Aerodynamics; Is a HS required on a rotorcraft with 'absolutely' rigid rotors?

[Dave_Jackson]

The preamble:

The airplane's flight-controllers; the rudder, the elevator (or stabilator), and the ailerons are attached directly to the fuselage. They therefore give the fuselage a rapid response to input.

The rotorcraft's flight-controllers on a craft with twin main-rotor are the pitch of the blades. These rotor disks are flexibly coupled to the fuselage and this results in a delay between the input and desired result.

It is obvious that a greater rotor rigidity results in a faster response. This implies that a helicopter with 'absolutely' rigid rotors [http://www.unicopter.com/B329.html#ARR (http://www.unicopter.com/B329.html#ARR)] will respond to inputs at a rate that is similar to those of an airplane.

Pitch change of the blades, when at the sides, will impart roll, just as ailerons do. Pitch change of the blades, when at the front and back, will impart pitch, just as a stabilator does.


The assumption:

Assuming that the craft has 'absolutely' rigid rotors (or the closes thing to absolutely rigid), when the blades are at the back they will act as if they are stabilators. Since they act as stabilators there should not be any requirement for this helicopter to have a horizontal stabilizer.

In addition, when these blades are at the front they will act as if they are a canard and this pseudo canard will also contribute to the longitudinal controllability of the craft.


Any thoughts?

[Deemar]

Two things (at least) that you need to consider when looking at controlability:

- The transient response - roughly the time taken between you making an "instantaneous" change in the position of the control and the point at which the aircraft adopts a steady roll/pitch rate in response to this control input.

- The steady state condition - what rate of pitch or roll can be achieved for a given control deflection.

What you are referring to with "flexible" couplings on a non absolutely rigid rotor will only affect the first of these (to a reasonable first approximation). I'm not sure exactly what the transient response time is for a flexible rotor system, but if I recall the first chapter of Stepniewski correctly, it only takes 1-2 rotations. This would imply a transient response time of about 0.2-0.4 seconds for a helicopter with a main rotor rpm of 300. Noticable, but not huge.

A fixed wing aircraft will have a similar situation. When you apply a rolling moment using the ailerons, the aircraft will take a certain amount of time to achieve its steady roll rate. The force on the ailerons has to accelerate the body from a roll rate of zero to the steady roll rate. The angular acceleration will be determined by the torque the ailerons can produce and the moment of inertia about the longitudinal axis. Eventually the roll rate will reach a steady state as a roll rate generates aerodynamic damping through the change in relative angle of attack for the two wings.

So just because the controls are rigidly connected to the aircraft does not mean the response will be instantaneous. Your transient response time will still be affected by the inertia of the aircraft and the size of the control force/torque.

I'd contend that the overall level of control authority on a helicopter is quite high. Witness the relatively small control (cyclic only, the collective and anti-torque can require substantially more) deflections required for most maneuvers compared to the overall travel available. For helicopters this is primarily driven by the fact that large changes in stick position are required for trim at different airspeeds.

But anyway, on to the crux of your question - could you do away with the horizontal stabiliser. I suspect you'll find the answer is no. This has to do with the phenomenon of flap-back, or more specifically how the strength of the flapback effect is affected by a small disturbance in the relative airflow (i.e. what happens when the helicopter pitches forward or back slightly from your trim position).

Now, when a rotor is tilted back slightly more relative to the airflow, the flapback moment will increase - an unstable situation. This situation is exacerbated with increasing speed. At a hover, who cares whether you have a horizontal stabiliser or not, there is no flapback effect as there is pretty much no airspeed. As you move faster and faster however, the helicopter will get harder and harder to fly due to the innate instability due to flapback increasing. This is like trying to fly a fixed wing aircraft when the CG is behind the aftmost limit.

Adding a horizontal stabiliser has a counteracting effect, just like the feathers on an arrow. When the nose of the helicopter pitches down slightly, the downforce on the stabiliser increases, pushing the boom down and acting to pitch thenose of the helicopter back up.

This effect applies regardless of the type of rotor head you are using. The absolutely rigid stuff will however add some nasty cross-coupling of pitching to rolling (although that may not concern you as all you designs seem to have two main rotors).

Daniel

[Graviman]

Dave,

Since i have yet to understand what interleavers specifically offer i generalise my response to cover all counterrotating helicopter configs. We are designing for high speed then (retreating stall avoidance).

Firstly you must define the offset hinge you mean by "Absolutely Rigid Rotor" so that i can give a meaningful answer. Comanche achieved 15% hinge offset using advanced carbon composite construction so has frequency 1.12 Nr. Guestimate Nr 400 RPM/60 = 6.66 rev/sec gives a blade natural frequency of 3.43Hz. Assuming you have a magic formula which doubles the blade stiffness for the same mass, then this gives you a frequency ratio of 4.85Hz (F=SQRT(k/m)/2PI). Put your "magic" blade back into Comanche and you have dynamic frequency of 8.24Hz or 1.23 Nr. So your "Absolutely Rigid Rotor" thus has a hinge offset of 26%. With a reasonable blade damping factor of 0.5 Cc, it has a pitch lead angle of 66.8 degrees. So still nearer 90 degrees than 0 degrees - and i'll bet Eagle worked hard to get that 15%.

As Deemar says, since you are designing a counterrotating machine you will not have the concerns of cyclic cross coupling to deal with since the crossed components will cancel. However a pitch lead of 66.8' will still result in rotor flapback, which will be the main source of lateral and longitudinal dihedral. Thus the config of the aircraft is almost an incedental point, particularly in hover. If anything this rotor system is tending towards neutral static stability, perhaps requiring that the SAS system extend its control from the damping of dynamic overshoots of any practical statically stable system. Combine this and Deemars point about longitudinal instability in forward flight, and i sure as **** wouldn't strap in!

Mart

[Dave_Jackson]

The following relates to a theoretical, albeit impossible, 'absolutely' rigid rotor. Subsequent adjustments would then be required to account for the discrepancy between an 'absolute' and an actual extremely rigid rotor.


