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Justin Koullapis
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About Resonance, and also the "Project 150"

Gentlemen,

I have read your posts on this subject with great interest?I have recently been giving resonance a lot of thought, and specifically how it relates to current and past horological creations.

It would seem to me that any system of coupled oscillators, bound loosely together, and which beat in relative sympathy, do not really count as being in resonance at all. Rather, I would argue that such a pair of oscillators are really ONE oscillator with a very complex geometry.

Take for example the balance bars on Harrison's clock, H1. The pair of dumbell-shaped brass balance bars are connected to each other in two ways, namely:

a) By means of a pair of helical springs connecting opposing dumbell-ends, and

b) By means of a pair of steel ribbons, fixed to a roller on each balance so that the two are inseperably bound?when one balance rotates clockwise, its partner is forced into rotating anti-clockwise.

So, the two balances are locked into phase with each other. What I am trying to illustrate is the existence of apparently seperate oscillators actually working as one. They can be mathematically reduced to just one oscillator, the frequency of which is some function of their geometry (I do not claim to be capable of actually doing the Maths, though!).

Now, in H1, the oscillators are "tightly" bound, inasmuch as the steel ribbon could expand or contract, and therefore, can definitely NOT be considered a "resonant" system. There are other timepieces whose multiple oscillators are commonly considered to be in "resonance", but are really in a status of forced, unnatural, communication, not as forced as in the example of H1, above, but still forced. Examples of these would be Janvier's dual-pendulum clocks, and Breguet's. In both cases, the pendulum supports are flexible or pivoted in some way, so as to impart shared motion between the two. I would venture that Mons. Haldimann's "Double Resonance Tourbillon" falls into the same category?the twinned balances are forced into sharing communication with one another, and thus become indistinguishable from each other. They become ONE. Not two in harmony.

The remarkable performance of all the "resonant" systems cited above may well have to do with a certain level of communication between the oscillators, but I still feel that they should more properly be considered to have a single complex oscillator with a very complex geometry.

Mons. Journe's "Chronom?tre ? R?sonance", however, has a pair of oscillators, finely adjusted to match each other, and solidly fixed with respect to each other. There is no conjuring here. Imperceptible vibrations are transmitted, perhaps through the medium of the report of the pallet stones against the 'scape wheel teeth, perhaps some reaction between the balance jewels and their respective pivots, perhaps the reaction of the balance spring against its mounting. Perhaps all three, perhaps none. I don't believe air movement has much to do with it?Breguet's air shield disproves this.

Regarding the reaction of the balance spring and its stud, may I offer the following insight, well-known, perhaps, to watchmakers: if you have a balance and spring assembly, out of a watch, and you raise and lower the balance spring by the stud at precisely the frequency to which the assembly is tuned (eg 18000 b/hr), the balance will oscillate in the normal way, proving that there is measurable reaction to the motion of the balance at the spring's stud. This reaction may well be communicated to the rest of the watch (just be worrried when your arm muscles begin to tic at 18000 beats per hour!).

Regarding the Conant-Tiffany clock mentioned in Jack's earlier post, can anybody cast any light on the system used to keep the pendula in resonance? It is referred to in the article, but not described. I think that the great achievement of this particular clock is the method of dividing the errors with differentials. Genius.

Lastly (finally!), may I draw your attention to the work being done in the United Kingdom in this regard: a team of horologists, among whom are very eminent clockmakers and mathematicians, is building a multi-pendulum clock, one of the objectives being to have the clock operate on a resonant system. Three pendulums have been tried, and four, and that with three, the pendulums communicate with each other very well without any external, interefering, coupling device. Indeed, as I understand it, LESS power is required to drive the three in resonance than just one on its own, a litmus test of a true resonant system. Just as in all the other cases, the oscillators have to be closely rated with respect to each other. With four pendulums, there are two pairs swinging at right angles to each other, and with three, they are mounted at the vertices of an equilateral triangle, swinging towards and away from the centre.

I don't think I have added any definitive word to the meaning of "resonance", but I feel a ditsinction must be made between genuine and forced behaviour in these systems. Please tear it to pieces; I am hoping to glean insight into the principle anyway.

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