Yaw at High Speed

[Tango]

Hi,

 

I raised this point not long after the initial release of DCS:BS, and never received a satisfactory answer to my query.

 

Starting off on the ground, all controls centered, and trim reset to center position.

 

Take off, pull up the gear, and just accelerate, in a straight line.

 

To keep pointing in a straight line in flight at 250 km/h, it is necessary to either roll right to counteract the yaw, or to add in notable right anti-torque input to keep straight and level.

 

Given the aircraft uses a co-axial rotor system, and all else being symmetrical, I can not understand why this anti-torque input is required.

 

If you attempt to keep the controls neutral (except the forward cyclic input, naturally), the aircraft will start to fly in circles.

 

Does anyone have any actual stick time in a Ka-50 and is able to comment?

 

It seems completely wrong that the aircraft requires corrections when the physics is suggesting it isn't required.

 

The only thing I can think of is that the lower rotor, having a larger diameter shaft, has more overall mass than the upper rotor system, thus has a larger torque reaction compared with the upper rotor, resulting in an overall anti-clockwise procession of the fuselage around the Z axis (as viewed from above) as a result.

 

Can anyone confirm this? It is driving me mad as I can't otherwise see a logical explanation for this.

 

I'd also expect this reaction to be worse at lower speed, as the aircraft doesn't have the benefit of slip stream in which to weathervane, helping with overall heading stability.

 

Best regards,

Tango.

[Boulund]

It might be because of the longer arm of the upper rotor, but it could very well be equally much because of the lower rotor's continous operation in downdraft?

[ZaltysZ]

It seems completely wrong that the aircraft requires corrections when the physics is suggesting it isn't required.

 

Physics isn't doing that. :smartass: Remember that, lower rotor experiences effects of downwash of upper rotor. Their lift isn't equal.

[GGTharos]

Bingo. It is the longer arm, thus the moment is more powerful and for this reason the forces brought on by the coaxial rotor are not perfectly balanced.

 

It might be because of the longer arm of the upper rotor, but it could very well be equally much because of the lower rotor's continous operation in downdraft?

[EinsteinEP]

http://forums.eagle.ru/showthread.php?p=649872&highlight=ghostbusters#post649872

[Tango]

EDIT: I still don't see it...

 

I can understand why a longer shaft would affect the roll reaction, but not the yaw.

 

How is the yaw induced?

 

Best regards,

Tango.

Edited August 16, 2009 by Tango

[EinsteinEP]

To politely disagree with GG, the torque and banking moments are not caused by rotor height. They're due to the rotor disks producing differing amounts of drag at airspeed (thus torque) and differing amounts of asymmetrical lift (thus bank).

[Zembla]

How is the yaw induced?

 

Higher speeds mean the torques on the blades are different. Just like changing the AoA of the rotor disk (which happens when using pedal input) will change the yaw.

 

Higher airspeed means the blades flying into the wind experience more drag. Additionally, the retreating blades experience a bit of a push, and the lift changes. Not only the lift changes though, because one way to yaw is to work with the change of yaw momentum because of a different blade attitude.

 

You really need diagrams for this stuff :p A picture, or a vector diagram shows more than a thousand words in these cases :)

 

-Z

[Yo-Yo]

To politely disagree with GG, the torque and banking moments are not caused by rotor height. They're due to the rotor disks producing differing amounts of drag at airspeed (thus torque) and differing amounts of asymmetrical lift (thus bank).

 

That is not right. The main reason of unbalance is the unequal arms. If the thrust of the rotors are equal the moments are not equal. The yaw moment is produced because of unequal hub arms along the X-axis.

[EinsteinEP]

That is not right. The main reason of unbalance is the unequal arms. If the thrust of the rotors are equal the moments are not equal. The yaw moment is produced because of unequal hub arms along the X-axis.

Hub arms? X-axis? Can you produce a diagram?

 

As I stated in the link a few posts above, the upper and lower rotors produce the same drag in a hover, so no net torque. With forward airspeed, the upper rotor disk produces more drag than the lower rotor disk, and, since the upper disk rotates clockwise, this prodcues a net counter-clockwise moment, hence the need for right rudder. The more airspeed, the more the difference in drag production, the more right rudder needed.

