B185 Supplement

Delta3

Robinson R-22 & Delta3									Dave Jackson	14/12/00
Prouty on R22									Al Hammer	14/12/00
	Interesting								Dave Jackson	14/12/00
		This little piggy went wee-wa all the way home.							Al Hammer	14/12/00
			We're wee-wa-ing						John Uptigrove	15/12/00
				wee-waa-ing around the patch					Al Hammer	15/12/00
			Wee-wa & Cross-coupling						Dave Jackson	15/12/00
				(more)					Dave Jackson	15/12/00
				No					John Uptigrove	15/12/00
					Yes				Dave Jackson	15/12/00
						Same thing			John Uptigrove	15/12/00
							John, I agree with you ...		Dave Jackson	15/12/00
In pursuit of the elusive 'wee-wa'									Dave Jackson	17/12/00
Not so fast Dave									Al Hammer	17/12/00
	hold the presses								Dave Jackson	17/12/00
		Terms reversed							Al Hammer	17/12/00
			Thanks Al ...						Dave Jackson	18/12/00
			Braiding the split hairs :-)						Dave Jackson	18/12/00
				Ok, Dave, Prouty has vindicated you.					Al Hammer	18/12/00
					here goes				Dave Jackson	18/12/00
Wee-wa and other strange things									CA BEATY	18/12/00
Just a wild idea									Dave Jackson	18/12/00
	Skewed teeter hinge								CA BEATY	18/12/00
		Thanks for the comments							Dave Jackson	19/12/00
			single pivot						John Uptigrove	19/12/00
				That is correct, John....					Craig Wall	19/12/00
				fame & fortune					Dave Jackson	19/12/00
					not really				John Uptigrove	19/12/00
						(chuckle) It's pretty hard, John,...			Craig Wall	19/12/00
			Drag hinges						CA BEATY	19/12/00
				Chuck, I hope you are willing to pursue this.					Dave Jackson	19/12/00
					Hub kinematics				CA BEATY	19/12/00
						Chuck, thanks for the detailed posting …			Dave Jackson	19/12/00
							The Coriolis hoax, Dave...		CA BEATY	20/12/00
								...	.	20/12/00
								...	.	20/12/00

Post new message in this thread

Date: 14-Dec-00 14:28
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: Robinson R-22 & Delta3

There have been a couple of interesting threads on the R-22 rotor hub during the last few months; [cross-coupling] & [Frank Robinson on R-22]. The intent of this thread is to expand on those previous ones.

The attachment at the bottom of this posting consists of a drawing of the R-22 hub and its 18-degree delta3 (by control system geometry), for pitch/teetering. The dimensions are quite accurate.

Chuck Beaty has previously discused the advantages of pitch/cone hinges. The right hand side of this drawing shows the R-22 hub, with the addition of a 33-degree delta3 (by control system geometry) , for a 1.54:1 cone/pitch hinge.

This thread may serve to expand the knowledge on teetering rotors, if Chuck and others are interested in posting to it, and also, if John Uptigrove is still considering modifications to his rotor head.

Related Web Sites

Dave J

Project: SynchroLite Progressing thanks to the technical contributions of others . past and present.

Attachments: R22 hub.gif

Date: 14-Dec-00 15:46
Author: Al Hammer (alhammer3@netscape.net)
Subject: Prouty on R22

In case you're interested, found this paraphrase of a comment by Ray Prouty..

this is an excerpt from a letter written by Ray Prouty: "...If you are on the ground and apply maximum cyclic pitch to the rotor when it is over the nose, the tip path plane will tilt up 90 degrees later on the left side (and down on the right) following the laws that apply to a gyroscope.

If you are in the air, the same thing happens as you call for an acceleration of a right roll by applying maximum pitch over the nose. (If the rotor has offset flapping hinges, the angle is not 90 degrees, but something less--maybe 85 degrees). However, once you achieve some rate of right roll, the situation changes and the tip path plane will not be responding at 90 degrees, but at some smaller angle depending on the design of the blades. This angle can be as low as 60 degrees depending on the design of the blades and results in rate crosscoupling.

Some helicopter designers arrange the cyclic control system such that a stick movement directly to the right produces maximum pitch over the nose and rely on the pilot to take care of the rate cross-coupling. Others, such as Robinson, rotate the controls to minimize this crosscoupling while accepting some acceleration crosscoupling.

There are some other sources of crosscoupling, so one value of control phasing will never be optimum....."

