**Conformal mapping** is a mathematical technique used to
**convert** (or map) one mathematical problem and solution into
another. It involves the study of complex variables while in college.
(**Complex variables** are combinations of real and **imaginary
numbers,** which are taught in secondary schools). Under some very
restrictive conditions, we can define a complex mapping function that
will take every point in one complex plane and map it onto another
complex plane. The mapping is represented by the purple lines in the
figure.

Many years ago, the Russian mathematician **Joukowski**
developed a mapping function that converts a circular cylinder
into a family of airfoil shapes. The mapping function also converts
the entire flow field around the cylinder into the flow field around
the airfoil. Since we know the velocity and pressures in the plane
containing the cylinder, we can derive the velocity and pressures
around the airfoil using the mapping function. Knowing the pressure
around the airfoil, we can then compute the lift.
The computations are difficult to perform by hand, but can be solved
quickly on a computer. Joukowski's transformations are computed in
the FoilSim program.

You can see the effects of conformal mapping by using the FoilSim II Java Applet. If you want your own copy of FoilSim to play with, you can download it at no charge.

Go to...

- Beginner's Guide Home Page

*byTom
Benson
Please send suggestions/corrections to: benson@grc.nasa.gov *