 

If you're referring to the dissymmetry of lift, this effect produces a banking moment, not a yaw moment, which is what the poster's question was about, but even the banking moment is not due to the difference in rotor disk heights, but due to the differing amounts of lift produced by each disk (as the lower disk is working in the upper disk's downwash). The upper disk creates a larger banking moment than the lower disk because it's producing more net lift, not because it's farther from the helicopter's CG.

[Yo-Yo]

Hub arms? X-axis? Can you produce a diagram?

 

As I stated in the link a few posts above, the upper and lower rotors produce the same drag in a hover, so no net torque. With forward airspeed, the upper rotor disk produces more drag than the lower rotor disk, and, since the upper disk rotates clockwise, this prodcues a net counter-clockwise moment, hence the need for right rudder. The more airspeed, the more the difference in drag production, the more right rudder needed.

 

If you're referring to the dissymmetry of lift, this effect produces a banking moment, not a yaw moment, which is what the poster's question was about, but even the banking moment is not due to the difference in rotor disk heights, but due to the differing amounts of lift produced by each disk (as the lower disk is working in the upper disk's downwash). The upper disk creates a larger banking moment than the lower disk because it's producing more net lift, not because it's farther from the helicopter's CG.

 

 

M = L*R so any change in lift or arm causes asymmetry. But if you estimate the rotor side inclination and calculate the banking arms you can see the value. Of course unequal thrust affects too.

Regarding the yawing moment - try to draw hovering helo. It's obvious that with the airframe pitch +7 deg the both hubs and CG are on the same vertical line. When the helo flies at high speed the pitch is - 5 deg so the CG and hubs are on the line inclined for 12 deg forward. And here they are - arms and yawing moments.

 

Upper/lower discs moments can vary too.

Edited August 18, 2009 by Yo-Yo

[EinsteinEP]

Yo-Yo,

 

I'm sorry, but I'm still not able to follow your explanation nor am I able to see why you think my detailed and researched explanation is wrong. I submit I may have made a mistake and will gladly review any criticism provided against it, I just have a hard time accepting the assertion that "that is not right" without any clear justification.

 

You throw around terms like "banking arms" and "side inclination" as if these are common conventions, but they are relative and ambiguous and can be interpreted to mean a great number of things. A simple diagram (e.g., via MS Paint) will help me understand what you're trying to convey, as it's not clearly obvious. You also have seemed to skip the part that explains how a 12 deg forward pitch of the CG and hubs generate a counter-clockwise yawing moment that's dependent on airspeed.

 

When I first started investigating this behavior, I made a number of free-body diagrams, including at the rotor blade level, the rotor disks, and up to the helicopter system. I poured through a number of aero books, researching helicopter dynamics, including the phenomena of dissymmetry of lift and gyroscopic procession, to arrive at the explanation I provided in an earlier post. Yet I still fail to see yaw moments are a function of rotor height or pitch angle, and not due to differing drag production of the two rotor disks. I like to think I'm not completely stupid (there are many valid reasons to question that, though!). Perhaps you can explain more clearly to enlighten me?

[sinelnic]

With all humbleness and not attempting to provide a solution but to help understanding to myself, may I be allowed to participate? I tried to create a graphical explanation for the roll induced by the different height of the two rotor discs in forward flight. I can of course be completely wrong, but I hope not by too much.

 

Fig 1 shows a crude simplification of the force that the "moving forward" blade generates on the mast. It's really more of a rotating force but having dampers in the joint between the blade and the mast, and considering the whole blade is generating lift, I believe it's safe to oversimplify this way. I may be wrong.

 

 

Fig 2 shows the decomposition of the force vector, one part goes to increase the lift, and the other "presses" against the mast

 

 

Fig 3 shows how, under my ad-hoc analysis, the moment calculation then shows why you get a roll just for having both rotors at different distances from the CG.

 

 

Did this help at all? I'm still researching Yaw.

[sinelnic]

Eureka! I think I got the Yaw. Please see the picture, the key is that rotors centers are disaligned with the CG if you take the HELICOPTER movement plane as the reference, hence the top rotor (F2) generates more moment on the HELICOPTER than the lower one:

 

 

Did I get it Yo-Yo? Did I? DID I?!?!?!?

