Introduction to UAV Systems. Mohammad H. Sadraey

Figure 3.8). As the airfoil angle of attack increases, the pressure difference between the upper and lower surfaces will be higher.

The wing three‐dimensional (3d) lift coefficient (C_L) is directly a function of the airfoil two‐dimensional (2d) lift coefficient, c_l. In turn, the variable c_l is a function of variations of pressure coefficients on the upper and lower surfaces. For the case of a small angle of attack (less than 5 degrees), the 2d lift coefficient is calculated from

Figure 3.8 Pressure distribution for an airfoil section

      (3.4)

      where C_pl and C_pu are pressure coefficients at the lower and upper surfaces respectively, and c is the airfoil chord. Thus, the lift is produced due to the pressure difference between the lower and upper surfaces of the wing/tail. References such as [8, 10, and 11] provide techniques to determine the pressure distribution around any lifting surface such as the wing. The variations of lift coefficient versus angle of attack are often linear below the stall angle. The UAVs are usually flying at an angle of attack below the stall angle (about 15 degrees).

The Northrop Grumman X‐47B (Figure 3.9) an experimental unmanned combat air vehicle (UCAV) has provisions for various payloads such as EO/IR/SAR/GMTI. Its aerodynamic design allows for a maximum speed of Mach 0.9+ and a range of 3,900 km. This UCAV with a blended wing‐body tailless configuration, a maximum takeoff weight of 44,567 lb (mass of 20,215 kg), and a wing span of 62.1 ft (18.9 m) is equipped with a single turbofan engine.

Figure 3.9 Northrop Grumman X‐47B UCAV

Figure 3.10 Net pressure distribution over an airfoil

Figure 3.11 Spanwise pressure distribution around a 3d wing

Figure 3.12 Downwash

Consider the net pressure distribution about an airfoil, as shown in Figure 3.10. It is apparent that a wing would have positive pressure on its underside and negative (in a relative sense) pressure on the top. This is shown in Figure 3.11 as plus signs on the bottom and minus signs on the top as viewed from the front or leading edge of the wing.

Such a condition would allow air to spill over from the higher pressure on the bottom surface to the lower pressure on the top, causing it to swirl or form a vortex. The downward velocity or downwash onto the top of the wing created by the swirl would be greatest at the tips and reduced toward the wing center, as shown in Figure 3.12.

      Aerodynamics textbooks (e.g., Reference [8]) are a good source to consult for information about mathematical techniques for calculating the pressure distribution over the wing and for determining the flow variables.

3.6 Drag Polar

Another important concept concerning the three‐dimensional air vehicle is what is known as the aircraft drag “polar,” a term introduced by Eiffel many years ago, which is a curve of C_L plotted against C_D. A typical airplane drag polar curve is illustrated in Figure 3.13.

      The drag polar will later be shown to be parabolic in shape and define the minimum drag (or zero‐lift drag), C_Do, or drag that is not attributable to the generation of lift. A line drawn from the origin and tangent to the polar gives the minimum lift‐to‐drag ratio that can be obtained. It will also be shown later that the reciprocal of this ratio is the tangent of the power‐off glide angle of an air vehicle. The drag created by lift or induced drag is also indicated on the drag polar.

      The drag coefficient is the sum of two terms: (1) zero‐lift drag coefficient (C_Do) and (2) induced drag coefficient (C_Di). The first part is mainly a function of friction between air and the aircraft body (i.e., skin friction), but the second term is a function of local air pressure, which is represented by the lift coefficient. Pressure drag is mainly produced by flow separation. The sum of the pressure drag and skin friction (friction drag – primarily due to laminar flow) on a wing is called profile drag. This drag exists solely because of the viscosity of the fluid and the boundary layer phenomena.

      The drag coefficient is a function of several parameters, particularly UAV configuration. A mathematical expression for the variation of the drag coefficient as a function of the lift coefficient is

      (3.5)

      This equation is sometimes referred to as aircraft “drag polar.” The variable K is referred to as the induced drag correction factor. It is obtained from

(3.6)

      where e is the Oswald span efficiency factor and AR is the wing aspect ratio. The aspect ratio is defined as the ratio of wingspan over wing mean aerodynamic chord (b/C). It is also equal to wingspan squared divided by wing area or b²/S. The variable AR is further discussed in this chapter.

Figure 3.13 Airplane drag polar

3.7 The Real Wing and Airplane

      A real three‐dimensional conventional aircraft normally is mainly composed of a wing, a fuselage, and a tail. The wing geometry