Main/OneNote/OSD/Research/Helicopter.md

> [!caution] This page contained a drawing which was not converted.  

Tip speed should not exceed 200 m/s.

For us that is roughly 6400 rpm.

Formula: 200*60/D/pi

- Rotor size and max weight are first things to consider.
- Normalizing Entities to compare between models --> make dimensionless
    
    - Non-dimensional induced velocity
        
        - ![Exported image](Exported%20image%2020231126172013-0.png)
    - Thrust coefficient
        
        - ![Α ](Exported%20image%2020231126172013-1.png)
        - VT is tip speed of blade
        - Thrust is divided by dynamic pressure times area --> gives Force [N]
    - Combined:
        
        - ![ст 
            Ст — 411 ](Exported%20image%2020231126172013-2.png)
- Power overview:
    
    - Induced Power is major part of power during hover
    - Power to overcome blade drag PO
    - ==Solidity== of rotor:
        
        - ![Exported image](Exported%20image%2020231126172013-3.png)
    - Skin friction drag:
        
        - ![Exported image](Exported%20image%2020231126172013-4.png)
          
          
        - ![Exported image](Exported%20image%2020231126172013-5.png)
    - Rotor efficiency: M = Pi/PO --> Figure of Merit
        
        - ![- (CT)3/2 
            2 ](Exported%20image%2020231126172013-6.png)
        - ki is induced power factor because of a variation in induced velocity

  
  

# Blade Aerodynamics

- ![dL 
    Disc Plane 
    Figure 3 A 
    Blade Section 
    Blade section flow conditions in vertical flight ](Exported%20image%2020231126172013-7.png)
- Angles:
    
    - Inflow Angle (small angle approx)
    - ![Exported image](Exported%20image%2020231126172013-8.png)
    - Theta: pitch control by pilot
    - Alpha: angle of attack seen by blade
- Aerodynamic forces
    
    - Lift and Drag
        
        - ![dL=-pU2.cdr.CL 
            dD=-pU2.cdr.CD ](Exported%20image%2020231126172013-9.png)
    - Thrust
        
        - ![Exported image](Exported%20image%2020231126172013-10.png)
    - Blade Torque
        
        - ![Exported image](Exported%20image%2020231126172013-11.png)
    - Thrust coefficient with a linear twist blade and the assumption of no stall and no compressibility
        
        - ![075% λ ](Exported%20image%2020231126172013-12.png)
          
        - ![Exported image](Exported%20image%2020231126172013-13.png)
        - Lambda: inflow factor
            
            - ![Exported image](Exported%20image%2020231126172013-14.png)
            - Relating the inflow factor to momentum theory (see above)
                
                - ![CT = sa 
                    3 
                    2 
                    CT 
                    2 ](Exported%20image%2020231126172013-15.png)
            - Relationship between inflow factor and pitch setting
                
                - ![Exported image](Exported%20image%2020231126172013-16.png)
    - Why are blades twisted? My assumption is that the angle of attack seen by the blade depends on the wind speed it experiences. This in turn, depends on the radius and the angular velocity of the blade. The closer you are at the hub, the larger is the inflow angle and thus the smaller is the angle of attack. That means if we twist the blade and add additional aoa close to the hub and remove aoa where the speed is high, we will have more lift in total and not have a stalling condition somewhere and not at other places.

  

# Flapping, Feathering & Lead-Lag

- Coriolis Force induces lag
    
    - ![In Newtonian mechanics the equation ot motion tor an object in an ineäial reference tram 
        F = ma 
        where F is the vector sum ot the physical forces acting on the object, m is the mass ot tr 
        Transforming this equation to a reference frame rotating about a fixed axis through the orl 
        F m — x — 2mu x — mu x x ) = ma' 
        where 
        F is the vector sum of the physical torces acting on the object 
        is the angular velocity, of the rotating reference frame relative to the inertial trame 
        v' is the velocity relative to the rotating reference frame 
        r' is the position vector of the object relative to the rotating reference frame 
        a' is the acceleration relative to the rotating reference frame 
        The fictitious forces as they are perceived in the rotating trame act as additional forces thi 
        • Euler torce —m— x 
        • Coriolis torce —2rn(w x v') 
        • centrifugal force —mu x (w x r' ](Exported%20image%2020231126172013-17.png)
-