Section i. introduction
Kutta began with a nod not only to Lilienthal but to more recent developments in aviation. These, he said, gave a great practical significance to the old, but difficult hydrodynamic problem of calculating the forces on a body immersed in a moving fluid such as air. Calculating the lift forces on a wing was particularly important. It should be possible to do this because the relevant flow can be understood (“aufgefafit werden kann”) as the superimposition of a circulation and a steady stream. For an explanation of the basic ideas of the circulatory theory, Kutta directed the reader to the first volume of Lanchester’s Aerial Flight and a 1909 article by Finsterwalder. Finsterwalder’s article was titled “Die Aerodynamik als Grundlage der Luftschiffahrt” (Hydrodynamics as the basis of airship flight), but it also dealt with the basics of the circulation theory of lift.29 Kutta’s choice of words, in saying that the flow can be so understood, simply indicates that if the flow is interpreted in this way, then the lift force becomes intelligible. There is, however, no reason to suppose that he doubted the reality of circulation. He was probably stepping carefully because of the highly artificial character of the concepts he was applying to the problem: friction was being ignored, the flow was to be treated as two dimensional, and the fluid was taken to be free of vorticity (that is, the flow was irrotational).
Kutta then made three observations about his own earlier work. First, he said that in 1902 he had discovered a general theorem about lift which was rediscovered by Joukowsky in 1906. He thus made a priority claim for the result that lift is proportional to circulation and is given by the product of density, velocity, and circulation.30 Second, he said that the 1902 predictions about lift were supported by Lilienthal’s data but acknowledged that the discussion had been confined to wings at zero angle of incidence. This restriction would not apply to the more general analysis he was about to offer. Third, in his earlier account, the magnitude of the circulation could be fixed by specifying that the flow was to be smooth at both the leading and trailing edge. This was possible because of the symmetry of the arc-like wing at zero angle of incidence. In the more general treatment, with an arc whose chord was at an angle to the flow, adjusting the circulation could only make the flow smooth at one edge, for example, the trailing edge. At the leading edge the fluid would divide, generally at a point on the lower surface, and some of it would be forced to flow around the leading edge. Because Kutta represented the wing by a geometrically thin line, this meant the fluid at the leading edge would achieve infinite speeds and pose a significant problem for the analysis.
Kutta indicated to the reader that the lift force on the wing would have to be broken down into two parts. Leaving the explanation until later, he stated that one part of the lift would be produced by pressure on the surface of the arc, while the other part could be represented as a tangential, suction force at the leading edge. He also signaled his intention to make his abstract, geometrical model of the wing more realistic by studying the effects of rounding off the leading edge.