middle-of-the-road setting -- neither the maximum AOA they can stand (without stalling) nor the minimum that will work at all.

If you draw a graph of lift/drag ratio (=efficiency) against angle of attack, you get soemthing like a lopsided version of a typical "bell curve." The sweet spot is in the lower portion of the mid-range of AOA.

With typical cambered airfoils, this "sweet spot" for AOA is 2-3 degrees. It's most important for the outboard portion to operate near this spot (because, at the high airspeed we see at the tips, the consequences of a poor AOA are worse than they are for poor AOA inboard). Still, for best performance, we'd like the inboard portions to be near THEIR sweet spots, too. This requires twisting the inboard sections down relative to the outboard sections.

The reason for this is more apparent if you think of twist as "lower incidence as you approach the hub" rather than "higher incidence as you approach the tip." It's not that we increase the tip AOA with twist; it's that we DEcrease the inboard AOA.

Example: Dragon Wings are twisted. At the hub, they have zero pitch. At the tips, they have a positive pitch (how much depends on blade length). An untwisted metal blade will typically have 1-3 degrees of pitch along its whole length; this is too much for the inboard section and causes a larger stalled area inboard as well as more drag on the unstalled inboard area.

I don't have the math to translate this into numbers. It involves a formula that expresses lift at a given slice of blade as a function of blade station (which, in turn, means expressing both AOA and airspeed as functions of station at a given RRPM) and then integrating over the range of stations.

I believe (but don't know for sure) that the notion of tapering chord toward the tip has to do with Reynold's Number. This is the principle that states that small-chord airfoils are especially inefficient at low airspeeds, but relatively more efficient at high airspeeds. A 7" rotor blade is a pretty small airfoil. By increasing chord at the root (where airspeed is low), you hope to win back a bit of efficiency in the inherently-inefficient inboard area.

When thinking about this, it's helpful to keep it in perspective. Cierva's earlier gyros used no blade area at all inboard -- just the plain spar out in the breeze, out to what looks like 30-40% radius or so. So the notion that we can gain a lot by optimizing the inboard section with lots of twist and huge chord, along with the notion it's critical to make "as big a driving area as possible," are clearly inaccurate.

P.S.: The downside of twisting the blades so that the AOA is more nearly constant along the blade length is that the whole blade tends to stall at once. This translates into an abrupt onset of hard blade flap once you the retreating blade gets too much airspeed for its RPM.

[darrellwittke]

Damn! Paul B. may be ahead in understanding rotor dynamics after all! So it's a red herring that positively twisted rotor blades gain efficiency from slower speeds. (This has been discussed a number of times, I just never caught on.) I was thinking the higher angle of attack of dragon wings at 4-5 degrees allowed them to carry more weight while turning slower. Same as the cartercopter, they would gain exponential drag reduction while carrying same weight as faster turning straight blades. All wonderfully wrong.

Thanks Doug, for finally getting me to understand! I appreciate knowledgeable guys like you educating hard-headed blokes such as myself. (Send a tutoring fee if you wish!)

Your example of the dragon wings having 2-3 degrees (for example) and going backwards to zero degrees at the hub was most helpful.

With tapered blades (through proper sizing) showing (anecdotally) efficiency gains, would my ideal blade (ie. a tapered AND positively twisted blade) be an aerodynamically workable ideal (disregarding manufacturing and cost factors?)

Thanks again, darrellwittke

[Al_Hammer]

Some tidbits from the experts:
My studies of two different gyroplane designs indicate that the high-speed performance would be somewhat helped by using a slightly positive twist (higher angle at the tip than at the root) for a disc loading of two pounds per square foot. However, some negative twist would be beneficial if the disc loading were seven. -Ray Prouty
=======================================
The most efficient angle of attack for an airfoil is where its lift-to-drag ratio is the highest. For most rotor airfoils, this angle is in the neighborhood of 8 deg. -Ray Prouty
==================
In the 1930's, Lock showed that best L/D leads to
maximum rpm for given airflow.
As a general rule
performance drops off rapidly if pitch is too high (rotor may not even rotate
at all). Performance drop off is quite gradual if pitch is too low.


I think Paul B has posted his belief that negative twist might be a benefit, the reason being that the tips are driven in a helicopter and a gyro, so why not twist them both the same?
The airflow in a helicopter is from the top and that changes the Angle of attack distribution significantly, requiring negaitive twist for efficient hover.
The twist actually hurts helicopter performance at forward speed.

