question for the geeks.......

 By: JMan : September 4th, 2011-07:47

I have a question regarding amplitude of a watch which is used as a measure for the accuracy. I understand why the deviation of amplitude would represent accuracy but often the total amplitude seems to be used synonymously. As in "....change increased the amplitude from 300deg to 330deg leading to better accuracy". Could somebody clarify why this is?



 By: ei8htohms : September 4th, 2011-09:19
Hello JMan,

Discussions of amplitude very often take place between two people with a less than completely thorough understanding of the subject.  

I once had a US watch industry executive (NOT my current employer) relay to me a story wherein he bragged to his Swiss counterparts that "his" watchmakers routinely got over 310o of amplitude where the Swiss watchmakers only got 300o .  I cringed when I heard this story because if his Swiss counterpart knew anything about watchmaking he surely thought to himself, "This guy is an idiot."  More amplitude is only necessarily better within a very limited, caliber specific context and only up to a point, beyond which it is undesirable.

Amplitude is not in any way a measure of accuracy, although it can sometimes represent a measure of the mechanical health of a movement.  If the amplitude (measured on a timing machine) is consistent across a variety of positions and within factory tolerances, a watchmaker knows a decent amount about the consistency of the power being delivered to the balance, which is critical to timekeeping.

*  *  *  *  *

Amplitude is critically related to timekeeping for basically four inter-related (and sometimes contradictory) reasons: 1.) isochronism, 2.) poise errors, 3.) rate stability in response to disturbances and 4.) the potential for rebanking.  

1.) All watches strive for isochronism as much as possible which literally means that the rate will be the same regardless of the amplitude.  A very well designed oscillator will only change rate by 5 or 10 seconds per day across 70 or 80% of the power reserve of the watch, but all watches suffer from non-isochronism in some regard.  To the extent that undesirable rate deviations increase as the amplitude decreases, keeping the watch running with as much amplitude as possible is a good thing.

2.) Poise errors are rate deviations in the vertical positions associated with irregularities in the distribution of mass of combined balance and hairspring system (the balance complete in watchmaker parlance). This is one of the sources for rate variations between the 9H, 6H and 3H positions (the vertical positions commonly measured for chronometers). Ideally the poise should be adjusted as much as possible to reduce this error, but it will always exist to some extent, and since poise error is closely tied to amplitude, it's best to have the amplitude of the balance optimally suited to minimize poise errors when worn. 

This is a complicated discussion no matter how you slice, but 220o  is the amplitude at which poise errors are negated completed and they become dramatically more pronounced below 180o  and above 300o .  If the watch loses 25o  of amplitude from the horizontal to vertical positions and approximately 50o  over the course of 24 hours (the usual run time for a hand wound watch with a traditional power reserve) and we want the amplitude curve to be centered around 220o  (in the vertical positions), we'll want our maximum amplitude at full wind to be 270o  if minimizing poise errors is our only goal.  Allowing for some loss in amplitude as the oils deteriorate, maybe we'd shoot for 275o  or 280o .  Please see Daniels Watchmaking for more info and alter calculations for automatics or extended power reserves as desired.

3.) A significant, real-world problem for mechanical watches, and especially those worn on the wrist, is the frequent shocks, seemingly random twisting and turning motions and other g-force inducing perturbations they are subjected to.  Good amplitude is a good defense against these perturbations because significant amplitude drops when disturbed represent a smaller percentage of the total amplitude and thus less deleterious to timekeeping. A high beat rate is an even better defense in this context and high beat escapements generally result in more consistent amplitude between the horizontal and vertical positions, so it's a win-win.

4.) The problem with too much amplitude (in addition to the magnification of poise errors mentioned previously, which is of minor consequence when compared to our current topic) is the risk of rebanking.  If the amplitude gets so high that the roller jewel on the balance strikes the back side of the pallet fork, it's VERY bad for timekeeping.  A watch that is rebanking can gain minutes per hour or can even break off the roller jewel and stop completely.  

As the lubricants deteriorate inside the barrel of an automatic watch (accelerated by the slipping of the mainspring bridle when fully wound), amplitude can sometimes increase and cause the watch to rebank even if it was running with a perfectly safe amplitude previously.  Also, periodic rebanking can be triggered by arm movements even if the amplitude is not explicitly excessive when the watch is stationary, something that is more problematic for watches with large, heavy balances.  For this reason, most manufacturers have pretty well defined amplitude guidelines for the various calibers they produce, with some watches running optimally with 310o  and others becoming dangerously high above 260o .