Al Hammer

Date: 14-Dec-00 19:17
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: Interesting

Prouty's two references to "design of the blades" in respect to phase angle is perplexing. I can't recall reading anything about a relationship of this type in any of his books.

It is difficult to see how the airfoil profile has any effect. Perhaps very heavy tip weights might have an effect because they will reduce the coning angle. Also, extremely heavy tip weights might reduce the ability of 'aerodynamic precession' to overcome gyroscopic precession. (I am using the term 'aerodynamic precession' as the aerodynamic force attempting to change the tip path plane.)

Later Edit: "design of the blades" may be a reference to Lock nbr.

Prouty does not delve very deeply into delta3, as I recall.

Dave J

Date: 14-Dec-00 20:31
Author: Al Hammer (alhammer3@netscape.net)
Subject: This little piggy went wee-wa all the way home.

Sure sounds to me like he is describing what F.R. called wee-wa, but Prouty calls it rate cross coupling.

Date: 15-Dec-00 09:36
Author: John Uptigrove (fun@mosquitoheli.com)
Subject: We're wee-wa-ing

I think you're right Al. Robinson is talking about rolling forward and Prouty is talking about rolling to the right. Effect is the same.

BTW I tried putting in a little control delta-3 but it was only about 15 deg. Unfortunately my through-shaft control method does not tolerate offsetting the pitch links very well as it introduces torsional forces to the linkage which it wasn't designed for. I made a quick run around the patch with it just to see if there were any noticable effects but couldn't notice anything significant. But the 5 minute test was so small it would be difficult to compare any differences. I didn't want to push my luck so I stopped there.

I didn't rotate the lower controls to compensate for the offset and it still flew the same. For some reason the offset matches the response time to give the same result. There must be some mathematical verification for this.

I still fail to see why a hefty 30 degree or so control delta-3 would not increase control power and reduce gust influence by a considerable margin. Perhaps the nutating thing Chuck discussed would show up at higher offsets. There must be some reasons no one (other than FR) does it.

The big difference between control delta-3 and teeter hinge delta-3 in my view is that the control version makes the rotor more swash plate compliant while the teeter version makes it more rotor shaft compliant, the former being the desirable one. I'll find a way to try it some day.

Date: 15-Dec-00 20:07
Author: Al Hammer (alhammer3@netscape.net)
Subject: wee-waa-ing around the patch

John, it's good that you can put in some changes and fly around the patch to check out the results. we've got so many variables kicking around in these recent discussions that is very dificult to understand any one concept in isolation. BTW, the R22 isn't the only one with swashplate offsets. The Linx, and the Squirrel have 72 and 78 degree offsets. It is to eliminate the cross coupling. Depending on altitude and temperature,aft cyclic will get you a right roll or a left roll component or none at all. The R22 design eliminates the cross coupling effects quite well, but at higher speeds more and more right stick pressure has to be held, and there is a cruise trim knob for that.

Date: 15-Dec-00 12:49
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: Wee-wa & Cross-coupling

Frank Robinson appears to be addressing two separate subjects that both entail cross-coupling. He discusses "two minor undesirable characteristics of rotor systems having 90-degree pitch links."

1/ ~ The duration of wee-wa is limited to the short time required for the rotor disk to realine itself after a pilot induced change of longitudinal cyclic. Frank Robinson says "… the rotor disc will have some lateral tilt while the rotor disc is tilting forward, sometimes referred to as "wee-wa.". This is refered to as Acceleration Cross-coupling, I think.

2/ ~ The other reason for delta-3 is to iliminate the need for the pilot to maintain left lateral cyclic during the whole time of forward flight. This is refered to as Rate Cross-coupling, I think.

It appears to me that the following scenario would apply to a helicopter that does not have delta-3. ~ When the pilot, in a hovering helicopter, instigates forward flight, he must apply a small amount of left lateral cyclic along with the forward longitudinal cyclic. This left lateral cyclic is then removed. It is then reapplied in an ever increasing amount as the forward velocity of the helicopter increases.

The preceding is cast in concrete ~ until someone comes along with a jack-hammer.

Dave J

Date: 15-Dec-00 13:39
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: (more)

The following is based on the pilot inputing an amount of forward cyclic and then holding that cyclic stick position.

There are 3 phases of interest during the transition from hover to fast forward flight,

The instigation of forward flight. Wee-wa
Initial, slow forward flight
Fast forward flight

Without delta3, the pilot instinctively applies left lateral cyclic during 1 & 3.

