## Speed Limits – Part 1

May 28, 2009 by Tim McAdams

One big advantage to a helicopter’s rotor system is the vertical thrust that allows the aircraft to hover. However, when this same rotor system is flown edge wise through the air it creates an aerodynamic problem that limits the helicopter’s forward speed. The term used to describe this is dissymmetry of lift.

To generate lift a helicopter’s rotor blades spin to create airflow. A rotor system’s RPM is fixed at a certain value for all phases of normal flight and increasing the blade’s angle of attack (the angle between the relative wind and the blade’s cord line.) with the collective control generates lift. In a hover with no wind, lift is essentially equal across the entire rotor disc. However, as the helicopter begins to move forward it creates a relative wind. One side of the rotor disc has a blade that is advancing into the relative wind (think headwind) and the other side has a blade that is retreating (think tailwind). The difference in airspeed each blade encounters between the two sides grows as the helicopter gains forward speed. This creates an imbalance of lift problem that early helicopter engineers had to solve to maintain controllability.

To help understand how they did it, consider the equation for lift.

Lift = CL ½ p S V2

CL = Coefficient of Lift, which is a function of angle of attack and blade shape

p = air density

V = airspeed

At a given moment in time, air density, total blade area and blade shape are all fixed values, so as each blade’s airspeed changes the rotor system must respond by changing the blade’s angle of attack to keep total lift constant. This is done primarily by allowing the blades to move up or down in a process known as flapping. Two bladed rotor systems (known as semi-rigid) use a single teetering hinge that allows the blades to flap as a unit (one go up, the other goes down). Rotor systems with more than two blades (typically known as fully articulated) use a flapping hinge on each blade allowing the blades to move up or down independently of each other.

How flapping works is by changing the angle of attack in response to the varying airspeeds the blade encounters as it moves around the rotor disc. When the advancing blade experiences a higher airspeed, the lift on that blade increases forcing it to move up. This upward movement changes the direction of the blade’s relative wind reducing its angle of attack. On the retreating side just the opposite happens. The reduced airspeed causes a decrease in lift causing the blade to move down, increasing its angle of attack. Each blade’s angle of attack changes in direct relation to its relative airspeed. As each blade’s relative airspeed increases, angle of attack decreases and vice versa to maintain equal lift across the disc as the helicopter’s airspeed increases.

As you might have guessed, this creates a problem on the retreating side. You can only increase an airfoil’s angle of attack so much before it stalls. As the helicopter continues to fly faster the retreating side must continue to increase its angle of attack to compensate. At some airspeed the retreating blade stalls and this is what limits the helicopter’s forward airspeed. This is referred to as retreating blade stall.

There is more to discuss on this subject so part 2 is coming up next time.

### 33 Responses to “Speed Limits – Part 1”

1. Chris Says:

Great review! Out of all the articles so far this was my favorite! THANKS!!!

2. JJG Says:

An excellent review from a different perspective for a relatively new pilot. Also, I am pleased that the AOPA provided something for us few helicopter pilots. Keep it coming, and thanks for all the good work.

3. Dave Finn Says:

Great to have helicopter content because we helicopter pilots are largely ignored by most popular aviation magazines – well done, easy to grasp the concepts and great illustrations. Looking forward to discussions of more unique properties of helicopters… rotor hop, vortex ring state, delta hinges, ground resonance, etc.

4. JDH Says:

An outstanding article on what happens in a “rotor disc”. Although not a rotary wing pilot, I’ve been a helicopter fan since my days in Viet Nam. Your article is almost word for word a discussion I had with a life long buddy, and military, now commercial helicopter pilot , who has flown everything from pre UH1’s through Chinooks. As was his explanation of what happens on the backside of the disc, yours was simple and easy to understand. I need that! Before I pass on to the great airport in the sky, I’ve got to get a couple of hours of helicopter time. Please do more of these!

5. JJ Says:

Very interesting article, but I’m still not clear on how the blade’s flexing up and down (flapping) changes the angle of attack, as opposed to that set by the collective. If I recall correctly, I thought rotor systems have a “swash plate” that adjusts the angle of attack for the advancing and retreating blades. What I’m not clear on is, when you set an angle of attack with the collective, how does the upward or downward flexing of the blade change the angle of attack?

