It is possible to quantify the longitudinal beat angle by an easily understandable mathematical formula:

As long as we assume that the lift of a representative blade element is proportional to A.o.A (i.e. without stall), and proportional to the square of the airspeed, then the compensation of the speed difference between the advancing and retreating sides by the A.o.A difference can be translate approximately as follows:

*(Vc*+*Vf)² */ *(Vc-Vf)²* *=** (αa + a1) / (αa – a1)*** (*)**

The solution to this equation is *a1 = 2 αa Vc Vf / (Vc**²*+ Vf*²*)

**(*)** In which* Vc* is the circumferential velocity, *Vf * is the forward velocity, *αa* is the average angle of attack, and *a1* is the longitudinal flapping angle

If, in flight, *αa* = 5°, *Vf* = 35 m/s, and *Vc* at ¾R = 120 m/s then *a1* = 2*5*120*35/ (120*²*+35*²*) = 2.7°

So, the angle of attack of this element on the retreating side is then *(αa + a1) = *5° + 2.7° = 7.7° (i.e below the stall)

Now if, during the run, *αa*= 8° (due to the large disc A.o.A), *Vf* = 10 m/s, and *Vc* at ¾R = 30 m/s then *a1* = 2*8*30*10/ (30*²*+10*²*) = 4.8° So, the angle of attack of this element on the retreating side is then *8°* + 4.8° = 12.8°

We see it is above the stall and the compensation is impossible. Thus, the flapping angle will increase to each round until the blades hits it stops.