Airfoil Design and Data

The publication of an airfoil catalog seems to be not very consequent today. There exist computer programs which allow the design of airfoils which are very good, if not optimally adapted to the requirements resulting from certain special applications. It may be better to design an entirely new airfoil for an application rather than to look for an appropriate one in some catalog. It is not very likely to find an optimal airfoil there which has the correct thickness, the correct lift coefficient range and the correct moment coefficient, being tested for the intended flap arrangement, the right Reynolds number and the right surface roughness, to mention only a few criterions for the selection.

In this chapter, an airfoil shape is supposed to be given, for example, by an empirical mathematical function as for the NACA four digit airfoils (See [4]) or by a set of coordinates. The airfoil is subjected to an infinite parallel flow of velocity V_∞ and density ρ at an angle of attack α. The undisturbed (static) pressure of the infinite flow is p_∞. There exist mathematical methods for computing the (inviscid) potential flow around the airfoil, either by conformal mapping, (see [4]) or by panel methods. In the present book, the potential flow analysis is made by means of a special higher order panel method which is described in detail in Reference [1]. Only a short summary of the characteristic features is given here.

The boundary layer properties depend only on the potential flow velocity distribution V(x) and the Reynolds number. Details will be described in Chapter 4. Boundary layer theory determines in many cases how V(x) must look in order to provide good boundary layer behavior. This fact has been a classical challenge for more than 40 years in developing inverse potential flow theories in which “the” velocity distribution V(x) is given and the airfoil shape is desired as a result. This inverse problem doesn’t look too difficult. It contains, however, several problems.

Before the boundary layer flow is discussed, some remarks should be made about the nondimensional variables in the formulas and the units to be used. In mechanics, a system of three units is normally used, like meters, kilograms, and seconds or inches, pounds, and minutes. Once such a system of units is selected, all variables and parameters must be measured in these units; for example, velocities in m/sec or inch/min, forces in Newtons N = m kg/sec², stresses or pressures in N/m², and so on. This is not always optimal. In many problems, certain reference values are selected; for example, a characteristic reference length L of the problem and a then transformed in such a way of such a transformation can be characteristic velocity V_R of the problem. All equations are that only ratios involving reference values appear. The result achieved in a much simpler way. Instead of the unit system mentioned above, another system with units in closer correlation to the problem to be solved is selected. In problems of fluid mechanics (without considering heat), an adequate system of units can be a characteristic length L, a characteristic velocity V_R, and a characteristic density p_R of the problem. Once the selection of the unit system is made, all variables and parameters must again be measured in the selected units. For example, a time must then be measured in L/V_R and a mass in ϱ_RL³. Additional examples are given in the following table.

The NACA 6-series airfoils achieved their laminar effect through the introduction of a segment with constant velocity on both surfaces for different angles of attack. This was previously discussed in Chapter 3.11. Thus, a certain range of angles of attack is created over which a favorable pressure gradient is present on both surfaces up to a certain chord location. The NACA 65₃-018 airfoil is a typical example of this design philosophy. This philosophy was based, however, only on a qualitative property of the boundary layer, i. e., that transition occurs later in a favorable pressure gradient. Today much more information on transition is available. A more realistic transition criterion was given in Fig. 4.4 and in Equation (4.27). At lower Reynolds numbers, the boundary layer will be laminar in an adverse pressure gradient as well. The ultimate limit for the laminar boundary layer is, in this case, laminar separation. At high Reynolds numbers, transition can occur in a favorable pressure gradient. It is therefore absolutely necessary to take the Reynolds number into account when specifying the velocity distributions for those portions of the airfoils over which a laminar boundary layer is to be exploited. The design method allows this problem to be solved in a simple and straightforward manner. This solution is first described for relatively low Reynolds numbers, which in many applications occur near the upper end of the laminar bucket where transition on the upper surface of the airfoil is of great importance.

Chapter 6 contains only airfoil data. Each airfoil is given on at least two pages which show the airfoil with several velocity distributions and the c_d-c_ℓ-plot. For simplicity, both are always given on pages that face each other. If necessary, some short comments are given on the right side of the first diagram.