Rigid Rotors & More ~ A challenge

[Dave Jackson]

"The ubiquitous nature of cross-coupling constitutes one of the chief reasons why piloting this type of aircraft requires such high skill levels developed through long training programmes" ~ Gareth D. Padfield

"In more distracting circumstances, however, he would benefit if the helicopter control system would make the aircraft quickly do what the pilot wants it to do, and nothing more." ~ R.W. Prouty
______________________

It has been said that there is nothing new in rotorcraft.

The following outlines a configuration that has never been built. Some of the features have been previously used, but never unified in one assemblage. It flies in the face of conventional rotor dynamics.

I challenge anyone with knowledge of aerodynamics to find fault with the following rotorcraft conceptualization.

Features;
~ Two main rotors with three blades each.
~ Intermeshing configuration.
~ Direction of rotation is forward on the inside.
~ Blades have absolute rigidity and cannot flap, lag or twist.
~ Hub has no pre-cone and no flap or lag hinge.
~ Hub is mounted to the fuselage via a totally rigid static mast.
~ Blades can only rotate about the feathering hinge and mast.
~ Phase lag angle (gamma) is 0 degrees.
~ 'T' tail with inverted high-lift horizontal airfoil, located above the rotor disk.

Hover to Forward Flight:

Forward cyclic is applied which results in maximum blade pitch over the tail (azimuth 0). The absolutely (really) rigid rotor disk and fuselage, together, pitch nose down and the forward component of the thrust causes forward flight.

The 'T' tail provides speed stability, in lieu of conventional rotor disks. A type of pitot tube adjusts the opposed lateral cyclic between the two rotors and thereby sets the relative pitch between the advancing and retreating blades. In addition, the rotorcraft incorporates the advancing blade concept (ABC). This causes the advancing blades to provide more thrust than the retreating blades and this in turn give the craft lateral stability through dihedral. As well, it negates retreating blade stall during fast forward flight.


Additional details, if desired: http://www.unicopter.com/unicopter.html

Will anyone pick up the gauntlet? :)

Dave J

[helmet fire]

I enter the fray unarmed and unprepared...but...in one foul swoop?
Gyroscopic precession! :p

Off the cuff, it appears that the totally rigid design proposed would not be controllable due to the lack of flap. So to move forward by increasing blade pitch to a maximum over the tail, with no flap, you have created more lift at the rear of the disc. Remember gryroscopic precession? I believe that the absolute rigidity you propose will meet the requirements of a gyroscope and thus be susceptible to gyroscopic precession (note: you have excluded aerodynamic precession by not allowing blade flap). So, with more lift at the rear of the aircraft, the gyroscope translates this into the two discs trying to roll outward from each other (assuming they both rotate forward on the inside). Thus if you wanted to go forward, i think you would have to have max blade pitch on the outboard side of both discs, thus translating into a tilt forward (90deg precession).

Lets assume that you did get this to occur, and the aircraft began to move forward. your next monster is dissymetry of lift. As the discs rotate forward in side, more lift would be created in the centre of the aircraft and the roll forces would be tring to roll each disc away from each other. Both discs will translate the dissymetry of lift forward as per gyroscopic precession resulting in a savage pitch up that will be only controllable by tilting the disc further forward. At the same time however, you have lost lift from the outboard retreating side of the discs which translates into a pitch up as well, thus doubling your fun.

The only out here is to force both discs to tilt down. As per above, the only way to achieve this is to increase pitch on the retreating outboard sides of the discs. Accordingly, you would not be going very fast before you had retreating blade stall on both discs manifesting itself as a massive pitch up that would be uncontrollable due to the fact that the only way to pitch down would be to further increase pitch on the already stalled retreating blades.

But all that aside, we have to assume you have discovered the material that is light enough for flight, has absolute rigidity as claimed, and is strong enough not tear the aircraft up the middle. BIG assumption here, and probably insurmountable with todays technology.

Dont know if any of the above makes sense, but I would love to hear your reasoning...

:) :)

[Dave Jackson]

helmet fire,

"Off the cuff, it appears that the totally rigid design proposed would not be controllable due to the lack of flap."

This concept is a radical departure from the conventional helicopter rotor. The function of flap must be forgotten. This configuration is more like two large intermeshing propellers, which have variable pitch blades.

________________

"So to move forward by increasing blade pitch to a maximum over the tail, with no flap, you have created more lift at the rear of the disc."

Correct.

________________

"I believe that the absolute rigidity you propose will meet the requirements of a gyroscope and thus be susceptible to gyroscopic precession. So, with more lift at the rear of the aircraft, the gyroscope translates this into the two discs trying to roll outward from each other (assuming they both rotate forward on the inside)."

You are correct. The rotors will be experiencing gyroscopic precession, but this is an advantage. The gyroscopic precession is small when compared to the aerodynamic force. This precession lags the aerodynamically forced tipping by 90-degrees. The two rotors are counter rotating and rigidly connected, therefore the two gyroscopic precessions will oppose each other and provide some dynamic stability for the craft.

________________

"Thus if you wanted to go forward, i think you would have to have max blade pitch on the outboard side of both discs, thus translating into a tilt forward (90deg precession)."

No. There is no precession on the aerodynamic force. The aerodynamic phase lag is 0-degrees.

_________________

"Lets assume that you did get this to occur, and the aircraft began to move forward. your next monster is dissymmetry of lift. As the discs rotate forward in side, more lift would be created in the centre of the aircraft and the roll forces would be trying to roll each disc away from each other."

There is no dissymmetry of lift during forward flight. As the speed increases the force of the 'free' air will, via a mechanically device, deliver opposite lateral cyclic to the two rotors. In other words, dissymmetry of lift is handled by blade pitch not by flapping.

In addition, there is no problem if the amount of lateral cyclic is not totally correct since the twin counterrotating rotors and the rigidity will handle it.

__________________

"But all that aside, we have to assume you have discovered the material that is light enough for flight, has absolute rigidity as claimed, and is strong enough not tear the aircraft up the middle. BIG assumption here, and probably insurmountable with todays technology."