The Robinson does this automatically with its delta3.

Dave J

Date: 15-Dec-00 14:09
Author: John Uptigrove (fun@mosquitoheli.com)
Subject: No

We-wa and cross coupling are the same thing. They are caused by pitch or roll of the rotor in any direction. The roll (or pitch) causes one blade to have a higher angle of attack relative to the other. As a result there is a tendancy to rise/sink a 1/4 turn later. It is totally independent of the angle between the rotor and swash plate. The delta-3 introduced to correct it however is, as it is only effective when the two are not parallel.

The forward motion we-wa is the same thing only it is caused by the different angle of the fore and aft coned blades relative to the oncoming headwind. The rear blade has a lower relative angle of attack than the front and so it we-wa's a weenie wittle bit.

Date: 15-Dec-00 15:05
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: Yes

I believe that wee-wa is one example of cross-coupling.

Reguarding your second paragraph, you are thinking of the coning angle and forward velocity, as was mentioned by previously Chuck Beaty. This is a constant situation during forward flight.

Wee-wa is a temporary thing. It takes place within a single revolution (possably 1/2 revolution) of the rotor. It takes place only when the plane of the rotor disk is in the process of changing.

The following is an excerpt from Frank Robinson's posting; "the rotor disc will have some lateral tilt while the rotor disc is tilting forward, sometimes referred to as "wee-wa." This occurs because while the rotor disc is tilting, the forward blade has a downward velocity and the aft blade has an upward velocity. This increases the angle-of-attack of the forward blade causing it to climb, and reduces the angle-of-attack of the aft blade causing it to dive."

Please note that Mr. Robinson uses the word "tilting" not "tilted".

The above posting with the Subject: (more) has been re-posted. It might help with the explanation.

Dave J

Date: 15-Dec-00 15:15
Author: John Uptigrove (fun@mosquitoheli.com)
Subject: Same thing

Regardless of what they are called they are caused by the same basic thing and have the same basic result. Not really that complicated.

Date: 15-Dec-00 15:32
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: John, I agree with you ...

... if you consider the act of tilting the disk in a forward direction as being basically the same as steady forward flight with a coned disk.

The end result is definitly the same; application of left lateral cyclic.

The following might be of interest. It supports one of your previous posting.

re: Relocation of pitch links for delta3

The non-rotating portion of the swashplate does not change. In other words the top of the rods which come from the mixer box are not rotated about the mast.

Both the top and the bottom of the pitch links, between the swashplate and the pitch horn are rotated an equal amount.

The mathematical verification supporting the equality of this rotation is

Δψ = 90° - tan^-1 * K_p = 90° - δ₃

Change in the azimuth = 90° - tan^-1 * [pitch-flap coupling] = 90° - [delta3 angle]

Dave J

Date: 17-Dec-00 13:32
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: In pursuit of the elusive 'wee-wa'

It appears that I'm sitting on the opposite side of the fence from a distinguished group of knowledgeable people, namely Chuck Beaty, Al Hammer and John Uptigrove. So for the fun a good argument and the chance to learn something, here goes…..

The opposition's position:

Wee-wa and is one-and-the-same as 'forward velocity with a coned disk'.

My position:

Wee-wa and 'forward velocity with a coned disk' are two distinctly different events. Their only commonality is that of lifting the retreating side of the rotor disk.

My argument:

I would guess that the name 'wee-wa' is derived from 'small "washout-out coupling effect"'. I would suggest that 'wee-wa' only takes place while the disk is in the active state of tipping forward. At this time the forward half of the disk is experiencing an increased angle of attack because it is descending.

Who will argue?

Dave J

Date: 17-Dec-00 18:23
Author: Al Hammer (alhammer3@netscape.net)
Subject: Not so fast Dave

I did not argue the opposite. I agree that there are two seperate events. I believe Prouty was describing what FR was calling wee-wa.

The tilting rotor can cross couple up to 60 degrees according to Prouty's comments. That is a pronounced effect and as you recall, Robinson said it was figured to be about 18 degrees. The controls were rotated 18 degrees in the R22 to just compensate for this wee-wa(and other effects). Robinson did not ever say that delta-3 was a consideration at all(I don't think.) Which leads us to wonder how much delta-3 is actually present and how much does it add or subtract from the wee-wa ? In forward flight the R22 tends toward the left if right stick isn't held in which seems to suggest that the delta-3 must not be cancelled by the control offset of 18 degrees. This isn't a flaw, just a decision to have low cross coupling at hover and low speed and to accept having to add right trim at cruise. Al

Date: 17-Dec-00 21:02
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: hold the presses

Al, There is no intent to compete with Lu Zuckerman for length of thread, but this subject is interesting., It is important to me also, considering the close blade-to-blade clearances in my intermeshing project.

