In addition to all of the effects discussed above, the rotor will also respond to changes in sideslip. This is because blade flapping is produced by conditions referenced to the flight path rather than to whatever orientation the fuselage might have at the time.
Imagine the helicopter of Figure 7.7 in forward flight with no sideslip and with the rotor trimmed perpendicular to the shaft. If the flight direction is suddenly changed so that the helicopter is flying directly to the right without changing fuselage heading or control settings, the blade over the tail becomes the advancing blade and the one over the nose the retreating blade. Since the cyclic pitch no longer corresponds to trim conditions, the rotor will flap down on the left side because of the asymmetrical velocity distribution—thus producing a rolling moment to the left.
In practice, of course, sideslip angles are less than the 90° used for illustration, but the trend is the same—the helicopter tends to roll away from the approaching wind. This is the same characteristic found on airplanes with dihedral (both wings slanted up) and is known as the positive dihedral effect on rotors even though the source is different.
It is a desirable characteristic that helps the pilot. With negative dihedral, a sideslip would tend to roll the aircraft into an ever-tightening spiral dive. Too much positive dihedral, on the other hand, also can be undesirable, as will be later pointed out in the discussion of lateral-directional stability in Chapter 9- Positive
FIGURE 7.7 Effect of Sideslip on Rotor Flapping
dihedral manifests itself during flight as a lateral stick displacement required in the direction of sideslip to maintain equilibrium.
The rolling moment due to the dihedral effect is also accompanied by a pitching moment. Again going back to Figure 7.7 and the helicopter when it is flying directly to the right, it may be seen that the blade pointing in the direction of flight was originally the advancing blade and had a low pitch. It still has a low pitch that will cause the rotor to flap down over the nose, producing a nose-down pitching moment.
Similarly, during flight to the left, the blade pointing in the direction of flight has a high pitch and will cause the rotor to flap up over the tail—also producing a nose-down moment. Thus steady sideslip in either direction requires aft stick displacement, an effect that does not exist on an airplane.
Somewhat surprisingly, if the same analysis is made on a rotor turning clockwise when viewed from above, the pitching moment direction is unchanged—nose-down for sideslip in either direction. This pitching effect is not always observable in flight, since other pitching moments may be generated by
changes in airflow conditions on the horizontal stabilizer and tailboom as they move out from behind the fuselage during sideslip.
The blade flapping is also responsible for a helicopter behaving better in gusty air than an airplane does. This is because the rotor blades flap individually in response to the gusts, allowing the rest of the helicopter to have a relatively smooth ride. The wing of an airplane, on the other hand, transmits its unsteady loading directly into the fuselage. This gust alleviation feature has been demonstrated by flying helicopters and airplanes of the same size in formation through gusty air, as reported in reference 7.1. The recording instrumentation showed that the helicopter had a smoother ride. The comparison is similar to that of an automobile with independent wheel suspension compared to one on which the wheels are rigidly mounted to the chassis.
As already discussed, the addition of hinge offset changes the characteristics of the rotor from being a system in resonance to one whose natural frequency is higher than the rotational frequency. An analysis of this system in hover gives equations for the frequency ratio, damping, phase lag, and cross-coupling as a function of the hinge offset. From Figure 7.8, it may be seen that the increment of moment about the hinge due to centrifugal force perpendicular to the shaft is:
AA1c f = mArCl2r(r — ^)(3
FIGURE 7.8 Geometry of a Flapping Blade
For the example helicopter, the hinge offset is 5% of the radius, and thus the corresponding first flapping frequency ratio is 1.04.
The equation an be rearranged for use in determining the effective hinge offset of a hingeless rotor. For these rotors, the value of (0jCl is generally calculated separately for the purpose of performing rotor dynamic analyses. Once this parameter is known at the operational rotor speed, the effective hinge offset ratio can be found as: