Drag Divergence Mach Number

The advancing tip operates at nearly zero lift coefficient at high speed, so the drag characteristics of the airfoil in this condition are important. As the free stream

Mach number is increased toward and beyond its critical Mach number, the local velocity on the surface first reaches the speed of sound and then exceeds it, until at some speed and at some position on the airfoil a shock wave is formed through which the velocity decreases to a subsonic value. Tests show that if the shock is weak and close to the nose, there is no significant drag penalty; but as the shock

FIGURE 6.27 Gamma Function as Affected by Mach Number

passes beyond the crest or, for this condition, the position of maximum thickness, the drag increases rapidly as a result of the momentum loss through the shock (wave drag) and m some cases as a result of separation of the boundary layer (shock stall). The free stream Mach number at which the drag coefficient increases significantly is known as the drag divergence Mach number. In many studies, it is defined as the Mach number at which the drag coefficient rises at the rate of 0.1 per unit Mach number. For helicopter applications, however, where the magnitude of the drag change may be more significant than the rate of increase, it is щоге appropriate to define it as the Mach number at which the drag coefficient is twice its incompressible value. Using this definition, the measured two-dimensional drag divergence Mach numbers of a number of airfoils at zero lift as reported in references 6.1, 6.13, 6.17, 6.21, 6.46, 6.47, 6.48, 6.49, and 6.30 have been compiled and are plotted in Figure 6.28a as a function of thickness ratio. It may be seen that the symmetrical airfoils of all families form a reasonably tight grouping, but that

(a)

Sources: Sipe & Gorenberg, “Effect of Mach Number, Reynolds Number, and Thickness Ratio on the Aerodynamic Characteristics of NACA 63A-Series Airfoil Sections,” USATRECOM TR 65-28, 1965; Van Dyke, “High-Speed Subsonic Characteristics of 16 NACA Six-Series Airfoil Sections," NACA TN 2670,1952; Wilson & Horton, "Aerodynamic Characteristics at High and Low Subsonic Mach Numbers of Four NACA Six-Series Airfoil Sections at Angles of Attack from -2° to 31 NACA RM 876 (L53620), 1953; Stivers, “Effects of Subsonic Mach Numbers on the Forces and

the six-series cambered airfoils generally have lower drag divergence Mach numbers. Even these airfoils can be brought into the grouping if the physical parameter is taken as twice the maximum upper ordinate instead of the thickness ratio, as shown in Figure 6.28b.

Just as with the maximum lift coefficient, the scatter of the points in Figure 6.28 represents differences in airfoils and differences in tunnels. Some airfoils have beneficial supercritical characteristics—either by design or by accident—and thus have measurably higher drag divergence Mach numbers than average. For other airfoils, the supercritical characteristics might be detrimental if an expansion wave is located ahead of the shock instead of a compression wave. The difference that a tunnel can make is shown by 5 points for the NACA 0012 airfoil.

A conclusion that can be drawn from Figure 6.28 is that for the same thickness ratio, aft camber as used in the six-series airfoils lowers the drag divergence Mach number, but that forward camber as used in the five-digit airfoils has little effect. This conclusion, however, must be qualified. If the nose is drooped so far that the lower surface becomes concave, the drag curve at zero lift can have the distinct characteristic shown for the 33008 airfoil in Figure 6.29 from reference 6.9. This is known as a “creepy” drag rise and is apparently due to a shock wave formed on the lower surface that locally separates the boundary layer in the concave region. Even airfoils with moderate forward camber may exhibit significant drag creep at small negative angles of attack such as might exist on the advancing tip at high speeds.