Daniel,

Re EDIT. Sorry Daniel :{ . The uniqueness of an 'absolutely' rigid rotor results in this subject being somewhat complex; for me at least. Initially, I rushed to answer you and Mart before reviewing work that had been done a number of years ago. The following response to you has been significantly revised.

Thanks for the thought provoking points that you bring up.

Without going into the transient response and the steady state condition, I believe that there are four distinct cyclic control situations.

1/ Teetering rotor: It is said that this rotorhub has the slowest response rate.

2/ Offset flapping hinge rotor: It is said that this rotor has a faster response rate visa vie the teetering rotor, due to the additional moments caused by the centrifugal effect of the blades.

3/ Virtual offset flapping hinge rotor: As the offset becomes exceptionally large its effective location will be beyond the cutout and located in the span of the actual blade. This distant location will lengthen the moment arms, reduce the mass that is contributing to the centrifugal effect and generate multiple lift vectors that are normal to a blade that is curved in the out-of-plane direction.

4/ Absolutely rigid rotor: This will have a single lift vector that is normal to the precone angle of the blades but offset from the mast by an azimuth and radius dictated by the cyclic control.


As to the crux of the question, I submit the following.

This is my understanding of flapback (http://www.unicopter.com/B267.html#Flapback). I do not believe that a helicopter with 'absolutely' rigid rotors is subjected to flapback, for the following reasons. The 'absolutely' rigid rotor will have a phase angle very close to 0-deg. This means that to lift the nose of the craft the greatest blade pitch will be when the blade is pointing forward at 180-deg azimuth, not when it is a 90-deg azimuth on the advancing side.

It is hoped that the transverse flow effect will provide the required amount of speed stability. If it does not then the the propeller can be considered. Its thrust value will be proportional to the craft's airspeed, therefore I think that by locating its thrust vector slightly above or below the center of total drag the speed stability may be satisfied.

If you disagree with the above, please say so.


Mart,

Since i have yet to understand what interleavers specifically offer.... All configurations offer some advantage(s). If you wish to further discuss effective disk loading please say so by continuing the previous thread.

Firstly you must define the offset hinge you mean by "Absolutely Rigid Rotor" ..... Comanche achieved 15% hinge offset using advanced carbon composite construction .... Assuming you have a magic formula which doubles the blade stiffness.... i'll bet Eagle worked hard to get that 15%. The Sikorsky S-69 ABC had a flapping frequency ratio of ≈ 1.4 You will find that this should give an equivalent flapping hinge offset of ≈ 50%. In addition, the S-69 had titanium spars, because back then they were not willing to risk using carbon composite. Just think what they might be able to do today.

Deemars point about negative longitudinal stability in forward flight, and i sure as **** wouldn't strap in! I believe that Daniel is talking about positive stability; excessive positive stability.

So your design does not overturn 60+ years of helicopter dynamics. You still need to consider ...... And IMHO, you still need to consider prefixing some of your factual statements with 'IMHO', or 'I assume', or 'Possibly'; just in case one or more ain't factual.

Dave

[Graviman]

Dave,

Effective hinge offset will give you exactly the same dynamics as an actual offset hinge. The calculation just assumes that the blade flapping frequency is higher than the rotor frequency, with effective hinge offset a convenient way for engineers to discuss the dynamics.

As you reaslise, the whole thing comes to lead angle anyway. So a rotor with anything near 90' will have flapback. If an absolutely rigid rotor were achievable the result would be a helicopter with no static stability, so pilot would have increased workload keeping attitude correct.

Can you expand on the transverse flow effect stabilising helicopter? Don't forget heli must be stable with no power.


All configurations offer some advantage(s). If you wish to further discuss effective disk loading please say so by continuing the previous thread.


Before we start that discussion again, i refer to the tandem config. Tandem offers the same effective disk loading but without the width requirements, and IMHO offers better potential for high speed aerodynamics with practically rigid rotors.


The Sikorsky S-69 ABC had a flapping frequency ratio of ? 1.4 You will find that this should give an equivalent flapping hinge offset of ? 50%. In addition, the S-69 had titanium spars, because back then they were not willing to risk using carbon composite. Just think what they might be able to do today.


This is incredible if it is true - are you sure of these facts? I calculate 39% effective offset and approx 55.6 degrees for lead (assume 0.5 Cc, depending on Lock Number), so we are still not near your 0 degree ideal.


I believe that Daniel is talking about positive stability; excessive positive stability.


OK, but the machine is longitudinally unstable so will require constant pilot intervention to damp down speed instability.


And IMHO, you still need to consider prefixing some of your factual statements with 'IMHO', or 'I assume', or 'Possibly'; just in case one or more ain't factual.


I thought it was a rumour network. ;) Probably a good thing with some of your dodgy calcs! :ok:

Mart

[Dave_Jackson]

Can you expand on the transverse flow effect stabilising helicopter?See; Potential Solutions (http://www.unicopter.com/UniCopter_Stability.html)


If an absolutely rigid rotor were achievable the result would be a helicopter with no static stability.Are you stating that the 4-deg precone will not contribute to static stability?


This is incredible if it is true - are you sure of these facts?I am never sure of anything.
Ask Stepniewski ~ Rotary-Wing Aerodynamics, page 39 and figure 1.11.


Probably a good thing with some of your dodgy calcs! Please elaborate.


Dave J.

[IFMU]

1/ Teetering rotor: It is said that this rotorhub has the slowest response rate.
Dave
I would have thought the Lockheed Cheyenne had the slowest response rate. The pilot flies the gyro bar, which flies the rotor. So you have a pure 90 degrees of phase lag for the gyro bar, plus whatever the inherent phase angle of the rotor. I'm not sure that I have the whole concept of their control scheme down, but I had oft heard that the extra phase delay was one of the prices paid for that design.
-- IFMU

[Graviman]

Dave,


Are you stating that the 4-deg precone will not contribute to static stability?


