Rotor reference axis So far we have used the same reference axis: Z aligned with the rotor shaft Y perpendicular to Z and along the blade (in the rotor plane). X in the rotor plane and perpendicular do Y A person with this set of axis will see the blade flapping, lagging and feathering. Although complicated it has the advantage of being linked to a physical part of the aircraft Slide 1
Rotor reference axis We could choose other axis on which the movement are not so complex: Slide 2
Rotor reference axis We have therefore defined four planes: Hub Plane (HP) perpendicular to the shaft No Feathering Plane (NFP) along the airfoil chord Tip Path Plane (TPP) with the boundary described by the blade tips Control Plane (CP) parallel to the swashplate Slide 3
Rotor reference axis No Feathering Plane (NFP): An observer see no variation of the cyclic pitch, that is θ 1c and θ 1s are zero. There is still the flapping movement Used for performance analyses Slide 4
Rotor reference axis Tip Path Plane (TPP) An observer see no variation in flapping, that is β 1c and β 1s are zero. The observer will see: Feathering Lagging Used for aerodynamic analyses The thrust resultant aligns within a degree of the Tip Path Axis (note that the TPP is not strictly a plane) Slide 5
Rotor reference axis Control Plane (CP) The observer will see no pitch variation The observer will see blade flapping and dragging Slide 6
Rotor reference axis Relations between axis Looking along the advancing blade Slide 7
Rotor reference axis Relations between axis Looking from the rear of the disk Slide 8
Rotor Trimming Slide 9
Rotor Trimming T T W T D D W Slide 10 W
Rotor Trimming T T W T D D W Slide 11 W
Forces and momentums applied Longitudinal trim Slide 12
Forces and momentums applied Lateral trim Slide 13
Force Equilibrium The contributions for the force are : Weight (W) Main Rotor Thrust (T MR ) Fuselage Drag (D) Fuselage Side Force (Y F ) Main Rotor Hub Drag (H MR ) Main Rotor Side Force (Y MR ) Vertical Tail (F VT ) Horizontal Tail (F HT ) Tail Rotor Thrust (T TR ) Slide 14
Force Equilibrium For simplicity we will assume: There is no side slip angle (Y F =0) There is no contribution from the Vertical Tail (F VT =0) There is no contribution from the Horizontal Tail (F HT =0) Thrust is aligned with the rotor shaft Slide 15
Force Equilibrium The vertical component equation is: The longitudinal component equation is: The lateral component equation is: Slide 16
Moment Equilibrium The contributions for the moment are: From the main rotor (M MR ) From the fuselage (M F ) From the horizontal tail (M HT ) From the vertical tail (M VT ) From the tail rotor (M TR ) Other sources (M O ) Slide 17
Moment Equilibrium Taking the moments about the rotor hub: Pitching moment Rolling moment Torque equilibrium Slide 18
Equilibrium Equations Using small angle assumptions: Slide 19
Forces The rotor thrust: Number of blades times the average of one blade lift per revolution The thrust coefficient Slide 20
Forces We could introduce the assumptions already made previously: Linear twist θ tw =const. Uniform inflow λ(r,ψ)=const. Rectangular blade c=const. And analytically we can obtain Slide 21
Forces We can use a similar process to calculate the other forces, with the rotor drag force H MR or H-force The H-force coefficient Slide 22
Forces the rotor side force Y MR or Y-force Using the same principle we could get the Y-force coefficient Slide 23
Moment Rotor torque Rotor rolling moment Rotor Pitching moment Slide 24
Inflow If we want to determine the trim value for both the main rotor inflowλ MR and the tail rotor inflowλ TR then two extra equation are needed. Using simple momentum theory Slide 25
Inflow In the previous expressions: µ MR cos α MR =V/(Ω MR R MR ) α MR is the main rotor disk angle of attack (=α) µ TR cos α TR =V/(Ω TR R TR ) α TR is the tail rotor disk angle of attack (=0 if there is no side slip) Slide 26
Equilibrium The vehicle equilibrium equation (with the inflow equations) can be written in the form F(X)=0 wherexis a vector of rotor trim unknowns: Slide 27