 

 

[Edit] Corrected forces to appear at the rotor centers, not at the tips, thanks EinsteinEP!!

Edited August 20, 2009 by sinelnic

[EtherealN]

Wow sinelnic, if that one actually comes up being true, that is a very good illustration.

 

Finding the yaw component in the sum of the forces would be interesting as well, but having been ownt by Yo-Yo before I will (for the time being) acquiesce to his superior knowledge.

 

EDIT: Wow... Talk about late response to an old browser window... I'll have to check back later to check yaw

[sinelnic]

I'll have to check back later to check yaw

 

Yeah you'd be better off going to bed because it's 2 AM in Moscow now (and later in any of Russia's 11 timezones). I'll stay here though, in case Yo-Yo is feeling insomniac for some reason :blink:

[EinsteinEP]

Welcome to the discussion, sinelnic! The more the merrier! I'm struggling to understand this myself and I really enjoy a decent discussion!

 

Your graphics re: banking (or roll moment) look good, reducing them to forces at the rotor hinge was brilliant. The net "side" forces (in red on your diagram), caused by the dissimilar lift created on each side of the rotor disk due to dissymmetry of lift, seem to describe the condition well, and shows how the banking moment is, indeed, a function of rotor disk height as well as the difference in lift due to dissymmetry of lift. It also explains why the moment increases to the left as airspeed increases. Well done!

 

Your yaw moment theory makes sense as well, as long as you move F1 and F2 back to the rotor mast heads, not the rotor tips!

 

This theory can also be easily tested:

 

Per the theory, the yaw moment is a function of rotor mast angle AND airspeed. If so, if the rotor mast is brought to vertical (+7 deg pitch per Yo-Yo, seems right) while in forward flight (say, 150 kph), the induced yawing moment should immediately go to zero. If it does, you've nailed it and all my work gets flushed down the toilet! ;) Good job! Can't wait to test!

Edited August 19, 2009 by EinsteinEP

[EinsteinEP]

Sinelnic,

 

I trimmed the heli for straight and level coordinated flight at 300m alt and 200 kph. I took my feet off the rudder pedals and pulled the cyclic back to pitch to +7 deg. Neither the banking moment nor yaw moment disappeared! (track attached for your review)

 

Although the diagram you drew was correct, the moment caused by F1 and F2 is still in the plane of the rotor mast, no matter how far up or down the helicopter is pitched. This means that the net moment will cause the helicopter to bank, not a yaw.

 

Is there some reason why the theory that the yaw moment is caused by the differing drag of the upper and lower rotors at airspeed is not worth even considering? Some blantant logic error? If so, please feel free to point it out. Seems to explain it pretty nicely...

Edited August 19, 2009 by EinsteinEP

[Obiwan]

Is there some reason why the theory that the yaw moment is caused by the differing drag of the upper and lower rotors at airspeed is not worth even considering?

 

 

I think the issue is way more complex than what's currently being discussed. Drag most certainly plays a role. My theory: In forward flight, the air entering the upper rotor has a lower angle of attack. The air gets pushed down, increasing the vertical component, and it hits the lower rotor with a higher angle of attack. Also, the pressure difference needs to be considered. The air pressue above a rotor (single rotor) is lower than the air pressure below. So in a two rotor setup, the air pressure above the lower rotor is higher than the air pressure above the upper rotor, caused by the pressure increase underneath the upper rotor.

 

In a stationary hover (no wind), I don't think the torque forces will be exactly even either. You again have the pressure difference, creating more drag on the lower rotor. However, since the total column of air is flowing down vertically, you have the same angle of attack, so the torque difference is small (but not zero!). The induced drag should be about the same, except that the air is denser for the lower rotor so you have more drag there. Once you move into forward flight, the induced drag of the upper rotor system dimishes. I'm a bit fuzzy on how much that changes on the lower rotor though. But your total parasitic drag is much higher on the lower rotor than on the upper rotor. Thus the torque difference is higher.

 

That's all arm-chair physics though, so I may be completely off base :)

While roll is explained with the height/arm etc, I believe the yaw is more a result of drag difference than anything else.

