The role of mathematics in the formation of mechanical engineering as an
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'
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
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
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.