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Rotor Flapping Characteristics
QUALITATIVE DISCUSSION OF FLAPPING
Before deriving the helicopter equations of equilibrium and motion, it seems well to develop a general understanding of rotor flapping, a primary factor in helicopter stability and control analysis.
As might be expected, the stability and control characteristics of a helicopter are different from those of an airplane primarily as a rotor is different from a wing. Whereas the wing remains more or less rigidly attached to the airplane airframe, the rotor tip path plane tilts easily with respect to the helicopter airframe in response to changing flight conditions and control inputs. This tilt produces changes in forces and moments at the top of the rotor shaft. A hingeless blade may have no single point at which flapping occurs, but an effective hinge offset can be determined that will give it the same stability and control characteristics as a blade with an actual mechanical hinge at that point. This concept will be used to eliminate any consideration of blade structural stiffness in the following analyses.
Several different flapping characteristics will be discussed in a cause-and – effect manner and then mathematically derived from the laws of physics. These characteristics are summarized in Table 7.1 for rotors with and without hinge
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TABLE 7.1 Rdtor Flapping Characteristics (for Counterclockwise Rotation) Result
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offset. (There are few modern rotors with individual blades hinged with no offset but two-bladed teetering rotors fall into this category for the purposes of this discussion.)
All these flapping characteristics can be explained on the basis that at the flapping hinge (or at an effective flapping hinge in the case of a hingeless rotor) the summation of moments produced by aerodynamic, centrifugal, weight, inertial, and gyroscopic forces must be zero.
Shaft Tilted in a Vacuum
If a rotor with no hinge offset is operating in a vacuum, there are no aerodynamic forces; only centrifugal forces acting in the plane of rotation. These can produce no moments about the flapping hinges. If the shaft is tilted, no changes in moments will be produced and the rotor disc will remain in its original position, as shown in Figure 7.1. If, on the other hand, the rotor has hinge offset, the centrifugal forces acting in the plane of rotation will produce moments about the hinges that will force the blades to align themselves perpendicular to the shaft.
