Wednesday, April 05, 2006

43200 vph: The Spring's the Thing

Seiko's 43200 vph movement made me think a little more (deeply?) about the whole issue of the trade-offs and raised some questions in my mind.

Being the geeky sort I created a little spreadsheet calculating the power of the oscillating balance and the energy store in the spring. As usual the old Rolex calibres are in the lead (based on my limited data set of balance wheel intertias - yes, I collect them; note to self, get out more in 2006) being 15 mgcm2 beasts and of course they oscillate away at the benchmark 28800 vph. Now assuming a given amplitude (may I?) we can compare the power delivered to the balance wheel/hairspring as a function of its inertia and frequency (cubed).

In relative units, if we make a Rolex 3135 100,
A JLC autotractor with a balance of 14 mgcm2 at 28800 vph gives us '93.3'.
A RM003 with a 10 mgcm2 at 21600 vph is '28.1'.
A JLC 8 day wheel of 3.8 mgcm2 going 28800 vph is '25.3'; a quarter of the power of the Rolex.

And of course, we can see how an 8 day movement can be delivered more easily with a lower power consumptive balance. Which brings me to the next step: the gas tank, the spring. So, we take the power reserve and power consumption multiplied together to give us the required energy store size, the size of the gas tank the size of the spring barrel(s).

Again taking the examples, we have Rolex '100' runs for what, 50h. So we'll call that '5000'.
The JLC autotractor = 93.3 * 50ish = 4665.
RM003 = 28.1 * 70 = 1967.
JLC 8 day = 25.3 * 192 (9 days?) = 4863.

So arguably despite all the fuss about twin barrel etc, in fact the energy stored in the spring pack of a Rolex 3135 could have powered the JLC 8 day. Hmmm.

So naturally, with a spreadsheet you can begin to perform some what ifs and investigate some truly marvelous and preposterous scenarios. What you notice however, and that dawns on you as obvious in retrospect is that for a given spring pack energy storage value, dividing it by the number of days reserve gives you the 'power budget' to expend in your balance combo; be it small wheel with higher vph or big wheel slower vph.

If we assume that the spring in the new ND58 43200 is comparable to the Rolex (and why not?), then with the 42 hour P.R. we can see that at 43200 vph, Seiko would have a 5.3 mgcm2 wheel (quite small). Returning to the above analysis, the ND58 would score '119' beating Rolex by ~20% on balance power! And of course, it's naturally at the expenseof power reserve (42 versus 50 ) for the same notional spring performance. (i.e 119*42= ~5000). So let's go further. Who's got the biggest most impressive spring? Well, to cut a long story short AFAIK from my data, the Freak is right up there. It powers a 7mgcm2 balance at 28800 for 168h (am I right?), so if we take that baby what do we get? Well if opt to stay at 42h power reserve to maximise out balance power, we can have a 8.3 mgcm2 balance at 43200 vph. Now that, ladies and gents, would be a '187' relative to the '100' for the Rolex. I believe it would be possible to do something quite signficant with the accuracy and stability of a watch with such a high power balance operating at such a high frequency. Here's hoping for further developments.

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