Adding ideal twist (which is not a constant twist)to the gyro rotor will allow the maximum amount of the blade span to be operating near the best AOA, as Doug said.
The idea is not to maximize the driving region. The driving and driven regions arrange themselves until there is a balance and at that point rpm is steady.
The diagram shows that both driving and driven sections are making lift. Because of the constant changing AOA long the span, the lift at each point is tilted. At the point where AOA is at some crucial value, the lift is pointing exactly along the axis of spin. . At all other points it either tilts forwrd or back of vertical, or there is no lift at all(stalled region.)

[darrellwittke]

are truly worth a thousand words. Thanks for the diagram Al. Got anything for tapered blades and their gains in performance through "reynolds numbers" wizardry?

And I also am aware of Paul B's stated belief in negative twist, I'm just baiting him but he has successfully resisted thus far :D .

Honestly, I am hoping that Paul B and the other aussies digest this and come to agreement with positive twist. I am very interested and curious about Patroney's tapered blades and can't help wondering how they would perform with positive twist.

Hope they join us, in the spirit of communication and knowledge sharing, not argument.

Oops, almost forgot, Prouty states 8 degrees being optimal, Doug R. stating 2-3 degrees, why the difference? (Helicopters operate at 8 degrees but cannot autorotate until pitch dropped to 2-3 degrees, I would deduce the pneumatic drive is not sufficiently strong to drive the outboard section when at 8 degrees? Hmmm, assuming that is correct, if you strengthen the pneumatic drive through either taper, twist or both, could you not increase driven section angle?)

I am not forgetting Doug R's admonition, the gains would be likely be quite small, just like to know what the optimum goal is.

Thanks again, darrellwittke

[Al_Hammer]

Darrell, thank you. Glad it helped. I'll have to do some digging into the taper thing..

Thanks

[Doug Riley]

Remember that pitch isn't AOA -- just as in fixed wings, incidence isn't AOA. The angle at which the air actually meets the leading edge of the blade is dependent on RRPM, rotor spindle angle, cyclic flapping and flight path, not just on the pitch angle that you set when building the blades.

Example: If the (untwisted) blade pitch is zero, the spindle angle is ten deg. to the gyro's relative wind, RRPM is such that the blade tips are going 375 mph and the gyro's forward speed is 60 mph, the advancing blade's calculated AOA at the tip at the "3 o'clock" position would be about 1.45 degrees, WITHOUT cyclic flapping. (You can arrive at this by doing a scale vector drawing with a ruler and protractor, or by chewing through the math). However, this AOA and airspeed on the advancing blade will cause some cyclic flapping which, in turn, de-pitches the advancing blade and up-pitches the retreating blade. This "blowback" angle can be calculated if you know the blade airfoil's lift vs. AOA curve. It's on the order of two degrees, and varies with airfoil section as well as airspeed.

The upshot is that you can't have both the advancing blade and retreating blade operating at the AOA that gives ideal L/D. One's going to have too much AOA and/or the other will have too little. Only in a perfect vertical descent can you get the blade to fly at a constant AOA all the way around its orbit. In forward flight the blade's AOA fluctuates constantly through its rotational cycle.

I imagine that a blade that's very wide at the root would increase efficiency a bit. The McCutchen hub is a modest attempt to use this effect. Vancraft put a full disk (24" in diameter or so?) over its hub for awhile, perhaps for the same reason. The current Sportcopters don't have this feature, however, so it must not have been worth it.

[gyromike]

I imagine that a blade that's very wide at the root would increase efficiency a bit. The McCutchen hub is a modest attempt to use this effect. Vancraft put a full disk (24" in diameter or so?) over its hub for awhile, perhaps for the same reason. The current Sportcopters don't have this feature, however, so it must not have been worth it.


Jim Eich also used wide-chord sections on his blade roots.
I don't know how well it worked though.

[Al_Hammer]

Chuck on "Plugging the Hole", and on Blade twist(from the old forum)

Date: December 20, 2002
Author: CA BEATY
Subject: Plugging the hole

Ray, the inner portion of the rotor is stalled, not a great loss in terms of disc area but greater loss that apparent at first thought.

High pressure air from the underside of the rotor rushes through the hole caused by blade root stall to the low pressure air on top of the rotor. Plugging the hole will improve the rotor lift/drag ratio.

