Cyclic Pitch Change in Hover

In Chapter 3 it was shown that a hinged rotor blade without offset is a system in resonance; that is, its natural frequency is identically equal to its rotational

frequency. A characteristic of a system in resonance is that its maximum response follows by exactly a quarter of a cycle its maximum force input. Thus, if cyclic pitch is applied to a rotor of this type, it will have its maximum flapping amplitude 90° later. Although the derivation of Chapter 3 ignored the existence of aerodynamic forces, they do not change the phase lag from 90°. The aerodynamic forces only add damping to the flapping motion and, as shown in Figure 7.3, the phase angle is always 90° for any damping level. For a zero offset rotor in hover, a 10 change in cyclic pitch will result in a 10 change in flapping. The mathematical derivation of this will be given later; from an intuitive point of view, however, it is because the rotor’s stable condition is with no cyclic angle of attack variations with respect to its tip path plane without regard to the relative position between the shaft and the tip path plane. Thus the rotor flaps just enough to cancel out the initial cyclic pitch input and to return it to its initial hover angle of attack configuration with respect to its tip path plane.

If the rotor has hinge offset, the phase angle is somewhat less than 90° and the flapping is not quite numerically equal to the cyclic pitch. This is because as offset is increased, the restoring moment due to centrifugal forces increases faster than the moment of inertia about the flapping hinge; as a result, the flapping natural frequency is higher than the rotational frequency. In short, the system is no longer in resonance. The frequency ratio will be less than unity and the phase angle will be less than 90°, as shown in Figure 7.3. The total magnitude of the flapping

will be slightly less than for a rotor with no hinge offset because of the restraint provided by the nonflapping inner portions of the blades.