Pitching Moments at High Mach Numbers

When the speed at a blade element is high enough that shock waves are formed, the resulting effects can drastically change the pitching-moment characteristics.

Source: Abbott & Von Doenhoff, Theory of Wing Sections (New York: Dover, 1959).

One of the most important changes is the so-called Mach tuck, a sudden nose – down pitching moment that was encountered on airplanes as their dive speeds first approached transonic conditions. When this occurs on the advancing tip of a helicopter rotor, it may produce high enough loads in the blades and control system to effectively limit the maximum allowable forward speed. For most airfoils that have been tested in two-dimensional wind tunnels, the Mach tuck characteristic comes slightly after drag divergence. This does not eliminate the Mach tuck problem, however, since drag divergence may be exceeded in many flight conditions.

Aft-cambered airfoils generally have a worse Mach tuck problem than do forward-cambered airfoils, as illustrated by the pitching-moment coefficient at zero lift shown in Figure 6.39, which is based on curves presented in reference 6.57. The basic source of the nose-down pitching moment is the change in the shape of the pressure distribution as the flow becomes supercritical and shock waves are established, first on the top surface and then on the bottom. This change is illustrated in Figure 6.40. Since the changes in pressure distribution patterns are caused by the shock waves, any reductions in shock wave strength, such as those obtained by supercritical airfoil design techniques, will be beneficial in decreasing the Mach tuck problem.

Trailing edge tabs that are used to adjust the pitching moment at low Mach numbers appear to retain most of their effectiveness at high Mach numbers, according to wind tunnel data presented in reference 6.57.

Symmetrical airfoils, of course, do not exhibit Mach tuck at zero lift, but they do produce compressibility-related pitching moments when developing some

Source: Dadone, “Helicopter Design Datcom,” Vol. I. “Airfoils,” USAAMRDL CR 76-2, 1976.

Source: Hughes, unpublished document.

lift. The presence and relative position of shock waves on both the upper and lower surfaces at about M = 0.9 causes the pitching moment to vary with angle of attack as the shock waves shift position. This produces a definite reversal in pitching-moment characteristics for small angles of attack such that the pitching moment generates an unstable blade twist—that is, an increased angle of attack twists the blade nose up and vice versa. This characteristic was identified in reference 6.61 as the cause of a significant dynamic problem involving an out-of­track phenomenon occurring every other rotor revolution on the Sikorsky NH-3A compound helicopter when the advancing tip Mach number exceeded 0.92. Figure 6.41 from reference 6.62 shows wind tunnel results for the NACA 0012 in the Mach number region from 0.80 to 0.96. It may be seen that at M = 0.90, even the lift curve slope exhibits a reversal. This odd behavior is not limited to symmetrical airfoils. Reference 6.57 shows that the VR-7 also has reversals in both pitching moment and lift at a Mach number of 0.82 and a ct of about —0.3.