1. School of Aviation Safety
Rotor Systems
Chapter 4
LCDR Frank ‘MOTO’ Collins
Helicopter Aerodynamics
(850)
FOR OFFICIAL USE ONLY:
THIS BRIEF CONTAINS SAFETY PRIVILEGED INFORMATION WHICH MUST BE SAFEGUARDED IAW OPNAVINST 3750 Series

2. Learning Objectives – Ch 4
List the three degrees of freedom for a rotor blade, and their purpose.
Draw or explain how flapping equalizes lift distribution over the rotor, using a blade element diagram.
Describe what rotor “blowback” is, and how the rotor’s thrust axis separates from the control axis as airspeed increases.
List the solutions to obtain a more ideal lift distribution over the rotor disk.
Describe the forces that are responsible for determining a rotor blade’s coning angle.
Explain how the mechanisms and design of the rotor blade affect flight.
Discuss the differences of the rotor axes in hover and in forward flight.
Topics of discussion.

3. Pilot in Rotor

4. Juan de la Cierva Autogyro
Juan de la Cierva developed many of the rotor features that we see on modern helicopters, even though his concern was with low speed fixed wing flight.
In the 1920s de la Cierva developed autogyros as a safety feature following a bomber crash that he witnessed. He figured that an aircraft that could fly slowly without stalling would be highly desirable.
De la Cierva’s initial design failed in test before it reached takeoff speed because it fell over and thrashed itself to death. This was puzzling to the designer because his small scale model hadn’t behaved thus.
One night, while at the opera “Aida” with his wife, Juan de la Cierva had a flash of inspiration. He realized that his small model had not exhibited a tendency to roll because the flexible rattan blades that he used had enough give to compensate for dissymetry of lift between the advancing and retreating blades. To allow for such flapping on the full scale design he incorporated a mechanical hinge.
Juan de la Cierva also later incorporated a vertical hinge to counter vibrations and structural stresses imparted by dissymetry of drag.

5. Pitch Control by Direct Rotor Tilt

6. Rotor Blade Degrees of Freedom
Feathering (q): Increases/decreases the pitch (AOA) of the rotor blades collectively (all blades same pitch change) or cyclically (independently) , depending on blade azimuth position.
Flapping (b): Solution to dissymmetry of lift between advancing and retreating blades. Relieves hub stresses.
Lead-lag (g): Relieves dissymmetry of drag forces. Relieves hub stresses due to conservation of angular momentum.
We talked during the first class about the complexities of studying helicopter/rotor wing aerodynamics. And one concern was the increased number of DOF over our F/W brethren.
Before we ask ourselves “What are our DOF for a rotor system?”
What is a DOF? [Unrestricted movement along or about an axis]
Examples:
- 1 DOF (spring-mass system/elbow]
- 2 DOF (wrist)/ 6 DOF (F/W aircraft)
- 9 DOF (F/W plus 3 listed feathering/flapping/lead-lag)
Juan de la Cierva (Spanish Mathematician and inventor) and the development of the Autogyro (1920’s)[Helo Aero, Prouty p.17].
- asymmetry of lift (flapping)
- lead-lag (drag and rotational inertia)
We will look at each of these rotor system DOF’s individually.
[FM 1-203, p. 5-6;

7. Teetering (Semi-rigid): 2 DOF; allows movement about the feathering hinge/pitch. Allowed to teeter to compensate for flapping. Advancing blade flaps up as retreating blade flaps down.
- Rigid in plane: any slight tendencies to lead or lag will be absorbed by the torsional flexibility of the rotor system and the stiffness of the blade root.
Fully Articulated: 3 DOF; allows for motion about all axis (flapping, lead-lag and pitch).
- Lead-lag: will be limited by in plane dampening, usually a shock similar to a car suspension system.
- Flapping: also limited; low NR will be limited by flap and droop restraints.
Rigid Rotor: feathering hinge only to allow for change in AOA; elastomeric blade grip or series of elastomeric bearings will allow blade to flap and lead-lag. Elastomeric blade sleeve will limit the amount of flapping and lead-lag.
p.59

