Flight Theory and Aerodynamics. Joseph R. Badick
lower surfaces have the same shape and are equidistant from the chord line. Symmetrical airfoils are common in rotary‐wing blades and in some aerobatic aircraft. Figure 3.16 shows examples of early airfoil design to more modern, supersonic designs.
Figure 3.15 Cambered versus symmetrical airfoil.
Source: U.S. Department of Transportation Federal Aviation Administration (2019).
Figure 3.16 Examples of airfoil design.
Source: U.S. Department of Transportation Federal Aviation Administration (2008a).
Classification of Airfoils
Most airfoil development in the United States was done by the National Advisory Committee for Aeronautics (NACA) starting in 1929. NACA was the forerunner of the National Aeronautics and Space Administration (NASA). The first series of airfoils investigated was the “four‐digit” series. The first digit gives the amount of camber, in percentage of chord. The second digit gives the position of maximum camber, in tenths of chord, and the last two give the maximum thickness, in percentage of chord. For example, a NACA 2415 airfoil has a maximum camber of 2% C, located at 40% C (measured from the leading edge), and has a maximum thickness of 15% C. A NACA 0012 airfoil is a symmetrical airfoil (has zero camber) and has a thickness of 12% C.
Further development led to the “five‐digit” series, the “1‐series,” and, with the advent of higher speeds, to the so‐called laminar flow airfoils. The NACA’s 23000 series created in 1935 were very popular and are still in use today. The laminar flow airfoils are the “6‐series” and “7‐series” airfoils and result from moving the maximum thickness back and reducing the leading edge radius.
Figure 3.17 NACA airfoils (NACA data).
Two things happen with this treatment. First, the point of minimum pressure is moved backward, thus increasing the distance from the leading edge that laminar (smooth) airflow exists, which reduces drag. Second, the critical Mach number is increased, thus allowing the airspeed of the aircraft to be increased without encountering compressibility problems. In the 6‐series, the first digit indicates the series and the second gives the location of minimum pressure in tenths of chord. The third digit represents the design lift coefficient in tenths, and the last two digits (as in all NACA airfoils) show the thickness in percentage of chord. For example, NACA 64‐212 is a 6‐series airfoil with minimum pressure at 40% C, a design lift coefficient of 0.2, and a thickness of 12% C. Sketches of NACA subsonic airfoil series are shown in Figure 3.17. National Aeronautics and Space Administration’s (NASA) FoilSim interactive simulation software developed by the Glenn Research Center comprises an excellent tool to explore the various shapes of airfoils and how air flows around them when airfoil characteristics are manipulated.
A modern design used worldwide on corporate, military, and air transport aircraft is the supercritical airfoil, which is flatter on top and more rounded on the bottom than a conventional wing. The upper trailing edge has a downward curve to restore lift lost by the flattening of the upper surface. The benefit of this design in the high‐speed realm of flight, as well as other supersonic airfoils, is discussed in Chapter 14.
Application 3.1
Symmetrical airfoils are found on many different types of aircraft, from light to heavy aircraft, and within general aviation to those designed solely for military operations.
Identify various aircraft that incorporate symmetrical airfoils into their design. Where are these airfoils located on the aircraft, and why was the symmetrical airfoil design utilized instead of a cambered airfoil design?
Development of Forces on Airfoils
Leonardo da Vinci stated the cardinal principle of wind tunnel testing nearly 400 years before the Wright brothers achieved powered flight. Near the beginning of the sixteenth century, da Vinci said: the action of the medium upon a body is the same whether the body moves in a quiescent medium, or whether the particles of the medium impinge with the same velocity upon the quiescent body. This principle allows us to consider only relative motion of the airfoil and the air surrounding it. We may use such terms as “airfoil passing through the air” and “air passing over the airfoil” interchangeably.
Pressure Disturbances on Airfoils
If an airfoil is subjected to a moving airflow, velocity and pressure changes take place that create pressure disturbances in the airflow surrounding it. These disturbances originate at the airfoil surface and propagate in all directions at the speed of sound. If the flight path velocity is subsonic, the pressure disturbances that are moving ahead of the airfoil affect the airflow approaching the airfoil (Figure 3.18). As the arrow indicates there are slight changes with the streamlines ahead of the leading edge of the airfoil.
Velocity and Static Pressure Changes about an Airfoil
The air approaching the leading edge of an airfoil is first slowed down and then speeds up again as it passes over or beneath the airfoil. Figure 3.19 compares two local velocities with the flight path velocity V1 and with each other. As the velocity changes, so does the dynamic pressure “q” and, according to Bernoulli’s principle, so does the static pressure “P.” Air near the stagnation point at the leading edge of the wing has slowed down, so the static pressure in this region is higher than the ambient static pressure. Air that is passing above and below the airfoil, and thus has speeded up to a value higher than the flight path velocity (both V2 and V3 are greater than V1), will produce static pressures that are lower than ambient static pressure. So as “q” increases, “P” static pressure decreases and a greater pressure differential is realized.
Figure 3.18 Effect of pressure disturbances on airflow around an airfoil.
Figure 3.19 Velocity changes around an airfoil.