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A New Start in Göttingen

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Book cover Ludwig Prandtl

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Abstract

As a result of the efforts of the mathematician Felix Klein, applied sciences were greeted with great interest at the University of Göttingen. Carl Runge took up an appointment in Göttingen in the same year. Runge and Prandtl directed the Institute of Applied Mathematics and Mechanics, which was founded in 1905. From 1907, Prandtl was also appointed to research into aerodynamics for airship technology, which was carried out in a small airship model research institute outside the university, in a wind canal constructed by Prandtl. Parallel to this, questions related to flow mechanics were given an ever increasing range. During this time, Prandtl became an expert in aeronautics which, in addition to airships, became more and more concerned with aircraft. In 1909, Prandtl married Gertrud Föppl, the daughter of his supervisor.

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Notes

  1. 1.

    Sommerfeld to his mother, 4th March 1894. ASWB I, p. 55.

  2. 2.

    Rowe (1989, 2001, 2004).

  3. 3.

    Schubring (1989).

  4. 4.

    Hashagen (2003, Chap. 21).

  5. 5.

    Manegold (1970).

  6. 6.

    Vereinigung (1906).

  7. 7.

    Klein to Althoff, 7. June 1905. GStAPK VI. HA, Nl Althoff, No. 798, Sheet 245.

  8. 8.

    Runge and Prandtl (1906, p. 96).

  9. 9.

    Runge and Prandtl (1906, p. 100).

  10. 10.

    Runge and Prandtl (1906, pp. 103–106).

  11. 11.

    Prandtl to the Dean of the Philosophical Faculty, 31st July 1904. UAG, Phil. I, 190a; Naumann to the curator of the University of Göttingen, 31st July 1904. UAG, Kur PA Ludwig Prandtl, Vol. 1. Reprinted in Rotta (1985, p. 55).

  12. 12.

    Prandtl to the Curator, 30th March 1907. UAG, Kur. PA Prandtl, Ludwig, Vol. 1.

  13. 13.

    Althoff to Prandtl, 4th July 1907. UAG, Kur. PA Prandtl, Ludwig, Vol. 1.

  14. 14.

    Verzeichnis der Vorlesungen auf der Georg-August-Universität zu Göttingen. http://gdz.sub.uni-goettingen.de/dms/load/toc/?PPN=PPN654655340. Please also refer to Wuest (2000); with a list and annotation of Prandtl’s lectures.

  15. 15.

    Verzeichnis der Vorlesungen auf der Georg-August-Universität zu Göttingen. http://gdz.sub.uni-goettingen.de/dms/load/toc/?PPN=PPN654655340. Please refer also to Richenhagen (1985, p. 298).

  16. 16.

    Runge and Prandtl (1906, p. 111).

  17. 17.

    Verzeichnis der Vorlesungen auf der Georg-August-Universität zu Göttingen. http://gdz.sub.uni-goettingen.de/dms/load/toc/?PPN=PPN654655340.

  18. 18.

    Runge and Prandtl (1906, p. 95).

  19. 19.

    Protokoll der Generalversammlung der Göttinger Vereinigung, 17. Dezember 1904. AMPG, III. Abt., Rep. 61, No. 2329.

  20. 20.

    Prandtl to the Kurator, 28th February 1906. UAG, Kur. 7464.

  21. 21.

    Prandtl’s report at the meeting of the Göttinger Vereinigung on the 10th December 1905. AMPG, III. Abt., Rep. 61, No. 2329.

  22. 22.

    Curator to Prandtl, 7th March 1906. UAG, Kur. 7464.

  23. 23.

    Prandtl to the curator, 19th February 1907. UAG, Kur. 7464.

  24. 24.

    Protokoll der Generalversammlung der Göttinger Vereinigung on the 13th and 14th July 1906. AMPG, III. Abt., Rep. 61, No. 2330.

  25. 25.

    Protokolle der Göttinger Vereinigung 1908 and 1909. AMPG, III. Abt., Rep. 61, No. 2331 und No. 2332.

  26. 26.

    Vereinigung (1908, p. 30).

  27. 27.

    Gründungsaufruf, 3rd May 1906. GStAPK, VI. HA, Nl Althoff, No. 531, Motorluftschiff-Studiengesellschaft, Sheet 214–215. Regarding the history of the foundation, please refer to Rotta (1990a, pp. 18–22).

  28. 28.