Weight was the big problem 70 years ago and it was beaten. As you say, weight will be the problem again but it can be beaten. Pultruded carbon and composite construction have the lightness and rigidity that will allow this craft to fly today. Man-made silk etc. will offer greater advantages in the future.


If you question any of the above, take a shot. :eek:

[vorticey]

hi dave
i think that a blade that wont flex, will snap. and the bulk of material used to make a ridgid rotor would make blades to thick and increase parasitic drag.
the ridgid rotor would move like you think with a 0deg lag and if the cabin is close in hight to the discs as they move though the centre, this would reduce induced airflow on the inside (incraesing rotor stall ias) and increase power required to the outside to hold the aircraft up.
the dihedral would not be acheived with ridgid rotors as an angle must be acheived, and youve got the leading edge in the middle not the outside.
gyroscopic procession would occer when the aircraft is tilting and would load the hubs ........and the more disc weight the hevier load on the hubs.

i dont think ridgid rotors are the go.

:confused:

[Dave Jackson]

Hi vorticey,

Thanks for provoking thought about potential problems. Hopefully, the answers are valid.

"If the cabin is close in height to the discs as they move though the centre, this would reduce induced airflow on the inside (increasing rotor stall ias) and increase power required to the outside to hold the aircraft up."

The inside of a rotor disk provides very little lift. For example, in hover the inner 30% of the Robinson's rotor disk only provides 5-percent of the total lift. The Brantly is an excellent example of not using the inner portion of the disk.

"I think that a blade that won't flex, will snap. and the bulk of material used to make a rigid rotor would make blades to thick and increase parasitic drag."

The extreme thickness will be mainly confined to the inner portion (root) of the blades. Here the profile need only be aerodynamic, to minimize drag (NACA 0033). As mentioned above, the outer portion of the blades will provide the lift and have a thinner profile. Preliminary blade loadings have been done and strength should not be a problem. The amount of flex (flap) will be determined by testing.

"dihedral would not be achieved with ridged rotors as an angle must be achieved, and you've got the leading edge in the middle not the outside."

With the intermeshing configuration, 70% of the advancing blade extends beyond the opposite side of the helicopter, and this 70%, combined with ABC, is the high thrust portion of the disk.

"gyroscopic procession would occur when the aircraft is tilting and would load the hubs"

True, but this should be an advantage by providing dynamic stability in steady flight.

"i don't think rigid rotors are the go."

I really hope you're wrong. ;)

[vorticey]

one other thing i can think of is as the aircraft tilts over forward, the weight of the helicopter (centre of gravity) is lifted to the back by the blade tips through the mast because the whole helicopter must tilt instead of just the disc. this would take more althority than normal. maybe not even achieve forward flight, especialy at weight??
in forward flight there would be a continuous bending moment in one direction on the mast increasing fatigue failure, bearing wear.
??

[CRAN]

Hi Dave,

While locating the advancing blade on the inside of this disk could work I feel that it may cause additional problems for the design such as n-per-rev rotor induced vibration on the fuselage structure. Indeed most manufacturer’s attempts to mount the rotor close to the fuselage in order to reduce hub parasite-drag have resulted in such problems and have had to be subsequently modified. Furthermore, a large amount of noise is likely to be generated in close proximity to the cabin.

The intermeshing rotor system will exhort more download on the fuselage than a conventional design - resulting in a loss of efficiency. I appreciate that the inner portions of the disk have been off-loaded so the significance of this is diminished - but its still present. One of the compromises of the really rigid-rotor-system, will be that it is necessary to have relatively low aspect ratio blades which are themselves less efficient. I think that the reduced efficiency of the rotor based on highly loaded rotor, plus intermeshing effects plus the weight involved in designing such a rigid system will mean little useful load will be possible. Hence, you will have to create a very large machine indeed to carry a single person and a useful fuel load.


I am intrigued to find out what your thoughts are on having the advancing side of each disk intermeshing, would it not be more beneficial to have the less effective retreating side intermeshing hence reducing interference losses.

Away from largely aerodynamic issues, I have the following thoughts on the general configuration:

The rigid rotor will be very heavy indeed in comparison to conventional designs.

Designing a safe ABC rigid rotor system presents a very difficult aero-elastic problem. What design tools/codes do you intend to use?

While the ultimate properties of carbon-fibre are very good indeed, the use of these materials in polymer composites is not straightforward. Composite materials are subject to considerable variability even with strict quality controls. Therefore, significant conservatism is required which diminishes the advantage of such materials. In working for one of the major helicopter companies recently I have seen when designing to the airworthiness standards and multiplying all of the required factors (variability, degradation (many), and safety) it is often easier and lighter to design in metal! Composite ARE good, but in practice they don’t always work the miracles some people have been led to believe that they can.

For a rigid design, your hubs (two of them!) will have to be enormously strong. The fatigue loads will be very considerable. Lot’s and lot’s of weight whatever you manufacturer them from!

These loads will be increased by not having any pre-cone (as the blade will naturally want to cone to equilibrium between lift and CF)

I like that static mast idea, obviously attaching the rotating bits at the top is an interesting design problem but the removal of shaft whirl issues is worth it in my opinion.

Assuming that you intend to have a single transmission for both rotors to isolate the opposing rotor loads from the fuselage the loads here again will be enormous and also cyclic. Therefore, this will require huge strength and very considerable weight to meet the static and fatigue strength and stiffness requirements.

One of the problems associated with having large concentrated masses in aircraft fuselages is crashworthiness. When subjected to crash inertia loads (6g vertically-down say (benign)) a substantial structure will be required in the aircraft to avoid these concentrated masses detaching from their attachments and crushing the cabin. Therefore, if you were to isolate the aerodynamic and inertial forces for the rotor system using a stiff transmission, you would not be able to attach it to a lightweight fuselage as it would not be crashworthy.