OK, this would produce a small amount of static stability if an absolutely rigid rotor were achievable. Since the calcs have demonstrated that the best lead angle is ~60 degrees, it is academic anyway. Nick has commented that a rigid rotor, although having a snappier response, "feels" less stable. Unless i find a way of magically gaining an equivalent lifetimes experience of flying helos, i'm inclined to believe him.


I am never sure of anything.
Ask Stepniewski ~ Rotary-Wing Aerodynamics, page 39 and figure 1.11.


Fig 1.11 - "Effect of flapping hinge on blade flapping frequency", is better calculated using eqn 1.30. This still gives 39% hinge offset with 1.4 freq ratio. By personal preference, i find Prouty clearer to understand.

What i meant was are you sure about the freq ratio of 1.4 in S-69? In truth the 400 rpm guestimate is probably a shade high, bearing in mind the 2-speed strategy used. If the 1.4 ratio was at say 200 rpm = 3.33Hz, this gives a blade natural frequency of 3.26Hz. At the 400RPM = 6.66Hz guestimate this then produces a system frequency of 7.42Hz, or a ratio of 1.11. So guestimated effective hinge offset would be 13.7%. Since i would expect the Comanche carbon fiber blade 1st bending natural frequency to be slightly higher, this seems about right to me.


Please elaborate.


IMHO, you need to develope a sense of humour when discussing your ideas. Personally, i enjoy debating ideas and just accept that if i am wrong i have still learnt something. All engineering is an expression of someones opinion - it is only right until a better solution comes along. You have chosen to champion the symmetrical rotorcraft, and that is fine, but don't get worked up when the numbers don't always support the concept...

Mart

[Graviman]

I would have thought the Lockheed Cheyenne had the slowest response rate. The pilot flies the gyro bar, which flies the rotor. So you have a pure 90 degrees of phase lag for the gyro bar, plus whatever the inherent phase angle of the rotor. I'm not sure that I have the whole concept of their control scheme down, but I had oft heard that the extra phase delay was one of the prices paid for that design.
-- IFMU

IFMU, teetering response delay is due to the heli having to "swing" into a position for any cyclic input. The rotor system is there is a turn or two, depending on whether or not you incorperate delta3. The Lockheed system may have taken several turns for a snap input, but the overall response was much more direct (ie low pass filter, with critical damping).

The best way to understand this system is that it was a mechanical interpretation of modern gyro stability augmentation systems. The pilot flew the gyro, and the gyro flew the helicopter. The dodgy part is that the pitch link geometry allowed feedback so that the gyro compensated for flapback - i have only really understood this recently. With modern software able to predict dynamic systems to very high accuracy, i still feel this system has the potential for a cost effective SAS. Being mechanical it would not suffer from the neglect that might trip up an electrical system.

Mart

[IFMU]

The pilot flew the gyro, and the gyro flew the helicopter.
This is where I would think the delay comes in. You fly the gyro. Your inputs go in 90 degrees early. The reaction happens 90 degrees later, with a delay equal to the time it takes for 1/4 of a trip around the circle. Then, assuming the lead angle of the rotor is 60 degrees (or whatever, 40, 70, ?) there is yet another delay as the rotor adds in its delay. Unless of course you have an absolutely rigid rotor, then you are only saddled with the 90 degree phase lag of the gyro bar.

Being mechanical it would not suffer from the neglect that might trip up an electrical system.
Mart
Which is exactly why I always had to fuss with my neglected carburetors, and have never had to touch my electronic fuel injection system. Whoops, that doesn't fit!

-- IFMU

[Dave_Jackson]

IMHO, you need to develope a sense of humour


Graviman,

I have absolutely no sense of humor when it comes to those who disseminate erroneous information under the guise of being factual; and then, attempt to sidestep 'their facts'.

These are understood characteristics in politics. They are dangerous characteristics in engineering.


Perhaps you would like to guesstimate the offset on this rotor?

http://www.unicopter.com/Temporary/Hiller.jpg

Hiller X-2-235 (rigid, 2-blades/rotor) (http://avia.russian.ee/helicopters_eng/hiller_x-2-235.php)

[Graviman]

I have absolutely no sense of humor when it comes to those who disseminate erroneous information under the guise of being factual; and then, attempt to sidestep 'their facts'.


Uh huh. :hmm:


Perhaps you would like to guesstimate the offset on this rotor?


Sure, my guestimate would be less than 15%.

We are talking about the frequency of the 1st bending mode of the blade, this depends on mass as well as stiffness:

Freq = SQRT(Stiffness/Mass) / 2PI

The Hiller X-2-235 demonstrates strong blades, so one can make the assumption that they are stiff. The tip is likely already heavy, so the addition of say 40kg at each tip would not cause large deflection (notice they are carefully distributing weight across both rotors). My conclusion is the frequency will still not be significantly higher than Nr.

Composite glider wings are very strong, but part of the DI was to shake them to look for structural discontinuities. From memory resonant frequency would have been about 2Hz. This is why these blades do not look such a high offset to me.

Further realisation (23/01/07):

Having two blades per rotor then, since there must be a crossover point for the blades, any pitch/roll torque would produce excessive vibration. This lead me to belive rotor may have been teetering with mechanical linkage between to two rotors. Rotor was later redesigned to have 3 blades, but my guestimate for offset stands for reasons given later.

Mart

[Graviman]

This is where I would think the delay comes in. You fly the gyro. Your inputs go in 90 degrees early. The reaction happens 90 degrees later, with a delay equal to the time it takes for 1/4 of a trip around the circle. Then, assuming the lead angle of the rotor is 60 degrees (or whatever, 40, 70, ?) there is yet another delay as the rotor adds in its delay. Unless of course you have an absolutely rigid rotor, then you are only saddled with the 90 degree phase lag of the gyro bar.


Agreed, but then the heli responds more-or-less instantly to the pitch and roll torque at the hub. I've never flown rigid, but every one i have spoken to says the response is faster. My understanding is that the Lockheed system worked well on the 475 and 186.