    Meeting of the governing body of the technical committee of the Motorluftschiff-Studiengesellschaft m. b. H. on the 28th October 1906. SUB, Cod. Ms. F. Klein 7C. Please refer also to Rotta (1990a, p. 25).

  29. 29.

    Enclose 3 to the meeting of the Studiengesellschaft, 30th October 1906. SUB, Cod. Ms. F. Klein 7C.

  30. 30.

    Klein to Studiengesellschaft, 15th December 1906. SUB, Cod. Ms. F. Klein 7C. Reprinted in Rotta (1990a, pp. 26–32 and supplement pp. 298–300).

  31. 31.

    Rotta (1990a, pp. 35–38).

  32. 32.

    Protokoll der Sitzung des Aufsichtsrats dated the 14th September 1907. GStAPK, VI. HA, Nl Althoff, Nr. 531, Motorluftschiff-Studiengesellschaft, Sheets 95–97.

  33. 33.

    Kehler to Althoff, 4th November 1907. GStAPK, VI. HA, Nl Althoff, Nr. 531, Motorluftschiff-Studiengesellschaft, Sheet 107–109.

  34. 34.

    Protokoll der Göttinger Vereinigung 1907. AMPG, III. Abt., Rep. 61, No. 2330.

  35. 35.

    Protokoll der Göttinger Vereinigung 1908. AMPG, III. Abt., Rep. 61, No. 2331.

  36. 36.

    Notes of Klein on “Hydro- und Aerodynamik (1908, 44 Blatt)”. SUB Cod. Ms. Klein 20 F.

  37. 37.

    Regarding the development of mathematical-physical seminars at German Universities, please refer to Olesko 1991, in which—taking the example of the Königsberg Seminar of Franz Ernst Neumann—above all, the role for teaching training was emphasised. On the subject of Klein’s seminars, please refer to Chislenko and Tschinkel, 2007.

  38. 38.

    Verzeichnis der Vorlesungen auf der Georg-August-Universität zu Göttingen. http://gdz.sub.uni-goettingen.de/dms/load/toc/?PPN=PPN654655340.

  39. 39.

    Runge and Prandtl (1906, p. 111).

  40. 40.

    Wuest (2000, p. 202).

  41. 41.

    Protokollbuch No. 27, Mathematisches Lesezimmer der Universität Göttingen.

  42. 42.

    Protokollbuch No. 27, pp. 11–17. Mathematisches Lesezimmer der Universität Göttingen.

  43. 43.

    von Kármán (1909). Regarding Kármán’s recollections of his academic beginnings with Prandtl, put to paper many years later, please refer to Kármán and Edson (1967, pp. 34–41).

  44. 44.

    Protokoll der Göttinger Vereinigung 1908. AMPG, III. Abt., Rep. 61, No. 2331.

  45. 45.

    Protokollbuch Nr. 27, pp. 18–24, 38–51 and pp. 52–66. Mathematisches Lesezimmer der Universität Göttingen.

  46. 46.

    Blasius (1907).

  47. 47.

    Boltze (1908), Hiemenz (1911).

  48. 48.

    The new variable is produced from the original variable by the transformation \( \xi = \frac{1}{2}\sqrt {\frac{\rho U}{k}} \frac{y}{\sqrt x } \) and \( \psi = \sqrt {\frac{kU}{\rho }} \sqrt x \zeta \). For a justification, please refer to Blasius (1907, p. 7).

  49. 49.

    cf. In this context Fig. 2.5 and Prandtl (1905b, p. 487).

  50. 50.

    Protokollbuch No. 27, pp. 67–81. Mathematisches Lesezimmer der Universität Göttingen.

  51. 51.

    Darrigol (2005, Chap. 6).

  52. 52.

    Cod. Ms. L. Prandtl 14, p. 29 and 30. SUB.

  53. 53.

    Sommerfeld (1900).

  54. 54.

    Eckert (2010).

  55. 55.

    Bodenschatz and Eckert (2011).

  56. 56.

    Prandtl to the curator, 29th October 1907. UAG, Kur. 1456.

  57. 57.

    Regarding the later career of Blasius, please refer to Hager (2003).

  58. 58.

    An index of the dissertations supervised by Prandtl can be found in Tollmien et al. (1961, Vol. 3, pp. 1612–1617).

  59. 59.

