Rotorcraft Theory (🩷◕‿◕🩷)

EG3081

What is rotorcraft?

A heavier than air aircraft with rotary wing generating lift by rotating around a vertical mast.

What are the two main types of rotorcraft?

Helicopters (powered rotors) and Autogyros (unpowered rotor during flight).

How do helicopter differ from autogyros?

Helicopter can hover, take off vertically, and have rotor control input.

Autogyros cannot hover and rely on airflow to power the rotor during flight.

Why do we study rotorcraft?

Rotorcraft principle are used in helicopters, drones, wind turbines, and ship propellers.

What is induced velocity?

The downward velocity imparted to the air by the rotor generating thrust.

What is the relationship between thrust and induced velocity in hover?

T=2ρπ(R^2)(vi^2)

What are the key assumptions of momentum theory?

Flow is incompressible and axially symmetric, velocity is constant across the disc, and far-field flow is at rest.

What is the purpose of a blade element theory (BET)

To calculate rotor thrust and torque by summing aerodynamic forces along the blade span

What is the vortex ring state?

A condition where descending airflow reverses upwards through the rotor, causing a loss of lift and control.

How can the vortex ring state be avoided?

By increasing forward speed or reducing the descent rate.

What is the role of the pre-rotator in autogyros?

It spins the rotor during take off to reduce the required speed take off distance

What is autorotation?

A state where the rotor spins freely, powered by airflow, allowing for emergency landings without engine power

How does forward flight differ from hover

In forward flight, blades experience asymmetric loading, with the advancing blade generating more lift than the retracting blade.

How can cyclic pitch control be used in forward flight?

Cyclic pitch adjusts blade angles to tilt the rotor disk forward for propulsion or laterally for balance.

What is the purpose of the blade flapping?

To compensate for asymmetric lift between advancing and retracting blades in forward flight

What is the retracting blade stall?

A condition where the retracting blade’s angle of attack exceed the stall limit, reducing lift.

What are the main rotor control imputs?

A collective pitch (𝜃_0) for uniform thrust and cyclic pitch (𝜃_1s, 𝜃_1c) for disk tilt.

How is yaw control achieved in a single rotor helicopters?

Through tail rotor thrust, counteracting main rotor torque

What is purpose of aerodynamic damping in flapping motion?

To reduce oscillations and stabilise the rotor’s response to disturbances.

The flapping motion creates opposing aerodynamic proportional to velocity , reducing oscillation.

What are stability derivatives?

Metric like forward speed damping (M_u), vertical damping (M_w) and pitching damping (M_q) that describe stability contributions.

What is the thrust coefficient (C_T)

C_T = T/(ρA(ΩR)^2)

What is the power coefficient (C_P)?

C_P = P/(ρA(ΩR)^3)

What is the figure of merit?

M = P ideal / Ptotal measuring rotor efficiency.

Higher indicate more efficient rotor.

How do tandem rotors differ from single rotors?

Tandem rotors uses differential thrust and tilt for pitch control, eliminating the need for a tail rotor.

What is unique about coaxial rotors?

They have two counter-rotating rotors on the same shaft to balance torque without a tail rotor

What are transverse rotors?

Two side by side rotors used for lateral balance via differential thrust.

How is induced velocity on hover calculated?

v_i = sqrt(T/(2ρA))

What is the thrust equation in vertical climb?

𝑇=2𝜌𝜋(𝑅^2)(𝑈_𝐴 + 𝑣_1)*𝑣_1

What is the thrust equation for windmill brake descent?

𝑇 = 2𝜌𝜋(𝑅^2) (𝑉_𝐷 − 𝑣_𝑖𝐷) 𝑣_𝑖 𝐷

What are the key factors affecting rotor efficiency?

Rotor speed (Ω), blade chord (c) and pitch angle (θ)

What are the limitation of the momentum theory

Assume steady, incompressible and axisymmetric floe cannot model unsteady effects like vortex ring state or windmill brake conditions.

What is the role of blade twist in BET?

Reduces inboard stall and improves efficiency and improves efficiency by distributing lift evenly along the blade span.

How does differential collective pitch affect yaw in tandem?

It creates torque to yaw the aircraft but must be balanced to avoid pitch instability.

why does vortex ring state occur more frequently in hover descent?

Hover descent produces a strong recirculation of airflow reducing effective thrust.

What are the two main issues driving the multi-rotor configurations widely used in the early rotorcraft development?

Torque balance.
Rolling moment in forward flight

How does the single rotor helicopter deal with the torque balance?

Tail rotor.

How does single rotor helicopter deal with the rolling moment in forward flight?