Which is exactly why I always had to fuss with my neglected carburetors, and have never had to touch my electronic fuel injection system. Whoops, that doesn't fit!


Good point well made. You'll notice i always champion high boost turbo diesel engines. The one i drive has mechanical injection. This one shows the performance potential (24 hours at on/off high power):
http://en.wikipedia.org/wiki/Audi_R10

What i meant is that criticism is often raised for single channel electronic systems because they can fail without warning. Sure reliability is getting very good, and three channel is the way to go. If a simple mechanical system could be developed which offered the same advantage as SAS, but never needed to be dissengaged then that can't be a bad thing.

I realise the Lockheed system had it's day, and this is the age of electronics. Engineering software has also moved on too, so i believe that this system could be developed to be very cheap and reliable. I accept that this is not a popular view, so i don't spend much time defending it.

Mart

[IFMU]

Agreed, but then the heli responds more-or-less instantly to the pitch and roll torque at the hub. I've never flown rigid, but every one i have spoken to says the response is faster. My understanding is that the Lockheed system worked well on the 475 and 186.Mart
If the rotor is absolutely rigid, and has no lag, but is controlled by a gyro bar that has a 90 degree phase lag, then the torque doesn't get there instantaneously. Instead it takes that 1/4 turn of the gyro bar before the inputs get to the rotor.
-- IFMU

[Dave_Jackson]

Graviman,What i meant was are you sure about the freq ratio of 1.4 in S-69? As mentioned earlier "I am never sure of anything."

As mentioned earlier, Stepniewski said on page 39 that "because of the truly rigid blades (v/n [the flapping hinge frequency] is +/- 1.4".

As not previously mentioned, Sikorsky said in 'Advancing Blade Concept (ABC) Development' that "Blade first flatwise and edgewise mode natural frequencies are both at approximately 1.4/rev".

Do you now believe that a 39% and higher hinge offset was feasible over 30 years ago. Do you now think that with today's pultruded carbon composite construction it might be remotely possible to get 1 or 2% further out on the blade????

If not then consider the following;

You said;Since the calcs have demonstrated that the best lead angle is ~60 degrees, it is academic anyway.You might be interested to know that the ABC's swashplate had a pilot adjustable phase angle from 0º to 70º.

_____________________


I ... just accept that if i am wrong i have still learnt something. I don't like learning someone whos attitude is that Newton wasn't the last person to know everything about everything!!!

[Graviman]

If the rotor is absolutely rigid, and has no lag, but is controlled by a gyro bar that has a 90 degree phase lag, then the torque doesn't get there instantaneously. Instead it takes that 1/4 turn of the gyro bar before the inputs get to the rotor.
-- IFMU

Agreed, IFMU. Lets say the system takes a full rotation to respond, to play the numbers safe. At say 300rpm we are talking 0.2 seconds, so the machine will not respond to pilot inputs above 5Hz. Pilot would likely need to throw a fit to generate 5Hz inputs.

Mart

[Graviman]

Dave,

Good grief... :rolleyes:


As mentioned earlier, Stepniewski said on page 39 that "because of the truly rigid blades (v/n [the flapping hinge frequency] is +/- 1.4".

As not previously mentioned, Sikorsky said in 'Advancing Blade Concept (ABC) Development' that "Blade first flatwise and edgewise mode natural frequencies are both at approximately 1.4/rev".


At low RPM agreed. Like i showed in my guesti-calc, the machine would have 39% offset in low gear and about 14% offset in high gear. Since i imagine high gear was selected for hover then hover lead angle would be ~78 degrees. Since i imagine low gear was selected for cruise then cruise lead angle ~56 degrees.


Do you now believe that a 39% and higher hinge offset was feasible over 30 years ago. Do you now think that with today's pultruded carbon composite construction it might be remotely possible to get 1 or 2% further out on the blade????


With the rrpms i mention yes.

Do you honestly believe the helicopter industry is involved in some kind of conspiracy to hide advanced technology? Maybe that sectret X2 photo was actually Elvis strapping back in to his UFO, for his return trip to Vega...


You might be interested to know that the ABC's swashplate had a pilot
adjustable phase angle from 0º to 70º.


Then why not just ask the pilot what settings he used, instead of stirring things up? I've found him to be extremely helpful on technical matters related to rotorcraft.


I don't like learning someone whos attitude is that Newton wasn't the last person to know everything about everything!!!

Maxwell, Einstein, and Schrodinger have had a few more things to say since then. I've enjoyed studying them all.

Mart

[IFMU]

Agreed, IFMU. Lets say the system takes a full rotation to respond, to play the numbers safe. At say 300rpm we are talking 0.2 seconds, so the machine will not respond to pilot inputs above 5Hz. Pilot would likely need to throw a fit to generate 5Hz inputs.
Mart
Mart,

I would think the rotor would respond to inputs above 5hz, but with the 0.2 second (using your example) delay between each input and output, regardless of its frequency content. Of course the amplitude of response would be a function of the rotor's dynamic characteristics and the frequency content of the input.

-- IFMU

[Dave_Jackson]

Graviman. Simply, quit trying to squirm out from under you erroneous 'statements of fact'. You are probably not fooling anyone.

You say that you are here to learn.
If true, then why didn't you learn from this;
In a PPRuNe message two weeks ago I made an incorrect statement. After being corrected by you, I apologized for the error.

Your inability to admit errors has abused my time, and may cost an employer much more.

.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Detachment line for the moderator should the following statement be perceived as political.


Consider the cost to the American people resulting from a certain individual's unwillingness to admit his errors.

[Graviman]

Dave,

Since i have absolutely no idea what you are talking about i'm not apologising for anything.

I have stated that the "absolutely rigid rotor" is impractical. I have backed up my statement with calculations. When faced with further examples, apparently contrary to my statement, i have backed up my facts with further calculations.

