The role of mathematics in the formation of mechanical engineering as an independent discipline

Symposium, Friday October 10, 1997

In the course of the nineteenth century and the first part of the twentieth century mechanical engineering developed into an established independent discipline. This development is accompanied by an increasing application in mechanical engineering of mathematical methods, directly in the form of geometrical methods, and indirectly in the form of mechanics and other physical theories. The purpose of the symposium is to investigate this growing role of mathematical methods in mechanical engineering.


Gerard Alberts: "What is so applied about applied mechanics"?
From the beginning of higher education in engineering, i.e. the École Polytechnique in France and the Polytechnische Schulen in Germany, rational mechanics was among the obligatory subjects. It was Newtonian mechanics in the shape in which it was canonised by Lagrange. Rational mechanics was quite different in style and practice from practical mechanics or mechanical engineering and was in fact not taught not to provide solutions to practical engineering problems. On the contrary, it was offered mainly in order to stimulate clear thinking, to generate a geometrical spirit in the minds of the future engineers.
The second half of the nineteenth century, however, saw the rise of a range of technical problems of an essentially dynamical nature. Problems like resonating motors, rolling ships and vibrating railway tracks, resisted solution by straightforward mechanical engineering or kinematical approaches, mainly because the forces of moving bodies came into play. Problems in this category were new, and -by lack of experience- no rules of the thumb were at hand. Even newer were the twentieth century problems of flight, aerodynamics and turbulence.
Only gradually engineers came to grips with such problems; neither the mechanical engineers, nor the professors of rational mechanics had much to contribute. Not the average engineers, but rather the scientifically oriented engineer succeeded in bending rational mechanics towards some partial understanding of turbulence, resonance etc. at the cost of heavy numerical investment. Around 1900 Heun, Runge and Kutta represented this practice. By 1920 they were joined by Von Mises and the "scientifically working engineers" of ZAMM and GAMM. The field came to be called applied mechanics, that is applications of rational mechanics. It involved not just intensive calculative effort, but also laboratory experiments.
Against this background I will concentrate in my paper on the story of applied mechanics in the Netherlands. In Delft in 1913, Van Iterson left his chair of mechanics at the Technische Hoogeschool after only three years in office to become director of the National Coal Mines. He slammed the door behind him in frustration for being denied laboratory equipment and further research facilities. In 1914 his successor Biezeno occupied the chair that was renamed and became the chair for applied mechanics. Biezeno kicked off in controversy, hitting in the direction of Dutch remnants of the German "Anti-Mathematische Bewegung". However successful, and internationally renowned, Biezeno and his group, and his colleague Burgers, were in the field of Applied Mechanics, it would last until 1948 before they were allowed to train students of their own. Applied mechanics clearly involves the application of mechanics. Still engineers wondered, not without reason, how applied -or rather practicable- its "exact" methods are from their point of view. Also in the Netherlands, controversy between mathematical and experience-based methods remained.

Fons Alkemade: "On the increasing role of fluid mechanics in engineering: J. M. Burgers and his work on pumps"
In the beginning of the twentieth century the Technological University of Delft realised that fluid mechanics was becoming increasingly important for the technical sciences. H.A. Lorentz suggested to appoint the physicist Johannes Martinus Burgers (1895-1981). At the age of 23 years Burgers became professor in Delft and started to work in fluid mechanics. Apart from his theoretical work on turbulence (to him we owe the simplified equation for turbulence, known as the Burgers-equation) Burgers also excelled in experimental work. In the laboratory of Aero- and Hydrodynamics, which was founded in Delft in 1921, he was one of the first to apply hot-wire technology to the problem of transition and turbulence in a boundary layer. In 1928 the National Committee for the Zuiderzee works asked him to work on the pumps that would be used to drain the Zuiderzee polders. In the lecture I will describe Burgers' solution to the problem of the design of the fans of centrifugal pumps as an example of the increasing role of fluid mechanics in engineering.

Bruno Belhoste (Paris): "The Role of Mathematics in Applied Mechanics Teaching to French Engineers in XIXth Century"
The purpose of this lecture is to examine how Mathematics was used in the various French XIXth-century engineering schools in connection with applied mechanics teaching. I will consider both of the analytical and geometrical traditions, developped in the "grandes »coles" (École polytechnique and its écoles d'application") and in the technical courses (Conservatoire national des arts et manufactures, etc.). This investigation will be mainly based on the study of courses made by prominent teachers (Navier, Poncelet, Belanger, Morin, etc.).

Marco Ceccarelli (Cassino): "On the Historical Development of Mechanisms' Drawing"
Technical drawings are a fundamental tool for the representation and the design of machines and mechanisms. In the lecture I will concentrate on the historical development of mechanisms drawing. The development reflects parallel developments in art but also theoretical developments in mechanical engineering. Moreover, we will see that there is an evolution from presumably even intentionally incomplete sketches to a naturalistic description of the way in which a mechanism functions. Later there is an evolution from synthetic schemes to much more abstract graphs to represent mechanisms.

