A conformal-mapping method for the design of airfoils with prescribed velocity distribution characteristics, a panel method for the analysis of the potential flow about given airfoils, and a boundary-layer method have been combined. With this combined method, airfoils with prescribed boundary-layer characteristics can be designed and airfoils with prescribed shapes can be analyzed.

*The flow about an airfoil in free air can be described
approximately by a boundary-layer flow near the surface of the
airfoil and by a potential flow everywhere else. Boundary-layer
theory can be applied to the flow about an airfoil in two ways.
First, the boundary-layer development can be determined for a given
potential flow velocity distribution. This is the direct or
analysis problem. Second, the potential-flow field, or at least
some of its properties, can be determined for a given
boundary-layer development. This is the inverse or design problem.
This second application of boundary-layer theory requires the
solution of the inverse potential-flow problem where the
potential-flow velocity distribution is specified and the airfoil
shape is computed. Thus, the viscous airfoil design (inverse)
problem can be described as the computation of a shape from a
potential flow velocity distribution which is consistent with a
desired boundary-layer development.
Because Tollmien, Schlichting,Ulrich, Pretsch, and others had shown that
favorable pressure gradients delay the transition from laminar to
turbulent flow, airfoils were designed with aft pressure
recoveries.
The experimental results for these airfoils confirmed
the theoretical predictions.
This breakthrough led to the laminar flow airfoil series.
Since that time, boundary-layer and potential
flow theories have been steadily improved.*

*Different computer programs have been developed for low-speed
(incompressible)airfoils.
The present paper describes one of these programs.
The potential flow inverse problem still plays a major role in airfoil design.
This problem has been solved exactly by means of conformal mapping.
The method is similar to that of Lighthill, is direct, and solves
most multipoint design problems in a very simple manner.
A potential-flow analysis method is also required
for comparison with wind tunnel tests of given airfoils and for
analyses of airfoils generated by the design method and then
modified by a flap deflection.
The airfoil analysis problem is solved using a distributed surface
singularity method.
Some of the details of this method are new and previously unpublished.
The boundary-layer method uses integral momentum and energy equations.
The present method does not contain a boundary-layer displacement iteration.
The program has been successfully applied at Reynolds numbers
from 20 thousand to 100 million.*

Italic text above is from TM 80210.

Although this program is of great historical importance and one still finds current papers that refer to calculations made with PROFILE, it is not the program of choice for someone learning about airfoil plus boundary layer calculations. I would recommend Xfoil for today's students. Xfoil is an interactive program for the design and analysis of subsonic isolated airfoils written by Mark Drela and Harold Youngren. Check the Virginia Tech site for valuable notes on running Xfoil.

- Go to the page of references for the Eppler program.
- Go to the download page for the Eppler program.