Yaw at High Speed

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.

I do not, but I can point you to a very interesting book, "Principles of helicopter aerodynamics" from Cambridge University Press. It has a very math-heavy chapter on coaxial rotors, but sadly some pages are missing in the google library. Maybe you can get it from some local library (it's US$ 100 in Amazon, too much)...

A little cheaper here: http://books.google.com/books?id=nMV-TkaX-9cC&dq=Principles+of+helicopter+aerodynamics&printsec=frontcover&source=bn&hl=en&ei=GFaMSoThJpCEswOpqc2wCQ&sa=X&oi=book_result&ct=result&resnum=7#v=onepage&q=&f=false

;)

Sadly, the book focuses on the power efficiencies of the coaxial rotor system, and does not address the yaw or banking moments we are investigating.

Something else interesting: have you noticed that, in forward flight, the lower rotor disk cones a great deal more than the upper rotor disk? This observation is what led me to the conclusions I've made, but perhaps I've misinterpreted it. Why do you believe the lower rotor disk cones way more than the upper?

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.

(It appears that) The helicopter system has been designed so that drag of the upper and lower rotor disks match at a hover, hence the blades of the lower rotor having a pitch of 1.25 deg less than the upper. This is the whole point of the coaxial design, so it's not a far-fetched assumption. As you point out, this wouldn't happen if the two rotor disks were identical.

As for how the downwash affects the lower rotor blades' angle of attack, actually the AoA gets REDUCED with the downstream. Airstream coming from above = negative angle of attack. The overall relative airspeed increases, however, which, as you point out, increases parasite drag.

Although the pressure of the airstream is affected, I'm not certain to what extent that plays as the effect is usually very localized. In fact as the airstream is sped up by the rotor blades, the static pressure reduces with velocity as the dynamic pressure increases. Will have to mull it over and will keep it in consideration in the future. Thanks for bringing it up!

Sorry Obi, somehow I missed your post in all the hub-bub. Thanks for joining in!

No problem. I'm used to being ignored ;)

(It appears that) The helicopter system has been designed so that drag of the upper and lower rotor disks match at a hover, hence the blades of the lower rotor having a pitch of 1.25 deg less than the upper. This is the whole point of the coaxial design, so it's not a far-fetched assumption. As you point out, this wouldn't happen if the two rotor disks were identical.

Right. By default, that's probably adjusted with rigging or center trim offset (if there is such a thing), just like disymetry is adjusted with a tilted mast or cyclic rigging. My point was that without such adjustment, the torque forces are not equal.

As for how the downwash affects the lower rotor blades' angle of attack, actually the AoA gets REDUCED with the downstream. Airstream coming from above = negative angle of attack. The overall relative airspeed increases, however, which, as you point out, increases parasite drag.

Grrr... right, my bad. I meant the angle of the airflow to the cord line is greater. Bad terminology on my bad. With cord line drawing and head-on wind pictured in mind, the angle of attack is indeed very negative.

Agree, though, that is a great discussion! /me goes back to lurking

Aerodynamics site

http://www.dynamicflight.com/aerodynamics/

If your interested in some basic aerodynamics and aerodynamics when being applied to an rotor system (eg helicopter or planes like the V-22 Osprey)

this is an great site. It has lots of info and explains very well how things work and why they work like that.

(i used it as reference for an Dutch paper about the Trust of an Helicopter)

For people not very familiar yet whit aerodynamics i suggest to start reading the upper left article 1st, then the one below untill you reached the bottom of that row, and then start on the Right row of articles.

There's no point in jumping into the deep if you dont know what AoA stand's for or what is meant by Relative Wind for example.

( http://www.dynamicflight.com/flight_maneuvers/ from the same site, though this explains manouvering a helicopter in general)

Thanks for the 411 and links Falcon. As you can see in the posts, what we're discussing (yaw and banking moments generated at airspeed in a coaxial helicopter) isn't explicitly called out in any of those links. We're bashing out our theories against each other and seeing what pieces stick together.

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.

Ooooh I see it then, that explains the right roll when accelerating. You really need to see this in 3D. So far what I get is that you first get right roll as described in my first series of drawings, then when you decrease F2 to balance moments by appliying cyclic, you end up having a net force in the direction of F1. Then if you jump to my fourth drawing, you get that net force generating just left yaw because roll is already balanced in the previous step. Amazing!

So this really helps in flying technique: first left cyclic, then right pedal. Adjust whenever you change airspeed, collective, and pitch relative to path motion. Nice!

A little cheaper here: http://books.google.com/books?id=nMV-TkaX-9cC&dq=Principles+of+helicopter+aerodynamics&printsec=frontcover&source=bn&hl=en&ei=GFaMSoThJpCEswOpqc2wCQ&sa=X&oi=book_result&ct=result&resnum=7#v=onepage&q=&f=false

;)

Sadly, the book focuses on the power efficiencies of the coaxial rotor system, and does not address the yaw or banking moments we are investigating.

Yes! that's where I got it from, but the two last pages are missing from the coaxial rotor chapter, and also the first ~60 pages where all fundamental equations are introduced... maybe Truth was there, we'll never know...