Theodore Theodorsen - Expanding On Significant Themes

Expanding On Significant Themes

Theodorsen was an innovative practical engineer at a time in which most of his contemporary theoretical aerodynamists were located at educational institutions and thus were not involved in practical engineering solutions. Theodorsen’s work is especially significant in that it still plays an important role in current research and technology.

The theory of arbitrary airfoils based on conformal mapping developed by Theodorsen, is a model of classical applied mathematics. It should be pointed out that there are two key concepts that made Theodorsen’s approach different from and a clear improvement on the methods that preceded it such as that of von Mises and von Karman. One was the important use of the complex variable not in the usual form of a polynomial or power series but in the form of an exponential to power series. The equation led directly to the basic boundary value equation which, as an integral equation, represents an exact solution of the problem in terms of the given airfoil data. This solution gave the exact pressure distribution around an airfoil of arbitrary shape. Seldom in aeronautics are solutions “exact”. This is one of the very few. The method has been automated so that complete pressure distributions for a given airfoil section can be obtained in a matter of seconds. The philosophy in Theodorsen’s approach was that an exact formulation is often simpler and preferable to an approximate one and that while approximations are essential in applied mathematics they should be delayed as far as possible.

Another topic that merits discussion is Theodorsen’s work on flutter. The approach here is again direct and clean, leading to an explicit exact solution as contrasted with previous implicit and approximate results. This exact flutter solution including results for control surfaces has had a keystone role in the development of flutter methods in the United States. It has enabled an engineering feel for the effects of variables and parameters in complex situations and has been available as a model against which approximate solutions can be compared.

Although Theodorsen leaned strongly toward basic theoretical analysis, he usually accompanied his work with experimental verification. He was highly innovative in engineering and experimental activities where he always sought a theoretical framework or was guided by physical intuition. He was responsible for proposing a wind tunnel for flutter work which employed a mixture of air and freon with variable pressure to greatly increase the scope of research with aeroelastic models throughout the Mach range and with lower horsepower requirements. The Transonic Dynamics Wind Tunnel now used exclusively for aeroelastic research is based on the same principles.

Another unique facility due to Theodorsen was the helicopter rotor tower for aerodynamic and noise research. Ideal propeller dynamics was given a definitive treatment in several reports and a book. Theodorsen was the earliest to obtain reliable skin-friction drag data at subsonic, transonic and supersonic speeds.