At least our endeavor is a little easer than Lu's. We want to prove something amongst a few people. He wants to prove something to the world.

OK ~ Here goes.

Al ~ "Robinson did not ever say that delta-3 was a consideration at all(I don't think.)"

Robinson ~ "…the 18-degree delta-three angle designed into the R22 swashplate and rotor hub."

Frank Robinson is obviously aware of delta3.

Al ~ "The tilting rotor can cross couple up to 60 degrees according to Prouty's comments."

Prouty ~ "This angle can be as low as 60 degrees depending on the design of the blades and results in rate crosscoupling."

1/ In this instance Prouty is speaking of rate cross-coupling. My position is that 'wee-wa' is acceleration cross-coupling.

2/ The only situation where I can find Prouty mentioning delta3 is when he is talking about the tail rotor. Here a large delta3 and a possibly unusual Lock number could well result in a phase angle of 60 degrees.

OK. This is the 'meat' of the argument. I disagree with your following statement.

Al ~ "I believe Prouty was describing what FR was calling wee-wa." ~ A Hammer

Prouty ~ "Some helicopter designers arrange the cyclic control system such that a stick movement directly to the right produces maximum pitch over the nose and rely on the pilot to take care of the rate cross-coupling. Others, such as Robinson, rotate the controls to minimize this crosscoupling while accepting some acceleration crosscoupling."

This is where I do not think that Prouty and Robinson are describing the same thing. Robinson does not specifically mention 'rate" or 'acceleration' when referring to cross-coupling but;

I believe the following to be rate cross-coupling.

Robinson ~ "The other undesirable characteristic in rotor systems having 90-degree pitch links is the lateral stick travel required with airspeed changes during forward flight at higher airspeeds."

I believe the following to be acceleration cross-coupling.

Robinson ~ " the rotor disc will have some lateral tilt while the rotor disc is tilting forward, sometimes referred to as "wee-wa."

Prouty and Robinson appear to be in agrement on rate cross-coupling but not on acceleration cross coupling. I am in no position to question Prouty but, he talks about "accepting some acceleration crosscoupling", whereas Robinson is saying that delta3 is removing most of the acceleration cross-coupling, which he refers to as "wee-wa"

Al ~ " In forward flight the R22 tends toward the left if right stick isn't held in which seems to suggest that the delta-3 must not be cancelled by the control offset of 18 degrees. This isn't a flaw, just a decision to have low cross coupling at hover and low speed and to accept having to add right trim at cruise."

This may not be related to delta-3. Who knows?

Dave J

Date: 17-Dec-00 21:51
Author: Al Hammer (alhammer3@netscape.net)
Subject: Terms reversed

Dave, without getting into a bunch of hair-splitting, I will just say that I believe you have those two terms backwards.(Rate, and acceleration cross coupling.)

Date: 18-Dec-00 13:25
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: Thanks Al ...

... will look into.

I appreciate the limited amount of time that you have available for pursuing a single subject so deeply.

In my case, it's a little different. The SynchroLite rotor is designed around the delta3 hub. I would rather split hairs now than split blades later. :-)

Dave J

Date: 18-Dec-00 15:16
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: Braiding the split hairs :-)

For anyone who is remotely interested in this thread, and is still following it, it looks like the answer has been found. The following is from Prouty's Helicopter Performance, Stability. and Control - p.460.

This was also a chance to test the Optical Character Recognition program, which came with the scanner. It only made one mistake. Not bad.

"For the example helicopter, this means that a 1° change in longitudinal flapping will be accompanied by a lateral flapping of —.07°. If the pilot wishes to use cyclic pitch to tilt the tip path plane nose up in a purely longitudinal direction, he will have to move the stick slightly to the right as he pulls it aft in order to cancel out the left roll that would otherwise be generated. This type of cross-coupling is sometimes called acceleration cross-coupling because it is associated with the rotor moments, which provide the initial acceleration during a maneuver. Once steady rates are established in the maneuver, the cross-coupling changes to rate cross-coupling, as will be shown later. Because these two types of cross-coupling have different values, it is not possible to compensate exactly for both by a simple mechanical rotation of control inputs between the stick and the swashplate, although some compromise may be used in an attempt to minimize both."

