De Bethune - The yurt and the equation

February 2012

Denis Flageollet, watchmaker and co-founder of De Bethune, along with David Zanetta, likes solitude. He set up his ateliers and his manufacture in the Jura mountains, near Sainte-Croix, on a high plateau, home to a few scattered villages. But, for him, this remoteness is not enough. Thus, he regularly takes refuge at an even more secluded spot—a Mongolian yurt that he puts up each winter at the edge of a small forest. Here, there is no electricity or heating. When he arrives at the yurt, even before lighting a fire under a pot to melt some snow for water, Flageollet turns off his mobile phone. As for telling the time, he reads it in the stars and in the trajectory of the moon.
Perhaps this voluntary isolation at the heart of nature is what Flageollet needs in order to “return to the essential” and to contemplate, in peace and quiet, the best way to open new avenues in the ancestral art of mechanical timekeeping. And to do so, he needs to traverse a thick layer of time, since the quasi-intangible principles of mechanical watchmaking were born with the discovery by Galileo of the laws of the pendulum, before later being put into motion by Huygens in 1675 (see the article “The mastery of time” by Paul O’Neil in this issue).
Since then, the balance spring coupled to a pendulum balance invented by Huygens has invariably governed the ways of mechanical watchmaking. During its history of more than 300 years, this escapement, which has the advantage over all the others of being perfectly isochronous, has continuously been improved, miniaturised, protected from temperature variations, the negative effects of gravity and then accelerated. Yet, the principle of its operation has never changed. The balance spring driven by the pallets remains, still today, the design foundation of the mechanical watch.
At the back of his yurt, Denis Flageollet set about thinking of the best way to improve the balance spring—to make it smaller, lighter, faster, more precise… In 2006, at BaselWorld, he presented an experimental, self-compensating balance spring made of silicon with a silicon escapement oscillating at 72,000 vibrations per hour, or 10 Hz. He remains convinced that the limit of 10 Hz cannot be exceeded by a classic escapement, mainly for reasons of reliability and mechanical wear and tear over time (even though, since then, Zenith presented a 50-Hz calibre and TAG Heuer produced a 500-Hz, which allows the mechanical indication of 1,000th of a second for 150 seconds of power reserve).
With this in mind, Flageollet went about exploring another system, the magnetic escapement.

De Bethune - The yurt and the equation

Birth of the “Résonique”
Between the yurt, the manufacture, the ateliers, and the small laboratory that he set up there, “a new watchmaking discipline in classic mechanical timekeeping” was born. Flageollet has coined a word for this new discipline—“Résonique”. A contraction of “resonance,” resonant frequency, and mechanical energy, the fundamental principle of Résonique is the synchronisation between a moving gear train and a vibrating mechanical oscillator. On paper, the principle is very simple and goes straight to the essential: a driving organ, for example, the barrel, transmits energy to a reducing gear. At the end of the gear is a magnetised rotor that transmits, in turn, energy to the oscillator to which magnets are attached. By resonance, the speed of the magnetic rotor synchronises with the frequency of the oscillator. Its movement, stabilised at the correct frequency, is maintained by the rotation of the magnetic blades.
The system is a trio of elements—composed of a rotor, oscillator, and magnets, that together act as the escapement, with the mechanical energy maintaining the vibration. The fact that the rotor operates continuously and not by jumps allows it to transmit the energy in a sinusoidal pattern rather than by brief impulses, which improves efficiency.

Mathematical simulations
At the beginning of his research, Flageollet brought in the services of a young physicist, Siddharta Berns, who, most importantly, converted the watchmaking “Résonique” principles into differential equations. These equations allowed them to carry out a whole series of simulations, which revealed that the synchronisation among the various elements of this new form of magnetic escapement passed through various stages. During these different steps, it was observed that the speed of the rotor and the amplitude of the oscillator stabilised.
The simulations allowed the various steps to be isolated “with physically realisable parameters,” including the addition of random perturbations so that the constancy of the synchronisation could be observed. This first step allowed De Bethune to create functional prototypes. We were able to see some of them in the ateliers, before leaving by moonlight for the snow-covered yurt with its wood fire burning.

De Bethune - The yurt and the equation

Up to 10 kHz...
The Résonique invention opens avenues of exploration that could very well end with a mechanical equivalent of a quartz movement in terms of precision and small size. Along with Berns, Denis Flageollet and the rest of the small team have already cleared a large part of the research.
The oscillator that they designed is made in one single piece, as is the escapement. The ensemble is completely silent and shock-resistant, with the escapement not requiring any lubrication. Wear and tear is thus minimal, and even theoretically non-existent, thus the lifespan is consequently longer.
The previous research conducted by the team on “classic” 10-Hz escapements has been quite useful in determining the “quality factor”. This factor defines the portion of energy to be transmitted to the oscillator to maintain its constant amplitude. The precision of the oscillator’s frequency is thus proportional to this factor. With a low amplitude, it follows that the quality factor can be very high, in fact, ten times the norm for balance springs.
The greater the power in the oscillating system, the greater the regulating power of the resonator and the lower its sensitivity to shocks. The chosen arrangement therefore was a high-frequency oscillator with low amplitude. According to the equations and the experiments, the speeds and precisions obtained do not consume any more mechanical energy than a traditional escapement, thus allowing very large power reserves within a very wide frequency range—between 10 Hz and 10 kHz. One of the prototypes is already operating at 1,000 Hz, or one 2,000th of a second, while waiting to achieve the 10,000th (over several hours).

Open source
This revolutionary invention—for once, the word does not seem exaggerated—opens many fields of exploration that exceed the resources of De Bethune alone. Moreover, Denis Flageollet says he is “convinced that, like achievements in the past, the evolution of timekeeping and its creativity will advance by the wide sharing of knowledge”.
Contrary to all of the common jealousy-based practices in the watch industry, Flageollet decided to make his results and his research public. The “Résonique”, this new mechanical system that “aspires to perfect chronometry issued from the domain of natural vibrations”, is therefore open to any researchers, constructors and watchmakers who want to study it.
This is one of the best and also one of the most uncommon gestures of transparency, one that can only help but move watchmaking forward, towards more of the “essential”. To arrive at this, it was, perhaps, necessary to retreat to the mountains for contemplation in a snow-covered yurt.

Reflections on Time, read more:

Source: Europa Star February - March 2012 Magazine Issue