I read this thread the way i read our exchange about disk loading. You are looking for an absolutely rigid rotor to back up your conviction about laterally symmetrical rotorcraft. You know that if it can be proven that flapback will stabilise a coaxial helicopter, then you have lost some ground. Since i have demonstrated that indeed a coaxial can be statically stable, i am now the target of your frustration.

If you had any common sense you would have realised that the reduction in flapback at the low RRPM ideal for high speed flight maybe justifies laterally offset rotors for static stability. Instead of launching into your own brand of politics, you would have argued the case on engineering principles. I would have countered with fly-by-wire being more cost effective than additional structure and separate gearboxes. Frankly, i'm too p*ssed off now to continue the debate.

Mart

[slowrotor]

On the question of helicopter stability-
Helicopters have speed stability, the rotor flaps back when the speed is increased and this results in a minor stabilty of not much value (in my opinion).
Other than speed stabilty, I can't think of any other useable stability in a normal helicopter rotor.
It's like a unicycle, the operator provides the stability.

[Graviman]

I would think the rotor would respond to inputs above 5hz, but with the 0.2 second (using your example) delay between each input and output, regardless of its frequency content. Of course the amplitude of response would be a function of the rotor's dynamic characteristics and the frequency content of the input.


Agreed IFMU. As long as the system response is faster than the pilot the phase lag never gets near 180 degrees. This means that the pilot response is always in phase with the rotorcraft so pilot induced oscillation does not develope.

In practice, i don't actually believe the Lockheed system would have been any slower in response than a conventional rigid. The gyro basically remained at the same attitude as the helicopter, with any error being the "signal" which adjusted the main rotor to make helicopter follow gyro. Thus pilot would have had very fast control over gyro. This would need to be proved out in modern dynamic simulation software like ADAMS or Simpak - not sure what is prefered in the heli industry.


On the question of helicopter stability-
Helicopters have speed stability, the rotor flaps back when the speed is increased and this results in a minor stabilty of not much value (in my opinion).
Other than speed stabilty, I can't think of any other useable stability in a normal helicopter rotor.
It's like a unicycle, the operator provides the stability


Slowrotor, the analogy i like to give is this:
Imagine yourself carrying a cup of coffee to your desk. You know that as long as you hold it right way up the coffee stays where it belongs - this is static stability. Now imagine that the cup is full to the brim and only carefull movements will avoid it sloshing over the rim - this is dynamic stability. A good coffee cup pilot can predict the movement so performs fast direction changes without spillage. The average coffee cup pilot (that would be me) figures that as long as he keeps his inputs below the sloshing frequency he can avoid spillage.

Helis, in principle, are no different. As long as there is a pilot to hold the cyclic in position the heli is statically stable. If the pilot wants to get a fast response he has to know the machine dynamics to dynamically stabilise the machine. So a heli can be said to be statically stable, but dynamically unstable.

Mart

[slowrotor]

Mart,
I am not buying.
Every helicopter I have flown that has cyclic control had "neutral" stability on the main rotor. Neutral stabilty is nearly the same as no stablity.

As long as there is a pilot to hold the cyclic in position the heli is statically stable. I would say that is neutral stability if a pilot is required to hold position.

Stability in my opinion, is something that restores the rotor to original setting after a gust. I have not seen this.

Yes, I read about static and dynamic stability in the books. It's just engineering fluff. Helicopters have little or no stability.

Just my opinion,as always
slowrotor

[Graviman]

Slowrotor,

No problem, it is probably just how we are defining the stability fluff. Agreed that the actual cyclic control that you hold has no stability, since i have often wondered why not fit a very weak trimmable centreing spring.

I think the difficulty with gust loading is that in the hover you are trying to stay above a point. The gust is trying to move the heli with the air mass, since this is how stability is defined in a fixed wing. The heli could be considered stable if the cyclic was frictioned on and the heli allowed to wander in whatever direction it wanted. My point is that it always wants to hover at the same attitude.

From the pilots perspective this makes the heli seem statically at least neutrally stable since the pilot has to continually input new cyclic positions to stay in the box. This is also just my opinion, like all engineering, but it seems to make sense.

Mart

[Dave_Jackson]

Graviman,

You went back to post #12, two days later, and did some typing. I am not familiar with this design .... The rotors must therefore be teetering .... Thus the effective hinge offset of this rotor is likely 0% - which is less than 15%.

If you had gone back to post #11 and done some reading there would have been no reason for the typing.

:ugh:

[Graviman]

Dave,

Rather than try to bludgeon me with a 60 year old photograph why not just try to determine the effective offset? As i say my guestimate is still less than 15%, because although the blades are very stiff materials of that era would have been far heavier than carbon fibre. If Comanche achieved 15% in hover using carbon fibre spars, and assuming hover RPM is not dissimilar, i really just do not see how the 1st bending frequency of these blades would be any higher.

It may be that the compromise required for this design was a much larger diam root, which would be adverse to aerodynamics. Material stiffness is determined by EI (Young's modulus x 2nd momemt of area). Since we are dealing with blade wave mechanics you are better sticking numbers into these formulae:

Shear wave velocity = (Youngs_Modulus/((1-Bulk_Modulus)*Density))^1/2

Bending wave velocity = (2*PI*Frequency*Thickness)^1/2 * (Youngs_Modulus/(12*Density))^1/4

These will calculate the range extremes for the static 1/4 wave natural frequency.

I do not have the figures to hand, but steel or aluminium will not beat carbon fibre. Thus for a similar design carbon fibre will produce a higher natural frequency

From the linked site:


The UH-1X, Hiller's first military contract, clearly ran counter to normal aircraft engineering, but then the team building it had experience only in designing ships, bridges, and similar beefy structures. The lack of even a single aeronautical engineer on Hiller's payroll to introduce that field's antipathy to heavy structures was, ironically, an advantage in the uncharted terrain being explored.


Mart

[Dave_Jackson]

slowrotor,

In addition to the Speed Stability, one or both of the following ideas looks like they might provide Angle of Attack Stability (http://www.unicopter.com/B329.html#Angle_Attack_Stability) on a helicopter equipped with 'absolutely' rigid rotors and without a horizontal stabilizer.