Dave J

Date: 18-Dec-00 19:16
Author: Al Hammer (alhammer3@netscape.net)
Subject: Ok, Dave, Prouty has vindicated you.

I agree with Chuck- it is a confusing subject. The problem I am having is in trying to follow the chain of reasoning:

The coning hinge geometry(delta-3) introduces a phase shift in the rotor response to control input

Some rotation of the controls will correct for this.

Is the 18 degree control rotation correcting for phase shift or is it compensating for acceleration cross coupling?

Robinson calls it an 18 degree delta-3 angle, but could it be that he is simply referring to the 18 degree swashplate rotation.?? If the 18 degrees is compesating for wee-waa, then there is nothing left over to compensate for delta-3. Maybe the amount of delta-3 from control geometry is minimal. What is the theoretical value according to your calculations?(HAHA) Al

Date: 18-Dec-00 22:52
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: here goes

The following is an attempt to answer to your posting. Others may refine it, - or destroy it.:-)

The coning hinge geometry(delta-3) introduces a phase shift in the rotor response to control input.

The teetering hinge (in the case of the R-22) geometry(delta-3) introduces the need for a phase shift in the swashplate.

Some rotation of the controls will correct for this.

Yes. Clockwise relocation of the rotating part of the swashplate only.

Is the 18 degree control rotation correcting for phase shift or is it compensating for acceleration cross coupling?

Cross-coupling takes place whenever there is movement of the cyclic stick or the collective stick. The 18-degree delta3 attempts to compensate for this acceleration cross-coupling and rate cross-coupling. The delta3 causes an increase in the effective natural frequency of the teetering motion and the 18-degree rotation at the swashplate gives a matching phase shift.

Robinson calls it an 18 degree delta-3 angle, but could it be that he is simply referring to the 18 degree swashplate rotation.??

He is referring to both.

Clockwise rotation of the top of the pitch link increases the delta3 angle.

Clockwise rotation of the bottom of the pitch link increases the phase angle.

It just happens that when the pitch link is perpendicular, ie. top and bottom rotated the same amount, the phase angle is exactly what is required to suit the delta3 angle.

If the 18 degrees is compensating for wee-waa, then there is nothing left over to compensate for delta-3.

The two take place at different times. Wee-wa [acceleration cross-coupling] exists when the cyclic stick is in motion and the rotor disk is in the process of tipping. The other [rate cross-coupling] exists for the duration of holding in the cyclic.

For example, when going from hover to fast forward flight, acceleration cross-coupling takes place the moment the cyclic stick is pushed forward. Rate cross-coupling starts to come into play as the forward speed increases.

This is explained much more clearly by Prouty, in the posting just before yours.

Maybe the amount of delta-3 from control geometry is minimal. What is the theoretical value according to your calculations?~~(HAHA)~~ to you. Your going to get an answer.

About a year ago I did the delta3 calculations for the SynchroLite. This was done for a reason that has not even been discussed in this thread. It was done to handle lead-lag. The ability to handle lead-lag is necessary because the Coriolis effect causes a rotational oscillation between the two rotor disks. As an aside;- Dick deGraw said that he did not take this into account in his Hummingbird and he experienced no problems. That sure says something about theorizing.:-) Perhaps oscillatory twisting in the two masts took care of the problem.. Back to today; the calculations worked out to 15-16 degrees.

From very rough consideration of the R-22 it appeared to me that the 18 degrees of delta3 would take care of the wee-wa [acceleration cross-coupling] and be a contribution toward the [rate cross-coupling].

Whew :-) Hope this 'theory' helps, if you're still reading.

Dave J

Date: 18-Dec-00 14:26
Author: CA BEATY (cabeaty@worldnet.att.net)
Subject: Wee-wa and other strange things

A really confusing subject. Wayne Johnson ("Helicopter Theory") devotes several pages of partial differential equations, La Place transforms and multiple integrations to the subject of rotor cross coupling.

As nearly as I can determine, with flap hinges on the center of rotation and no delta-3 coupling, sideward tilt of the rotor is caused by:

(1) Angle of attack difference front to rear as a result of coning.