*  *  *  *  *

As you can see, it's a complicated subject and it should not be generalized about casually in my humble opinion (and I have left escapement and pinning-point errors out of this discussion entirely for the sake of simplicity).  This is one of the reason it bothers me when publications like WatchTime include timing machine readings in their reviews and then associate some kind of score with the readings as if such a practice is anything other than nonsensical.  

Don't misunderstand, I'm sure some of the watchmakers advising on these reviews are very knowledgeable, but it gives the reader an erroneous sense of their own understanding when the reviewer says, "The amplitude was only 290o  at maximum, so we could not give the full 10 points in this category."  This kind of casual reductionism of complicated topics is NOT helpful. For you car guys, imagine if a car mag reviewer said, "This car only only red-lines at 5500 rpm, so we deducted a point from its overall score." Huh?


Great and highly educating post, a true classic! ...

 By: Marcus Hanke : September 4th, 2011-09:32
...thanks, John! I printed it and put it into my copy of Raymondin/Monnier, because your expalantion is so much easier to understand than the stuff written there.


Great information!

 By: mkvc : September 4th, 2011-10:54
Thanks for much improving my understanding of the subject.

Had to read it twice to make sure I was following...

 By: Zhege : September 4th, 2011-11:24
Thanks for posting, very informative.  I almost wrote "useful", but the only real use it has is to make me more aware of something I know very little about smile smile

Excellent post, John

 By: nickd : September 4th, 2011-13:29
Excellent post!

As you say, amplitude is more of an indicator of good design and manufacturer, and I wonder if things like balance wheel inertia, "power curve" and reserve de marche would be better indicators of potential performance?  If people can obsess about car power curves and motor, then these can't be beyond understanding...if manufacturers are willing to communicate them.  A bit like quoting power and torque rather than where it red-lines.

If you look at the discussions around the Le Locle Chronometrié competitions, the only time amplitude gets mentioned is when a tourbillon has an unusually high amplitude.  On the other hand, there's lots of comment around the fact that in the non-tourbillon category manufacturers generally enter tractors with oodles of torque and lovely clean power transmission, plus a decent height to allow for precision tolerances and overall solidity.  Given that the manufacturers are pathologically secretive we don't know the inertias of the balances in the movements but it's reasonable to assume, given the movements, that inertia is a major factor, especially as they're testing for shock and vibration.


What I'd love to see

 By: ei8htohms : September 4th, 2011-14:48

I'd love to see curves like these published across entire power reserves. smile

Any chance of...

 By: BDLJ : September 4th, 2011-16:29

seeing the source data for that graph? smile

Thanks for the posts, John. Informative and fascinating as ever.

it just looks like ~4000 rows of this

 By: ei8htohms : September 4th, 2011-16:38
t [s] Rate [s/d] Amplitude [°]
2 12.8 290.0
4 12.5 290.0
6 12.3 291.0
8 11.8 291.0
10 11.7 292.0
12 11.8 293.0
14 11.5 294.0
16 11.3 295.0
18 11.7 296.0
20 11.7 296.0
22 11.5 297.0
24 11.7 298.0
26 12.0 298.0
28 12.0 298.0
30 12.1 298.0
32 12.2 297.0
34 12.4 296.0
36 12.4 296.0
38 12.3 295.0
40 12.5 294.0
42 12.8 294.0
44 12.7 292.0
46 12.5 292.0
48 12.8 292.0
50 12.8 291.0
52 12.4 291.0
54 12.3 292.0
56 12.2 291.0
58 11.7 292.0
60 11.4 293.0
62 11.2 294.0
64 11.1 295.0
66 11.1 296.0
68 10.8 297.0
70 10.9 297.0
72 11.3 298.0
74 11.3 298.0
76 11.4 298.0
78 12.0 298.0
80 12.2 297.0
82 12.1 297.0
84 12.4 296.0
86 12.6 295.0
88 12.6 294.0
90 12.5 294.0
92 12.6 293.0
94 12.5 292.0
96 12.6 292.0
98 12.3 291.0
100 12.3 291.0
102 12.4 291.0
104 12.0 291.0
106 11.6 291.0
108 11.6 292.0
110 11.4 293.0
112 10.9 294.0
114 10.9 295.0
116 11.0 296.0
118 10.8 297.0
120 10.7 299.0
122 10.8 299.0
124 10.8 300.0
126 11.2 300.0
128 11.3 300.0
130 11.6 300.0
132 11.9 300.0
134 11.9 299.0
136 11.8 299.0
138 12.2 298.0
140 12.2 297.0
142 11.9 297.0
144 12.1 297.0
146 12.1 296.0
148 11.7 296.0
150 11.5 296.0
152 11.4 296.0
154 11.3 296.0
156 11.2 297.0
158 10.8 298.0
160 10.6 299.0
162 10.6 300.0
164 10.4 301.0
166 10.2 302.0
168 10.5 303.0
170 10.5 304.0
172 10.3 305.0
174 10.5 306.0
176 10.8 306.0
178 10.8 306.0
180 11.0 306.0
182 11.2 305.0
184 11.4 305.0
186 11.7 304.0
188 11.7 303.0
190 11.9 302.0
192 12.3 301.0
194 12.2 300.0
196 11.9 299.0
198 12.4 298.0
200 12.3 297.0
202 12.0 296.0
204 11.9 296.0
206 11.8 295.0
208 11.5 295.0
210 11.2 296.0
212 11.1 296.0
214 11.1 296.0
216 11.1 297.0
218 10.9 297.0
220 11.0 298.0
222 11.3 298.0
224 11.2 298.0
226 11.2 298.0
228 11.7 298.0
230 11.8 297.0

