Drag at Moderate Angles of Attack and Mach Numbers

For conditions in which there is no separation and no significant compressibility effects, the drag of the airfoil is primarily due to skin friction, whose coefficient is a function of the local velocities on the surface and whether the boundary layer is laminar or turbulent. Figure 6.30, from reference 6.1, shows the effect of Reynolds number on the calculated minimum drag coefficient for fully laminar and for fully turbulent boundary layers. Also shown are wind tunnel results for several airfoils. Laminar flow can usually be maintained only on the nose of the airfoil where the flow is accelerating. Thus no airfoil can take full advantage of laminar flow; but some, such as the six-series airfoils, keep the flow accelerating further back than others and thus have a larger region of laminar boundary layer. As a matter of fact,

Pressure Distributions on Four NACA 64A-Series Airfoil Sections at Angles of Attack as High as 28°,” NACA TN 3162, 1954; Abbott & Von Doenhoff, Theory of Wing Sections (New York: Dover, 1959); Wiesner & Kohler, “Tail Rotor Design Guide,” USAAMRDL TR 73-99, 1973; Davenport & Front, “Airfoil Sections for Helicopter Rotors—A Reconsideration,” AHS 22nd Forum, 1966; Graham, Nitzberg, & Olson, “A Systematic Investigation of Pressure Distributions at High Speeds over Five Representative NACA Low-Drag and Conventional Airfoil Sections,” NACA TR 832, 1945; Gothert, “Airfoil Measurements in the DVL High-Speed Wind Tunnel,” NACA TM 1240.

Droop

the six-series airfoils were originally known as laminar flow airfoils and were especially designed to take advantage of this effect. Wind tunnel tests of these airfoils showed that, compared to other airfoils, the drag coefficient had only a small rise as the angle of attack was increased until at some angle of attack most of the boundary layer suddenly became turbulent. This resulted in the drag bucket illustrated in Figure 6.31. Subsequent use of these airfoils on airplanes in the 1940s and 1950s proved disappolhting from a drag standpoint, since dirt, bugs, and surface imperfections triggered premature transition to turbulent flow and nullified the promising characteristics that had been measured on carefully shaped and polished wind tunnel models.

There is some indication—primarily based on the observations of reference 6.51—that a rotor blade, even one with leading edge erosion, can maintain laminar flow more easily than a wing, possibly because built-in surface imperfections are usually less and also because pitting is less detrimental than protrusions.

Even though the six-series airfoils were disappointing from a skin friction standpoint, it was found that some of them had lower drag characteristics for certain combinations of lift coefficients and Mach numbers than did the older airfoils. Figure 6.32 shows drag data for two 15% thick airfoils, a NACA 23015 and a 66.2-215 taken from reference 6.17. At low lift the drag characteristics of the two airfoils are similar, but at higher lift the six-series airfoil has higher drag at low Mach numbers but dips to lower drag at high Mach numbers. At the time

Mach Number

Mach Number FIGURE 6.32 Drag Characteristics of Two 15 Percent Thick Air­foils

Source: Graham, Nitzberg, & Olson, “A Systematic Investigation of Pressure Distributions at High Speeds over Five Representative NACA Low-Drag and Conventional Airfoil Sections," NACA TR 832, 1945.

these test results were published (1945), the low drag could not be explained and the dips could only be called "peculiar.” We now know that these dips are characteristic of the class of airfoils that has come to be known as supercritical, which benefit from an advantageous pattern of expansion and compression waves, as shown in Figure 6.16. It is typical of all these airfoils that the region of low drag is limited to a narrow range of operating conditions. The design task for the

airplane aerodynamicist is to design airfoils in which this region coincides with the cruise Mach number and lift coefficient of the airplane. Since the helicopter rotor experiences a much wider range of operating conditions than a wing, it is more of a challenge to adapt this concept to a rotor blade; attempts to do this are outlined in references 6.52 and 6.53. Some whirl tower tests of rotors with six-series airfoils, or modifications of this family, indicate a small but measurable advantage in hover over the older airfoils. These tests are reported in references 6.16, 6.54, and 6.55. It is not known whether these benefits were due to increased laminar flow or to supercritical characteristics. Figure-6.33 shows a comparison of two-dimensional data backing up these whirl tower results.

Comparison of one airfoil with another with respect to drag characteristics should be done at the same Reynolds number if possible. Figure 6.34 shows the results of tests on a single airfoil at several Reynolds numbers. It may be seen that at the same Mach number and lift coefficient, the coefficient of drag decreases as the Reynolds number—or chord—is increased. The effect is present in other sets of wind tunnel data, though usually not as dramatically as in this case. It appears that from the standpoint of minimum profile power, a rotor with a few wide – chord blades is better than one with many narrow-chord blades. It is also evident that those computer programs that use tabulated values of aerodynamic coefficients may introduce sizable errors unless the data are based on the Reynolds number corresponding to the chord of the blade. When new tests in pressurized wind tunnels are being planned, consideration should be given to running at

Mach Number FIGURE 6.33 Drag of Two Arifoils at 0.6 Lift Coefficient

Source: Benson, Dadone, Gormont, & Kohler, “Influence of Airfoils on Stall Flutter Boundaries of Articulated Helicopter Rotors,” JAHS 18-1, 1973.

FIGURE 6.34 Effect of Reynolds Number on Drag Coefficient

Source: 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.

constant equivalent chords by matching the test Reynolds number to the Mach number whenever possible.

The airplane people have found that a wing can have a blunt trailing edge without a significant base drag penalty if the trailing edge thickness is less than that of the boundary layer on the upper surface. This can result in an allowable trailing edge thickness of about 1% of the chord, as used on the Lockheed S3-A antisubmarine airplane. This feature might be considered for those blades that need high chordwise stiffness.

Effect of Unsteady Aerodynamics on Drag

The oscillating airfoil experiments of references 6.23 and 6.33 used surface – pressure surveys, which are good for measuring instantaneous lift and pitching moment but are not usable to establish the instantaneous drag. Fortunately, another set of tests reported in reference 6.56 used strain gauge balances instead of pressure measurements and thus measured the instantaneous drag. Figure 6.35 shows typical lift and drag loops. It may be seen that the delay in drag corresponds
fairly well to the overshoot in lift and thus can be characterized by the same increase in the stall angle of attack.