Flapping That Is Caused by Pitch and Roll Angular Velocities

A factor that is important to helicopter flying qualities is the damping moment the rotor produces when the helicopter is subjected to pitch or roll angular velocities

by external means such as gusts. This damping is produced by the tilt of the tip path plane, which lags behind the motion of the shaft by an amount that is proportional to the rate of pitch or roll, as illustrated in Figure 7.6. It has already been shown how the aerodynamics on the blade causes the tip path plane to tend to stabilize itself in an equilibrium position with respect to the shaft. A rotor attached to a shaft that is continuously tilting, therefore, will follow the shaft. The rotor disc may be considered to be a gyro that must be precessed by a moment applied 90° before the direction of tilt. The moment can only be generated by aerodynamic means, which in turn can only be produced by asymmetric flapping velocities. To maintain a steady nose-up pitch rate, for example, the airload must be higher on the blade at |/ = 90° than on the blade at {/ = 270°: this asymmetry is generated by a downward flapping velocity—with respect to the shaft—at |/ = 90° ( and an upward flapping velocity at |/ = 270°. The maximum flapping amplitude with respect to the shaft, therefore, is down at \f = 180° and up at у = 0°, and the

tip path plane follows the motion of the shaft at a lag angle that is proportional to the rate of pitch and the rotor moment of inertia.

During a steady nose-up pitching maneuver, some lateral flapping also is generated as a result of the decreased angle of attack at у = 180° and the increase at у = 0°’ caused by the rate of pitch itself. This difference in angle of attack is compensated for by lateral flapping that produces enough flapping velocity at these two blade positions to cancel out the effect of the pitch rate. The production of both a lateral and a longitudinal flapping by a pure pitch rate is a source of cross­coupling, which applies equally to rotors with and without hinge offset. The cross­coupling ratio, bi/ax is a function of blade inertia, being highest for light blades.

Consider the converse case in which the steady pitch rate is being produced by the pilot in a deliberate maneuver instead of by external means. Since the rate is steady (no acceleration), no hub moment is needed if we ignore the damping moments generated, by the airframe. Under this condition, the longitudinal and lateral cyclic pitch required to maintain the maneuver will be exactly equal to the longitudinal and lateral flapping that would have been produced by a pitch rate caused by external means. This is a consequence of the equivalence of flapping and feathering explained in Chapter 3.