    Prandtl (1905b). This discourse appeared as a self-contained chapter in an encyclopaedia article completed in July 1905 about “Technical thermodynamics” Schröter and Prandtl (1905).

  60. 60.

    Prandtl (1904a).

  61. 61.

    Prandtl (1904e). Regarding the Mach bullet images, please refer to Hoffmann and Berz (2001).

  62. 62.

    Prandtl (1906), Prandtl (1907).

  63. 63.

    Settles et al. (2009).

  64. 64.

    Naumann (Prussian Ministry of Education and Cultural Affairs) to the curator of the University of Göttingen, 11th January 1909. UAG, Kur. PA Prandtl, vol. 1.

  65. 65.

    Prandtl to the curator 27th February 1909. UAG, Kur. PA Prandtl, vol. 1.

  66. 66.

    Berliner Illustrierte Zeitung to Prandtl, 15th April 1909. Cod. Ms. L. Prandtl 1, 9, SUB.

  67. 67.

    Protokoll der Generalversammlung der Göttinger Vereinigung, 7th and 8th July 1909. AMPG, III. Abt., Rep. 61, No. 2332.

  68. 68.

    Rotta (1990a, p. 51f.).

  69. 69.

    Appeal for participation in a discussion about the founding of an airship association, UAG, Kur. 3569.

  70. 70.

    Wuest (1988). Regarding the history of scientific balloon flight, please refer to Höhler (2001).

  71. 71.

    Cited according to Rotta (1990a, p. 53).

  72. 72.

    Prandtl (1909).

  73. 73.

    Protokoll der Generalversammlung der Göttinger Vereinigung, 17th and 18th June 1910. AMPG, III. Abt., Rep. 61, No. 2333.

  74. 74.

    Prandtl (1910a).

  75. 75.

    Rotta (1990a, pp. 87–95). Please also refer to illustrations in Cod. Ms. L. Prandtl 6, SUB und Kur 7464, UAG.

  76. 76.

    Rotta (1990a, pp. 69–74).

  77. 77.

    Fuhrmann (1912).

  78. 78.

    Cited in Vogel-Prandtl (2005, p. 48).

  79. 79.

    Please refer also to the correspondence in GOAR 2655.

  80. 80.

    Ludwig Föppl: Erinnerungen an Ludwig Prandtl. In the private ownership of the Vogel family.

  81. 81.

    Cited in Vogel-Prandtl (2005, p. 47).

  82. 82.

    Cited in Vogel-Prandtl (2005, p. 47).

  83. 83.

    Föppl (1925, p. 45).

  84. 84.

    Cited in Vogel-Prandtl (2005, p. 49).

  85. 85.

    Ludwig Föppl: Erinnerungen an Ludwig Prandtl. Privatbesitz Familie Vogel.

  86. 86.

    Cited in Vogel-Prandtl (2005, pp. 52–55).

  87. 87.

    Vogel-Prandtl (2005, pp. 53–55).

  88. 88.

    Prandtl to Klein, 4th May 1904. SUB, Cod. Ms. F. Klein, 2F, 3.

  89. 89.

    Prandtl to the Curator, 30th March 1907; Althoff to Prandtl, 4th July 1907. UAG, Kur. PA Prandtl, Ludwig, vol. 1.

  90. 90.

    Cited from Rotta (1990a, p. 99).

  91. 91.

    Cited from Lemmerich (1981, p. 55); regarding the history of the KWG, please refer also to Vierhaus and vom Brocke (1990).

  92. 92.

    Protokoll der Göttinger Vereinigung, meeting on the 24th and 25th April 1911. AMPG, III. Abt., Rep. 61, Nr. 2334.

  93. 93.

    Denkschrift über die Errichtung eines Forschungsinstituts für Aerodynamik und Hydrodynamik in Göttingen, 16th February 1911. AMPG, Abt. I, Rep. 1A, No. 1466. Also reprinted in Rotta (1990a, pp. 99–102).

  94. 94.

    Rotta (1983).

  95. 95.

    Denkschrift über die Errichtung eines Forschungsinstituts für Aerodynamik und Hydrodynamik in Göttingen, 16th February 1911. AMPG, Abt. I, Rep. 1A, No. 1466. Also reprinted in Rotta (1990a, pp. 99–102).

  96. 96.

    Protokoll der Göttinger Vereinigung, meeting on the 24th and 25th April 1911. AMPG, III. Abt., Rep. 61, No. 2334.

  97. 97.