Flapping motion

What is the difference between the helicopter and autogiros?

1. The rotor powered by the engine in the cruise flight.

2. Autogiros cannot take-off vertically without the help of pre-rotator.

3. Hover capability.

4. The helicopter may be larger than than the autogiros.

5. Autogiros sometime are not equipped with rotor control input.

Why does not the autogiro need a tail rotor?

The rotor of the autogiro does not connect with the engine, and it cannot transmit torque to the vehicle

What is the FUNDAMENTAL difference between the helicopter and the autogiro?

The rotor powered by the engine during cruise flight

The function of the swashplate?

Adjust the blade control angle at different azimuth angle.

What is the difference between the thrust and lift?

Thrust is in the rotor axial direction.
Lift is normal in the inflow direction

The assumptions of the momentum theory?

1) Existing a steam tube which is an axially symmetric surface passing through the rotor disc perimeter which isolates the flow through the rotor.
2) Incompressible flow.
3) Velocity imparted to the fluid is constant across the disk.
4) Far away from the disk, the air is at rest.

What is the definition of induced velocity?

The velocity increment due to the rotor is called Induced Velocity.

What is the condition of the momentum theory applicable to the vertical descent flight?

|U_A| > 2* v_i,hover

What is a Figure of Merit used for?

It is used to evaluate rotor performance in hove

What is the difference between calculating the rotor power from the momentum theory, compared to the blade element theory?

The power from the momentum theory is the induced power (induced + parasite power in forward flight), and the power from the blade element theory is the all rotor power consumption.

Why can’t the rotor provide any thrust in the vortex-ring state?

The vortex ring state sucks the downstream flow back, increasing the normal velocity Vn significantly, which makes most of the blade in the stall condition.

What is the most reasonable pilot control strategy to get rid of the vortex ring state?

Push longitudinal cyclic pitch to increase forward speed.

From the view of the blade element theory and considering the attack angle and the inflow condition, indicate why the rotor needs the pre-twist angle?

The pre-twist angle allows most of the blade element (especially the blade tip section) to be in the optimal attack angle (maximise the ratio between lift and drag).

Demonstrate the function and mechanism of the pre-rotator?

Reduce the take-off distance of the auto-rotator and even allow the autogiro to have vertical take-off capability.

Demonstrate the mechanism of the pre-rotator?

Let the engine link with the rotor on the ground to make the rotor rotate, which will disconnect with the rotor after take-off.

Demonstrate the control strategy of the collective pitch during the autorotational landing?

Reduce the collective pitch to maintain the rotational speed, and when the vehicle is close to the ground, increase the collective pitch to add additional vertical acceleration to reduce the vertical speed.

In the autorotation process, is the helicopter similar to the autogiro’s rotor. If so, how?

In the autorotation process, the helicopter is similar to the autogiro’s engine, providing no torque to the vehicle.

Which azimuth angle will be the highest point if we only consider the dynamic pressure difference in forward flight?

180 degrees

Which azimuth angle will be the highest if we only considered the coning angle in forward flight?

270 Degrees.

Which azimuth angle will be the highest point if we only consider the longitudinal cyclic pitch (use it to increase forward speed)?

0 Degrees

If we want to provide additional right force along from the rotor in an anti-clockwise rotor, which direction should the swashplate change?

Tilt backwards.

By optimising the pre-twist angle, which component of the power consumption will be reduced?

Profile Power.

By optimising the geometry of the fuselage, which component of the power consumption will be reduced?

Parasite Power.

Which component of power will increase due to the tip blade compressibility effect?

Profile Power

Why is the induced power reduced with forward speed increases?

The local dynamic pressure is higher.

Which components provide the mass, damping and stiffness terms of the rotor flapping dynamic equation?

Inertia force, aerodynamic force, and centrifugal force: respectively.

What is the flapping offset influence on the flapping frequency and flapping phase delay angle?

Increase the flapping frequency angle and reduce the flapping phase delay angle

Why the flapping phase angle is close to 90 degrees?

The natural frequency of the flapping motion is close to the rotational speed, and the excitation frequency is equal to the rotational speed. Thus, the system is in the resonance condition, in which the phase delay is 90 degrees.

What causes the lead-lag motion and why the rotor must have the lead-lag hinge?

The lag (lead-lag) motion is due to the Coriolis forces provided by the flap and the lead lag hinge is used to reduce this harmonic load damage on the rotor hub.

With forward speed increase, how will the reverse flow area change and how will it influence the rotor aerodynamic?

The reverse flow area will increase with forward speed, and it would reduce thrust and increase the rotor drag.

How will the flapping offset provide additional control moments and how will it influence the pitching and rolling damping?

