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Period of Modern Aerodynamics: From the End of the XIX Century Onward

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Aerodynamic Theory

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Abstract

Of the two aspects in which air reaction appears, known today as lift and drag, we have noted in the preceding section researches on the second one only.

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Notes

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  95. At this point Prandtl observes in a footnote that according to earlier experience, this has occurred only in turbulent boundary layers and at velocities beyond the critical, referring the reader on this subject to his note on resistance of spheres. (Über den Widerstand von Kugeln, Nachrichten der Kön. Ges. d. Wiss. zu Göttingen, p. 177, 1914).

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  96. Quite recently A. Betz has published a brief note entitled “Formation of Vortices in Ideal Fluids and Helmholtz’s Vortex Theorem” (Wirbelbildung in idealen Flüssigkeiten und Helmholtzscher Wirbelsatz, Zeitschrift für Mathematik und Mechanik, vol. X, p. 413, 1930) in which he demonstrates in a very simple manner that the possibility of the formation of surfaces of discontinuity is compatible with the hypothesis of a perfect fluid. The basis of his explanation is that the Helmholtz theorem on the impossibility of the formation of vortices in a perfect fluid holds good for vortex cores of finite section and not for surfaces of discontinuity. Now it is always possible to conceive ideal conditions (one of them was imagined by Felix Klein) in which surfaces of discontinuity (which as is well known are quite equivalent to vortex sheets) are formed in a perfect fluid.

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  100. Easier and more direct demonstrations of this theorem have been given later.

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  109. Fig. 34 of Prandtl’s report is the reproduction of Fig. 68 of Lanchester’s “Aerodynamics”, reproducing that wall diagram exhibited by Lanchester in his Lecture of the year 1894, and representing the incurvation of the streamlines on account of the presence of a plate of an “appropriate smoothly curved form, whose leading and trailing edges are conformable to the lines of flow”.

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  119. A detailed account of the work carried out in Germany on this subject is to be found in the paper by J. W. Maccoll “Modern Aerodynamical Research in Germany” (The Journal of the Royal Aeronautical Society, No. 236, vol. XXXV, August, 1930.

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  1. William Frederick Durand
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Durand, W.F. (1934). Period of Modern Aerodynamics: From the End of the XIX Century Onward. In: Aerodynamic Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-39765-7_35

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