Physical Description of Blade Flapping
The basic physics of blade flapping are relatively elementary, although on an actual helicopter during flight, the combined harmonics of the flapping displacements result in a more complicated blade motion. To this end, it is convenient to explain the net blade motion in terms of the contributing elements. This is the approach followed by Gessow & Myers (1952).
4.6.1 Coning Angle
The coefficient & is the average or mean part of the flapping motion that is independent of time or blade azimuth, fs. In hovering flight, — fio, which, as mentioned previ
ously, is called the coning angle. The presence of a coning angle has been pointed out to be the angle that results from the moment balance about the flapping hinge as a result of the centrifugal and aerodynamic forces. Because the centrifugal loads remain constant for a given rotor speed, the coning angle vanes with both the magnitude and distribution of lift across the blade. For example, a higher gross weight of the helicopter requires a higher blade lift to hover, which tends to increase the aerodynamic moment about the hinge, resulting in a higher blade coning angle. Also, it is already known from the previous discussion in Chapter 3 that the inflow velocity has an effect on the blade spanwise loading. As the magnitude of the inflow increases, for a given overall total rotor thrust the blade must become more highly lift loaded toward the tips. This produces a higher aerodynamic moment about the hinge and, therefore, a higher coning angle. Because the time-averaged inflow (induced velocity) through the rotor disk changes with forward speed, the rotor coning angle will mimic the variation in mean inflow through the disk with forward speed, as discussed in Section 2.14.6.