The flapping offset gives a moment to let the rotor thrust contribute to the control moment, which is called the hub moment. The flapping offset can make the rotor provide additional pitching and rolling damping

For a rotor system with no flapping offset and its rotational direction is anti-clockwise:
When the helicopter is in forward flight:
Indicate the direction of increment of the rotor thrust, forward/backward forces, and rotor tilting angle (flapping motion) provided by pushing backwards the longitudinal cyclic pitch controller.

Higher rotor thrust, more backward forces, rotor tilt backwards.

For a rotor system with no flapping offset and its rotational direction is anti-clockwise:
When the helicopter is in forward flight:
Indicating the direction of the additional rotor thrust, forward/backward force and rotor tilting angle (flapping motion) provided by introducing additional lateral cyclic pitch?

Sideward force (direction: act as damping), rotor tilt sideward

For a rotor system with no flapping offset and its rotational direction is anti-clockwise:
When the helicopter is in forward flight:
Collective pitch influence on the rotor forward/backward forces and flapping direction.

Exaggerate the flapping motion, making the rotor tilt backwards and sideward.

When the helicopter is in hover, and the rotor is not tilted backward or sideward:
Vertical velocity influence on flapping motion.

Not create any sideward tilt, and coning angle will be changed

When the helicopter is in hover, and the rotor is not tilted backward or sideward:
If a man is walking from the cockpit to the tail part of the vehicle, how will the trim control input, pitching altitude, rotor flapping, and tail rotor thrust change?

Collective pitching will be higher, additional nose-up pitching altitude, the longitudinal cyclic pitch should be pushed forward, the rotor is flapping forward, and tail rotor thrust will increase.

For a single-rotor helicopter configuration, they usually have a pre-setting angle. It means the rotor hub shaft tilts forward:
When this helicopter is in hover flight, the trim pitching angle of this type of rotorcraft should be….

nose up

For a sing-rotor helicopter configuration, they usually have a pre-setting angle. It means the rotor hub shaft tilts forward.
Compared to the traditional rotor design with no pre-setting angle, how will the pitching altitude and longitudinal cyclic change in the forward flight.

The pitching altitude will be more nose-up, and longitudinal cyclic control input will be more backwards.

Here is the x3 rotorcraft and its power consumption figure. This helicopter can fly at a higher forward
speed compared to the traditional helicopter

Compared to the trimmed collective pitch of this vehicle and the vehicle sharing the same size but without the wing system in hover and high-speed forward flight.

The trim collective pitch of X3 would be higher in the hover but lower in the high-speed flight.

Here is the x3 rotorcraft and its power consumption figure. This helicopter can fly at a higher forward
speed compared to the traditional helicopter.

Indicate the reason why this vehicle ground effect is lower than the single-rotor helicopter configuration.

The rotor wake is affected by the wing system, and therefore the airflow momentum that can hit the ground would be reduced.

Here is the x3 rotorcraft and its power consumption figure. This helicopter can fly at a higher forward
speed compared to the traditional helicopter

What are the two main reasons related to the rotor that limits the helicopter’s maximum flight speed?

Advancing tip compressibility effect, stall condition in the retracting side.

Which vehicles can be categorised as rotorcraft?

• Tiltrotor Aircrafts.

• Quadrotor Drone
  (basically anything with a rotor system)

What is the aim of developing the flapping motion for rotorcraft?

Balance the rolling moment in forward flight.

What is the most essential difference between the helicopter and the autogiro.

Whether the rotor is powered by the engine during the cruise flight

What type of rotorcrafts can fly forwardly without the flapping motion?

Tandem Configuration, Side-by-side Configuration and Quadrotor Drone.

What can the figure of merit not exceed?

The figure of merit cannot exceed 100%.

Which of the following statements related to the momentum theory is right

(a) It cannot be used in the vertical descent flight
(b) It can be used to evaluate the vortex-ring state’s induced velocity
(c) Its accuracy is still acceptable in the small speed vertical descending flight
(d) The hover equivalent induced velocity is always larger than the absolute value of the
induced velocity

(c) Its accuracy is still acceptable in the small speed vertical descending flight

Which of the following statements related to the blade design is right
(a) The lift coefficients at different radius locations are the same.
(b) Incidence angles at different radius locations are the same.
(c) The blade control angle at the tip is always lower than that at the root.
(d) The thrust calculated by the blade element theory is related to the induced velocity.

(c) The blade control angle at the tip is always lower than that at the root
(d) The thrust calculated by the blade element theory is related to the induced velocity.

When the rotorcraft is hover, which blade section is easier to be in the stall condition?

0.00R - 0.25R