Forward center of gravity:

If the lift moments are equal around the effective rotor disk then the center of lift will be at the center of the effective disk. If the center of gravity of the craft is ahead of the center of lift then an updraft should result in a stabilizing action by wanting to pitch the nose down. This will have been achieved without a horizontal stabilizer.


Decalage (http://www.unicopter.com/B329.html#Decalage) might be implemented.

The method will be to locate the thrust line of the propulsor above the center of total drag. This will want to pitch the nose of the craft down during cruise. To offset this negative pitch; the angle of attack in the aft quadrant of the disk will be less than the average angle of attack, and the angle of attack in the forward quadrant of the disk will be greater than the average angle of attack.

For example: Assume that the angle of attack of the blades are 2º when at the reared and are 4º when at the front. The effective rotor disk is now subjected to an updraft, which increases overall angle of attack by 2º. The lift at the rear will be increased by 100%, whereas the lift at the front will be increased by only 50%. This will cause the craft to pitch nose down thereby giving Angle of Attack stability; without a horizontal stabilizer.


Dave

[slowrotor]

Dave,
Some helicopters have horizontal tail, some do not.
The horizontal surface on a helicopter is to point the fuselage into the wind for less drag.

The method will be to locate the thrust line of the propulsor above the center of total drag
This seems contrary to modern gyroplane (gyrocopter) design. The new designs have "centerline thrust" to prevent loss of aircraft by forward dive "bunting", (I think is the word).
Have you read about gyroplane centerline thrust?

[Dave_Jackson]

slowrotor,

Thanks for mentioning the gyrocopters and centerline thrust.

Dave

[Graviman]

Dave,

For the purpose of continued discussion, and to overcome rotorcraft withdrawal symptions, let us assume the following:
1. The rotor Nr is optimised for hover.
2. The rotor system weight is not a concern.
3. Blade aerodynamics are not a concern.
4. The blade natural frequency is equal to the rotor Nr frequency.
Points 1,2 & 3 allow low Nr, oversize roots (or pylons ;) ), and compromised aerofoils to allow point 4.

By my calculations this gives a rotating blade system frequency of 1.414 Nr, so that the effective hinge offset is 40%. Since the Lock number is not known, let us assume materials and construction allow a damping factor of 0.354 Cc. This gives a swashplate lead angle of 45 degrees. This is not quite the absolutely rigid rotor you are proposing, but it does allow me to consider your arguement from the point of view of a machine with reduced flapback stability.

For the purposes of discussion i will ignore the flapback effect (90º lead component), so as to concentrate on the other stability effects (0º lead component). Forgive me but this will take some mental aerobatics on my part. :}


For example: Assume that the angle of attack of the blades are 2º when at the reared and are 4º when at the front. The effective rotor disk is now subjected to an updraft, which increases overall angle of attack by 2º. The lift at the rear will be increased by 100%, whereas the lift at the front will be increased by only 50%. This will cause the craft to pitch nose down thereby giving Angle of Attack stability; without a horizontal stabilizer.


Ok i can see this. You are basically saying that by pushing the CofG forward the rotor has its own longitudinal dihedral. My only concern is the limitations of this effect, perhaps still requiring the stabilising effect of a horizontal stabiliser. In theory gliders would fly if the CofG was at the main wings, but definately pop straight out of a spin if CogG is more forwards. An odd side effect of this arrangement was tail stall "bobbing" if stick was pulled too far back in a launch (leading edge saw high AOA).

Mart

[line marker]

I am interested in receiving gyrocopter plans and design models to build a prototype for myself, and to incorporate the stability ideas you have discussed in this forum.
please respond soon

[Dave_Jackson]

line marker,

Due to the very high rigidity of the rotors, the idea on this thread is about as far as one can get from gyrocopters, in the domain of rotorcraft.

Can you elaborate a little on your desires?

Dave

[Graviman]

Dave,

I have ammended post #26 to give you a means to estimate a rotor blade natural frequency (ie while not rotating). For simplicity, let us say that the target to beat is >5Hz. Use the bending wave to guestimate 1/4 wave freq (iterate several times with freq).

With the best will in the world, i honestly just cannot believe that that Hiller blade would resonate in first bending above 5Hz. Despite a very impressive PR photo, i really just don't see this as an "absolutely rigid rotor". Post #12 edited to explain why.

Mart

[BGRing]

So a heli can be said to be statically stable, but dynamically unstable.
True.
the fluff is just saying that Dynamicaly unstable is where , if the instability was left alone. it would get worse. IE a trimed up for level flight encounters a disturbance heli climbing diveing clinbing diveing would not stay the same. it would get worse with each. same for a hover.

[Dave_Jackson]

Mart,

This might be of interest.

From Rigid Coaxial (ABC) Rotor System ~ Stability and Control Characteristics. "The blades are extremely rigid with the first bending mode frequencies of 1.4 P flatwise and edgewise and 11.3 P in torsion. The high rigidity allows close rotor spacing (7 percent diameter) with adequate margins on blade tip clearance even in extreme maneuvers".

Another report gives the following;
Rotor diameter: 36 feet.
Rotor separation: 30 inches.
Design rotor speed: 650 ft/sec (helicopter), 450 ft/sec aux. propulsion)



Dave

[BGRing]

Pitch change of the blades, when at the sides, will impart roll, just as ailerons do. Pitch change of the blades, when at the front and back, will impart pitch, just as a stabilator does.
Even a ridgid rotor disk will react to controles just as a Teeter or Semi articulated Rotor disk, IE not Similar to Stabilators, (Remember Attitude and Induced flow is near similar all the way around, keep looking at the Disk as the thing you hang from. not a wing and canards etc) Here (http://ms.align.com.tw/bb2/mpeg/070215A.wmv) is a rigid rotor setup. (Though its Cyclic controle inputs are aided by a Bell-Hiller Fly padle system) Flame me if you like. I probably deserve it.