A more practical issue from the user point of view is the problem of fuselage attitude. Since no relative flapping occurs between the fuselage and the rotor then in order that the aircraft translate the fuselage must tip with the rotor. In the cruise therefore the fuselage attitude would be extremely nose down (drag penalty), unless you incline the rotor shafts forward for a level attitude in cruise. This would require a much more shaft tilt angle than seen on contemporary designs (over twice as much) giving a disconcerting nose up attitude in the hover. In this case what happens to forwards and downward visibility in a flare following an autorotation or a quick-stop? Furthermore the large variations in cabin pitch attitude will significantly reduce the effect and usefulness of the horizontal stabilizer on your T-tail as it is likely to find itself operating at very strange incidence for a lot of the time.

Dave this is an extremely difficult problem and I think therein lies the one reason why the configuration has not been tried by the big manufacturers – the cost would be enormous! If you can overcome these problems and produce a viable and safe design (emphasis on the later of course) then you are a very clever guy.

Good Luck
Cran.
;)

[Dave Jackson]

vorticey

"one other thing i can think of is as the aircraft tilts over forward, the weight of the helicopter (centre of gravity) is lifted to the back by the blade tips through the mast because the whole helicopter must tilt instead of just the disc. this would take more althority than normal. maybe not even achieve forward flight, especialy at weight??
in forward flight there would be a continuous bending moment in one direction on the mast increasing fatigue failure, bearing wear."

The two rotor disks are located just above the fuselage. One of the reasons for this is to make the moment arm between the center of the rotor disks and the center of gravity as short as possible.

You are correct. The initial tipping will place large loads on most of the craft and it must be design accordingly. Once in forward flight, the drag of the fuselage will hold the CG back.
____________________

CRAN

Thanks for taking the time to identify a number of valid concerns. Hopefully, there are satisfactory answers to some and there will be satisfactory answers to the others. Please advise if you disagree with any of the 'solutions'.

"While locating the advancing blade on the inside of this disk could work I feel that it may cause additional problems for the design such as n-per-rev rotor induced vibration on the fuselage structure."

This web page shows: Downwash on Fuselage (http://www.unicopter.com/1074.html) The two small circles represent the inner radiuses of the blades' thrust. The significant portion of the fuselage is located within these circles. In addition, consideration is being given to having a 'D' profile with the flat side down for all or part of the blade that is inside this radius.

Low vibration frequencies of around 16 Hz are discomforting to the occupants. In this area, the UniCopter has a strong advantage. It has smaller diameter and high RRPM rotors, plus six blades. For comparison, the vertical 2P vibration on the two-bladed Robinson R22 is about 18 Hz. The UniCopter's should be (700/60)*3 = 35 Hz. (in roll) and 70 Hz. (in heave)


A large amount of noise is likely to be generated in close proximity to the cabin.

Concern noted. Thanks.

The intermeshing rotor system will exhort more download on the fuselage than a conventional design - resulting in a loss of efficiency. I appreciate that the inner portions of the disk have been off-loaded so the significance of this is diminished - but its still present. One of the compromises of the really rigid-rotor-system, will be that it is necessary to have relatively low aspect ratio blades which are themselves less efficient. I think that the reduced efficiency of the rotor based on highly loaded rotor, plus intermeshing effects plus the weight involved in designing such a rigid system will mean little useful load will be possible. Hence, you will have to create a very large machine indeed to carry a single person and a useful fuel load.

Many of these point are valid, but I don't feel overly bad about the gross-weight / payload ratio. It will be definitely worse than that of a conventional helicopter, but it should be noted that the intermeshing configuration is probably only surpassed in rotor efficiency by the side-by-side configuration. One reason for this is that the elimination of the tail rotor results in an 8% power saving.

The following are a few design statistics on the UniCopter. The blades are 8'-4" long and supports only 125 lbs. each, in hover. A small amount of tip dihedral should assist with the blades 13:1 aspect ratio. The disk loading is only 2.4 lb/ft^ and the blade loading is 23.3 lb/ft^.

Over time, the use of lightweight composites for transmission components and high temperature composites for engine components must improve the gross-weight / payload ratio of helicopters.


"I am intrigued to find out what your thoughts are on having the advancing side of each disk intermeshing, would it not be more beneficial to have the less effective retreating side intermeshing hence reducing interference losses."

I believe that Flettner started by having the retreating side intermeshing and then he changed it. Since then, all intermeshing helicopters have the advancing side intermeshing. The only exception to this is a helicopter proposal by Stepniewski in 1997 (http://www.unicopter.com/Stepniewski_Concept.html). Incidentally, his concept incorporates ABC.

My own thoughts are;
~ 1/ On a helicopter in forward flight, the retreating blade has most of its thrust concentrated near the tip. The 'breast-stroke' configuration will locate this concentrated thrust outside the downwash of the other disk and thereby give a more balanced disk loading.
~ 2/ On the UniCopter, with its advancing blade concept (ABC) most of the lift will be on the intermeshing blade. This means that the lateral moment arm is shorter and this should result in less rotor-induced oscillation about the for/aft axis.


Your comments about strength, strength, strength and weight, weight, weight are only too too true. :)
Unfortunately, this may be the penalty that must be paid for a helicopter that could be easier to fly than a plane.

>Designing a safe ABC rigid rotor system presents a very difficult aero-elastic problem. What design tools/codes do you intend to use? "

CRAN Would you be willing to elaborate a little more on your concerns regarding the aero-elastic problem?

There is total agreement with your comments about composite construction.

Thanks for your remarks about crashworthinness. It could be a difficult problem and it never even crossed my mind.

Your concerns regarding the attitude of the fuselage will definitely require more consideration. Would you be willing to take a rough guess at what the angles might be for fast forward flight and for flare? I am trying to keep the depth and the drag of the fuselage to a minimum for speed stability. A couple of additional thoughts are that of; 1/ linking the cyclic and/or collective to an elevator or stabilator and 2/ providing the craft with a means of limited horizontal thrust that is aligned with the centers of parasitic drag and gravity.

You have certainly provoked thought. Thanks again for a very constructive critique.