8. Precession
Precession takes into account Phase Lag and the applied aerodynamic forces
Function of rotating system
Maximum displacement occurs 90 degrees after force introduction
Before we go on, we need to understand the idea of precession.
A rotating system like a rotor head with 360 degrees of motion experiences maximum displacement from an applied force 90 degrees after the point where the force is applied. The force acts where applied, but its associated maximum displacement is delayed.
This is why controls are typically placed 90 degrees out from where they are needed (the lateral servo is along the longitudinal axis).
On some installations, servo arm size and length of pitch change link can make moving the servo necessary to apply the force at the right point. Additionally, the resonant frequency of articulated heads can be altered by the distance from the hub to the hinge.
p.60

9. Feathering
Collective and cyclic feathering are the only means available to the pilot in “adjusting” the rotor system. (baring the effects of pedal adjustments through the mixing unit if applicable)
The pilot does not literally “move the head”. Pitch changes are made by the pilot and the head moves as an aerodynamic reaction.

10. Fwd Flt - Velocity Distribution
j = 180 WR
Nose W
Advancing Tip Speed
WR+Vf
j = 270
j = 90
WR-Vf
Reverse flow region
Retreating Tip Speed
Tail WR
j=0
p.56

11. Dissymmetry of Lift
Dynamic Pressure (q) of advancing blade is much greater than retreating blade, therefore more lift is generated on the advancing side. In order for the system to be stable both sides of the disk must produce the same amount of lift, therefore a change in airflow from advancing side to retreating side must be allowed so that the lift over the entire disk is equal.
p.56

12. Fwd Flt - Lift Distribution
Without Flapping
Retreating Blade
Advancing Blade
With Flapping
View: Looking Forward
p.56

13. Flapping
Equalizes lift moment on opposite sides of the rotor disk (Dissymmetry of lift solution)
Longitudinal flapping equalizes lift laterally (dissymmetry of lift).
Causes - Blowback
Lateral flapping equalizes lift longitudinally (transverse flow effect)
Causes - Roll towards Advancing Blade
Conservation of angular momentum – A the C.G. of the blade changes due to flapping the blade must either speed up or slow down.
p.55

14. Blowback Virtual Axis Control Axis Shaft Axis Control Axis
Shaft Axis: Location of the rotor shaft out of the main transmission
Virtual Axis (Thrust Axis): Always perpendicular to the rotor disk
Control Axis: Perpendicular to the swashplate. In a no wind hover condition the control axis and virtual axis are the same.
Blowback is the separation of the Virtual Axis (Tip Path Plane) from the Control Axis (Swashplate).
The Virtual Axis blows back.
p.61

15. Longitudinal Flappingq
Up flap velocity
Plane perpendicular to SHAFT AXIS
Advancing Blade
(flaps up)
Tip path plane = VIRTUAL AXIS
Swashplate
Fwd
Aft
Down flap velocity q a
Retreating Blade
(flaps down)
p.61

16. “Transverse Flow” Effect
Transverse Flow Effect: Non uniform induce velocity.
--Better Lift on Front , Not so good off the back. Less lift in the back. Precession causes a 90 deg delayed reaction.
--Tendency is to roll toward the advancing blade
Better lift in front. More induced flow over rear blade. Higher induced velocity means reduced AOA. This lower AOA is sensed 90 deg later. The advancing blade flaps up to reduce AOA. This is a further reduction in AOA. Therefore, the helo wants to roll toward the advancing blade.
Less induced flow over front blades. No change in AOA. Higher AOA in front than rear. Due to precession this high AOA is sensed 90deg later over the retreating blade. Higher lift on retreating side and less over the advancing side causes the helo to roll right.
Pilot compensates by applying left stick, or the aircraft mixing unit (AFCS) compensates for this.
Topic covered in Ch-9: Forward Flight. This is Lateral Flapping.