That's exactly..

 By: BDLJ : September 4th, 2011-21:50

...what I'd like to see smile

You'd then be able to interrogate the data by manipulating the scales....but as you wrote, you'd need a fair few samples and a decent amount of background info before you could make any inferences....fascinating, though.


Per watch...?

 By: nickd : September 4th, 2011-23:54
I can see the use of this on a per-watch basis, but could you do it as a generalisation for all instances of a movement if it's so sensitive to adjustment, or are some production movements so consistent that it's feasible? 


realistically? probably yes

 By: ei8htohms : September 5th, 2011-07:24
Hi Nick,

This is only a couple hours worth of data, so it's definitely only useful on a per watch basis and even then more for curiosity's sake.  If you look at the total amplitude and rate trace over the full run-down of a watch it tells you a little more about the generalized performance of that caliber, but would often be highly variable still, especially on watches with curb pin regulators. I'll try to gather some data sets of this type on a couple different watches that I can share.

A few years ago I put together an Excel based tool to perform Fourier Analysis on this type of data in the interest of identifying sources of variability in the power train that might be causing amplitude and rate fluctuations.  For you math geeks, it applies a Fast Fourier Transform to the amplitude and rate data and graphs out what I refer to as the "Periodicity Spectrum" (probably not a strictly correct term).  Spikes in the Periodicity Spectrum will indicate the source of periodic fluctuations as well as the amount of the periodic variation (to some extent).  Then you compare these spikes to the known periods of the rotations of the wheels and the passing of their teeth and you can see where your greater sources of variability are.  

This is the chart derived from the amplitude and rate data I posted previously, indicating periodic amplitude fluctuations at approximately 300 seconds and at approximately 50 seconds.  These most likely correspond to the teeth of the barrel engaging with the center wheel pinion and the teeth of the center wheel engaging with the third wheel pinion.  The amplitude (size) of the  spike itself must be taken with a grain of salt, since the Fourier Transform resolves only for perfect sinusoidal fluctuations which in this case are "best fit" approximations of the real world fluctuations.   

It works pretty well for identifying worn teeth, wheels that are out of round or if your second hand is touching the crystal, but not so much for anything else in my experience and the time that it takes and the hassle involved with gathering the data are not usually justified by the utility of the results (especially because these most easily identified conditions can readily be identified by a careful examination of the components themselves in almost all cases).  It's still a tool that I'm pretty proud of intellectually, but I lost interest in refining it as much as I probably could (yet) once I realized how limited its use would be.  

The resolution of this sort of tool is quite limited by the way the data is collected also.  For extended data sets the machine records at larger intervals (every 5 or 7 seconds for example) and there's no way to control this with machines I'm using currently.  Clearly for this type of analysis you'd like to record a data set for every single tick of the escapement, but alas this is not possible.  

The way a timing machine interpolates amplitude based on the sounds of the escapement is also a pretty rough science and doesn't stand up well to rigorous interrogation of the data in my opinion.  You could probably get a lot better results if you used a laser or optical gate on the arms of the balance to collect your amplitude and rate data.  Enough fiddling with a Microset 3 could perhaps yield resuilts or of course Witschi makes the Velocimetre SMEV which would probably give you better resolution for this sort of analysis, but the investment in a machine like that is really only justified at the manufacturing level.



 By: nickd : September 5th, 2011-08:33
Hi John,

I'd wondered if people used FF transforms for watch analysis.  It's used for precision clocks, and I love the idea of long term studies of precision clocks such as various Shortts or the Littlemore showing the earth's natural resonant frequencies and the pull of the moon.


Now that...