Dave J

[Buitenzorg]

Dave, off the bat I see four potential problem areas. CRAN may have touched on any or all of them. I’m also assuming that you envision eventual commercial application(s) of your design, so it’s not a purely experimental research project.

1. I share other posters’ doubt that materials presently exists that possess both the required stiffness and strength, as well as being light enough in weight to be lifted off the ground in an economical manner, and cheap enough to incorporate in a machine that must turn a profit. If you put a big enough engine on it, it’ll fly; commercial applications for the Harrier, anyone?

2. If the design were to be as stiff in all aspects as you envision, a large amount of aerodynamically generated vibration would be passed directly to occupants’ teeth fillings, as well as to other expensive hardware. Designing a rotor system that will be naturally smooth throughout the flight envelope is a very challenging problem indeed. Bö-105 pilots have tales to tell here.

3. The ABC concept involves NOT compensating for dissymmetry of lift within any one rotor disk, but instead the dissymmetry of lift of one rotor disk is compensated for by the equal-but-opposite dissymmetry of lift of the other rotor disk, right? Then at high forward speeds, both rotor masts as well as the fuselage and/or transmission will be subject to enormous bending moments. Components strong enough to withstand this (and repetitive, oscillatory stress => fatigue problems) will have to be very heavy; too heavy to fly maybe?

4. The rotor masts are to be very short as rolling and pitching moments are to be transferred directly to the fuselage from each rotor blade. This puts the rotors very close to the fuselage, so the rotor downwash striking the top of the fuselage will cause a greater loss of efficiency than e.g. the longer masts of the Kaman intermeshing designs.

I just love being negative, it’s so easy!

[Dave Jackson]

Buitenzorg,

"I just love being negative, it’s so easy!"

As long as it doesn't get personal, it's so appreciated! :)


"I’m also assuming that you envision eventual commercial application(s) of your design, so it’s not a purely experimental research project."

This project is a challenging addiction. If, thanks to the technological input of others, past and present, it looks feasible, I intend to fund and have built a 'cheap' full-scale operational prototype.

The UniCopter's fundamentals have been on the Web for over a year. No one can now patent it, to the exclusion of others, not even me. If an operational craft proves to be viable, the ultimate reward will be seeing it in commercial, recreational, or military applications. There are many 'ifs' to come; but so far no fatal shot has brought it down.

_________________________________

Your points about strength, weight and vibration are inline with CRAN's, and others.

The following responses beg for criticism.

1. & 3. A blade spar will be built and tested; probably in 6 months. This will be the first hurdle in testing for strength, weight and deflection.

2. The high RRPM and six blades will negate the very objectionable frequencies. Isolation mounts between the drive frame and the fuselage should absorb much of the higher ones. The rigidity will allow gusts to get into the fuselage but they should be no worse then those experienced in a plane. As well, the tail feathers are not in the downwash.

4. This may have been satisfactorily answered in the reply to CRAN.


Much appreciated.
Dave J

[CyclicRick]

Here's a thought.
I'm no genius but the thought came to my mind that reading all this info is fascinating, you chap's know your stuff by the sound of it and not just on this subject.
There are companies, Universities and various other institutions who possess the most sophisticated computer technology regarding aerodynamics, stucturues etc.
Why not put all these ideas to the test? These systems could give you real and accurate analysis of all the points made.
It seems a bit of a shame that alot of these seemingly (to me) good ideas stay just that....good ideas.

Go for it, you might be on a winner, who knows?

:)

[Dave Jackson]

A couple of weeks ago CRAN and others were kind enough to mention some of their concerns, about a helicopter that incorporated extremely rigid rotors.

It appears that one simple solution might solve the following four major concerns:
~ 1/ The increased parasitic drag, due to a large nose down attitude in
fast forward flight.
~ 2/ The changing slope of the pilot between fast-forward, hover and flare.
~ 3/ The necessity for high rotor strength and the resultant high weight.
~ 4/ High rotor induced vibration.

The solution is to provide a means of forward thrust, which is inline with the center of the parasitic drag. This eliminates the nose down pitching and, in addition, it transfers some of the rotor's thrust to the pusher prop.

Any criticism?

[helmet fire]

Dave,

I note that your list of problems does not include gyroscopic precession, as per your discussion above. A rigid spinning thing IS a gyroscope, and therefore, despite your points, I believe the forces will be an issue for you.

Your last post sounds like you are proposing adjusting the angle of the rotors rather than the fuselage

tilting the rotors perhaps? wait a minute....... lets call it a tilt fuselage!!

:D :D :D

[CRAN]

Hi Dave,

Cyclic pitch on the main rotor will is be required as you are aware for trim in all flight regimes. The really rigid rotor system will impart large fuselage pitch and roll motions as a result of trimming the aircraft. This is turn will cause the position of the centre of drag to move relative to the CG or hub (whatever reference you choose)

The resulting perpendicular offset between the drag centre and the line of action of thrust from your prop will produce a moment that must be reacted. You may have sufficient control power in your rigid rotor system but this will induce a source of control cross coupling between forward thrust and aircraft fuselage attitude, airspeed and a number of other factors. All very non-linear and will add considerable difficulty to the piloting task.

One example would be (there are more) the tendency of both rotors to flap back as you increase forward speed. Since the rotor is rigid the whole fuselage will flap back - moving the line of action of the propulsive thrust force (drag remaining the in the direction of freestream velocity). The prop - which I assume is mounted below the centre of the main rotor axis will aid this nose up tendency. The nose up tendency will slow the aircraft down so the pilot will add more power: the rotation of the fuselage increases until control is lost.

Again the rigid rotor would probably have enough control power to overcome this but the pilot would have to co-ordinate collective, cyclic, pedals, main rotor throttle, and propulsive thrust prop pitch - not to mention what the various instruments and talk on the radio and look outside......lot's of work!

There has been a lot of CAA research done at Glasgow University in Scotland on similar cross-coupling in autgiro's - have you seen it?