(2) Non uniform flow through through the rotor, front to rear at low airspeeds, causing a fore and aft lift differential that precesses the rotor sideways, exacerbated by a tilt rate.

(3) Tail rotor thrust.

A rotor with central flap hinges (or teetering) and no delta-3 coupling is resonant at the rotational speed so force/displacement always has a 90º phase angle unaffected by rotor mass/aerodynamic characteristics.

Things that raise the resonant frequency above the rotational speed such as hingeless blades, offset flap hinges and delta-3 coupling cause the phase shift to be less than 90º; the amount depending on the frequency ratio and dampening. Dampening is determined by the blade mass/aerodynamic lift ratio.

I have never been conscious of any cross coupling on a gyro with Bensen type rotor system.

The A&S-18A employs about 45º of delta-3 coupling to lower pitch following a jump and people who have flown this machine tell me it's a squirrel with strong cross coupling; jab the stick in pitch and it rolls; jab the stick in roll and it pitches. Swash plate phasing can minimize cross coupling only over a limited speed range.

Date: 18-Dec-00 17:33
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: Just a wild idea

From your comments, "with flap hinges on the center of rotation" and a previous posting of yours about pitch-cone coupling, comes the following.

Department of Demented Designs

What sort of weird or wonderful situation would exist if a helicopter rotor were built with the follow parameters?

2 blades.
Identical to a teetering rotor except that the blades are independently hinged on a common pin.
This hinge pin to have delta3, by a negative azimuth rotation of approximately 18 degrees (flap hinge geometry).

I wonder if this would result in a functional rotor, which has pitch-flap coupling and pitch-cone coupling, all from one hinge pin?

Dave J

Date: 18-Dec-00 18:44
Author: CA BEATY (cabeaty@worldnet.att.net)
Subject: Skewed teeter hinge

Sure, it'll work, you would still need drag hinges but I'm not sure 18º will do anything. Wouldn't raise the flap frequency enough to seriously affect phase angle/cross coupling and wouldn't pull pitch enough to significantly improve autorotation.

Make up some model rotors using 18" pieces of yardsticks (Do you still use spruce yardsticks in Canada?), run them in front of a box fan and you can get a pretty good empirical feel for behavior. You can try delta-3 coupling simply by skewing the teeter hinge on a see-saw rotor. My experience is that nothing really weird starts happening until you approach 30º of delta-3 and around 45º, you'll begin seeing some nutational response where the rotor dithers in response to a cyclic step input.

Date: 19-Dec-00 00:33
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: Thanks for the comments

Your remark about 'still needing drag hinges' is interesting. Drag hinges have not been incorporated into the SynchroLite, since it appears to me, in theory, that they are not needed. The lead-lag can be taken care of by the in-plane motion of flap-hinge-geometry delta3. My thinking is obviously wrong because Kaman is in agreement with you. They use drag hinges in conjunction with their flap-hinge-geometry delta3 teetering hinge. Pictures of the K-225 & K-Max rotor hubs

I have been unable to understand why drag hinges are needed. Your reasoning behind the need for them would be of considerable value.

___________________

The thinking behind this idea, if there was any thinking, was to duplicate the functionality of the Robinson hub, but make it simpler, by using one hinge instead of three.

It may be fun to build a model and/or John might want to consider it for the Mosquito. Eh! John

Dave J

Date: 19-Dec-00 07:40
Author: John Uptigrove (fun@mosquitoheli.com)
Subject: single pivot

I think we already discussed the idea of a single coning/teetering hinge a while back although without the delta-3 added. I recall Craig quashed my dreams of fame and fortune by telling me someone had already come up with the idea and used it in the "Rotachute" (I believe).

My affection for machining diminishes with every part I have to make so I'll leave it to you to prove the concept to be a real winner, then I'll incorporate it.

Date: 19-Dec-00 08:05
Author: Craig Wall (crow@concentric.net)
Subject: That is correct, John....

...Raul Hafner used the interleaved flapping hinges on the Rotachute with a single pin and a delta three offset. The idea was that the blades could be folded upward together and the machine airdropped, whereupon the blades would begin spinning while still nearly parallel, and then the rotation would spread them out to the normal coning angle.

I do know that airdrops of scale models were carried out and the deployment was successful and reliable- the "Rotachute" name was intended to refer to a simple strap-on rotary wing replacement for a standard parachute. To my knowledge no manned drops were carried out, but the Germans and Russians may have pursued this as well.