6. Chris Says:

Excellent, excellent, excellent ! Most dissertations on this subject don’t emphasize (or even mention) relative wind, the key to understanding flapping in a two blade rotor system.
Keep the articles coming !….

7. Wiz Says:

In response to JJ-
Technically, a helicopter pilot does not set the angle of attack.

The flight controls, operating through the swashplate or similar mechanism, set the pitch angle: the angle between the blade chord line and the direction of rotation. This is different than the angle of attack – the angle between the blade chord and the relative wind. In a “perfect hover” (no wind, no movement), the pitch angles and angles of attack are as close as they’ll ever be. But as the aircraft moves laterally, the relative wind varies across the disc, and it encounters the dissymmetry of lift that Tim describes in his article.

Flapping is an aerodynamic condition that is not controlled by the pilot. As the advancing blade sees more relative wind, it starts to create more lift, and the blade flaps up in response. This “flapping up” motion changes the direction of the relative wind, effectively lowering the angle of attack and reducing lift.

Likewise, as the retreating blade sees less relative wind, it flaps down in response, again changing the direction of the relative wind, which then increases the angle of attack and increases lift. The net effect of the flapping is an equalization of lift across the disc.

This all happens so fast: for a helicopter with Nr at 400rpm, a blade will make a complete rotation every 0.15 seconds – the blade flaps up and down literally faster than the blink of an eye.

On semi-rigid and fully articulated rotor systems, the rotor blades are hinged at or near the mast. The blades rotate up and down on these hinges in response to aerodynamic flapping. On a rigid (hingeless) rotor system, flapping is accomplished through a combination of elastomeric bearings and blade flexing (special composite blades allow this to happen). So on most helicopters, flapping and flexing are two different things.

Sorry to be so long-winded – but I hope this helps!

8. jack herrin Says:

visa versa——–should be vice versa
jack herrin
530-221-8533

9. GSB Says:

Also in response to JJ (excellent explanation Wiz):

It might help you to get a feel for flapping and relative wind by thinking of a bird’s wings. When the bird flaps his wings in forward flight, that motion combined with forward speed changes the relative wind. Flap down = increase angle of attack. Flap up = decrease angle of attack. Of course bird aerodynamics are more complex than this, providing propulsive power amongst other things, and the bird is using his or her muscles to cause the flapping, whereas helicopter blades flap in reaction to the aerodynamics. But this analogy always helped me with remembering how the flapping and forward speed combine to change angle of attack.

10. Keith Nelson Says:

Excellent explanation. I’m preparing to begin rotor-wing training in the Army and every article that Mr. McAdams has written is quite informative. I just started reading the Rotorcraft Fying Handbook and couldn’t quite wrap my mind around the concept of flapping. Thank you for the insightful explanations of this article and previous articles as well. I look forward to reading the next article.

11. Don Holliday Says:

If you look at the costs of operating rotorcraft, “visa versa” is probably more accurate, though not from a technical sense.

12. Don Holliday Says:

What is “rotor hop?” I can’t find a definition/explanation of the term anywhere?

Don

I believe “rotor hop” is when the blades are not tracking correctly, another words the blade tips are not passing through the same spot in space as they rotate around the mast. This can be felt in the seat as a up and down “hop”

14. Kimberley Says:

I think I’ll stay outta this one.

Thanks for all the comments and additional information. Sometimes it is easier to understand some of these concepts when a person hears several explanations from different perspectives.

Jack, thanks for catching the “visa” error, I made the correction.

Tim

16. John H Says:

In response to JJ. I don’t think anyone gave a good answer to how an upward motion changes the direction of the relative wind. But try this: Imagine if the blade flexed so far up that it actually became vertical, describing a tulip shape. At that extreme its lift would be toward the mast, instead of up. So flapping puts the blade somewhere between horizontal and that extreme. That means that the lift vector must tilt more and more inward as the amount of upward flap increases. It’s still advancing into, or retreating from, the wind, but that’s not so important to answering your question. The same thing would happen if you were lifting a heavy load, except that you’d have an equal upward flex on both blades, giving you a tulip shape.