You will probably want to have the prop at the back for mechanical simplicity and weight reasons but this will give you real difficulty with the cross-coupling mentioned above. Putting the prop at the front would help with some but not all of the modes.

The system will alleviate the large nose down attitude in forward flight but not the cabin attitude in the flare (though you could probably put up with this with adequate forward/downward vis. designed in).

The system won't significantly improve rotor induced vibration as the rotor thrust will be largely unchanged (approx. 90% i'd guess), there will still need to be cyclic pitch and the addition of a wake from the propulsive prop will feeding more interactions into the rotor wake causing further unsteady air-loads.

Weight will be worse - still need all the rigid bits PLUS an additional transmission for the prop, and pitch-change or speed change mechanism, additional control; in addition, a beef'd up structure to take the horizontal loads.

I'm not keen on this approach - with a configuration that is already inherently complex you must strive to keep the rest a simple as possible.

Hope things continue to go well.

CRAN

:)

[Dave Jackson]

helmet fire

Gyroscopic Precession:

"I note that your list of problems does not include gyroscopic precession, as per your discussion above. A rigid spinning thing IS a gyroscope, and therefore, despite your points, I believe the forces will be an issue for you."

I hope it's a positive issue. :D

It is said about helicopters, that stability and size are inversely proportional. If this is true, then in the light UniCopter the stability caused by gyroscopic inertia should be a benefit.

A few points that support this are;
~ 1/ In a gyroscope, all of the reoriented mass is rotating. In a helicopter with extremely rigid rotors, only a small portion of the reoriented mass is rotating. The much heavier fuselage is not rotating.
~ 2/ Aerodynamic precession appears to be much more of a factor then gyroscopic precession in helicopter rotors. With an absolutly rigid rotor the aerodynamic precession is at 0-degrees.
~ 3/ Currently, the rigid rotors don't even have sufficient inertia for autorotation. All their additional weight (and strength) is located in the hubs and at the root end of the blades.

A plea for help.

Satellites maintain their orientation in space by having two gyroscopes on a common axle and rotating in opposite directions. The UniCopter should benefit from this feature, as well.

There are algorithms for determining conventional gyroscopic precession 90-degress after the point of force. Will someone suggest how to determine the rate of rotation AT the point of force, on a device that has two counterrotating gyroscopes on a common axis?

-----------------

Excessive Nose-down Fuselage
"Your last post sounds like you are proposing adjusting the angle of the rotors rather than the fuselage."

Your adjustable 'partial' tilt rotor ain't a bad idea. :) My previous posting has the rotors plus fuselage varying only slightly from the horizontal and most of the forward thrust is provided by a variable pitch propeller. Another 'partial' solution is to have an adjustable seat (http://www.unicopter.com/1077.html).

[heedm]

Dave,

The Unicopter would normally have a net angular momentum of zero, so there would be no 'gyroscopic' stability due to the rotation of the rotors.

1/ In a gyroscope, all of the reoriented mass is rotating. In a helicopter with extremely rigid rotors, only a small portion of the reoriented mass is rotating. The much heavier fuselage is not rotating.

That's accurate, but it still doesn't give any more stability.


2/ Aerodynamic precession appears to be much more of a factor then gyroscopic precession in helicopter rotors. With an absolutly rigid rotor the aerodynamic precession is at 0-degrees.

If it's zero degrees then there is no aerodynamic precession, so can you even use that theory? :D

Seriously, with an absolutely rigid rotor, there is no flapping of the blade due to hinge or flex, so the dynamics will be very different from what we're used to with helicopters. Fortunately, making it absolutely rigid allows you to forget many things helicopter and just use generic spinny thing physics. If you push on the rotor disc at an off-axis point, the disc will rotate. Since it's already spinning the net rotation will be the same as a gyroscope. Since you have very strong hubs, mast, etc. then that 'push' on the disc also translates into a moment acting on the helicopter. I'm convinced that the net effect will be the helicopter pitching down and rolling left (6 o'clock push up with a ccw rotor)

That was for a single rotor. With yours the same thing will happen, but the effects for each rotor will cancel themselves out over the whole helicopter. Unfortunately, they don't disappear. Pitching inputs will create forces that try to roll the discs together or apart. Rolling inputs will cause one disc to want to tilt forward and the other backward.

Net effect? I think your helicopter will respond quickly to inputs and have relatively little uncommanded movement, but will either last for two minutes before catastrophic failure at the head or will be so heavy that the lightest pilot could only take a two minute fuel load. Okay, maybe that's a little pessimistic, but I can't think of a way of keeping things rigid and reducing weight.



3/ Currently, the rigid rotors don't even have sufficient inertia for autorotation. All their additional weight (and strength) is located in the hubs and at the root end of the blades.

That will help things with respect to the undesirable loads at the heads. Keeping the moment of inertia low will degrade autorotation characteristics, but will help with what I mentioned above.


A plea for help.

The satellites need a gyroscope to keep track of their orientation. The problem is, keeping it up to speed requires that a torque is applied. The antitorque will cause the satellite to spin, and will then require attitude control. To alleviate this constant antitorque problem, an opposing gyro is attached for every gyro required. It takes care of the antitorque and it gives more accuracy through redundant measurements.

In answer to your question, the algorith "to determine the rate of rotation AT the point of force, on a device that has two counterrotating gyroscopes on a common axis" will be precisely the same as the algorithm to calculate rotation of a stick. Net angular momentum is zero. With the gyroscopes there will be torsional forces along the length of the axle, but that doesn't change the whole body result. (IIRC the "common axle" is no significant length, basically two wheels that are paper width from touching...easy to do in a vacuum).


Just my thoughts here, but the adjustable seat may help, but I don't think it's the "right" fix for the attitude problem. It introduces a seperate mechanism that only fixes one portion of the attitude problem. Have you considered vectoring the thrust of the pusher prop and/or adding an elevator?


You've captured my attention with this project. I do see merit in much of the design, but there are still some pretty major hurdles to overcome. I'll let you know if I get any ideas. Sorry, can't help much with funding the project ;) .