Teun Koetsier: "On the Mathematization of Kinematics of Mechanisms"
In particular in the second half of the 19th century, kinematics enjoyed great popularity among both mechanical engineers and mathematicians. A figure of major importance was the German engineer F. Reuleaux. We owe the way in which we look at mechanisms today to Reuleaux. In the course of the 19th century many new mechanisms had been invented and it was difficult to classify them in a sensible way. First in lectures and then in his 1875 book Reuleaux introduced a new abstract point of view with respect to mechanisms, which led to a new system of classification.
Reuleaux's abstract view of mechanisms was one of the factors that led the German mathematician Ludwig Burmester to a systematic study of the applicability of geometrical methods in kinematics of mechanisms. In 1888 Burmester's Lehrbuch der Kinematik appeared, partially based upon earlier work. Over more than 900 pages an extensive treatment of planar theoretical kinematics was given and the results thus obtained were applied to a wealth of examples from kinematics of mechanisms. The book contains graphical methods to determine the instantaneous velocities and accelerations for a given mechanism in any position. Similar methods for the kinematical analysis of mechanisms were developed in the United Kingdom by the engineers Alexander Kennedy, who translated Reuleaux' book into English, and R. H. Smith. Burmester's work, however, was much more influential. Important is also the so-called Burmester theory, developed to design mechanisms.

Klaus Mauersberger: "Die Entwicklung des wissenschaftlichen Maschinenbaus in Deutschland im Spannungsfeld von visuellem Denken und mathematische Abstraktion" (Ein Beitrag zur Methodendiskussion in den Ingenieurwissenschaften im 19. Jh.)
Im Selbstverständnis der sich entfaltenden polytechnischen Bildung und in der breiten methodischen Diskussion innerhalb der Ingenieurwissenschaften rang man im 19. Jahrhundert um jene eigenständigen Konzepte, welche zwar die naturwissenschaftlichen Grundlagen und die Mathematisierung theoretischer Ansätze einbezogen, die aber vielmehr auf die Spezifik einer eigenständigen technischen Wissenschaft abhoben. Bei aller Affinität zu den Naturwissenschaften, namentlich zu den glänzenden Erfolgen der Mechanik, hatten die Techniker rechtzeitig erkannt, daß eine Reduktion der Entstehung der Technikwissenschaften auf die Anwendung der Ergebnisse der Naturwissenschaften mit Hilfe mathematischer Methoden, eine viel zu engen Sicht auf die Genese ihres Fachgebietes darstellt. Neuere wissenschaftshistorische Untersuchungen über die Beziehung von Struktur und Funktion des technischen Wissens, seiner Herausbildung, Reife und Anreicherung mit theoretischen Elementen haben die Erkenntnis bestärkt, daß die Entstehung der Technikwissenschaft als die Fusion und Interaktion verschiedener Wisssensformen begriffen werden kann, welche in der historischen Entwicklung zu einem lebhaften Spannungsfeld unterschiedlicher Herangehensweisen, Denkstile, Erfahrungshintergründe und methodischer Konzepte geführt hat.
Im Wissenschaftlichen Maschinenwesen wurden seit Anbeginn neben der heute üblichen physikalischen und mathematischen Modellierung technischer Vorgänge auch andere Lösungsmöglichkeiten, Methoden der Analyse und Denkweisen berücksichtigt. Der Prozeß der Verbalen Beschribung und mathematischen Modellbildung ist eng verbunden mit dem visuellen und nichtverbalen Prozeß der Wahrnehmung, geistigen Vorwegnahme und konstruktiven Synthese. In die Natur des technischen Entwurfs- oder Erfindungsvorgangs einzudringen heißt auch, Unwägbares einzubeziehen. Erfinder und Konstrukteure arbeiten mit diesem "geistigen Auge", arbeiten genauso mit Intuition wie mit ihren intellektuellen Fähigkeiten. Die deutliche Hinwendung zu einem visuellen Denken und später zu visualisierbaren Methoden herrschte im Mascinenbau bis zur Mitte des 19. Jahrhundert vor und geriet ausgangs des Jahrhunderts in Wiederstreit mit einer zunehmenden mathematischen Abstraktion im theoretischen Apparat der Maschinenwissenschaften. Noch in der Gegenwart werden nichtmathematisierbaren Aussagen etwa für die Wertung, Interpretation und Abschätzung von theoretischen Ergebnissen in Bezug auf die praktische Realität herangezogen. Noch heute hängt die Kreativität des Ingenieurs auch von diesem visuellen, nichtverbalen Denken ab, wenngleich sich Intuition und Erfahrung gründlich gewandelt haben.