What would be the acceptable beat error range on a vintage pocket watch?

[John Wong]

Been working on these aviation pocket watches and have them tested on a newly-bought timegrapher. My Hamilton M23 shows the result of a beat error and amplitude that are 1.2ms and 235° respectfully, yet the Jeager aircraft clock in the background has a BE of only 0.3ms. Athough being a horological newbie, I still know that a modern fine watch should have a BE that is well within 0.5ms.
My question is, for century-old vintage watches, like a Hamilton M23 or a much older fusee pocket watch, what kind of a beat error reading is considered to be good enough for them? And how come my Hamilton M23 with a 1.2ms beat error still keeps exceptionally good time?

 

[karlmansson]

I’ve heard that anything below 1ms is fine for time keeping but I try to keep mine at 0,2 or less.

 

[thesnark17]

- Higher beat errors will make the watch self-start later in the winding cycle when being wound from a stop.
- They also cause lower amplitude, since an increasing amount of the impulse energy is being wasted as the beat error measurement gets larger. - Large beat errors may cause a watch to rebank at full wind if the amplitude is high enough (usually 310-330º), since the larger swing in one direction allows the roller to hit the back side of the pallet, even though the overall amplitude is not large enough to cause a rebank. (More amplitude than that, and the watch is probably rebanking anyway, beat error or no beat error...)
- At the extreme, the watch will not run at all, but the extreme is well past the 9.9ms point where my timegrapher maxes out.
- Irregular escapement wear is another theoretical issue that could occur in a watch with a very high beat error, run over a long period of time.

Aside from the amplitude issue, it shouldn't affect the timekeeping at all. Such a small deviation from the ideal of <1.0ms would be causing an almost unmeasurable drop in precision in your Hamilton by causing an almost unmeasurable drop in amplitude.

Bear in mind that when the M23 and earlier watches were designed/built, there was no way to measure beat error, since the timegrapher wasn't invented until the early 1940s. Beat error was known to exist, but either the watch started easily and worked well (=low beat error) or it didn't (=high beat error in the absence of other problems). Vibrograf (an early timegrapher maker) indicated in early documentation that a beat error of 2.0ms is not a cause for concern.

For myself, I don't worry about it if it's under 2.5ms on an old pocket watch. When I adjust beat error, I try to get under 0.5ms, but these old pocket watches require more work to get the beat error down, and have a higher risk of accidents in the process. Usually it takes 4 or 5 adjustments for me to get the error down to 0.5ms, each time involving removing the balance from the cock. Sometimes I settle for <1.0ms.

I don't see that a fusee watch would be different in theory, except that I imagine the ease of adjustment might be even worse, depending on the example. If it requires repinning the hairspring to change the beat error, I would tolerate a high beat error if it was otherwise running well.

Modern wristwatches that are adjustable without disassembly are a different matter altogether.

 

[gmorse]

Hi thesnark17,

I don't see that a fusee watch would be different in theory, except that I imagine the ease of adjustment might be even worse, depending on the example. If it requires repinning the hairspring to change the beat error, I would tolerate a high beat error if it was otherwise running well.

With verges, which are usually undersprung, it's not a big deal to unpin the balance spring from the stud and reposition it, or rotate the spring collet. With fusee levers that are mostly oversprung, it can be more of a fiddle, but still not that daunting. Of course, if you need to keep the pinning point the same to maintain the rate, then the earlier fusee levers with undersprung balances can be a pain, because the spring collet sits between the wheel and the roller, so a special tool is needed to rotate it if you don't want to remove the roller.

Regarding acceptable beat errors, I regard 1ms as achievable and acceptable for fusee levers. With verges it depends on the general state of them but it's something to aim at.

Regards,

Graham

 

[thesnark17]

I don't do much work with fusee watches, and the hairspring repinning I have done tends to make me not want to do more. On the other hand, collets don't scare me. It's weird to be nervous about one end of the hairspring and not the other, now that I think about it.

So my comments are more from the point of view of someone who is familiar with American and Swiss watches, and not wanting to speak too much for English and very old watches, where I know I don't know what I'm talking about.