[Dave Jackson]

Hi heedm,

It looks like we agree about rotational inertia and two counter-rotating rigid rotors. The interesting part may be;[list=1] to maximize the inertia for autorotation, and
to minimize the inertia for lowest weight, and
to optimize the inertia for ideal dynamic stability.
[/list=1]
Is it correct to assume that we agree on the following non-helicopter statement?

A device consisting of two counter-rotating gyroscopes, which are located on the same vertical axle, will physically resist any tendency to pitch or roll but will offer no resistance to yaw.


"In answer to your question, the algorithm "to determine the rate of rotation AT the point of force, on a device that has two counterrotating gyroscopes on a common axis" will be precisely the same as the algorithm to calculate rotation of a stick. Net angular momentum is zero. With the gyroscopes, there will be torsional forces along the length of the axle, but that doesn't change the whole body result. (IIRC the "common axle" is no significant length, basically two wheels that are paper width from touching...easy to do in a vacuum)."

I don't fully understand the above. Could you elaborate a little?


"Have you considered vectoring the thrust of the pusher prop and/or adding an elevator?"

CRAN is questioning the pusher prop also. One of his concerns is complexity. My, previous, thinking is to locate the thrust close behind the mean center of parasitic drag. The prop will have a variable pitch, which is linked to the forward portion of the longitudinal cyclic only. This prop will provide a large portion of the forward thrust, but not all of it. This way, the rotor's cyclic should maintain control of the craft. More thinking is going to be required in this area.

An elevator could offer advantages. It's probably going to entail looking into the potential contributions of longitudinal rotor cyclic, prop thrust variability and the elevator.

Hopefully, each hurdle will eventually be overcome. :) Thanks.

[Dave Jackson]

CRAN

Thanks for outlining your concerns. I agree with many of your points, particularly the few pros and many cons that come with an additional thrust device, the propeller. They have been noted for further evaluation.

"One example would be (there are more) the tendency of both rotors to flap back as you increase forward speed. Since the rotor is rigid the whole fuselage will flap back - moving the line of action of the propulsive thrust force (drag remaining the in the direction of freestream velocity). The prop - which I assume is mounted below the centre of the main rotor axis will aid this nose up tendency. The nose up tendency will slow the aircraft down so the pilot will add more power: the rotation of the fuselage increases until control is lost."

Some of you concerns are based on the existence of 'flap back'. I think that this subject needs reevaluation when it is applied to the unorthodox 'absolutely rigid rotor'. This subject also needs to be handled very carefully. :) I made an error when discussing 'flap back' a few months ago, and two very knowledgeable people, Nick Lappos and Roberto Celi, politely put me in my place.

On a conventional rotor in steady forward flight, the maximum blade tip climb will be at azimuth-90 (azimuth-0 being at the tail]. The maximum blade tip elevation will be at azimuth-180 and hence 'flap back'. The forgoing assumes a phase lag of 90-degrees. As rotor rigidity increases the phase lag decreases. With an absolutely rigid rotor the maximum climb will still be at azimuth-90 but the phase lag will be 0-degrees. This means that the maximum blade tip elevation would be at azimuth-90, if it were allowed to. In this situation, there are opposing lateral forces, which are attempting to split the two rotors apart, but there is no flap back.

If you should agree with the forgoing, then some of the other concerns have to be reassessed. I believe that the primary one is that of negative pitch stability due to the parasitic drag of the fuselage, which is located below the rotor disks and without flap back to offset it. The craft was given a high 'T' tail to give it speed stability.


"There has been a lot of CAA research done at Glasgow University in Scotland on similar cross-coupling in autgiro's - have you seen it?"

The gyro rotorcraft conference has spoken highly of this on several occasions but no, I have not seen it. They consider Dr. Stewart Houston, along with Jean Fourcade and Chuck Beaty as the preeminent gyro gurus.

Your additional thoughts on 'flap back', in the light of this unorthodox rigid rotor, will be much appreciated.

Dave

[CRAN]

Firstly, I should apologise for my shoddy explanation of my concern on the effects of flap-back on your aircraft - it was a rushed response. In the context of an 'ideal' absolutely rigid rotor then you are absolutely correct. No arguments. However an absolutely rigid rotor is physically unrealisable and therefore some flapping and hence 'some' flap-back will occur (the exact nature of it being dependent on the blade dynamics). The extent of this flapping will depend on how stiff you can make the rotor and still get off the ground.

[I'm just trying to be realistic about the system.]

I am willing to accept that the stiffness of the rotor and the centrifugal stiffening effect due to the high rrpm could render this effect insignificant, but the mechanism does exist. (i.e some flapping must occur.)

As we have said before the flight mechanics and structural dynamics of this aircraft represent a considerable challenge and you must take great care with any explicit or implicit assumptions you make in your analysis.

Best Regards
CRAN

[Lu Zuckerman]

To: Dave Jackson

Once again I may expose my ignorance relative to the subject at hand but here goes:

If you have an infinitely rigid rotor you in effect have a gyroscope. In this case, two gyroscopes rotating in opposition to each other. If I understand it correctly the advancing blade or rotation on the right side is counter clockwise as viewed from above and the left rotor is rotating clockwise as viewed from above. If you move the cyclic forward from a hover (assuming zero wind) the greater lift will be on the retreating side. This will generate a perturbing force on the two rotors causing them to move as a gyroscopic rotor 90-degrees later in rotation, which will cause the nose to fall and the tail to rise because of the 100% interlock between the rotors and the fuselage. At least I think that is what will happen.

If my conclusion is correct then you should look into establishing directional control in the same manner as the V-22, which is almost identical to the CH-47. (Differential input).

Over: :confused:

[Dave Jackson]

Hi Lu,

You provoke thought, thanks.

You're hitting on a number of subjects. Here are a couple of answers. I'll get back on the others.
____________________________

The enclosed segment has been moved to [Gyroscopic Precession - Revisited] and is about to be cut from here. :eek:

"If you have an infinitely rigid rotor you in effect have a gyroscope."

