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
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 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!)
- the identification of the measure of performance
- the approach to changing the shape so that the performance is improved
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 Clmax 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 Cl 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 Cl is easily removed. The lower surface flow is now attached, and
remains attached down to a Cl of about 0.2. We must check to see that we
have not hurt the Clmax too much.
Here is the new section at the original design condition (still less than
Clmax). The modification of the lower surface has not done much to the upper
surface pressure peak here and the Clmax 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 CL greater than a certain
value. This could involve slowly increasing the amount of laminar flow at
low Cl's and checking to see the effect on the maximum lift. The objective
may be defined numerically. We could actually minimize Cd with a constraint
on Clmax. We could maximize L/D or Cl1.5/Cd
or Clmax / Cd@Cldesign. 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 Cl for best Cl/Cd is
different from the airplane CL for best CL/CD.
Another type of objective function is the target pressure distribution.
It is sometimes possible to specify a desired Cp distribution and use the
least squares difference between the actual and target Cp'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
1. By hand, using knowledge of the effects of geometry changes on Cp and
Cp 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.