But it's not as simple as attaching a large plywood disc to the hub bar.

In forward flight with the rotor tip plane axis tipped rearward of the rotorhead axis as a result of cyclic flapping, the plywood disc would be forced to oscillate at 2/rev about the blade feathering axis.

Cyclic flapping and cyclic feathering are equivalent, depending only on the axis from which the rotor is viewed.

Viewed from the tip plane axis, there is no cyclic flapping, only cyclic feathering. The advancing blade has a lower angle of attack than the retreating blade. A plywood disc bolted to the hub bar would be locked to the blade feathering axis.

Viewed from the rotorhead axis, there is no cyclic feathering, only cyclic flapping.

Jim Eich attacked this problem (the hole) a number of years ago by attaching giant airfoils to the hub and the blade root ends. He bent up Clark Y sort of airfoils with a chord of a foot or so.

With the auxiliary airfoils set with the bottom surfaces parallel to the hub bar, there was a decrease of performance (they were stalled) but nosed down a couple of degrees, there was a performance improvement. You might contact Jim and ask him about his experiment -I probably have some of the details garbled.
=================================
Date: March 03, 2003 1
Author: CA BEATY
Subject: Twisted 30' rotors

Paul, I don't know why the variation of angle of attack along the blade span is so difficult to visualize.

Consider a gyro with 30' rotor diameter in a vertical descent. It will descend vertically at something over 1200 ft/min or 20 fps. Say the rotor is turning at 320 rpm.

The wind on the blade as a result of rotation is 503 fps at the tip and of course, zero at the center.

But the actual wind on the blade is the vector sum of vertical descent speed and speed resulting from rotation.

At the tip, the angle of relative wind is atan(20/503) = 2.3 deg.

At midspan, it is atan(20/251) = 4.6 degrees

Three feet from the center of rotation, it is atan(20/100.5) = 11.3 degrees.

At the center of rotation it is, of course, 90 degrees.

At the tip, the blade angle of attack is too low to produce a good lift/drag ratio. Inboard, the rotor is stalled.

A gyro doesn't operate only in a vertical descent. Forward flight produces a more complex flow pattern; the advancing blade isn't exposed to as much variation of angle of attack and the retreating blade, more. For optimum forward flight, the advancing blade needs less twist than the retreating blade and the best compromise, according to Haffner, is something in the range of 5 degrees.

But small amounts of twist in either direction don't have a gross effect on rotor performance. If your blades with wrong way twist subjectively performed better, you need to look at factors other than twist; i.e., the test pilot's preconceived biases, blade surface condition or perhaps the two rotors weren't operating at the same tip speed.

And no, I didn't save all of Chuck's posts, but I grabbed a fair bunch of them just before Norm went off the air. Larry Goodhind has a complete database, but he is also among the missing myhtical figures, and anyway, he isn't giving out anything without Norm's consent, so we go round and round, just waiting for one of these people to resurface with the silver chalice.

[darrellwittke]

I sure do enjoy Chuck B's posts, their enlightenment can keep me up late at night mulling it over.

I also do like Dean Dolph's (I believe) suggestion of a permanent section on rotor dynamics etc... It was said that it would be good for the newbee's but I believe all of us non-technical sorts would benefit. I know I keep asking some of the same questions over and when I get the answers (as in above, partially) I go "Doh, I knew that!" With a permanent section I could review it to refresh my memory and keep knowledgeable people from burning out on repeating themselves over and over.

Chuck B's patience is truly amazing after seeing him post and educate us on Norm's and this forum.

However, enough maudlin sentiments, how about them tapered rotor blades/reynolds number theory and efficiency comparisons to positive twist blades?

Sincerely, darrellwittke

[Rotor Rooter]

Al, as per your instructions, this posting is added to a previous 'on-topic' thread. ;)

While searching 'ideal twist', I came across your post of an earlier post by Chuck B. The mention of a solid root disk [plug] on a gyrocopter got the neurons firing. It relates to the following picture from the book 'History of the Helicopter'. It also relates to a person with a name somewhat like 'Vanack' who has an idea for a helicopter with a very large disk and with short blades at the circumference.

http://www.UniCopter.com/Platt-LePage.jpg
__________________________________

To provoke thought;

The use of plugs on a helicopter will produce negative lift during forward flight, if they are aligned with the tip-path-plane. However, the tip-path-plane of the gyrocopter is tilted aft during forward flight ~ I think.

