Technische Mechanik in Action:. Kutta’s Arc and the Joukowsky Wing

Die Stromungs – und Druckerscheinungen, wie sie in bewegten Flussigkeiten, insbe – sondere auch der Luft, an den dareinversenkten Korpern beobachtet werden, haben schon seit langerer Zeit der hydrodynamischen Theorie einen viel bearbeiteten, nicht ganz einfachen Gegenstand geboten. Seit Otto Lilienthals Errungenschaften, und der neueren Entwicklung und Losung des Flugproblems haben diese Fragen auch grofie praktische Bedeutung erlangt.

w. m. kutta, “ Uber eine mit den Grundlagen des Flugproblems in Beziehung stehende zweidimensionale Stromung’ (1910)1

The flow and pressure phenomena, as they can be observed on bodies immersed in a moving fluid, particularly the air, have long provided for hydrodynamic theory a much worked on, but far from simple, object of study. Since Otto Lilienthal’s achieve­ments and recent developments in solving the problem of flight, these questions have acquired great practical significance.

In the next two chapters I show technische Mechanik in action by giving an overview of the early German (or German-language) development of the cir­culatory theory. In this chapter I deal with the “infinite wing” paradigm, that is, with an analysis deliberately confined to a two-dimensional cross section of the flow in which the wingtips are ignored. I then devote the next chapter to the more realistic theory dealing with a wing of finite span and the three­dimensional flow around it. It was Wilhelm Kutta in Munich who triggered the striking progress in the field of two-dimensional flow that was made in Germany before and during the Great War. His work is my starting point. Where Rayleigh used a simple, flat plane as a model of a wing, Kutta used a shallow, circular arc. Both men treated the air as an inviscid fluid, but where Rayleigh postulated a flow with surfaces of discontinuity, Kutta postulated an irrotational flow with circulation. Joukowsky, a Russian who published in German, then showed how to simplify and generalize Kutta’s reasoning. A variety of other workers in Gottingen, Aachen, and Berlin, starting from Kutta’s and Joukowsky’s publications, carried the experimental and theoreti­cal analysis yet further. Appreciating why these developments constitute an exercise in technical mechanics, rather than mathematical physics, requires

engaging with the details of the scientific reasoning. As a first step I place Kutta and his achievement in their institutional setting.