Inform the noob 21600 bph vs 28000 bph

[Matt]

This is one of those 'piece of string' problems in which the words 'all things being equal' eventually come to play a major part.

So let's break the problem down into a few separate parts and examine them independently.

First, let's imagine a perfect watch: It is perfectly poised, perfectly balanced and so on. In this watch, positional variation has been, to all intents and purposes, eliminated. If gravity has no effect on it, you would expect that acceleration and rotation would have no effect on it as well.

However, there is a problem. As anyone who has driven an old car will know, there are some rattles that occur at very specific engine speeds. These rattles happen because the vibration from the engine hits the frequency at which the thing that rattles rattles, and so it will rattle away in harmony. (and on my car it's a slightly loose exhaust heat shield). There will be a frequency range in which the heat shield responds to the vibration. vibration outside of that range will not much effect it. You can get the same effect with guitar or piano strings and an experienced tuner can use the way that the two strings interfere with each other to fine tune the instrument. So why is this a problem for watches?

You can begin to imagine why there is a problem most clearly with an old fashioned pendulum clock.

Here's one I prepared earlier:



In a house it ticks precisely once a second and can manage accuracy of a few seconds a month. However, now imagine it in a ship pitching or rolling sharply once a second. Obviously as the pendulum is tuned to swing once a second, this pitching will effect the pendulum a lot as it is at precisely the frequency it responds to This is one of the reasons why you don't tend to see pendulum clocks on ships. They don't work.

This was something that clock makers rapidly got around - rather than using a pendulum (which is badly effected by acceleration in a straight line) as a resonator, they started using a resonator that rotated rather than swinging - a balance. As the acceleration and deceleration of this resonator was rotational it was less effected by the effects of pitching and rolling,

Obviously a ship pitching and tossing is still slightly rotational but the arcs are so big that the effect is more like linear acceleration. However, It's worth noting that a ship's chronometer will always hold the balance flat and in gimbals to minimise even this small effect. The reason it is flat is to avoid it being in the same rotational plane as the majority of rotation - imagine a chronometer with the balance at the vertical and the pivots pointing fore and aft - in this position any rolling action will have the maximum effect.

So to return to wrist watches and the problem. Obviously a wristwatch with a pendulum simply wouldn't work - it's just too easily affected by linear acceleration. That's why we use a balance, but as we can now see, a balance will still be badly affected by rotational acceleration if the acceleration happens to be at a frequency that it is sensitive to and in a plane that it is sensitive to. Imagine a balance at ninety degrees to your wrist - every time you twisted your hand the balance would be upset. However, balances are flat to your wrist and so largely unaffected by this action. However, our arms are not that long and a lot of their action is rotational in that plane (especially when walking or, to give a classic example that upsets watches, fly fishing)

You can see the sorts of lateral and rotational forces that might effect a watch very easily, because as well as trying to minimise them, manufacturers also take advantage of them to wind an automatic watch. So we know that even in a plane that is flat to the wrist there is lateral and rotational acceleration that can have an effect on a balance. The question is how much of an effect? This brings us back to the question about beat rates - the simple fact is that the closer the rotational acceleration is to the resonant frequency of the balance the greater the effect will be. There are two ways of changing this. Either you avoid jerky rotational movements or you move the frequency of the balance further away from the frequency of the movements. Generally the latter solution is preferred. Thus the higher the beat rate of the watch, the less our natural movements will interfere with it.

Hopefully it is clear that even the perfect watch will be more precise at a given beat rate (all things being equal) However, the problem is that watches are not perfect - they do have problems with positional variations, they have escapements which are not balanced, springs that are not balanced, in most cases they have forms of regulation that are not balanced and in the case of lever escapements the tick and the tock do not even give an equal impetus to the balance. In each of these cases linear acceleration also gets a look in. Once again, this will cause an effect and once again the effect will be down to how close the linear acceleration is to the frequency of the balance, spring or escapement. Once again, raising the frequency of the balance reduces the effect of the linear acceleration because it just can't be that sharp on a human arm.

So that's why a faster beat rate is preferable - it reduces the amount of interference on the amplitude of the balance by the natural movements of the wearer's wrist.

However, that's not even half of the story.