17. Lateral Flapping V Transverse Flow effect Ch 9
Upward component of Inflow
Downward component of Inflow
Transverse Flow effect
Non uniform induce velocity.
Better lift in front. Less lift in the back. Precession causes a 90 deg delayed reaction.
More induced flow over rear blade. Higher induced velocity means reduced AOA. This lower AOA is sensed 90 deg later. The advancing blade flaps up to reduce AOA. This is a further reduction in AOA. Therefore, the helo wants to roll toward the advancing blade.
Less induced flow over front blades. No change in AOA. Higher AOA in front than rear. Due to precession this high AOA is sensed 90deg later over the retreating blade. Higher lift on retreating side and less over the advancing side causes the helo to roll right.
Pilot compensates by applying left stick, or the aircraft mixing unit (AFCS) compensates for this.
Ch 9

18. Flapping
Flapping results from a change in aerodynamic forces as blades ‘fly’ to tilt the tip path plane
May be due to change in aerodynamic forces from differential linear velocity (V2 component)
- Longitudinal Flapping (Blowback)
May be due to change in aerodynamic forces from differential induced velocity component (AOA – CL component). Causes a roll towards the advancing blade.
- Lateral Flapping
Also, Will be due to changes in aerodynamic forces due to cyclic feathering (AOA – CL component)
- Cyclic Flapping
Conservation of angular momentum – A the C.G. of the blade changes due to flapping the blade must either speed up or slow down.
Flap Down: The Retreating Blade – When a blade flaps down its center of gravity moves out from the axis of rotation onto a larger radius and its velocity slows down.
Flap Up: The Advancing Blade – Flapping up moves the blade forward on the hinge (lead-lag hinge) as the blade speeds up and flapping down moves it aft as the blade slows down.

19. Flapping S-56 at 120 or 150 kts. (1956 video)
Some said H-1 or H-3 rotor blade rotor flapping. Not really flapping, but close – due to camera location.
It is a NACA 0012 blade used on both the H-1 and H-3.

20. Precession
Precession takes into account Phase Lag and the applied aerodynamic forces
Function of rotating system
Maximum displacement occurs 90 degrees after force introduction
But why aren’t servos 90 degrees from their intended action
Effect of hinge location (e) and servo arm size
Point of pitch control rod and blade attachment.
Before we go on, we need to understand the idea of precession.
A rotating system like a rotor head with 360 degrees of motion experiences maximum displacement from an applied force 90 degrees after the point where the force is applied. The force acts where applied, but its associated maximum displacement is delayed.
This is why controls are typically placed 90 degrees out from where they are needed (the lateral servo is along the longitudinal axis).
On some installations, servo arm size and length of pitch change link can make moving the servo necessary to apply the force at the right point. Additionally, the resonant frequency of articulated heads can be altered by the distance from the hub to the hinge.
p.60

21. Lead-Lag Advancing Blade (Flaps Up) Moves Forward on lead-lag hinge
Compensates for:
Conservation of Angular Momentum
Dissymmetry of Drag
Advancing Blade (Flaps Up)
Moves Forward on lead-lag hinge
Retreating Blade (Flaps Down)
Moves Aft on lead-lag Hinge
Advancing Blade
Flapping up
moves the blade forward on the hinge (lead-lag hinge) as the blade speeds up and flapping down moves it aft as the blade slows down.
Retreating Blade:
Flap Down:
When a blade flaps down its center of gravity moves out from the axis of rotation onto a larger radius and its velocity slows down.
Dynamics of Lagging Hinge with Offset
1. Inertial Force
2. Centrifugal Force
3. Aerodynamic Drag Force
p.58

22. Lead-Lag Diagram Vforward Front Rear Advancing Blade Flapping up
moves the blade forward on the hinge (lead-lag hinge) as the blade speeds up and flapping down moves it aft as the blade slows down.
Retreating Blade:
Flap Down:
When a blade flaps down its center of gravity moves out from the axis of rotation onto a larger radius and its velocity slows down.
Front
Rear

23. Velocity Distribution
j = 180
Nose WR W
Advancing Tip Speed
WR+Vf
j = 270
j = 90
WR-Vf
Reverse flow region
Retreating Tip Speed WR
Tail
j=0

24. Non-uniform induced velocity
Dissymmetry of Drag Di vi
Rear BLADE CARRIES MORE drag. Rear blade is more torque.
--Nose Blade: Less Induced Flow -> means less drag and a higher AOA because more lift produced
--Tail Blade: More Induced Flow -> means more drag and a lower AOA because less lift produced
Set rear blade higher. Left cyclic input. Sets AOA on blade. – Left turns require more torque.
Why: Due to non uniform induced velocity.
What is the most effective rotor blade: The advancing blade due to the V-squared blade.
2nd most efficient: Nose blade – over nose, best lift vector
3rd most efficient: retreating blade
Least effective: blade over tail. But the most “torque-ee-est” blade.
Non-uniform induced velocity

