Dynamic Effects on Pitching Moment

As with lift and drag, the change in pitching moment due to stall is delayed if the angle of attack is rapidly increasing as the airfoil goes through its static stall angle

Source: Prouty, “Aerodynamics” column, Rotor & Wing International, Vol. 18, no. 9 (August), 1984.

of attack. Since the dynamic pressure on the retreating blade is small, any pitching – moment characteristics associated with stall would be expected to be of little importance to the aerodynamicist in terms of their effects on performance or stability. The dynamicist, however, has recognized that the delay in the pitching – moment break while going up through stall, and the corresponding delay in returning to unstalled conditions on the downstroke, can lead to negative damping, which may excite the torsional vibration mode of the blade. If the direction of change in pitching moment is nose down while the angle of attack is changing nose up, or vice versa, the damping is positive. The top portion of Figure 6.42 illustrates this with a simple schematic representing an airfoil model mounted on a shaft through a moment balance and restrained by a damper. If the inertia of the model is neglected, the moment measured by the balance is just that caused by the damper, and a plot of moment versus angle of attack as the shaft is oscillated will trace out a counterclockwise hysteresis loop. Thus a plot of aerodynamic pitching moment from an oscillating airfoil test will show positive damping for regions enclosed by counterclockwise loops, but negative damping for regions enclosed by clockwise loops. The lower portion of Figure 6.42 from reference 6.63 shows the hysteresis curves for a NACA 0012 as it oscillates ±6° about mean angles of 0°,

12°, and 24°. The data show positive damping for the low and high mean angles representing nonstalled and fully stalled conditions, but show both positive and negative damping through the stall region. The negative damping region represents a condition where energy is being extracted from the airstream and put into the oscillating blade. This is the source of stall flutter, which, if allowed to persist, could result in serious structural problems. Fortunately, helicopters generally subject their blades to the stalling conditions only during a small portion of the retreating side. For this reason, only a few cycles of oscillation can occur before the angle of attack drops below stall and has positive damping. The phenomenon manifests itself on some helicopters in the form of high control system loads and vibration levels. Detailed discussions of these aspects of stall flutter may be found in references 6.64 and 6.65.