Blade Flapping is a helicopter design feature, used to overcome a burden of theirs called Dissymmetry of Lift. I recommend reading that node (and perhaps its stablemate Retreating blade stall) before continuing, though a brief summary follows anyway.

A helicopter produces lift with spinning rotor blades. Each one of these is effectively a wing, which produces lift as a function of surface area, angle of attack and airspeed. However because the rotor is spinning in what may be a prevailing wind, or because the helicopter is flying in a particular direction, its airspeed is never quite constant. As each rotor blade turns it changes orientation relative to the prevailing speed and direction of the air; therefore its own airspeed, and thus the amount of lift it generates, also changes. When a rotor blade is travelling forwards to meet the wind its total airspeed is the sum of its own airspeed and the airspeed of the wind meeting it.

If a helicopter rotor is turning at (say) 200 knots and the helicopter is flying forwards at 100 knots, a rotor blade approaching this wind will have an effective airspeed of 300 (200 + 100) knots. A rotor blade retreating from this wind will have an effective airspeed of only 100 (200 - 100) knots. Clearly the approaching and retreating rotor blades will generate significantly different amounts of lift. Without correction, this would cause a helicopter to pitch up or down (depending on the direction the rotor blades turn) if it were moving forwards, backwards, sideways or hovering in windy conditions. Flapping rotor blades are one of the main methods of counteracting lift dissymmetry.

# Why

The lift generated by the main rotor disc must be equalised. It is not acceptable for one side of the rotor disc to create more lift than the other; not only would maneuvrability suffer but it's plain unsafe. A big gust of wind could pitch the helicopter uncontrollably, as could lateral movement at any significant speed. To eliminate this problem, lift must be controlled and equalised between rotor blades at all times. The amount of lift a rotor blade produces is a function of its surface area, angle of attack and airspeed; since the rotor blade surface area is fixed and airspeed is beyond the remit of the designer, the only way of controlling how much lift it produces is to control its angle of attack.

The angle of attack of a wing surface is the angle between its chord line (an imaginary line between a wing's trailing and leading edges) and its relative wind. Up to a point, the greater this angle the more lift the wing produces. After that peak is reached the amount of drag produced becomes restrictive and less lift is produced. Rotor blades can stall just like conventional wings.

In a hover, the wind direction relative to the rotor blades is generally level with the tip plane path (a flat disc traced in the air by the spinning rotor tips):

```                                 @@@@@
@@@@@    A
@@@@@@         |
@@@@@@               | <--- Angle of Attack
@@@@@                     |
@@@@@@                          V
@@@@@ ################################     <<--- Relative wind direction/tip plane path
```

Although the collective and cyclic controls of a helicopter physically change the pitch (and thus the angle of attack) of each rotor blade constantly, these are not used to balance the lift produced by the rotor disc. I do not know why this is precisely, but I presume it is prohibitively complex to add yet another augmentation to the already-complex systems controlling rotor blade pitch. However if there were some way of changing the wind direction relative to each rotor blade it would have the same effect as physically changing the angle of the rotor blades.

This sounds quite ridiculous, but bear with me. The wind direction relative to any object is tied to its horizontal and vertical motion. If you were to move your hand in a horizontal line, the wind hits a different side of it than it does if you move it diagonally downwards. The blade flapping system uses the natural motion of the rotor blades to change the angle of the wind hitting them, effectively changing their angle of attack and with it, the amount of lift they produce.

The earlier diagram roughly represents a rotor blade of a helicopter hovering in still air. The blade is tilted but air is still approaching it from horizontal because there is no vertical movement; the rotor is turning horizontally. Now say the helicopter starts to move forward: as a rotor blade turns to face the wind its effective airspeed increases, meaning it creates more lift. The excess lift causes the rotor to flap upwards on the hinge at its base. Since the relative wind is equal and opposite the direction and speed of the rotor blade's movement, the relative wind will be downwards at the same angle and speed that the rotor blade is going upwards.

If the rotor blade rose 5° from horizontal, the relative wind would approach from a direction 5° from horizontal. However, the rotor blade pitch has not changed, so the effective angle of attack is less!
```From this:

@@@@@
@@@@@@    A
@@@@@          |
@@@@@@               | <--- Angle of Attack
@@@@@                     |
@@@@@@                          V
@@@@@ ################################    <<--- Relative wind direction/tip plane path

To this:                                  __
@@@@@_____| A
@@@@@@            |
@@@@@           _____  |  <--- Angle of Attack
@@@@@@       xxxxxxxxx     |_V
@@@@@    xxxxxxxxx
@@@@@@xxxxxxxxx
@@@@@ ################################    <<---   Tip plane path

x = relative wind direction

```
So, as the rotor blade is moving the fastest it actually produces no more lift because its angle of attack is reduced; the brief period of excess lift only allows the blade to flap upwards in order for this reduction to occur. Likewise, as the rotor blade enters the retreating side of the rotor disc and descends through reduced speed, the relative wind flows past the rotor blade at an increased angle; its angle of attack is increased so that it does not produce any less lift. This constantly equalises the lift produced by all parts of the rotor disc and means the helicopter does not become unstable in windy conditions or when moving at high speed.

Of course past a point, at excessively high speed, it is impossible to eliminate lift dissymmetry because the retreating rotor blades eventually have such a low airspeed that they cannot provide sufficient lift: retreating blade stall occurs. Further, this blade flapping must have a physical limit, which if reached can have serious consequences for the helicopter and occupants, should the rotors flap so far that the rotor hub comes into contact with the rotor mast.