Fake watches: It has been a recognized fact for several decades that the tourbillon, invented by Abraham-Louis Breguet to compensate for the effects of gravity in pocket watches, was not designed to perform the same task in wristwatches. Double tourbillons and triple axis tourbillons have somewhat improved their effectiveness, but are still far from achieving their ideal.
Scientists at Instant-Lab EPFL in Neuchâtel investigated the question. They designed a “theoretical object” that is successful, or almost. A fundamental step towards achieving the “perfect” tourbillon that will finally be able to fulfill all its chronometric promises. The ball is now in the watchmakers’ court.
In 1996, Europa Star published a critical evaluation of the tourbillon by Jean-Claude Nicolet, a professor at the La Chaux-de-Fonds School of Watchmaking. His analysis came to the scathing conclusion that “in creating the tourbillon, Breguet thought it was eliminating the effects of gravity. It was a mistake on his part. He only managed to mask them a bit.” Nicolet then compared the ingenious watchmaker to a “wizard who makes an elephant disappear.”
This was tantamount to blasphemy, and the watchmakers’ reaction to this critical assessment was equally scathing. No one disputed the scientific argument; the main accusation was that we set out to “kill the goose that laid the golden eggs” that the tourbillon was becoming. At the time, in 1996, it was estimated that around a thousand tourbillons had been made over the course of two centuries, such was their rarity. Since then, and despite expressed reservations about the true chronometric benefits of a tourbillon in a wristwatch, tourbillon fever has taken hold. Today, probably as many tourbillons are produced in a year as in the previous two centuries.
Since then, however, watchmakers have become increasingly aware of the tourbillon’s limitations, especially in wristwatches, and have been exerting their ingenuity to overcome them. The result has been new configurations, double tourbillons, gyrotourbillons, triple axis tourbillons, 30° inclined tourbillons (which, let’s say, achieved the best results in the history of the International Chronometric Competition) to name just a few examples.
But no one has succeeded in designing the perfect tourbillon for a wristwatch, because to equalize all deviations in speed, its axis would have to sweep in all directions evenly. And that’s a pain in the ass, because all the mechanisms available to date have an intrinsic mathematical flaw. We will come back to this.
Noémie Mandon is a young French woman who recently graduated from the Cluny Institute of Technology of Arts and Crafts (which mainly teaches mechanical, industrial and energy engineering). For her last year of study, an academic exchange gave her the opportunity to study mechanical engineering at EPFL in Lausanne, Switzerland. She was attracted to micromechanics, and more particularly to mechanical watchmaking, because of its beauty and sophistication. And she was also driven by an interest in research and innovation.
She came to the EPFL Instant-Lab run by Professor Simon Henein in Neuchâtel, to work with Ilan Vardi (see our article Breaking the second barrier). Ilan Vardi revived a topic that had been dormant for quite some time: tourbillon geometry. It became the subject of her master’s research project.
The aim of his research was to build a theoretical object using a mathematical design, with the aim of correcting the intrinsic defect of tourbillons to “almost totally” compensate for the effect of gravity: averaging it, as in Breguet pocket Replica Watches Store, but for all directions. But doing this also meant finding a means to vary the rotation speed of the tourbillon, which in tourbillons available today is constant for each axis. In mathematical design, a theorem is implemented mechanically.
Ilan Vardi, the project manager, assembled a talented team to help Noémie Mandon (he emphasizes the collective, team aspect of the work). It included Roland Bitterli, a scientist at Instant-Lab, in charge of “making sure the object didn’t become intractably complex”, Patrick Flückiger, a PhD student who in 2019 won the Omega Student Award with a master’s project in a new type of Foucault Pendulum, and Quentin Gubler, an engineer and watchmaker at Ulysse Nardin, where he worked on various projects related to conformal mechanisms.
Is the tourbillon really useless?
Invented in 1795 to compensate for the effects of the earth’s gravity on a pocket watch,
that is, a watch placed vertically in a jacket pocket,
the purpose of the tourbillon is to average the vertical positions, thus improving the precision of the watch. In this sense, it achieves its purpose. “Proof of this”, adds Ilan Vardi, “is that the tourbillons automatically pass the COSC tests in the four vertical positions”.
But things start to get more complicated in wristwatches. On the wrist, the position of the tourbillon in relation to gravity changes continuously in all directions. “Useful only when the balance axis is perpendicular to the direction of gravity”,
the tourbillon no longer fulfills its original role in a wristwatch. Because, while you can average positions in a single (vertical) plane, you can’t do it in three-dimensional space.
To solve this problem, watchmakers gradually turned to multi-axis tourbillons,
beginning with Anthony Randall, who invented the first double-axis tourbillon in the late 1970s. Many other proposals followed, including the Double Tourbillon 30° of Greubel Forsey,
which allows the tourbillon axis to sweep a circle at a constant latitude,
then the Gyrotourbillon invented by Eric Coudray for Jaeger-LeCoultre,
after which came the three-axis tourbillon, versions of which have proliferated.
In search of a uniform distribution of points on a sphere.
But, as Noémie Mandon explains, we know that “in order to average out the effects of balance wheel orientation relative to gravity in a wristwatch, the distribution of points on the dial swept by the balance axis has to be as uniform as may be possible.”
The uniform distribution Luxury Fake Watches of points on a sphere is an important mathematical problem and has been the subject of numerous scientific articles. Although we know how to distribute points evenly in a rectangle, “for spheres there is no theoretical solution.” As will be explained below, the simplest method of distributing points on a sphere leads to overconcentration at the poles. To understand the consequences of this phenomenon for multi-axis tourbillons, a friend of Anthony Randall’s,
the English engineer Guthrie Easten, highlighted this non-uniformity in 1985. He found a compelling image to illustrate it.
The simplest method of distributing points on a sphere leads to overconcentration at the poles. This lack of uniformity in the distribution of the points implies “a lack of compensation for
the effect of the position of the tourbillon in relation to gravity”.
Imagine a tourbillon in the center of a Chinese paper lantern. Its axis is equipped with an ink gun that,
with each oscillation of the exhaust, shoots a drop of ink into the lantern. If the effect of the multi-axis tourbillon were perfect,
the ink droplets would be evenly spaced along the surface of the dial. But at the poles, unfortunately, we find an abnormal concentration of droplets.
Because? Because the rotations of a multi-axis tourbillon are constant in latitude and longitude,
they do not cover the same longitudinal distance, depending on what latitude they are at. When it reaches the pole, the distance traveled cancels out. This lack of uniformity in the distribution of the points implies “a lack of compensation
for the effect of the position of the tourbillon in relation to gravity”.