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Physically Similar Systems - A History of the Concept

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Springer Handbook of Model-Based Science

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Abstract

The concept of similar systems arose in physics and appears to have originated with Newton in the seventeenth century. This chapter provides a critical history of the concept of physically similar systems , the twentieth century concept into which it developed. The concept was used in the nineteenth century in various fields of engineering (Froude , Bertrand, Reech ), theoretical physics (van der Waals , Onnes , Lorentz , Maxwell , Boltzmann ), and theoretical and experimental hydrodynamics (Stokes , Helmholtz , Reynolds , Prandtl , Rayleigh ). In 1914, it was articulated in terms of ideas developed in the eighteenth century and used in nineteenth century mathematics and mechanics: equations, functions, and dimensional analysis. The terminology physically similar systems was proposed for this new characterization of similar systems by the physicist Edgar Buckingham . Related work by Vaschy , Bertrand, and Riabouchinsky had appeared by then. The concept is very powerful in studying physical phenomena both theoretically and experimentally. As it is not currently a part of the core curricula of science, technology, engineering, and mathematics (GlossaryTerm

STEM

) disciplines or philosophy of science, it is not as well known as it ought to be.

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Abbreviations

STEM:

science, technology, engineering, and mathematics

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Acknowledgements

Work on this paper was supported in part by a Visiting Fellowship at the Center for Philosophy of Science at the University of Pittsburgh in 2010, during which my project was the history of the concept of physically similar systems . This paper also incorporates some earlier work published in Chaps. 6 (The Physics of Miniature Worlds) and 7 (Models of Wings and Models of the World) of Wittgenstein Flies A Kite: A Story of Models of Wings and Models of the World. Thanks also to Brian Hepburn and George Smith for conversations about Newton’s use of similar systems , and to Jasmin Ozel for translating parts of Forchheimer’s Hydraulik.

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  1. Department of Philosophy, Wichita State University, 1845 North Fairmount, KS 67260-0074, Wichita, USA

    Susan G. Sterrett

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  1. Susan G. Sterrett
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Correspondence to Susan G. Sterrett .

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  1. Department of Humanities, University of Pavia, Piazza Botta 6, 27100, Pavia, Italy

    Lorenzo Magnani  & Tommaso Bertolotti  & 

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Sterrett, S.G. (2017). Physically Similar Systems - A History of the Concept. In: Magnani, L., Bertolotti, T. (eds) Springer Handbook of Model-Based Science. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-30526-4_18

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  • DOI: https://doi.org/10.1007/978-3-319-30526-4_18

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