On a helicopter during autorotation, the area nearest the disk is stalled, but this may be due to the fact that the helicopter blades have negative twist and the pitch at the root will therefore be fairly high. I don't know what the mean angle-of-attack of a gyrocopter's rotor disk is during cruise but if it is any where near 8º then the circular plug may act like an airfoil and provide additional lift, plus eliminate blade 'root loss'.

Opposing the perceived advantages is the fact that this so-called airfoil has its pitch axis at 50% of its chord and this may create unwanted forces in the cyclical control stick as the forward velocity of the craft increases.

Will an extremly negative camber (like a Frisbee) significantly move the plug's pitch axes aft toward its center?

Will this musing provoke thought and response , or boredom? :confused:

[Al_Hammer]

Too bad Darrell's not with us anymore to see the completion of this discussion. I just checked my private messages and re-read a PM he sent me last year.

Not all that many people have written messages to me in the the years I've been on the forums, but even though he didn't know me, Darrell was quick to thank me for a link I'd given him and he was eager to talk about the rail bike that he designed and built. He seemed to have an abundance of creative energy- musing at one point over whether he could adapt a Segway type of gyro stabilised system to ride the rails.

Sorry, Dave, didn't mean to get off topic, but "Remembering" , (the title of Darrell's post), kind of got in the way.

[Rotor Rooter]

Hi Al,

It would be interesting to hear comments on this idea of 'plugging the hole', particularly from knowledge people like Chuck B.
_____________________________

Using Chuck's posting of December 20, 2002 as the foundation for a discussion, I would politely question the following two statements.
"But it's not as simple as attaching a large plywood disc to the hub bar."Perhaps it might be workable to attach a large convex disc [such as those large round aluminum disks that are used for sliding down snowy slopes] to the hub bar, if the angle-of-attack of the rotor-tip-plane is not excessive."In forward flight with the rotor tip plane axis tipped rearward of the rotorhead axis as a result of cyclic flapping, the plywood disc would be forced to oscillate at 2/rev about the blade feathering axis."I agree that any point on the rotating disk can be considered as experiencing 1/rev flapping about the rotor head axis, if one look at the point as being on a rotating blade. However, the rotation of this disk will have no aerodynamic effect. Therefore the disk can be considered as being a fixed wing.

Superficially, it appears that a central convex disk should provide addition lift to a gyrocopter, at minimal cost, weight and drag.

Dave

[Al_Hammer]

Perhaps it might be workable to attach a large convex disc [such as those large round aluminum disks that are used for sliding down snowy slopes] to the hub bar, if the angle-of-attack of the rotor-tip-plane is not excessive.

Dave, I don't see how you can eliminate the aerodynamic effects of a 2 per rev wobble of the "plug." If the plug were bolted to the top of the teeter block, for example, it would tilt the leading edge up each time the advancing blade reached the 12 0'clock position. Not only would this change the AOA of the plug twice per rev, but it would also oscillate the mass of the plug and cause vibration.

[Rotor Rooter]

Al,
If the plug were bolted to the top of the teeter block, for example, it would tilt the leading edge up each time the advancing blade reached the 12 0'clock position. The 'leading edge' of what, are you refering to?


Both you and Chuck have mentioned a 2/rev oscillation. Therefore there is a misunderstanding, and it is probably on my part.

As I understand the gyrocopter's rotor:

The tip-path-plane will maintain a constant attitude in space, as long as the are no perturbations or movements of the cyclic stick. If this is true, then the tip-path-plane is not experiencing any X/rev oscillations.

The hub-bar-plane is basically aligned with the tip-path-plane. If this is true, then the hub-bar-plane is not experiencing any X/rev oscillations.

Therefore if a convex disk [plug] is rigidly bolted to the hub bar, the plug-disk-plane will coexists with the hub-bar-plane and it should not experience any X/rev oscillations either.

The 'dome' of the convex plug will just clear the top of the teetering hinge components.

Is the above incorrect?

[Al_Hammer]

The tip path plane is not oscillating, but the blades are feathering with respect to the plane. This occurs as a result of the teetering of the hub.
At 3 and 9 0'clock positions, the blades are at the mid point of their teeter and they are basically parallel with the spin plane of the rotorhead. At that point they are not lined up with the tip path plane, but they are still travelling in the plane. At 6 and 12 0'clock the blades are once again lined up parallel with the tip path plane as they reach the max teeter angle.