 By: BDLJ : September 5th, 2011-16:51 some interesting data. My FFT skills are almost dead, but that's the kind of analysis/tool I'd love to see more of.

Brilliant work, John

I've thought about trying to put together some sort of

 By: grumio : September 5th, 2011-22:09
optical pickup for measuring rate & ampltiude myself.

I've built home-made optical pickups for other purposes before using the light source and receivers from an old fashioned 'roller ball' computer mouse. Positioning the pickup to work reliably, and calibrating it, would both be a little tricky, but not impossible.

Feed the output into a PC via a sound card, plus a little software, it's theoretically possible. One day I'll get around to it...

Thanks also ei8htohms for your initial answer to ampltiude question - I found it a very succint summary of the various issues.


If you end up putting something like that together...

 By: ei8htohms : September 6th, 2011-09:58

Send me the "how to". The I'd love to have something like that!


There's a chapter...

 By: nickd : September 6th, 2011-10:57 Robert Matthy's Accurate Clock Pendulums on both the sensors and the electronics for use on clock pendulums.  The book itself is worth the read for the sheer pleasure (if you're that way inclined). 


thanks for the book reference

 By: JMan : September 7th, 2011-13:02
Hi Nick or John,

Are there any other books that you could recommend that explain the technical design aspects of a watch? In the vein that is being discussed in the currently? Thanks.


Daniels Watchmaking is quite good

 By: ei8htohms : September 8th, 2011-04:10
The portions of the book specifically dedicated to these issues are pretty small (most of the book focuses on hand fabrication of watch components) but very informative.

DeCarle's Practical Watch Adjusting is also an excellent resource.


Too much or virtually nothing...

 By: nickd : September 8th, 2011-05:11
If you speak French and have university-level maths/physics there's a set of four tomes from the EICN at le Locle (swiss technology university department specializing in microtengineering, with a sub-speciality of horlogery). Its' called Théorie de la construction horlogère pour ingénieurs . Apparently all you will ever want to know 6

There are older books, such as Théorie générale de l’horlogerie by L. Defossez which was the reference in the 1950s, but it's out of date and in French.

Traité de construction horlogère
is a modern French reference that apparently goes into depth (I;ve not seen it). l

There are apparently good German books, but my German is barely adequate to stop me starving so I can't comment.

Otherwise, there's the WOSTEP Theory of Horology which is a pre-university level text book that covers basics but not design criterai and tradeoffs.  Warning: it'll whet your appetitie and leave you hungry for more smile

Apart from that, as John says, there are snippets in Daniels Watchmaking, but he often avoids details and maths.  His The practical Watch Escapement is good if you want to dive into the detail of escapement theory.



 By: JMan : September 8th, 2011-07:27
The Theory of Horology seems like the right kind of book. A bit on the expensive side though........

Send me details!

 By: BDLJ : September 6th, 2011-20:28
Interesting project...

Doesn't Brian Mumford..

 By: Tom the Tinkerer : September 8th, 2011-02:38
already make an optical pickup for watches? and the interface for converting it to a usable signal with the micro set thingy? (Never seen one, touched one or used one, but like the ideas)



 By: nickd : September 8th, 2011-03:14
Brian does make them, but the cost is not negligible, and for some applications they're overkill.


iA quick look at his website...

 By: grumio : September 8th, 2011-03:43
suggests that the optical pickups available for the Microset machines are used for timing clock pendulums. Again, never actually seen one, only read about them online.

There is one attachement he sells for vibrating bare hairsprings, but I can't immediately see how you could use it to measure a balance in a complete movement.


We are fortunate to have John here :-)

 By: KIH : September 4th, 2011-16:04

John, as always, wonderful and informative post.  We learn so much here from you!


Indeed. My thanks to John . . .

 By: Dr No : September 5th, 2011-10:06
. . . for sharing his valuable holiday time with us.



Thanks for this, John!

 By: Gary G : September 4th, 2011-19:09

A great exposition of a topic that was previously completely opaque to me. I now sense the fog lifting just a bit...


Gary G

appreciate the thorough response.......

 By: JMan : September 4th, 2011-19:27
John: Thanks for the education. I just finished my first read. But the topic is technical enough that I need to re-read your response to completely digest all the information you have presented. But it was my initial inclination that there was not going to be one "amplitude" that was optimal to all watches. If this is correct, I am in complete agreement with you that saying the redline of a car is 5500rpm is a useless piece of data about the power delivery - except that it may in a round about way indicate how the engine could behave. Thank you for making the forum a great place to spend time.

Very informative.....

 By: David Elliott : September 4th, 2011-19:39
It's definitely a complicated subject, and you definitely educated me a bit more on it.  Thanks.

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