25. Feathering, Flapping, Lead-Lag
Note:
Ordered Effect:
Longitudinal Flapping
Lateral Flapping
Feathering – the change in pitch due to cyclic position. Constant collective
Flapping – Advancing blade flaps up, but video show flapping down. Due to where we are looking
- Cyclic flapping
- Velocity flapping (longitudinal blowback)
- non induce velocity (Lateral flapping)
Cyclic flapping is evident.
Velocity flapping is happening, but you can not see this flapping. – Could see velocity flapping if you started from a hover and accelerated.

26. A Few Problems to Lift Distribution

27. Spanwise Lift Distribution?
This is Ideal, but not Achievable.
p.62

28. Spanwise Lift Distribution
This is Hover Lift Distribution if there is no blade twist.
p.62

29. Solutions for Spanwise Lift Distribution Problem
Blade Twist (Washout)
Used to even out induced flow across the disk.
Optimum condition is uniform induced velocity over disk.
Geometric Twist
Change angle of twist
Aerodynamic Twist
Change Shape of Airfoil
p.63

30. Geometric Twist
Blade twists down as go out

31. Aerodynamic Twist

32. Aerodynamic Twist
Outboard segment – less Cl since we don’t want as much lift outboard

33. Aerodynamic Twist Change the airfoil shape Root Tip
Thicker at root
Higher Cl values
Tip
Thinner Tip
Smaller chord > less surface area
Airfoil and Taper yield Aerodynamic Twist

34. Spanwise Lift Distribution
Ideally Twisted
(In Hover)
Twist + Flapping

35. Taper

36. Taper

37. A balance of lift and Centrifugal Force
Coning
A balance of lift and Centrifugal Force
Coning: result of CF and lift. For the rotor in a hover: An equilibrium condition exists between the aerodynamic forces on the blade and the centrifugal forces on the blade.
At a point:
Integrated along the length
Per blade the Centrifugal Force is
approximately 10x that of the Lift Force
p.64

38. Control Moment Teetering Rotor Head
Control moment produced as Thrust vector is moved, without the production of lift there is no moment.

39. Control Moment Fully Articulated Rotor Head
If the flapping hinge is displaced from the center of rotation then cyclic inputs will incur a control moment coupling even without the production of lift.
p.66, See Fig 12

40. Questions
Describe 2 types of flapping.
Longitudinal, Lateral.

41. Questions What is Blowback. Blowback: Longitudinal Flapping:
The separation of the virtual axis from the control axis in forward flight; tends to make the nose pitch up.

42. FYI – Lateral Flapping To be covered in CH 9.
Transverse Flow Effect: Also know as Lateral Flapping:
Non-uniform induced velocities in forward flight; tends to make the helicopter roll toward the advancing blade.
(CCW rotation --> right roll)

43. Questions State 2 solutions to the spanwise lift distribution problem.
Geometric and Aerodynamic Twist

44. Learning Objectives – Ch 4
List the three degrees of freedom for a rotor blade, and their purpose.
Draw or explain how flapping equalizes lift distribution over the rotor, using a blade element diagram.
Describe what rotor “blowback” is, and how the rotor’s thrust axis separates from the control axis as airspeed increases.
List the solutions to obtain a more ideal lift distribution over the rotor disk.
Describe the forces that are responsible for determining a rotor blade’s coning angle.
Explain how the mechanisms and design of the rotor blade affect flight.
Discuss the differences of the rotor axes in hover and in forward flight.
Topics of discussion.

45. Extras

46. Collective Feathering

47. Spanwise Lift Distribution
Untwisted
Ideally Twisted
This is Hover Lift Distribution : With and without blade twist.

48. Lift Distribution View: Looking Forward p.62 Without Flapping
Retreating Blade
Advancing Blade
With Flapping
View: Looking Forward
p.62

49. Geometric Twist
Ideal Twist