You have to forget gyroscopic precession & the helicopter rotor. For gyroscopic precession to take place, the rotating device must have considerable [Angular Momentum] A helicopter's rotor does not have enough.

Consider a toy gyroscope on a vertical axis. Bring it up to speed. A minute later it is still spinning, and the disk is still horizontal.

Now lets consider a 'type' of 2-bladed helicopter rotor, which has round 'no lift' blades. We'll make it from a 30-foot long by 2" diameter steel pipe. Drill a hole through both walls at 15-feet from the end and weld in a rod (axle), which extends out both holes. Now spin the horizontal pipe, somehow, on its vertical (rod) axis to about 400 rpm. When released, it will slow and fall over within a second or two.

They ain't the same thing.
____________________________

"If I understand it correctly the advancing blade or rotation on the right side is counter clockwise as viewed from above and the left rotor is rotating clockwise as viewed from above. "

A small point. Flettner originally had them rotating in the direction you mention. He then changed them so that the higher inside blades are advancing. (i.e. Port ~ CCW and Starboard - CW). This was done to give speed stability.

Back with more. :)

[Lu Zuckerman]

To: Dave Jackson

Now lets consider a 'type' of 2-bladed helicopter rotor, which has round 'no lift' blades. We'll make it from a 30-foot long by 2" diameter steel pipe. Drill a hole through both walls at 15-feet from the end and weld in a rod (axle), which extends out both holes. Now spin the horizontal pipe, somehow, on its vertical (rod) axis to about 400 rpm. When released, it will slow and fall over within a second or two.

This is a very poor example. A circular body passing through an air stream or an air stream passing over a circular body will initiate what is known as “vortex shedding”. Vortex shedding at 400 rpm will set up such a severe high frequency vibration as to cause the rotating object either to self-destruct or to break away from its’ driving axis. If you rotated the pipe as described but in a vacuum you would not have vortex shedding but you would have a device that would exhibit gyroscopic rigidity in space and gyroscopic precession if you had a means of perturbing the rotating mass. The vibration will be the result of the vortex shedding frequency but mainly due to the vibratory frequencies being different at each station on the rotating pipe.


A propeller on an aircraft is similar to your pipe example and your totally rigid rotorhead but it is rotating about a horizontal axis as opposed to a vertical axis. When the aircraft is maneuvered in any way the movement of the aircraft causes a perturbing force on the rotating mass of the propeller and the propeller wants to precess. It cannot precess because the propeller drive shaft is rigidized by the bearings contained within the crankcase so the blades will bend within their elastic limits.

On the V-22 there is a similar situation. When the aircraft is maneuvered in the airplane mode the Proprotor, which is not rigid will precess (flap). This precessing is detected and electronically corrected by inputs to the servomechanism. You will note that when in the airplane mode there is no advancing and retreating blade and the air stream passing over the Proprotor is uniform so in this case you have to accept gyroscopic precession over aerodynamic precession. Also, since the blades are independent from each other each blade is a part of a rotating mass and as such each blade will individually respond to the perturbing force and although independent from each other they respond as a solid disc.

[Dave Jackson]

Lu,

I don't disagree with your remarks about the propeller.

Previously mentioned was, " For gyroscopic precession to take place, the rotating device must have considerable [Angular Momentum]. A helicopter's rotor does not have enough."

This [Angular momentum] involves RPM and mass. A propeller has a much higher RPM and, proportionately, a much higher mass than the helicopter rotor.
______________

I actually hope that the UniCopter's two counterrotating rigid rotors do exhibit a little gyroscopic precession. This is desired to give the craft dynamic stability in pitch and roll.

Counterrotating Gyroscopes (Dynamic Stability):

Assume that the rotational part of a gyroscope is mounted on a stationary vertical axle. Assume, also, that we are looking down at the gyroscope (plan view) and that the locations of interest are the four primary points of the compass.

If the gyroscope was rotated CW an upward force on the West will cause the North to rise and the South to lower, due to precession. If the gyroscope was then rotated CCW the same upward force on the West will now cause the South to rise and the North to lower.

If we put two counterrotating gyroscopes on the same rigid axle and again apply an upward force on the West the opposing North and South forces will cancel each other. The axle can freely yaw but there is resistance to pitch and to roll.
_____________

If you want to pursue gyroscopic precession further, we should go to the [Gyroscopic Precession - Revisited] thread, so that other can beat up on you, also. ;)

Now to tackle your main point. :)

Dave J

[Dave Jackson]

Lu,

"If you move the cyclic forward from a hover (assuming zero wind) the greater lift will be on the retreating side. This will generate a perturbing force on the two rotors causing them to move as a gyroscopic rotor 90-degrees later in rotation, which will cause the nose to fall and the tail to rise because of the 100% interlock between the rotors and the fuselage. At least I think that is what will happen."

I believe that you previously accepted the fact that an teetering rotor has a precession of 90-degrees and that a rotor with some rigidity (flapping hinge offset) has a precession of less than 90-degrees. If you increase this rigidity all the way to 'absolute' rigidity you will reduced the precession all the way to 0-degrees.

For further information on this, see my paragraph to CRAN a few postings back and his subsequent agreement.
__________

Here's a little mental analogy, for the fun of it. Take a toy gyroscope and with its axle vertical and 'weld' the axle to the top of a can of beer.

If you try to roll this assembly to the right when the gyro is not rotating, the assembly will roll to the right.

Now drink all the beer so that the can is very light and spin the gyro up to a zilloin rpm CCW. If you now try to roll this assembly to the right, the assembly will roll forward. [Gyroscopic precession]

Now **** the beer back into the can, file most of the mass off of the gyro and only spin it at 60 rpm.
If you try to roll this assembly to the right which way will it go?

This is the analogy with the Unicopter. The full can of beer is the heavy fuselage, the filed down gyro is the light rotor(s) and the 60 rpm is the slow rotor rotation.