Edited August 19, 2009 by Obiwan

[sinelnic]

Mr Einstein, thanks indeed for your kind words even though I'm blatantly attacking your theory!! It's a pleasure to discuss in this way and I'm sure we'll all benefit from this by becoming smarter, prettier and better human beings. I'd like to become taller too, but I'm not sure this is the correct way :P

 

Now please consider that I'm only basically educated in this matters and I'm just amateurly conjecturing stuff here. The main drive for my drawings came from Yo-Yo's words, they were implying we were using the wrong reference system for the analysis and, during lunch, I got the image of a "spherical" system instead of a planar one. Since paradigm change always led me to understand some previously inaccessible problem, I thought I'd give it a try. But I'm in no position to challenge anything, just to guess creatively.

 

That being said, let me try and explain the main issue I have understanding your drag theory. It is the following: you state "In a hover, the two rotor disks of the Ka50 contra-rotating coaxial rotor helicopter are designed so that they produce the same amount of torque (due to drag) in opposite directions. The lower rotor actually produces less lift/drag than the upper rotor for the same relative airspeed, but since it is working in the higher airspeed downwash of the upper rotor, they match torque production at a hover setting." -> I might be completely wrong, but I'd think that if the lower rotor has to produce the same amount of torque than the upper rotor while working in a downwash, it should actually produce MORE torque in "normalwash". If the air is going down, the rotor blades face less air resistance when cutting through it at the same AoA, because that AoA is intended to push the air down and get the corresponding opposite drag and hence the lift; in fact if the downwash were strong enough it would be "accelerating" the blades, not resisting them. So the lower rotor in a downwash should work harder to get air resistance, either by rotating faster (not the case I think) or by having a higher AoA. Am I drinking too much Vodka? If I'm on a plane and I get into a downwards air current, I have to pitch up and/or add power to keep altitude, right?

 

So if the above is right (and please correct me if I'm wrong, but please teach me in the process), then when departing a hover you'd get right yaw instead of a left one. Whenever I take off and move to effective translational lift, this is exactly what happens to me. Please try a rolling takeoff from a runway (for visual reference) with no wind and verify my experience. I'm off my country this week but will gladly post a track on saturday showing this.

 

Once we get into the high airspeed zone, my elucubrations continue, the F1-F2 forces difference in my second post (at the mast, I stand corrected :)) grow bigger than the pure drag-induced opposite right yaw. Don't get why though. Will keep on thinking. Vodka is not helping :).

 

Regarding your experiment, I couldn't try your track because I'm not at home, but can I assume you gained a lot of altitude while pitching up? (there's no way you would avoid this without touching collective, which would introduce more variables to the experiment) But if you gained altitude, you were in fact flying diagonally up and thus keeping the same deviation of the rotor discs centers to the CG relative to the helicopter motion path, thus nullifying the intended effect. Or am I drinking too much Vodka again?

 

It's actually very difficult to try this, in every scenario that I can think of, whenever you try to make an immediate rotor center and CG realilgnment against the motion path, you end up modifying the motion path itself!! (like for example when departing a hover, you pitch down... and the heli flies down!!)

 

Let's keep this up! we'll eventually get it, leave this forum and create our own flight simulation company, and charge 15 bucks for exclusive access to WIP content. Oops sorry, that was completely off-topic.

[sinelnic]

Ok, for the reason for the transition from right yaw to left yaw, my theory is that I'm actually experiencing right yaw while climbing at very slow speed (but above ETL), so that the flight path is tilted up so that it corrects the rotor discs vs CG alignment while having strong right yaw induced from the above mentioned effect in a high collective scenario (even more right yaw). Once we reduce climbing and accelerate enough the alignment looks more like my second post. Oh I need to fly, dang!

[Yo-Yo]

First of all I must say that Sinelnic's drawings are right.

After that I have to say that I was mistaken writing about the hovering thrust of upper and lower rotors. The ratio is only 1.2:1. To obtain equal torque the lower rotor blades pitch is less by 1.25 deg.

This is for the axial flow mode when both rotors have almost common airflow and have strong interaction.

At high speed the rotors interaction is low because of two factors -

1) the inductive velocities become low in comparison to the inbound transverse air velocity

(IAS*sin(ROTOR_AoA))

2) the wake of upper rotor is skewed and goes by the lower.

