Airfoil Design Methods

The process of airfoil design proceeds from a knowledge of the boundary layer properties and the relation between geometry and pressure distribution. The goal of an airfoil design varies. Some airfoils are designed to produce low drag (and may not be required to generate lift at all.) Some sections may need to produce low drag while producing a given amount of lift. In some cases, the drag doesn't really matter -- it is maximum lift that is important. The section may be required to achieve this performance with a constraint on thickness, or pitching moment, or off-design performance, or other unusual constraints. Some of these are discussed further in the section on historical examples.

One approach to airfoil design is to use an airfoil that was already designed by someone who knew what he or she was doing. This "design by authority" works well when the goals of a particular design problem happen to coincide with the goals of the original airfoil design. This is rarely the case, although sometimes existing airfoils are good enough. In these cases, airfoils may be chosen from catalogs such as Abbott and von Doenhoff's Theory of Wing Sections, Althaus' and Wortmann's Stuttgarter Profilkatalog, Althaus' Low Reynolds Number Airfoil catalog, or Selig's "Airfoils at Low Speeds".

The advantage to this approach is that there is test data available. No surprises, such as a unexpected early stall, are likely. On the other hand, available tools are now sufficiently refined that one can be reasonably sure that the predicted performance can be achieved. The use of "designer airfoils" specifically tailored to the needs of a given project is now very common. This section of the notes deals with the process of custom airfoil design.

Methods for airfoil design can be classified into two categories: direct and inverse design.

Direct Methods for Airfoil Design

The direct airfoil design methods involve the specification of a section geometry and the calculation of pressures and performance. One evaluates the given shape and then modifies the shape to improve the performance.

The two main subproblems in this type of method are

the identification of the measure of performance
the approach to changing the shape so that the performance is improved

The simplest form of direct airfoil design involves starting with an assumed airfoil shape (such as a NACA airfoil), determining the characteristic of this section that is most problemsome, and fixing this problem. This process of fixing the most obvious problems with a given airfoil is repeated until there is no major problem with the section. The design of such airfoils, does not require a specific definition of a scalar objective function, but it does require some expertise to identify the potential problems and often considerable expertise to fix them. Let's look at a simple (but real life!) example.

A company is in the business of building rigid wing hang gliders and because of the low speed requirements, they decide to use a version of one of Bob Liebeck's very high lift airfoils. Here is the pressure distribution at a lift coefficient of 1.4. Note that only a small amount of trailing edge separation is predicted. Actually, the airfoil works quite well, achieving a C_{l_max} of almost 1.9 at a Reynolds number of one million.

This glider was actually built and flown. It, in fact, won the 1989 U.S. National Championships. But it had terrible high speed performance. At lower lift coefficients the wing seemed to fall out of the sky. The plot below shows the pressure distribution at a C_l of 0.6. The pressure peak on the lower surface causes separation and severely limits the maximum speed. This is not too hard to fix.

By reducing the lower surface "bump" near the leading edge and increasing the lower surface thickness aft of the bump, the pressure peak at low C_l is easily removed. The lower surface flow is now attached, and remains attached down to a C_l of about 0.2. We must check to see that we have not hurt the C_{l_max} too much.

Here is the new section at the original design condition (still less than C_{l_max}). The modification of the lower surface has not done much to the upper surface pressure peak here and the C_{l_max} turns out to be changed very little. This section is a much better match for the application and demonstrates how effective small modifications to existing sections can be. The new version of the glider did not use this section, but one that was designed from scratch with lower drag.

Sometimes the objective of airfoil design can be stated more positively than, "fix the worst things". We might try to reduce the drag at high speeds while trying to keep the maximum C_L greater than a certain value. This could involve slowly increasing the amount of laminar flow at low C_l's and checking to see the effect on the maximum lift. The objective may be defined numerically. We could actually minimize C_d with a constraint on C_{l_max}. We could maximize L/D or C_l^1.5/C_d or C_{l_max} / C_d@C_{l_design}. The selection of the figure of merit for airfoil sections is quite important and generally cannot be done without considering the rest of the airplane. For example, if we wish to build an airplane with maximum L/D we do not build a section with maximum L/D because the section C_l for best C_l/C_d is different from the airplane C_L for best C_L/C_D.

Inverse Design

Another type of objective function is the target pressure distribution. It is sometimes possible to specify a desired C_p distribution and use the least squares difference between the actual and target C_p's as the objective. This is the basic idea behind a variety of methods for inverse design. As an example, thin airfoil theory can be used to solve for the shape of the camberline that produces a specified pressure difference on an airfoil in potential flow.

The second part of the design problem starts when one has somehow defined an objective for the airfoil design. This stage of the design involves changing the airfoil shape to improve the performance. This may be done in several ways:
1. By hand, using knowledge of the effects of geometry changes on C_p and C_p changes on performance.
2. By numerical optimization, using shape functions to represent the airfoil geometry and letting the computer decide on the sequence of modifications needed to improve the design.