17. Jim Hogue Says:

To confuse the issue even more, blade (rotor) hop can have a vertical and/or horizontal component. Vertical hop occurs when the blades have a significant enough difference in pitch settings at flat pitch. Control arm adjustments can bring the tips closer to the same track throught the air to get rid of the up and down hop from dyssymmetry of lift that can occur, for instance, with putting on new blades. This used to take hours with the UH-1 using masking tape and a broom handle and red and black grease pencil on the blade tips. Use your imagination about how we did that. Horizontal hop (which is actually sideways shaking) occurs when there is a weight imbalance across the rotor disc. This gets a little difficult to grasp but the center of rotation of the rotor disc gets away from the center of the mast creating an annoying rolling motion of the aircraft under the disc. Believe it or not weight is added to the heavier blade to bring the center of rotation back to the center of the mast.

18. Jim Says:

Sorry, weight is added to the lighter blade to bring the center of rotation back to the mast. The center of rotation in an a weight imbalanced system moves out into the hub of the heavier blade. Weight was added to the blade that struck the measuring device the hardest, which common sense says should be the heavier blade, but not true, the heavier hit was from the lighter blade because it swung a greater arc with the center of rotation off the mast into the hub of the heavier blade. Drawing pictures makes this easier.

19. Bill Says:

All of this is great ! Those of us that only fly fixed wing are always curious about how those bumble bees fly… and all of the comments and explanations were helpful… thank you ! Have any of you ever looked at the Lockeheed Cheyenne ?

20. Daniel L. Newhall Says:

Is there perhaps something in the geometry of the hinges of the hub which decreses the pitch angle as the blade rotates up on the hinge?

21. Dan Olson Says:

I think there is an error here. The flapping hinges simply allow the helicopter to be freely suspended from the rotor system.
The equalization of lift from the advancing blade to the retreating blade is accomplished by the swash plate. It decreases the angle of attack of the advancing blade while increasing the angle of the retreating blade. This can be seen easily on the ground by sitting in the pilot seat and (with rotor stopped crosswise to the fuselage axis, engine stopped) moving the cyclic fore and aft. You will see the pitch on the advancing blade decrease the exact same amount that the retreating blade increases.
This is also the same motion that tilts the rotor forward or aft for forward or aft transition from hover. In hover the change in pitch applies a tilting force left or right that is altered by gyroscopic precession 90 degrees in the direction of rotation. It is complex to visualize but when you see it with the rotor stopped it is easier to understand.
The same motion of the swash plate that produces the initial tilt of the rotor also accomplishes the lift equalization for continued forward flight.
I am a Viet Nam era UH-1 crew chief and have CFI ASEL CFII CFIG. I am also a licensed professional engineer.
Thanks for listening.

22. Ehud Gavron Says:

Dan, the swashplate increases the angle of the advancing blade and equally decreases the angle of the retreating blade, but this in and of itself is not sufficient to change the relative lift of the two blades and the dyssymetry of lift.

Flapping means the advancing blade flaps up, moving the CG inward and compensating for the blade not being able to “lag” as if it had a lead-lag hinge on a fully-articulated rotor-system. The retreating blade flaps down, moving the CG outward, and therefore producing more lift without needing to “lead”.

The flapping hinges do not cause the “helicopter to be freely suspended from the rotor system”. The underslung rotor system does that without regard for a flapping hinge.

The swashplate does not equalize lift. It provides some of the input necessary to this — the flapping of the rotor blades does the rest.

I am not a Viet Nam era UH-1 crew chief and have respect for all of you who risked your lives for our country flying over dangerous enemy territory.

Respectfully,

Ehud

23. Dan Olson Says:

Ehud, I suggest you watch the rotor blades from behind during forward flight. You will see that both the advancing blade and the retreating blade are at the same height. I have been the tail end charlie of a flight of Hueys in trail. All the rotors are horizontal except for coning of about 3 or 4 degrees. You can also see that the advancing blade is at a reduced angle of attack while the retreating blade is at an increased angle of attack. The limit of this is when the retreating blade reaches its critical angle of attack and stalls. This is “retreating blade stall” and is one of the factors that sets Vne (never exceed speed) for a helicopter.
And the CG does not move. The CG is the center of gravity. This will remain fixed unless some internal load is moved about. If the center of LIFT were to move as a result of a pitch change from the swashplate, then the rotor would tilt. When the rotor tilts, the overall lift vector of the rotor tilts and results in translation or banking in that direction.
In steady flight the lift vector is ALWAYS perpendicular to the rotor. In steady forward flight the rotor is tilted forward to provide a forward component to equal the drag of the fuselage. In steady turning flight the rotor is tilted in the direction of the turn and the fuselage swings out directly under the rotor from the centrifugal force of the turn.
Thanks again,
Dan