As the blade pitch is close to maximum (15-18 deg as far as I remember) the 1.25 deg pitch difference produces less than 10% of thrust difference.

The rotor side inclination is approx. the same for both rotors so the side forces are aprrox. equal.

OK, let's compare THE ARMS producing SIDE moment. If you estimate where CG verical position might be you can see that arms ratio is about 1.7-1.8 so the moments ratio will be the same.

To have moments equal it is necessary to apply left cyclic input to reduce the upper rotor side force and then side FORCE unbalance appears! Ok, the moments are in balance but now you have excessive force directed left. And now let's go back to Sinelnic's drawing - the origin point of resultant side force lying at the mast is in front of CG longitudal position so you have LEFT yaw moment and must apply RIGHT pedal. By the way, to eliminate unbalanced side force it's necessary to have right bank too.

Edited August 19, 2009 by Yo-Yo

[sinelnic]

^^^ :drunk: ^^^

 

Thank you Yo-Yo! While thinking of this I think I understood the why of your nickname, thinking of this stuff can make one a rotor head, let's hope we all can avoid blade collision :).

 

I'm now having problem with the lower rotor difference in hovering thrust. When you say "The ratio is only 1.2:1. To obtain equal torque the lower rotor blades pitch is less by 1.25 deg.", you mean that if both rotors had the same blade pitch, the lower rotor would produce 1/1.2 (that's 1 divided by 1.2) thrust compared to the upper one (because of downwash)? If so, to produce 1:1 thrust, shouldn't the lower rotor increase blade pitch to generate more thrust? Where am I wrong, oh Master?

Edited August 19, 2009 by sinelnic

[Yo-Yo]

^^^ :drunk: ^^^

 

Thank you Yo-Yo! While thinking of this I think I understood the why of your nickname, thinking of this stuff can make one a rotor head, let's hope we all can avoid blade collision :).

 

I'm now having problem with the lower rotor difference in hovering thrust. When you say "The ratio is only 1.2:1. To obtain equal torque the lower rotor blades pitch is less by 1.25 deg.", you mean that if both rotors had the same blade pitch, the lower rotor would produce 1/1.2 (that's 1 divided by 1.2) thrust compared to the upper one (because of downwash)? If so, to produce 1:1 thrust, shouldn't the lower rotor increase blade pitch to generate more thrust? Where am I wrong, oh Master?

 

No, I mean that if both rotors had the same pitch they would produce approx. the same thrust BUT the lower rotor would have more drag and no yaw moment balance would be. This effect is due to the downwash that is additionally swirled. That's why the drag of lower rotor is higher if it produces the same thrust.

[EinsteinEP]

No, I mean that if both rotors had the same pitch they would produce approx. the same thrust BUT the lower rotor would have more drag and no yaw moment balance would be. This effect is due to the downwash that is additionally swirled. That's why the drag of lower rotor is higher if it produces the same thrust.

To see if I understand:

 

1.) At the same pitch angle, the rotor blades of the lower disk produce the same thrust as those in the upper rotor, but higher drag. This is due to the downwash and swirl from the upper rotor which increases the relative airspeed to the lower rotor blade, but reduces the angle of attack. An airfoil moving at a higher airspeed with a lower angle of attack can generate the same lift as the same airfoil at a slower airspeed, but the higher airspeed airfoil produces more drag (due to parasite drag effects which are a function of airspeed squared).

 

Did I capture it so far? I hope so, because it makes sense to me.

 

2).

In the Ka-50, the pitch of the lower rotor blades is reduced by a small amount (1.25 deg) to further reduce the angle of attack in the downwash which reduces the lift produced by the lower blades which reduces drag so that the amount of torque generated by the upper and lower rotors matches in a hover.

 

Am I still on track?

 

I'll stop here for feedback. This is fun!

 

On a similar note, but not to sidetrack this awesome discussion,

does anybody have an electronic copy of Kamov's "Aerodynamic Features of Coaxial Configuration Helicopter"? All the links I can find to it are dead and I'm hoping it may shed some light on this discussion.

Edited August 19, 2009 by EinsteinEP
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