    Rotta (1990a, pp. 102–114).

  98. 98.

    Minister of Education and Cultural Affairs (Freiherr von Trott zu Solz) to Prandtl, 6th February 1911. Cited in Rotta (1983, p. 32).

  99. 99.

    Rotta (1983).

  100. 100.

    Denkschrift über die Errichtung eines Forschungsinstituts für Aerodynamik und Hydrodynamik in Göttingen, 16th February 1911. AMPG, Abt. I, Rep. 1A, No. 1466. Please refer also to Rotta (1990a, p. 100).

  101. 101.

    Rotta (1983, p. 64f.).

  102. 102.

    Trischler (1992, pp. 70–83).

  103. 103.

    Trischler (1992, p. 78).

  104. 104.

    Euler to Prandtl, 20th March 1911, reprinted in Rotta (1990a, p. 62).

  105. 105.

    Prandtl (1912b). Please refer to the exchange of letters in GOAR 3731.

  106. 106.

    Rotta (1990a, pp. 64–68).

  107. 107.

    Prandtl (1912b, pp. 19–22).

  108. 108.

    Prandtl (1912a).

  109. 109.

    Rotta (1990a, p. 189f.), Bloor (2011, p. 133).

  110. 110.

    Prandtl (1912a, p. 34).

  111. 111.

    Kutta (1902), Kutta (1910), Joukowsky (1906), Joukowsky (1910).

  112. 112.

    Prandtl (1912a, p. 35).

  113. 113.

    Föppl (1911, p. 184).

  114. 114.

    Please refer to Sect. 4.5.

  115. 115.

    Rotch (1912, p. 44). Regarding Eiffel‘s work on aerodynamics, please refer to Eiffel (1911), Fontanon (1998) and Damljanović (2012).

  116. 116.

    Prandtls travel report to the Ministry of Education and Culture dated 1st November 1913. GStAPK, I.HA. Rep.76, Va, Sekt. 6, Tit. IV, No. 21, vol. 1 (Die wissenschaftlichen Reisen der Professoren und Privatdozenten an der Universität zu Göttingen. I: vom Dezember 1891 bis Dezember 1923), pp. 292–294.

  117. 117.

    Prandtl to W. Knight, 1st December 1919. AMPG, III. Abt., Rep. 61, No. 836. Regarding the (unsuccessful) attempt at making contact with Eiffel after the First World War, please refer to Eckert (2005, p. 113).

  118. 118.

    Föppl (1912, p. 121). O. Föppl to Prandtl, 21st February 1912, GOAR 2655.

  119. 119.

    Eiffel (1912).

  120. 120.

    Prandtl (1913a, p. 77). Eiffel also provided Prandtl following his visit to Auteuil in October 1913 with construction plans for the fan in his wind tunnel. Eiffel to Prandtl, 28th October 1913. GOAR 3684 (“Suivant votre demande, je vous adresse ci-inclus un dessin de mon ventilateur hélicoidal…”).

  121. 121.

    Prandtl (1914), Wieselsberger (1914).

  122. 122.

    Cod. Ms. L. Prandtl 14, p. 12. SUB.

  123. 123.

    Prandtl (1914, p. 180).

  124. 124.

    Prandtl to Eiffel, 16th July 1914. GOAR 3684.

  125. 125.

    Eiffel to Prandtl, 17th July 1914. GOAR 3684.

  126. 126.

    Prandtl (1913b, c).

  127. 127.

    A. Föppl to Prandtl, 6th June 1912. GOAR 2655.

  128. 128.

    Ludwig Föppl: Erinnerungen an Ludwig Prandtl. In the private collection of the Vogel family. Also cited by Vogel-Prandtl (2005, pp. 57–60).

  129. 129.

    Ludwig Föppl to Gertrud Prandtl, 11th December 1958. In the private possesion of the Vogel family.

  130. 130.

    Ludwig Föppl: Erinnerungen an Ludwig Prandtl. In the private possesion of the Vogel family.

  131. 131.

    Ludwig Föppl: Erinnerungen an Ludwig Prandtl. In the private possesion of the Vogel family.

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  1. Deutsches Museum, Munich, Bayern, Germany

    Michael Eckert

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Eckert, M. (2019). A New Start in Göttingen. In: Ludwig Prandtl. Springer Biographies. Springer, Cham. https://doi.org/10.1007/978-3-030-05663-6_3

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