Why a Helicopter Can Fly

The secret of rotating wings

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Abstract


We explain how the rotor blades of a helicopter acting like a pair wings generate lift and the expense of torsion of the rotor axis to overcome drag.


Rotor Blades Act Like Wings

Based on the Knol Why a Propeller Gives Thrust  based on Why It Is Possible to Fly we explain how the rotor of a helicopter acting like a propeller with rotating wing blades, generates lift L at the expense of torsion of the rotor axis to overcome drag D with lift/drag ratio L/D > 10. Classical explanations are incorrect or insufficient as evidenced by e.g.
  • Helicopter Flight TheoryYet, though the term “planing” is helpful in creating a visual image of the action of a lifting surface, it must be said that this does nothing to explain how the actual lift forces are produced or show the real effect on the air mass. The theoretical aspects cannot be adequately explained here…
  • Helicopter Aviation: The shape of the airfoil causes a low pressure area above the airfoil according to Bernoulli’s Principle, and the decrease in pressure on top of the airfoil exerts an upward aerodynamic force. 
  • Principles of Helicopter Aerodynamics: Aerodynamically the airflow through the helicopter rotor is extremely difficult to define and even after many years of study it still defies a fully adequate description.

                                                           Toy helicpoters.

Shortcut to the Action of a Wing

Below we give a pictorial description of how a wing generates lift and drag as a result of a perturbation of zero lift/drag potential flow arsing from a mechanism of instabillity at rear separation:

Sideview of velocity and pressure, and topview of streamwise vorticity of Naca0012 wing at aoa = 14. Observe the turbulent streamwise vorticity emanating from top separation, as sketched above. Computed solution of the Navier-Stokes equations with small friction force boundary condition [3].


Principle of action of a wing: Potential flow (upper left) with zero lift/drag modified by low-pressure counter-rotating rolls of streamwise vorticity from instability mechanism at separation (upper right), switching the pressure on rear wing (bottom) to give both lift and drag (H high, L low pressure).
                                Lift and circulation (x2)  of  Naca0012 as functions of the angle of attack. 

Variable Angle of Attack

We see in the above figure that the lift L scales linearly with the angle of attack aoa for aoa < 15 (and that circulation theory is incorrect). Further, L scales quadratically with the velocity of the rotor blade vs the air, and since the velocity is bigger advancing than retreating, it is necessary to change the aoa cyclically as each blade revolves, so that the lift becomes is equally distributed. This is done by a rotor hub:

                                  

If the relative velocity is twice as big advancing than retreating (at forward speed of about 200 km/h), then the lift with the same aoa  would be four times as large advancing than retreating, an unbearable lift force variation.
The drag D acting in the horisontal plane of rotation of the blades creates a torsion which is balanced by a
a tail propeller. 
With L/D = 10 and a rotor speed of 75 m/s each horse power can lift 10 kg, so 200 horse powers would
suffice to lift a 2000 kg helicopter, ideally.