 

[WoodyR]

Where did the "≤ 1 mS" beat error rule-of-thumb originate? I've not seen a quantitative technical explanation. Can somebody please provide a reference and/or link?

Thanks - Woody

 

[karlmansson]

Can't provide a link I'm afraid but I think I've seen documents pointing towards anything under 1ms would have no appreciable effect on time keeping and rate. I would however take this with a grain of salt as a measure of time will be relative to the base rate of the escapement. A beat error of 1ms will for instance be more in a watch with a beat rate of 21600bph than in a watch with a beat rate of 18000bph. 1ms will take up a higher percentage of the vibration period.

I think there are some timing machines that measure beat error in angle, relative to the provided bph and lift angle of the watch. This, to me, is a better measurement and probably the "true" measurement of the error as it is the angular error that you are also adjusting.

Not only should you be concerned with getting a low beat error, I think one of the primary uses of beat error measurement is to check that the beat error doesn't change with position to any substantial degree. This can point to an improperly adjusted terminal curve or crooked or improperly spaces regulator pins.

 

[Skutt50]

Thanks to Graham we have this link in another thread:

https://www.historictimekeepers.com/documents/Watch%20Adjustment.pdf

On page 28 there is a reference to the 1 ms beat error.

Quote:
A beat error of
under 1 millisecond has no measurable impact on timing.
End quote.

 

[praezis]

A beat error of 1ms will for instance be more in a watch with a beat rate of 21600bph than in a watch with a beat rate of 18000bph. 1ms will take up a higher percentage of the vibration period.

I think there are some timing machines that measure beat error in angle, relative to the provided bph and lift angle of the watch. This, to me, is a better measurement and probably the "true" measurement of the error as it is the angular error that you are also adjusting.

You are absolutely right, Karl. This issue is not yet realized by many, as nearly all TMs just offer ms as beat error.

If you want to know, if xx ms is ok or not, that number does not yet tell too much (1ms however will be ok in any case).
Essential is, how many degrees out of the middle is the balance in rest? That is the reason of the beat error.
The very same error of 4 degrees will show:
1.0 ms @ 28800, 300° Ampl. (B.E.= 4°)
1.7 ms @ 18000, 300° Ampl. (B.E.= 4°)
2.9 ms @ 18000, 180° Ampl. (B.E.= 4°)

Not only should you be concerned with getting a low beat error, I think one of the primary uses of beat error measurement is to check that the beat error doesn't change with position to any substantial degree. This can point to an improperly adjusted terminal curve or crooked or improperly spaces regulator pins.

The "ms" beat error will change at least between vertical and horizontal position, as the vertical amplitude uses to be lower than the horizontal.

Quote:
A beat error of
under 1 millisecond has no measurable impact on timing.
End quote.

I did not read the whole document, but is there a reason for just this limit claim?

Frank

 

[Skutt50]

I did not read the whole document, but is there a reason for just this limit claim?

There is not much of an explination. Here are some quotes describing the Beat Error......

Quote;
If the balance spring is still winding when it should be unwinding (beat error) after the balance has passed the neutral point, it will impact timing. The balance spring must be fully relaxed when the balance is at its neutral point.
End quote.

Quote:
Beat error is initially adjusted with the mainspring completely let down.
The balance spring collet is rotated on the staff until the impulse jewel is
centered in the pallet notch when the balance is at rest.
However, visually setting the beat error is not precise. This is due to the
fact that the balance rotates more in one direction than the other
depending on whether the balance spring is winding or unwinding. Final
adjustment must be made with an electronic instrument. A beat error of
under 1 millisecond has no measurable impact on timing.
End quote.

My earlier posting was mainly in response to Woody's request for some source to the 1 ms claim.

 

[WoodyR]

There is not much of an explination. ....

Thanks for all the replies, folks!

I, too, skimmed Dewey's article and didn't find an explanation. I suspect the rule-of-thumb predates him.

