Ludwig Prandtl and the Gottingen School

Der alte Gottinger Professor Dirichlet wurde sich wohl gefreut haben, wenn er dieses Resultat hatte sehen konnen; glaubte man doch gerade seine Potential-Theorie durch die einfache Tatsache, das ein Widerstand existiert, ad absurdum gefuhrt zu haben. j. ackeret, Das Rotorschiff und seine physikalischen Grundlagen (1925)1

The old Gottingen professor Dirichlet would have been so happy if he could have seen these results. People just believed that his theory of potential had been reduced to ab­surdity by the simple fact that there was resistance to motion.

The theory of lift may be divided into two parts: (1) the theory of the wing profile, that is, the wing sections of the kind studied by Kutta and Joukowsky, and (2) the theory of the planform of the wing. The planform is the shape of the wing when seen from above. Wings can be given very different planforms. The designer may chose a simple, rectangular shape or give the wing a more aesthetically pleasing curved leading or trailing edge. The wingtips may be rounded or square, and, most important of all, the wing may be made long and narrow (high aspect ratio) or short and stubby (low aspect ratio). It was known experimentally that some features of the aerodynamic performance of a wing depended on the profile, whereas others (such as the slope of the curve relating lift to angle of attack) depended on the planform and, particu­larly, the aspect ratio. Some of the features that depend on the profile were discussed in the last chapter, for example, the angle of attack at zero lift, the distribution of pressure along the chord, and the experimentally determined, but theoretically obscure, point of maximum lift. The minimum drag as well as the pitching moment were also found to depend on the profile. Now the discussion turns to the distribution of the lift along the span of the wing and the properties that a wing possesses in virtue of its finite length and the flow around the wingtips. Bringing order and understanding to these phenomena (and predicting unsuspected effects and relationships involving the aspect ratio of a wing) was the outstanding achievement of Ludwig Prandtl and his co-workers at the University of Gottingen.2 Before looking into the technical details of this achievement, I discuss the intellectual background of the work and its institutional context.3