There Is Nothing so Practical as a Good Theory

Getting a grip on instabilities or outwitting the forces of nature seems—like dreaming we can fly—an archetypal desire. Who doesn’t know such games and tests of courage in small and big children? Acrobats even make a career of it—engineers as well.

Stability is an ancient but central topic in the engineering sciences. Stabilizing a machine or a process to a point where safe and profitable operation is possible, despite the impact of constant error, is one of the core tasks of engineering. Solutions, such as simple systems that can be kept stable, have been common for quite some time. Complex systems, on the other hand, were non-existent until Aurel Stodola, while in Zurich, asked the right colleague the right question—a correct answer was given, too.

Aurel Stodola, born in a part of the former Austrian Empire, which belongs now to Slovakia, was appointed professor of mechanical engineering and machine design in 1892 at the Eidgenössische Technische Hochschule, now ETH Zurich. He taught and conducted research there in various fields, including in control engineering, until his retirement in 1929. In the first half of the 1890s, Stodola was occupied with a large theoretical study of water turbines that, among other things, was based on practical tests of experimental turbines. Eventually he succeeded in simplifying the mathematical modeling, but was not able to find a general solution to the problem of stability. During this research project, Stodola proposed the problem to Adolf Hurwitz, a mathematician appointed professor at ETH Zurich in the same year. Hurwitz, from Hildesheim, Germany, then managed to develop a mathematical method generally applicable to studying the instability of complex systems. Stodola, having been very pleased with this mathematical solution, included Hurwitz’ discovery in his paper published in the Schweizerische Bauzeitung, a scientific journal for engineers. In turn, Hurwitz published the results of their fruitful collaboration in the Mathematische Annalen a year later, and wrote not without pride that Stodola had already applied the findings to a system at a turbine plant in Davos “with brilliant success”.

Was this a groundbreaking scientific idea originally developed at the Swiss polytechnic? No! In Cambridge UK, the British mathematician Edward John Routh had developed the same mathematical procedure and published his idea about 25 years before Adolf Hurwitz. Routh’s work on stability had probably remained unknown to the engineers on the main European continent due to the language barrier and the lack of the method’s practical relevance. In 1898, Routh’s book “The Dynamics of a System of Rigid Bodies”, which contained his stability criterion, was translated into German. Stodola referred to it a year later in a paper. It was not until 1911 that the Italian mathematician Enrico Bompiani proved that the Routh and Hurwitz criterion were, in fact, identical. Since then, the Routh-Hurwitz Stability Criterion has become a standard application in control theory.

The birth of the Routh-Hurwitz Stability Criterion impressively illustrates how scientific research and the brilliant ideas it generates can emerge in various different ways and quickly find the path to practical implementation.

At Cambridge, a contest was the starting point for scientific work on the topic of “The Criterion of Dynamical Stability”. The discovery of the stability criterion long remained known only to a small group of scientists. In Zurich, an engineer who worked on the construction of a turbine plant was enthusiastic about the solution. He even published the stability criterion—in an easy to use guide—in a magazine for engineers. It is in this manner that a solution to a practical problem is solved through theoretical findings. In turn, its practical application has become today’s standard.

Still, the central aspect of this anecdote is rather that true breakthroughs and innovation often arise when boundaries are exceeded. Stodola was a brilliant engineer, yet his mathematical competencies fell short of what was needed to come up with the Hurtwitz-criterion. Conversely, Hurwitz would not have addressed the question of stability had not Stodolas coincidentally asked him. This ping-pong between the disciplines makes for an interesting approach. ETH Zurich has always strived to implement this approach—it is a principle of enablement that must continue in the future.