The assumption:
I understand this is just Pie in the Sky. so ...
Assuming that the craft has 'absolutely' rigid rotors (or the closes thing to absolutely rigid), when the blades are at the back they will act as if they are stabilators. Since they act as stabilators there should not be any requirement for this helicopter to have a horizontal stabilizer.
you will still need to keep the tail down if your frontal drag area of heli fuse is greater than rear. Remember fuse is kinda climbing now (When in High speed forward flight) with a rigid rotor system.

In addition, when these blades are at the front they will act as if they are a canard and this pseudo canard will also contribute to the longitudinal controllability of the craft. same as my first comment
(Remember Attitude and Induced flow is near similar all the way around, keep looking at the Disk as the thing you hang from. not a wing and canards etc)

[Dave_Jackson]

BGRing,

Thanks for mentioning your concerns.

This hypothetical rotorcraft has an 'absolutely' rigid rotors (http://www.unicopter.com/B329.html#ARR). Therefore, it will be difficult to compare it to a conventional helicopter, because, to my knowledge, no one has ever built or flown such a craft.

The following may be where a misunderstanding has come about. You say keep looking at the Disk as the thing you hang from. On this craft there is no articulation between the fuselage and the rotor disk.


you will still need to keep the tail down if your frontal drag area of heli fuse is greater than rear.The craft has a 4 or 5-degree precone and the belief (hope) is that it will act somewhat like a dinner plate in that the front of the disk wants to rise and the rear of the disk want to lower.

Should this appear flawed, please say so.

Dave

[BGRing]

The craft has a 4 or 5-degree precone and the belief (hope) is that it will act somewhat like a dinner plate in that the front of the disk wants to rise and the rear of the disk want to lower.

Should this appear flawed, please say so.


Ok this is probably where i learn some thing new. But To ME it Appears Flawed. (Leave me to think more on it)

For now, Here is what i was thinking;)

I understand the Pre cone but .. Just because it is Totaly Rigid shouldn't change the way a disk tilts. (All be it you are now in a Craft that is some 4-5 deg or more extra forward attitude in forward flight. Due to the rigid Structure between Blade,Grip,Hub,Mast<Here i may have misled you when i said hang. I did not mean Swing>)

So to acheive forward flight the disk must tilt forward (WHOLE CRAFT) and so if the Stabilator Canard theory were true. then you wouldn't get a Disk (Whol Fuse) tilt. or it would only tilt till a Certain Speed. ???????

OK I Got a Head Ache now. I think i am seeing your Point.... (Even about the No need for a HS , Due to Heli wanting to Level against Disk Wanting to Tilt. Though, Fuse Drag Front and Aft of mast? should be a Factor in the Desin)

:O

Hang On . I keep thinking about the Induced flow Diagram and the Flow Through Diagram for forward Flight. And weither the Fuse is Swinging or Rigididly held afft. the Disk must still be Flying the same.. (:ugh: Hmm You Got me Thinking)

Give me a week or Two.. then...

PS did you see the Vidio link i added in my last post. These things are RIGID.

[NickLappos]

Since there is no such thing as an "absolutely rigid rotor" then anything is possible once you make it!

[Graviman]

Dave, at first glance those figures are compelling so let me do some quick calcs. The 1.4P bending gives 39% effective hinge offset as discussed. A tip speed of 650 ft/sec at a diam of 36 feet gives 36 rad/sec; 5.75Hz or 345rpm. Now this compares to a "similar" size machine the Agusta 109 (also 36' diam MR) with 6.41 Hz or 385 rpm as slightly slow. Since retreating blade stall is not an issue, then in hover this Nr comparison make sense.

So why my doubt? The quoted reference does not make it clear that the 1.4P is at 345 rpm. Remember S-69/XH-59 had a gearbox to reduce Nr for high speed flight. I do not know the ratio so let me assume half, ie 2.87Hz or 172rpm. Now if 1.4P applies at 172 rpm, this gives a system frequency of 4.02 Hz.
Now since 2PI Fsystem = SQRT(( Kblade + Krotor) / m) - simple harmonic motion
so that Fsystem^2 = Fblade^2 + Frotor^2
then this gives blade natural frequency of
Fblade = SQRT( (4.02 Hz )^2 - (2.87 Hz)^2 ) = 2.81 Hz - seems OK to me.
Now putting this blade natural freq back into the system rotating at quoted 345 rpm gives
Fsystem = SQRT( (2.81 Hz )^2 + (5.75 Hz)^2 ) = 6.40 Hz or 1.11P
Putting this number back into the Prouty formula gives an effective hinge offset of 13.8%. Since i vaguely recall Nick mentioning the effective hinge offset at hover was ~12% then my figure seems to stand.

Now i may have made a mistake, but by laying the work out carefully you can check my logic. It demonstrates that even the ABC did not have an "absolutely rigid rotor".

Mart

[Dave_Jackson]

BGRing,PS did you see the Vidio link i added in my last post. These things are RIGID. Yes. :ok: Are you the pilot?

The web page Trim, Stability & Control ~ Musings on Trim (http://www.unicopter.com/UniCopter_TrimMusing.html) is related to this discussion.
__________________

Nick,Since there is no such thing as an "absolutely rigid rotor" True, but there is such a thing as an 'Absolutely' Rigid Rotor (http://www.unicopter.com/B329.html#ARR).

As you say, a HS will probably be required, even on a craft with very, very rigid rotors.


This thread was started as a simplistic attempt to determine IF a HS would be necessary IF rotors could be made with absolute rigid.

Then, the relationship between the amount of rotor rigidity and the size of a HS could be evaluated for a real application.


Dave

[Dave_Jackson]

Mart,

Interesting. I would have thought that the hinge point would have been further out.

The values may be for the slow RRPM used during cruise. This is because the ABC causes the two disks to move toward each other, on one side, during forward flight. In addition, the maneuvers may be more severe during forward flight. Nick will know the answer to this.



