With variation of the flapping angles the plane of rotation and the coning axis deflect backward and to the side in the direction of the advancing blade through the angle т (Figure 38a). As a result of the tilt of the coning axis backward by the angle a^, there is an increase of the blade flapping angle to 8 = + a^ at the 180° azimuth and a reduction to 8 = a^ – a^
at the 0° azimuth (Figure 38b). Tilting of the cone axis to the side by the angle b^ leads to change of the flapping angles: at the azimuth 90° 8 = ад – b^; at the azimuth 270° 8 = a. Q + b^ (Figure 38c).
Figure 38. Blade flapping motions and tilt of main rotor cone axis. 1 – cone for p = 0; 2 – cone for у > 0.
Tilting of the cone axis backward by the angle a^ leads to deflection /55
through the same angle of the thrust vector and the formation of the longitudinal thrust component H (Figure 39a). This force is the projection of the main rotor thrust on the hub rotation plane. Since it is directed aft, it is a drag force and is analogous to the induced drag of an airplane wing. The
Figure 39. Main rotor thrust force components.
larger the flapping motions, the larger the backward tilt of the cone axis and the larger the longitudinal force H resisting helicopter forward motion. Consequently, the flapping motions in the forward flight regime must be restricted.
If the deflected thrust T is projected on the hub axis, we obtain the force required for helicopter flight
Ty =.T cos au
In view of the smallness of the angle a^(2 – 3°) we can take a^ « 1. /56
Then T и T.
The sideward tilt of the cone axis (Figure 39b) leads to the appearance of the side force Sg, which is the projection of the main rotor thrust on the hub rotation plane
S = T sin b.• s 1
Since this force is directed to the left, this direction is unfavorable for single-rotor helicopters. Therefore, the blade flapping motions must be restricted in order to alter the sideward tilt of the cone angle from the
left to the right. Moreover, restriction of the flapping motions is also necessary to reduce main rotor vibrations.