Bensen continued the efforts by doing both drop tests and a rocket launched test of a "supersonic parachute", as GE press releases called it- I have a picture of a German V-2 rocket nosecone descending with rotorblades extended and Bensen trotting up in the background to recover it- with a big boyish grin on his face.

I also have images of his very early gyrogliders that used the Hafner Rotachute blades and hub, and he had to include a mast ABOVE the hub, with a pulley and cable arrangement to act as a droopstop- the cables run out about 18" to the blade from the pulley at the top of the 1 ft mast, and the cable is continuous so that as one blade rises the other falls. I suspect he did away with the interleaved hinge and went to a solid hub bar with the very next rotor, although he retained the delta three angle in that next iteration- the plans for the B-6 have the solid hub bar but show the delta three offset. It wasn't until the B-7 that he went to the 90 degree teeter hinge we all know and love.

Craig Wall

Date: 19-Dec-00 08:46
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: fame & fortune

I don't think Craig, in his previous or very interesting current posting, 'quashed your dreams of fame and fortune'. From Craig's comments, it would appear that they are using these features for a different purpose.

While we are waiting around until January to see if there still is a life for ultralight helicopters, you have to do something with all your free time.

Dave J

Project: SynchroLite Progressing thanks to the technical contributions of others . past and present.

Date: 19-Dec-00 10:41
Author: John Uptigrove (fun@mosquitoheli.com)
Subject: not really

The point was, Dave, that for a few fleeting moments I was the inventor of this fine concept and was headed for riches. Then I was informed, and not too surprisingly, that someone had thought of if earlier, about 50 years earlier. Oh well, back to work.

Date: 19-Dec-00 12:37
Author: Craig Wall (crow@concentric.net)
Subject: (*chuckle*) It's pretty hard, John,...

...to think of something that hasn't already been thought of. The trick is to move the concept to another part of the envelope. (I'm sure I'm not telling you anything you don't already know.)

The Rotachute interleaved-single-pin-delta-three arrangement is a good case in point: the design is obviously lifted from the folding props used on sailing auxiliaries from the 19th century (if not from a taffrail log whirlygig). The inventors of that no doubt lifted the concept from somewhere else- an ancient Chinese butter churn or a magic trick prop or something equally prosaic.

(Of course, one-bladed samara provide a confirmation that autorotation can be initiated in free-fall; wanting two blades makes sense for aircraft, but at least they knew beforehand that it was possible to start them from a fixed trailing position without destroying them in the process.)

I'm sure you could find ten other examples of similar mechanical configurations if you tried long enough. Even today, most chemistry departments possess shaft stirrers that open up once inside a reaction flask, past the narrow neck. The delta three refinement is just that- merely a refinement to get the proper behavior under load.

Craig (...mapleseeds 'R' us...) Wall

Date: 19-Dec-00 09:58
Author: CA BEATY (cabeaty@worldnet.att.net)
Subject: Drag hinges

Dave, the CG of a coned rotor during cyclic flapping is forced to follow a 2/rev circular path if there is no undersling and no drag hinges. Skew of the flap/cone hinge makes no difference.

Here's a simple test of the kinematics: Can you tilt the rotorhead axis, using the cone/flap hinge as the center without shifting the rotor CG?

Date: 19-Dec-00 12:56
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: Chuck, I hope you are willing to pursue this.

I understand your comment regarding 'the CG of a coned rotor during cyclic flapping being forced to follow a 2/rev circular path if there is no undersling and no drag hinges'.

The rotor configuration that I am having a problem understanding is a conventional teetering rotor with undersling. This is the type of rotor configuration that is used on the Kamans and is designed into the SynchroLite. During 'normal' operating conditions, they should not be experiencing much movement in the CG.

The unique situation with the Kaman and SynchroLite rotors is that because of the 90-degrree azimuth offset between the rotor disks, combined with the Corollas effect, there will be lead-lag between the pair of rotors. This is the same concern that I think you addressed a while back when you mentioned your idea of a single rotor with 4 blade and 2 teeter hinges.

I feel that the in-plane movement of Wayne Johnson's page 239 flap-hinge-geometry type delta3 should negate the need for drag hinges. Dick deGraw did nothing to handle lead-lag.

Kaman and you believe in the need for drag hinges, so it must be correct. My problem is that I still cannot see the need for drag hinges. Can you tell me where I am going wrong?