They considered using carbon spars in the XH-59A but then rejected them because it was too new a technology. In a table they compared the various spar materials under consideration. The carbon was shown as giving a better strength to weight ratio. As I recall, in an article on the new X2 there is mention of reducing the gap between rotors. This might imply that the use of carbon will be to increase rigidity and not so much to do with weight reduction.

Just random thinking.


Dave

[Graviman]

Dave, that does make a great deal of sense to me. The biggest problem would be that at high speed any variation in vertical airspeed, from thermals mostly, could result is high buffet loads. ABC may use blade bend/twist coupling to reduce these loads, similar to D3 on S76 for example, but too much coning would be a problem. I seem to remember that boron fibres give composites the highest stiffness to weight. Carbon fibres on X2 can't be far behind though.

Why don't we continue the discussion based on the assumptions of post #30? This will also help me gain greater insight into how hingeless dynamics differ from teetering dynamics - briefly explained in post #25 of this thread (http://www.pprune.org/forums/showthread.php?t=264231&page=2). At an initial guess, based on Nicks comments, i would say the main difference must be a higher acceleration level to the pitch/roll rate control of the cyclic. This would explain the "snappier response" from the direct hub moments.

Some day, i may even have a go at hingeless. Until then i have to defer to profs. Lappos, Robinson and Prouty. ;)


BGRing, i've not been able to access your server to see the video yet so can't comment.

Mart

[BGRing]

Dave. No I am not the Pilot. I Aspire to Be that good One day.

The Pilot is one of the Worlds Best Extream 3D Flyers, he and his Brother are near as good as Eachother.

That heli is Elec. And is the boots. It is near par with a Nitro one.
they also have Turbine ones. Scale and all sorts. In the last 3-4 years. These things have Developed Exponantialy. I had one in 88 and have only just got one again just recently. Elec.

Thanks for the link. This should help me , I Hope : ) well at least stop my :ugh: .

Gravinman;
http://align.com.tw/html/en/c_rindexe.htm
The particular Vidio was;
"Las Vegas 2007 FUN FLY
(PILOT:Danny Szabo)"

PS, not my Server : ) its a Taiwan one. This is where the Popular "T-Rex" brand Heli are made.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Actualy. the Heli in the vidio is not a Totaly Rigid Head.
1/ there is a Hard rubber dampner in the head teeter axis (Harder give Sharper Responce)
2/ All RC Heli have no restriction on the Lead lag (Except a little friction) they can lead or lag in the Grip on a single bolt Axis past 90deg either way. (Though this dose not happen in flight, Of cause)

But the Blades them self are as ridgid as they can make without compromising the weight and Balance Chordwise.

PS they spin in excess of 2000 RPM

[Dave_Jackson]

Mart,blade bend/twist coupling to reduce these loads, similar to D3 on S76 for example Will you provide a link to some information on this? Thanks.


Why don't we continue the discussion based on the assumptions of post #30? Where do you want to go with this? Any calculations that I do will be out of date by the time they are done. This is because by then man-made silk and nanotubes will have replaced carbon. :eek:


Dave

[Graviman]

Dave, there was a thread a while back on D3 related to the S76, but i couldn't find it in my brief search. Nick explained how D3 is used to unload rotor during an updraught encounter, since the blade flap also causes pitch reduction. This means that the rotor loading is reduced as the updraught is encountered and tries to push the aircraft up. At the same time it was explained that it can reduce flapback, which means that the vertical gust will not cause the usual pitch change in a heli - particularly if the HS has dominant control in pitch. Increase in pitch is often used as a means to increase rotor load, in high speed autos for example. I commented that the tradeoff for better gust response would be reduced lateral stability. From previous discussions we already know about the additional side effect of increasing revolutions for say R22 head to follow the cyclic, so no need to expand that further.

In a hingeless design you cannot have D3, since this implies a flapping hinge. The next best thing is to lay the blade up in a way which produces pitch reduction as the blade bends upwards. Although this will produce some control forces, a power augmented system will be fine - pretty much all hingeless have motor or hydraulic control. That's all i meant by that comment.

---

What i would like to get out of this thread is an increased understanding of the dynamics of hingeless rotors. Studying Prouty, guided by Nick, with the odd lab in an R22 has helped my understand teetering helicopters to some level. By considering a rotor at the limits of effective hinge offset i can begin to understand the benefits and problems associated. Again i suspect Nick will have picked up on all sorts of handling peculiarities which are not mentioned in the texts.

Mart

[Dave_Jackson]

Mart,

Re delta3.

Your remark was interesting because I was playing around with the concept of 'delta3 by blade ply orientation' last week, It was being considered as a possible addition to control/stability for the 2-blade teetering rotor w/ gyro, which we were discussing. :ok:

Obviously it's not a concept; it's a reality. Perhaps a subliminal recall of Nick's remarks. :O

If interested, it is item D/ on this web page; http://www.unicopter.com/0941.html

_________________________


On numerous occasions it has been mentioned is that helicopters have a 'softer' response to perturbations than fixed-wing craft have. It has also been mentioned that stiffer rotors result in 'harder' responses.

An nagging question has always been 'Is this 'harder' response any worse than that which would be experience by a fixed-wing craft under the same conditions?'. Anybody have an answer?


Dave

[Graviman]

Dave, teetering will transmit less pitch/roll moment to the fuselage when in gusty air. If the gust period is shorter than the time for the helo to respond, it goes unnoticed. A hingeless will immediately try to roll or pitch as the rotor flaps back, becoming worse as effective hinge offset increases.

I imagine that the vertical response would be similar to a hingeless rotor. In this case D3 would benefit both the teetering and hingeless. The horizontal stabiliser will also help to keep the fuselage attitude with respect to airflow, as well as overpowering any flapback divergence.

Fixed wings often have flexure designed into the spar to reduce gust loading. If you look at the wings of a commercial liner you can actually see the tips reduce AOA when they flex up. As the aircraft becomes more responsive the wings get stiffer, to allow the pilot faster control.

Mart