Single main rotor helicopter

[Marco9518]

Hello everyone!
I am currently developing a thesi to become an aeronautical engineer.
I am trying to reproduce the NASA report "a mathematical model of a single main rotor helicopter for piloted simulation".
I already built a simulink model but i am having a bit of trouble looking at the equations.
I uploaded a picture of the equation's set. I can't explain the L equation highlighted.
How can the lift be 0 when the angle of attack is 90 or -90 deg? cos(90) is zero, but at that alpha the lift should be maximum.

Thank to who will answer!

 

[Arjan82]

Lift is always defined perpendicular to the inflow. So if at cos(90), then I guess the blades are not rotating and your chopper is falling straight down. But the lift is now defined perpendicular to the inflow, which is directed in the horizontal plane, so you will not ever get any lift from this 'lift'... :) Only some from the drag component, which is directed vertical in this case.

 

[Lnewqban]

What angle does alpha represent in that equation?

 

[berkeman]

I am trying to reproduce the NASA report "a mathematical model of a single main rotor helicopter for piloted simulation".

Here is a link to that report for background info for everybody:

https://ntrs.nasa.gov/citations/19830001781

 

[FactChecker]

How can the lift be 0 when the angle of attack is 90 or -90 deg? cos(90) is zero, but at that alpha the lift should be maximum.

Why do you say this? At that angle of attack, there will only be drag. That would be the air hitting the blade broadside. (Is this angle of attack with respect to the blade motion or to the vehicle motion?)

 

[Marco9518]

Lift is always defined perpendicular to the inflow. So if at cos(90), then I guess the blades are not rotating and your chopper is falling straight down. But the lift is now defined perpendicular to the inflow, which is directed in the horizontal plane, so you will not ever get any lift from this 'lift'... :) Only some from the drag component, which is directed vertical in this case.

Thank you a lot for your answer. So at the moment i am modelling the fuselage alone and i am not taking into account any other component. As soon as i figure this out i will add the rotor inflow. For what i understand it is than possible for the lift to be zero at that angle of attack.

 

[Marco9518]

Why do you say this? At that angle of attack, there will only be drag. That would be the air hitting the blade broadside. (Is this angle of attack with respect to the blade motion or to the vehicle motion?)

Thank you a lot for your answer. So at the moment i am modelling the fuselage alone and i am not taking into account any other component. Talking about the angle of attack, they did not make very clear the reference axis. I supposed it to be with respect to the fuselage motion.

 

[Marco9518]

What angle does alpha represent in that equation?

The way i formulated it, it represents the angle between the direction of the flow and an ipotetical "chord" that goes from the nose to the tail of the fuselage.

 

[Lnewqban]

The way i formulated it, it represents the angle between the direction of the flow and an ipotetical "chord" that goes from the nose to the tail of the fuselage.

It seems to be the lift contribuited by the fuselage while the helicopter is vertically descending for landing, which should equal its drag.
In that case, I can’t understand that equation; sorry.