24. Dan Olson Says:

Check You Tube for videos of helicopters. One in particular is “NH-90 NATO Frigate Helicopter”. This shows a helicopter in forward flight approaching a ship to land while the ship is under way at 25 knots. The rotor is horizontal, not higher on the advancing side.
Dan

25. Kurt McKibben Says:

Hello folks,

Maybe we should write something about cyclic feathering to differentiate flapping and feathering. The collective controls pitch angle of all blades equally, via pitch horns. The cyclic controls pitch angles of each blade individually, via the swash plate. Flapping is an aerodynamically forced movement on the blades, via the physics of the lift equation. You build a rotor system to accommodate flapping no matter what because it’s physics you can’t deny. For anyone to say they can see blade flapping with the naked eye is nuts. The blade is flapping up and down so fast you can’t see it happen. It’s very small, and is just enough to equalize lift across the disc. You don’t see this with the naked eye, and the plane of rotation still resembles the horizon. THIS IS ALL CHALK BOARD TALK TO EXPLAIN THE PHYSICS for the correction of dissymmetry of lift.

Flying behind in a line of choppers and viewing different pitch angles from one side of the rotor disc to the other side is just viewing a function of cyclic input to maintain a given direction of flight. IE. forward, backward, sideways. If those same helicopters made a right turn those blades would change again side to side from a new cyclic input to turn right, via the swash plate.

You were looking at a cyclic control setting to create the blade configuration necessary to maintain air speed in forward flight.

Zen,,,,,,,,,,,,,,,,,,

Kurt McKibben

26. Kurt McKibben Says:

Oh, by the way Dan, now that you have my attention, the CG moves constantly through out all flights as fuel burns out of the tanks. We figure CG with full fuel and with empty fuel before takoff to assure we can be within CG limits the entire flight for a possible autorotation anytime if an emergency arises.

For CFI’s there is an FOI ( Fundamendals Of Instruction) FAA test question that states how important it is to learn the correct information in the first place. This is refered to as “Primacy.” It means the first thing a person learns are remembered best. To learn something wrong first, means you have to go back, do unlearning, and break bad habits before you learn the correct information. It is difficult to break bad habits and relearn information that was false.

No wonder flight instruction is so expensive!!!!!

Kurt McKibben
CFI Rotorcraft, Helicopters

27. Kurt McKibben Says:

Thank you Tim McAdams!! Exelent discussion!!! I learned the CL: coefficient of lift is a combination of angle of attack AND blade shape.

I wish I could write as well as you do!! Thanks again

Kurt McKibben
CFI, Rotorcraft, Helicopters

Thanks Kurt and everyone else who have contributed their thoughts and ideas. I like to put a topic out there and have readers who really have a good understanding of the subject provide comments. I think we all learn a lot that way.

29. George Carey Says:

I understand the limitation of forward flight being due to the stall speed of the retreating blade. Is there not also a limitation of the advancing blade approaching the speed of sound? Is the limitation a tradeoff between these two speeds? If it were just the stall speed of the retreating blade you could increase the Nr rotor speed. If you do that though then you increase the advancing blade speed toward the speed of sound.

30. Ehud Gavron Says:

Yes, but that isn’t as big a factor as it might seem. For example, on the R22’s high-speed rotor the tip-speed of 672FPS works out to (x3600/5280) 458MPH. That’s 300MPH slower than the speed of sound at sea level (760MPH).

Thus if this were a primary factor, it wouldn’t come into play until a forward airspeed of 300MPH (260 knots). Instead the forward airspeed is truly limited more by retreating blade stall.

Of course Airwolf had both bases covered… “Give me both turbos, Dom!”

Ehud

31. George Carey Says:

Thanks for the note Ehud. What you say makes sense but what if the main rotor RPM was increased? For a given forward airspeed would this not increase the speed of the retreating blade further above it’s stall speed? You could then increase the forward airspeed by that amount. Of course then the advancing blade speed would also be higher and limited by approaching the speed of sound. This is why it seems that main rotor RPM is set to give you a happy medium between the retreating blade stall speed and the advancing blade reaching the speed of sound.

I remember Airwolf but it has been a long time!

George

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