Somebody originally made the claim. I like to think it was based on geometry and dynamics or an experimental study - both would have to be extensive since the rule-of-thumb doesn't limit itself to any particular movement or movement type. To be clear, I'm not asking to be argumentative. Rather, I'm genuinely interested in leaning the technical (mathematical, geometric, dynamic) origin of the rule.

Thanks again! Woody

 

[praezis]

Skutt50, thank you

If the balance spring is still winding when it should be unwinding (beat error) after the balance has passed the neutral point, it will impact timing.

This is not true. It is true for a half swing only, but is compensated by the same inverse error in the other half swing.
Mr. G. B. Airy explained it already more than 100 years ago

The balance spring must be fully relaxed when the balance is at its neutral point.

In my understanding this is the neutral point (relaxed hairspring). But obviously the line balance center - pallet fork center was meant.

Woody,
there is no such hard limit as "1 ms" and so no one will explain it. As I showed above, a "ms" limit is nonsense but 1ms still a practical rule of thumb.

The manufacturer of a known timing machine gave the only reasonable answer I found till now: max. limit for the esc. error is 15 degrees. Up to here the unpowered escapement will still rest in lift position.
If you convert deg to wishy-washy ms, 15 degrees equates 9.6 ms @ 200 deg amplitude @ 18000 bph. Adjustment to 1/10 (to be really sure) of that real limit = 1.0 ms will be excellent.

Frank

 

[thesnark17]

It seems to me that discussing it as an angular error is helpful. As stated in an earlier post, 1ms error in a 36000 bph watch will be more consequential of of an error than 1ms in a 28800 bph watch, which in turn will be more consequential than 1ms in an 18000 bph watch, and so on. At 36000 bph, the balance moves a whole lot further in 1ms than at 18000 bph. (About twice as far, in my back-of-the-envelope math!)

Because the actual error in the escapement is angular error in degrees (not a timing error), the timing measurement changes as the watch amplitude declines. This is because the swing of the balance is (theoretically) isochronous, which means it takes the same amount of time to swing 300º or 180º. It will take less time to swing through the 4º section of the arc that is "out of beat" when the watch runs at 300º than it does at 180º. The real error doesn't change, and the amount of energy needed to swing the balance through the "out of beat" arc-section doesn't change either, but the measurement in ms changes. (Examples in this paragraph quoted from the earlier post; thanks again for writing it!)

Based on all of this, I suspect that the 1ms rule has no basis whatsoever except that it works. Vibrograf gave 2ms as unproblematic in practice; they would have been referring to 18000 bph when they said it. Hamilton being Hamilton, we know that they would not settle for "good enough" - they would want some margin beyond that - so they gave 1ms as factory spec. Watchmakers noticed that newer, hi-beat calibers were more sensitive to beat rate, and the word got around to aim to get under 1ms. Turns out it makes good mathematical sense, as 1ms error on an El Primero is about the same amount of error as 2ms on a railroad watch. But still merely a rule of thumb.

There comes a point where the measurable effect of any remaining beat error is indistinguishable from the background measurement "noise" (noise floor) that results from the accumulation of all the other errors in the watch. I suspect that point is much higher than we tend to think in the average watch, due to accumulated errors of wear, damage, and abuse.

And now that I think about it, with Hamilton being Hamilton, I wonder whether they derived the noise floor empirically for a new watch via mass measurement of their watches, and then chose a limit that keeps the beat error below the noise floor. If that process actually happened, that would make 1ms an empirically derived rule for 18000 bph watches in superb condition in c.1945, subject to improvement over time as manufacturing processes got better. (All the references that I have ever seen to the Hamilton rule quote an unnamed Hamilton engineer and suggest that testing took place in the factory. But who am I to say how they did it?) Empirical testing is no substitute for a good theory, but it works a whole lot better in real life.



In regard to the previous post: is 15º the limit for the watch self-starting? Because I have seen one or two watches run acceptably with beat errors as high as ~12 ms, clean traces and amplitude over 200º. They were not self-starting though - required a twist at full wind.



To the previous two posters: this comment was being written when you replied, so apologies if I covered the same ground again.

 

[praezis]

In regard to the previous post: is 15º the limit for the watch self-starting?

That is how I understood their statement in the manual.