Section vii. concluding remarks

Kutta ended with some ideas about extending his mathematical methods to a variety of different wing profiles with rounded leading edges and with flaps attached to the trailing edge. He mentioned the need to develop a more gen­eral form of the Schwarz-Christoffel theorem and indicated the demanding amount of computational effort that would be involved, but Kutta did not feel that the limits of his approach had been reached and hinted at their fur­ther application to biplanes.

Kutta’s next paper, in 1911, utilized the same mathematical techniques as those adopted in 1910 but it dealt with more complicated cases.33 The analysis was generalized in two ways. First, Kutta showed how to apply his conformal transformations to an aerofoil whose cross section was composed of not one but two circular arcs in the form of a crescent or sickle shape. Such a sickle­shaped profile was used in the successful Antoinette monoplane, and von Mises has suggested that its practical use was prompted by Kutta’s analysis.34 Second, Kutta generalized the approach in order to describe the flow over a number of wings that could be arranged to make a biplane or a triplane or even a multiwing arrangement in the form of a “Venetian blind.” Again, all of these forms had actually been used, or experimented with, by those who tried to build flying machines.

Having made these two outstanding contributions to aerodynamics, Kutta fell silent. He never published anything again. The reason for the silence is unknown.