In the diagram below the hub is perfectly level at the instant the blades reach 3/9 0'clock. A still photo taken now would not reveal whether the blades were flapping or not, since in either case the pic would look the same at this position.
90 degrees later at 6/12 0'clock the hub bar will be teetered up at the flapping angle.

[Rotor Rooter]

Al,

Thanks for the postings and diagram. You and Chuck are right.

I am wrong.
http://www.unicopter.com/Stupid.gif


Now ~ if the disk can still be attached to the hub bar but the disk is pivoted on bearings whose axis is the feathering axis. And, if the center of lift on the disk can be ............. :D

[Al_Hammer]

Congratulations on admitting your error, Dave. As a consolation prize I am posting this photo taken during some R&D testing of our new product for the recreational gyroplane market. :D

[Rotor Rooter]

Is that a rocket or did the JTO bottle come loose? :)

While discussing ideas http://www.unicopter.com/Idea.gif a new one has been posted on a separate thread in the Helicopter section.

[StanFoster]

Al & Doug:


I just want to step in and say a big thank-you to your constant positive inputs to this forum. This is a big part of what makes this place such a nice visit.....


Doug: It was very enlightening to have talked to you for that short time at Bensen days.

Stan

[Doug Riley]

Stan, I wish we could have visited longer and under happier circumstances.

I suppose you could attach the "flying saucer" to the rotor spindle (perhaps via beefed-up teeter towers on a Bensen-type head) instead of the hub. That would get away from the cyclic feathering, but would involve an awkward cantilever structure.

I guess the main reason that people who've tried this (there have been a few) haven't stayed with it is that it doesn't accomplish much.

A rotating round wing is about the sorriest wing you can come up with. It has an aspect ratio of either 1 (which is lousy) or zero (which is worse), depending on how you do the numbers. Its edge is both a leading edge and a trailing edge, so it's either too sharp or too blunt, depending on its role at the moment. But most of all, it's just small. A wing like that at 50 mph would be lucky to make 4 pounds of lift per square foot and would create a lot of drag in the process.

[Ga6riel]

you can calculate lift for yourselves if you want to play with numbers

Lift = .5 x slug x V^2 x area x Cl

or .5 x (.00238) x (ft per sec squared) x (sq ft of wing) x (lift coeficient)
low speed lift coeficients u can get from NACA charts, i use around 1.2, to 1.4 near stall (low speed) and around .4 high speed just to eyeball the numbers

[Rotor Rooter]

Just some random thoughts.


Mount the non movable disk to the tower with a fixed forward angle of attack of +/- 8º and let the rotating parts extend up through it's center.
Mount a moveable disk to the tower and link it to the cyclic so that it tips longitudinally and laterally at some percentage of the cyclic movements.
If the disk is shaped somewhat like a Frisbee it might have a better L/D ratio than that of a flat plate.
The convex shape may shift its center of lift closer to the center of the disk.

http://www.unicopter.com/Nerd.gif

[Ga6riel]

indeed the X-wing rotorcraft rotor (which had to work both ways) and some boats (proas) use ogival forms for lift. While lift is ok, drag is more, from memory, also its no longer @25% chord

[Al_Hammer]

I just want to step in and say a big thank-you to your constant positive inputs to this forum. This is a big part of what makes this place such a nice visit.....

Stan, thanks very much for including me in those generous remarks.
Your own contributions to the forum aren't too shabby either.

[StanFoster]

Al: I am just a shutter bug....you guys that explain these aerodynamics so well....gives me a lot of confidence going up. I like to half way know whats going on......and why the thing even flies.

You..Doug.......Chuck Beatty ...Udi...and excuse me cause I know I am leaving out others.....but anyway...the accumulative resources you guys so generously pour out here make this my favorite website.

Ok....I will be quiet and read with interest. :)



Stan

[Doug Riley]

Gabriel, I think lift coefficients of 1.0 or more would be optimistic. When a friend and I tested small H-stabs, with a proper 0012 airfoil and aspect ratio = 2 (see photo), the best C.L. we could get out of them was 0.8 at 14 degrees AOA. Based on that, I'd expect a small disk on a gyro rotor to be at 0.4 or less.

IOW, lift would be 2-3 lb/sq. ft. at 50 mph.