Theory and Practice

The way Kutta’s creative achievement was reconfigured in terms of the Jou – kowsky transformation, and then subsumed under a sequence of ever more general results, is striking. But generality alone was certainly not the driving force of the development that I have described. The goals that were being pur­sued were not abstract ones. Kutta, Joukowsky, Deimler, Blumenthal, Trefftz, Betz, von Karman, and von Mises were confronting mathematical puzzles, but their puzzle solving operated within a set of identifiable parameters, and those parameters were set by the practicalities of aeronautics. These men were all aiming to make their mathematical tools work for them so that the ideas involved could be brought into closer contact with the problems faced by

engineers who designed wings and built aircraft. Their tools were abstract ones (ideal-fluid theory, conformal mapping, geometry and mechanics), but they were harnessed to engineering goals and exploited or modified accordingly.

The stance the German, or German-language, experts took toward their mathematical apparatus was neither that of the pure mathematician nor that of the physicist. Neither rigor nor purity were central concerns, nor was it their primary goal to test the physical truth of their assumptions. They tested their conclusions for utility rather than their assumptions for truth. Expedi­ency was a prominent characteristic of their mathematical and experimental activity. When Betz looked for deviations between theory and experiment, he was tracking the scope of his approach, not trying to expose its falsity (which he took for granted). While no one directly asserted the literal truth of ide­al-fluid theory (though Prandtl came close), no one evinced much anxiety about its evident falsity either. Not a single author, in any of the papers de­scribed here, even mentioned the problem of how a circulation might arise in an ideal fluid. It was an issue of which they were aware, but it was not a stumbling block.

The particular blend of mathematics and engineering that was visible in Kutta’s 1910 paper was sustained throughout all the subsequent developments that have been examined in this chapter. The most vital ingredient in the blend was the orientation toward specific artifacts and the engineering problems associated with them. There is no evidence throughout the developments I have described that practitioners felt the need to make a choice between mathematics and their practical concerns. On the contrary: the former was seen as a vehicle for expressing the latter. Those working in aerodynamics were confident in their ability to combine mathematics and practicality. The continuity and homogeneity of their work suggest an increasingly secure dis­ciplinary identity. Workers in aerodynamics were beginning to form an intel­lectual community, and they had an institutional basis. Finsterwalder called their discipline “modern” applied mathematics. I have followed August Foppl and brought it under the rubric of technische Mechanik.

The particular form of the unity of theory and practice embodied in tech – nische Mechanik was eloquently affirmed in a lecture given in 1914 by Arthur Proll of the TH in Danzig.66 Speaking at a meeting of the recently formed Wissenschaftliche Gesellschaft fur Flugtechnik, Proll chose as his topic “Luft – fahrt und Mechanik” (Aeronautics and mechanics). Proll surveyed a wide range of topics, including stability and the strength of materials, but he began with the work on lift that had started with Kutta. He described the basic ideas of the circulation theory and reproduced the flow diagrams worked out by Deimler. For Proll this was a clear illustration of how a “good” theory can work hand in hand with practical concerns (“wie eine ‘gute’ Theorie mit der Praxis derart Hand in Hand arbeiten kann”). Responding to the rhetoric of the antimathematical movement, he went on:

Der Kampf ums Dasein mit den Erfordernissen des praktischen Lebens legt auch der wissenschaftlichen Spekulation gewisse Fesseln an und zwingt sie, Uberflussiges oder Unsicheres uber Bord zu werfen. Das ist eine erste gute Frucht der gegenseitigen Verstandigung von Theorie und Praxis, und eine solche finden wir auch hier bei der Aerodynamik vor. (95)

The struggle for existence and the demands of practical life impose certain constraints on scientific speculation and force us to throw overboard what is superfluous or insecure. This is the first fruit of the mutual understanding of theory and practice and it is what we actually find here in aerodynamics.

PrOll was not simply reporting a sequence of results in his field. He was mak­ing the case for a certain style of work and the methodology that it involved. He was celebrating the utility of technical mechanics in the face of familiar criticisms and characterizing that utility by using the slogan of the unity of theory and practice. He was saying what that unity meant for the practitio­ners of technical mechanics.67 This was not lost on his audience, and not all of them accepted his understanding of that unity. Not everyone with an interest in aeronautics was a specialist in technical mechanics, and for them Proll’s claims were not necessarily congenial ones.

On member of the audience was Prof. Friedrich Ahlborn, whose interest in hydrodynamics was empirical not mathematical. Ahlborn was a specialist in, and a pioneer of, the photography of fluid flows.68 For Ahlborn the math­ematics of ideal fluids was just the plaything of theorists who did not realize that experiment alone would yield understanding. In the discussion follow­ing Proll’s lecture, Ahlborn was the first on his feet in order to explain these facts to the assembled company. The work Proll had just described, he said, was mere theory and could be ignored. Ahlborn’s remarks about the Prandtl – Fuhrmann work on airships were scathing. As for the new Joukowsky aero­foils, Ahlborn warned aeronautical engineers that they should not assume that they will make good wings. Only experiment could establish that.69 Proll, he implied, had ignored experiment. Prandtl, who was also in the audience, sprang to Proll’s defense. The lecture, he insisted, had not been one-sided. Proll’s theme was the unity of theory and practice in aeronautics and that, surely, implied the unity of theory and experiment. If Ahlborn was not con­vinced, he, Prandtl, was.

To those who were outside the culture of technical mechanics, the work done by the insiders could seem of little value. This did not just apply to those, like Ahlborn, with no mathematical aptitude. It also applied to those whose mathematical expertise was beyond question, for example, to Cambridge-trained mathematical physicists. As G. H. Bryan had made clear in his review of Joukowsky’s book, the methods that had proven so fertile in the hands of Blumenthal at Aachen, or Betz at Gottingen, were of no interest to him. They seemed too elementary to be of any value, and they appeared to have nothing to teach a good Tripos man. British experts complained that the Kutta condition was arbitrary and, in any case, could not be applied to a rounded edge. Betz, by contrast, felt free to experiment with different posi­tions of the stagnation point and to explore the flow over a rounded and realistic trailing edge. The mathematically precise position of the stagnation point, he argued, was not of great practical significance. The British, unlike their German counterparts, were greatly exercised by the problem of how a circulation could ever arise in an ideal fluid. But where the German group, in one institutional setting, had surged forward and constructed a cumulative, puzzle-solving, and practically oriented tradition, the British mathematicians, in a different institutional setting, turned their backs on the opportunity, and they felt entirely justified in doing so.