Lateral Flapping Angle
The coefficient fas represents the amplitude of the pure sine motion (see Fig. 4.8). This represents the lateral or left-right tilt of the tip path plane. In addition to the natural tendency for the disk to tilt back with a change in forward flight speed, the disk also has a tendency to tilt laterally to the right. This effect arises because of blade flapping displacement (coning). For the coned rotor, the blade AoA is decreased when the blade is at тД = 0° and increased when у/ — 180°. Again, another source of periodic forcing is produced, but now this is phased 90° out of phase compared to the effect discussed previously. However, because of the 90° force-displacement lag of blade, in this case it results in a lateral tilt of the rotor disk to the right when viewed from behind (i. e., a — fas motion). Notice that in the hypothetical case with no coning, the blades see the same increase in AoA at i/r = 0° and 180° and there will be no lateral tilt.
4.6.2 Higher Harmonics of Blade Flapping
The coefficients @2о fas, and so on, represent the amplitudes of the higher harmonics of the blade motion. In practice, these are found to be very small and of no substantial significance but appear as a slight warping or wobbling of the rotor tip path plane. For
(a) Pure lateral tilt (no coning) (b) Lateral tilt (with coning)
Figure 4.8 Pure lateral flapping of the rotor, with positive displacements shown.
rotor trim and performance evaluation it is considered acceptable engineering practice to neglect all harmonics above the first. However, the effects of higher harmonic flapping on the vibration and aeroelastic stability characteristics of the rotor are important.