Thanks;

Dave J

Date: 19-Dec-00 14:51
Author: CA BEATY (cabeaty@worldnet.att.net)
Subject: Hub kinematics

View the attached sketch, Dave, and imagine tilting the rotor head with the drag hinge locked out. Will the blade rotate about its feathering axis or swing about a conical path? I see nothing of page 239 of Wayne Johnson that accommodates in-plane motion.

When a rotor is viewed from the tip plane axis while keeping in mind that momentum is conserved permits us to avoid the Coriolis math and reduce rotor motion to a simple problem in kinematics. Mother Nature mandates that the blade mass spins in a simple circular orbit that must be accommodated by the proper hinges at the hub.

A teetering rotor is a form of Hooks joint and the drive shaft does not run at constant angular velocity in the presence of cyclic flapping. Bell and Hiller solved this problem by floating the engine/transmission assembly on rubber biscuits and letting the rubber accommodate the 2/rev variation of angular velocity.

With a syncopter having a pair of Hooks joints at 90º to one another, some accommodation must be made: perhaps torsionally soft shafts or maybe close in drag hinges. Still a nightmare though; 2 high inertia flywheels tied together by gears and shafts. What is the natural resonant frequency frequency of this assemblage? Anywhere close to 2/rev and 4/rev aerodynamic excitations?

I've flown a couple of 3-blade rotors that had neither flap or drag hinges; -floating or gimbaled hubs. When the hub is allowed to follow the tip plane, flap and drag hinges aren't kinematically necessary but I was always concerned about in-plane aerodynamic loads and decided not to fly them again unless/until I fit strain gauges to the feathering bearing spindles.

Attachments: flap hinge.jpg

Date: 19-Dec-00 20:14
Author: Dave Jackson (jackson.dave@shaw.ca)
Subject: Chuck, thanks for the detailed posting …

.. but I'm not yet ready to convert. :-)

I see nothing of page 239 of Wayne Johnson that accommodates in-plane motion.

My belief is that figure(a) does provide in-plane motion.

… the drive shaft does not run at constant angular velocity in the presence of cyclic flapping.

Based upon the statements below, I think that the drive shafts can be run at a constant angular velocity.

_____________________

The following uses the two sketches on Wayne Johnson's page 239 as the examples. The sketches ~ for any other interested person. The only major change to both his sketches is that of substituting the phrase 'underslung teetering hinge' for his phrase 'flap hinge', since we are discussing a common teetering hinge not two offset flap hinges.

The Robinson's delta3 is figure(b), and this has no in-plane motion.

The Kaman's and the SynchroLite's delta3 is figure(a), and it does appear to have in-plane motion. When the blades teeter, either up or down, about the underslung teetering hinge, they will also advance in-plane. The Coriolis effect is a result of the teetering and this in-plane movement is in synchronization with this teetering.

Based on this, I believe that an appropriate amount of delta3 can be calculated so that the in-plane lead-lag counteracts the Coriolis effect. This means that neither of the masts is subjected to oscillatory torsion.

If the above is correct, then why does Kaman see the need for drag hinges?

Dave J

Date: 20-Dec-00 08:10
Author: CA BEATY (cabeaty@worldnet.att.net)
Subject: The Coriolis hoax, Dave...

....Was perpetrated by Cierva to bamboozle his competitors.

To have a Coriolis torque, you must have radial movement of mass in a rotating system. The commonest example is to stand at the center of a carousel and walk toward the rim. Your body, as it gains kinetic energy, exerts a torque opposing the rotation of the carousel.

Now, think of a shallow sheet metal cone with, say, a 170º included angle driven at its apex by a constant velocity universal joint. The cone rotates about its own axis even when the drive shaft is at, for example, a 10º angle. A paint dot near the rim of the cone would in fact move nearer and farther from the drive shaft axis as it rotates and one might imagine that it speeds up and slows down in response to Coriolis forces but it doesn't. The cone is rotating about its own axis and every molecule of metal spins in a circle at uniform angular velocity.

Slit the cone into segments to mimic rotor blades and nothing changes. This is an example of the "floating" hub rotor.

But even in the more usual rotor system with hub rigidly fixed to the drive shaft, the rotor cone rotates about its own axis at uniform angular velocity, accommodation being provided by flap/drag hinges rather that a CV joint.

You'll never understand the dynamics of a rotor, Dave, until you clear your mind of the Coriolis block.

Date: 20-Dec-00 16:24
Author: .

Date: 20-Dec-00 23:17
Author: .