Independents

Jack Forster
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A little bit. . .

. . .from me; I just read an interesting article archived to a physics newsgroup on the famous Tacoma Narrows bridge collapes, which is often presented in physics textbooks (having not seen the inside of a physics textbook in years, I must take this on faith) as an example of resonance in a mechanical system.

The definition of resonance, as you mentioned, is generally an oscillator being externally driven by something that gives it a periodic 'push' at something close to one of its natural frequencies. The question then arises of how wind gusts, which are aperiodic, could have driven the bridge into resonance in the first place. The usual mechanism proposed is something apparently called 'vortex spillage' where turbulence across the bridge periodically spills a vortex off the trailing edge. This is a good theory but modeling of airflow across the bridge shows vortex spilling happening at a much slower rate than the actual oscillations of the bridge. I don't know what this has to do with horology/chronometry exactly but I thought it was kind of interesting . It's also an interesting example, by the way, of just how much conventional wisdom- even apparently expert conventional wisdom and professional consensus- is sometimes not as reliable as one might think.

The basic definitions I've seen of mechanical (vs. acoustic, nuclear, or chemical) resonance all pretty much say the same thing: that it consists of an oscillator being driven periodically by a force applied at something very near one of the natural frequencies of the oscillator. As I understand it there are other ways to couple periodic mechanical phenomena than resonance. The Journe Chronometre a Resonance is an interesting case in point. I didn't realize this until recently but apparently the two balance wheels are not, when the watch is 'resonating,' actually rotating in synchrony with each other. I always thought that as the left wheel was rotating clockwise the right was rotating counterclockwise, and the air friction between the two was essentially locking them in phase with each other. It turns out (or so I'm told) that the two balance wheels are actually both rotating clockwise, then counterclockwise. This means that they're actually producing aerodynamic drag on each other at the boundary layer of the balance (right at the outer surface of the rim). If the aerodynamic coupling scenario is true then in a way, what you've got in that watch is exactly the opposite of resonance; in fact you've got two oscillators dampening each other rather than driving each other to greater amplitude. One of the basic requirements of a resonant mechanical system, as I understand the definitions I've read, is that one system is driving another, not dampening it. If the two balances are really resonating with each other, then you should be able to remove the mainspring from one of the two movements and the unpowered balance should still begin to oscillate at it's natural frequency (you could actually do this experiment, if you wanted to monkey with your Journe , I suppose you'd have to take the pallet fork out of the unpowered side as well.) This would clearly show that one oscillator was driving the other, albeit still leaving open the question of how the movements are coupled.

In the case of the new Beat Haldimann watch there seems to be an unambiguous mechanism for linking the balances- that is, the 'resonance arm' connecting the outer terminal curves of the two hairsprings. On the assumption that this watch actually represents two resonating oscillators, I suppose the next question is whether or not the resonators offer, even theoretically (leaving aside practical engineering constraints which may swamp any theoretical benefit, peace to those of you who find my admiration of the theoretical benefits of the tourbillon overstated) any advantage in timekeeping. As I understand it, all other things being equal (ha ha ) the Q of an oscillator is dependent on the mass of the oscillator and frequency, the relationship expressing the ability of the oscillator to resist external perturbations. The advantage that I can see to a resonator- potentially- is that coupling the two balances doubles the effective mass and thereby increases the Q of the system overall. On this view, once again all other things being equal, a resonance watch (defined as one with two balances mechanically coupled so as to induce resonance) should offer better long-term stability of rate. In practice whether or not this occurs would depend on a lot of other variables including stability of lubrication, etc. etc. Dr. Daniels would no doubt say that for such a mechanism to fulfill its potential it must be fitted with a co-axial escapement (or at least a detent escapement. . .)

Jack

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