If you don't buy this, I'm having a beer. :D :D

[Lu Zuckerman]

To: Dave Jackson,

You stated:

"Now **** the beer back into the can, file most of the mass off of the gyro and only spin it at 60 rpm.
If you try to roll this assembly to the right which way will it go?

This is the analogy with the Unicopter. The full can of beer is the heavy fuselage, the filed down gyro is the light rotor(s) and the 60 rpm is the slow rotor rotation".

My response:

It will most likely assume the position that you moved it to. (Rolled the can to the right). There are two reasons for this:

1) By filing the weight off of the rotor you have decreased the mass of the gyro rotor thus severely reducing any precessional energy contained within the spinning mass

2) At 60 RPM there would be minimal energy in the spinning mass even if you had not filed most of the weight from the rotor.
In a previous posting they mentioned a toy gyroscope that can maintain rigidity in space as long as the rotor is turning at or above the minimal speed to maintain that rigidity. As the rotor spins down due to friction the energy decreases allowing the gyro to tumble. However there is still sufficient energy to respond to a perturbing force which is what causes the gyro toy to rotate in the direction of rotor rotation although some of this can be attributed to friction.

Are you stating that your conceptual helicopter has a totally rigid head(s) that rotate at only 60 RPM? If that is the case, then you will have to defy the laws of aerodynamics and physics to get the helicopter off the ground and then to respond to control inputs.

Care for a Labatts Blue?

[Dave Jackson]

Hi Lu,

"It will most likely assume the position that you moved it to. (Rolled the can to the right)."
I agree.

Next next time you're in Vancouver the 'Blue' is on me.

[heedm]

Dave,

Everything rotating body will display "gyroscopic precession". Doesn't matter how fast/slow it turns, doesn't matter it's mass, mass distribution, etc.

It gets too complicated when multiple bodies get together to form a rotating system, so it's best to ignore GP. In fact also ignore aerodynamic precession...it just confuses the issue by generating argument about which precession theory applies to helicopters. Neither one does. They are both convenient explanations.

Examine the theory behind GP or AP. You will find it is the same rotational dynamics behind each. The blade wants to flap at it's natural frequency. If the natural frequency is the same as the rpm of the rotor, then the apparent lag is 90 degrees. If the natural frequency is higher, the lag is lower.

A gyroscope can be considered to be a bunch of point masses that are spinning around an axle and are free to "flap". Each point mass is just like a high school physics pendulum. The natural frequency depends on the length and the restoring force, sq. rt. of g/l in high school physics. Since the restoring force for the point mass is the centrifugal force (it's okay to use centrifugal force...just not a real force) then the force depends on the distance from the center, and the speed of rotation. In the end, we find each point mass has a natural frequency that is exactly the same as the rotational speed of the gyroscope. Reading the above paragraph, that means the apparent lag on a gyroscope is exactly 90 degrees. This shows that GP is just a special case of the blade frequency theory that is a much better way of looking at helicopters. QED

_____________

The full beer can with a slowly spinning gyro will do what you want, but it will require a small corrective force to keep the intended tilt in the right direction. That small corrective force corrects the gyroscopes reaction to the impressed moment.

______________

Lu, with the propellor example, the engine moves in response to the planes movement, that energy is absorbed by mounts, but some still transmitted to the aircraft. IIRC there are some aircraft with reversing gears between the engine and propellor to get closer to a zero angular momentum condition.

[Dave Jackson]

heedm

Thanks for your more detailed explanation.


"Everything rotating body will display "gyroscopic precession". Doesn't matter how fast/slow it turns, doesn't matter it's mass, mass distribution, etc."

"The full beer can with a slowly spinning gyro will do what you want, but it will require a small corrective force to keep the intended tilt in the right direction. That small corrective force corrects the gyroscopes reaction to the impressed moment."

Agreed. In the UniCopter, it should not be a very strong force and therefore when integrated with the other rotors opposite "gyroscopic precession", it should dampen any oscillations in pitch and roll. [I previously erred and called it static stability when it is actually dynamic stability]

[Lu Zuckerman]

To: heedm
A gyroscope can be considered to be a bunch of point masses that are spinning around an axle and are free to "flap". Each point mass is just like a high school physics pendulum. The natural frequency depends on the length and the restoring force, sq. rt. of g/l in high school physics. Since the restoring force for the point mass is the centrifugal force (it's okay to use centrifugal force...just not a real force) then the force depends on the distance from the center, and the speed of rotation. In the end, we find each point mass has a natural frequency that is exactly the same as the rotational speed of the gyroscope. Reading the above paragraph, that means the apparent lag on a gyroscope is exactly 90 degrees. This shows that GP is just a special case of the blade frequency theory that is a much better way of looking at helicopters. QED

Let's see how many people object to this statement.

Early on in discussions about gyroscopic precession I mentioned exactly the same thing (but in my words) regarding a book I read while working at Boeing (V-22) and the gyroscopic rotor you described above was illustrated and explained in the book. When I mentioned it I was crucified but those were the days everyone was preaching aerodynamic precession and flapping to equality. Terms that I was totally unfamiliar with.

[Dave Jackson]

Lu & Heedm,

Help!!! The original theme of this thread has been stolen. :eek:

I'm moving my first 'precession' comments to [Gyroscopic Precession - Revisited]. If you guys want to cut and past in sequence, we can rebuild the conversation over there. :)

Lu. You're next :D :D :D

[Dave Jackson]

Hi CRAN,

However an absolutely rigid rotor is physically unrealizable and therefore some flapping and hence 'some' flap-back will occur (the exact nature of it being dependent on the blade dynamics). The extent of this flapping will depend on how stiff you can make the rotor and still get off the ground."

I agree that absolute rigidity is unrealizable. My thinking is to make the blade as rigid as is feasible, then; a/ mold it with a slight downward curvature, or, b/ give the tip some anhedral, or, c/ give the pitch bearings a slight negative pre-cone.

The intent is to give the disk a zero coning angle when it is hovering at gross weight and then accept the small deviation (+ & - coning) during flight.